segunda-feira, 11 de junho de 2018




On my CV:
After a graduation in medicine I made my M.S. in philosophy at the UFRJ (Rio de Janeiro), Ph.D. at the University of Konstanz (Germany) and post-doctoral works at the Hochschule für Philosophie (Munich) and at the universities of Berkeley, Oxford, Konstanz, Göteborg, and at the École Normale Supérieure. 
My main articles published in international journals were collected and better developed in the book Lines of Thought: Rethinking Philosophical Assumptions (Cambridge Scholars Publishing, 2014). Also from interest may be a short theory on the nature of philosophy in the book The Philosophical Inquiry (UPA, 2002). Presently I am writting a book aiming to recuperate the credibility of the old orthodoxy in analytic philosophy of language. This book, to be called Philosophical Semantics, shall be also published by CSP in 2017/2. 

I am full professor at the Department of Philosophy of the UFRN, Natal, Brazil, though with ergonomic limitation.

Advertisement of some published books (see Amazon.usa):



Claudio Costa/UFRN/Brasil

A natural number can only be a trope if there is a way to understand it as some kind of spatiotemporally localizable property. In this paper, I develop a strategy to explain applied natural numbers as having this property. I also show how this strategy can be extended to what is common to all equinumerous applied numbers, namely, to abstractly considered natural numbers.
Key-words: trope theory, natural number, ontology, philosophy of mathematics

Trope theory aims to give an ontological account of the whole world based on empirical building blocks called tropes. I characterize a trope as a spatiotemporally localizable property, notwithstanding its vagueness. This characterization is easily applicable to properties like qualities and forms, external or internal, simple or complex, the last ones being homogeneous or heterogeneous. It is also easily applicable to relational properties, insofar as they are spatiotemporally localizable. Material objects are bundles of compresent tropes. Even very diffuse things like the electromagnetic field of the Earth or the Thirty Years War should be understood in tropical terms since they can be seen as made up of very diffusely located spatiotemporal properties.
  A vulnerable point of trope theory is that it seems unable to explain the so-called abstract entities like those of mathematics. Against this limitation, my aim in this paper is to sketch a strategy to explain natural numbers as tropes. This can be of obvious interest since natural numbers are touchstones of mathematics.


A preliminary point concerns the usual strategy to construct universals as sets or sums of strictly similar tropes (Williams 1953 I: 9; Campbell 1981). The universal of redness, for instance, is the set of all tropes of red that are strictly similar one another. However, this answer has well-known shortcomings. First, some consider sets to be abstract entities, universals in a Platonic or some Aristotelian sub-Platonic sense. Second, there is a well-known problem concerning our treatment of strict similarities: Either they are instances of the universal of strict similarity, contaminating trope-theory with realism on universals, or they are also tropes. If they are tropes, however, then two strict similarities between tropes must be strictly similar one another, what commits us to conceding a second-order strict similarity. But then we would soon need a third-order strict similarity of second-order ones, falling into an infinite regress. A further problem is that sets can change the number of their elements, which means that sets of strictly similar tropes could easily change their size, while universals cannot change their size since they do not have sizes. An appeal to open sets would not be helpful since although they exist in our minds and as written symbols, it is doubtful if they exist at the ontological level.
  My way to deal with the problem is free from these burdens. It is simpler and inspired in the particularism of English empiricism. Instead of appealing to sets, I suggest that to build tropical universals we proceed like a geometer building a proof by means of an example drawn on a blackboard: the example serves as a model for all cases (Berkeley 1710, Intro., sec. 12). Doing so, all that we need in order to construct a universal is just one trope that we arbitrarily choose to use as a model. Then we define the universal as either this model or any other trope that is strictly similar to this model. That is, calling T* the trope T used as a model, we can define the universal as follows:

Universal for a trope T (Df.): T* or any other trope strictly similar to T*.

Giving a simple example, suppose I am acquainted with a patch of vermillion of cinnabar, a very specific color. Now, suppose I intend to use this trope as the model-trope Tv*. This allows me to build the universal of this color as the trope Tv* or any other trope strictly similar to Tv*. Certainly, Tv* in practice does not need to remain the same. You can choose any other strictly similar patch as a model. That is, the models can be randomly chosen. In this way, we are free from the urge to build higher-order strict similarities, since we may consider any chosen trope T in terms of its first-order strict similarity or lack of strict similarity with Tv*. Moreover, there is no question about size in this operational view of universals, since we dropped the appeal to sets.


Coming to our attempt to build numbers as tropes, empiricist accounts can give us a first clue. Locke, for example, saw the number as a primary quality (1690, Book II, Ch. viii). Indeed, the bed in my room has the property of being one, independently of the sensory system of the perceiver. For applied small natural numbers, this seems to work: I can perceive two, three, or even six coins at a glance; and some savants can perceive more than hundred coins at a glance, although they are also unable to perceive large numbers without counting. Penelope Maddy noted that the ten fingers of her hands are located on her hands (1884: 87). Moreover, applied numbers can even move together with their bearers. For instance, the 26 stones that make up Stonehenge were originally transported to Wiltshire from Wales.
   Although these applied numbers seem to satisfy our definition of tropes, since they are spatiotemporally localizable, they are surely not at the same level of the counted bed, coins, fingers and stones. Since Frege, we have known that applied numbers are dependent on the conceptual ways we have to divide up the world. Thus, I count my 10 fingers but only my 2 hands, we count 26 stones but only a single Stonehenge in Wiltshire. Even if we agree to consider these applied numbers as tropical entities, we must consider them as dependent on the kind of thing counted, namely, as higher-order properties of concepts associated with the higher-order property of existence (Frege 1884: sec. 55)… Now, understanding the concept (differently from Frege) as a conceptual rule, not as rule actualized in someone’s mind, but as a dispositionally localizable trope, we can read existence as the (higher-order) property of this dispositional rule of its effective or warranted application. Moreover, this effectively possible application of a rule must be also a higher-order localizable dispositional trope-property indirectly belonging to what is said to exist, since it will be the higher-order tropical property of such a dispositional conceptual rule of being applied in some domain, which the real application of this conceptual rule proves. (Because of this, a thing can exist even if its conceptual rule does not actualize, insofar as if this rule were actual it would be effectively applicable to it, which makes the existence of things independent of the actual existence of cognitive subjects or rules.)
  Now, when we count different applications of a conceptual rule, what we get are applied numbers added to existence. Consider, as Frege would do, the case of the empty concept of ‘moons of Venus’. Symbolizing the conceptual rule for ‘moon of Venus’ as V, we can symbolize the idea that Venus has 0 moons as ~x (Vx). The concept ‘moons of Earth’ applies to only one object. Symbolizing the conceptual rule expressed by ‘…moons of Earth’ as E, we can render the idea that the earth has one moon as x [Ex & (y) (Ey → y = x)]. Symbolizing the conceptual expression ‘…moons of Mars’ as M, we can symbolize the idea that Mars has two moons as x [(Mx) (My) & ~(x = y) & (z) (Mz → (z = x) v (z = y))]… Important is that these existences and applied numbers can be seen as spatiotemporally localizable higher-order possible properties or tropes belonging to possible first-order tropical possible conceptual rules. The number 2 associated with the concept ‘moons of Mars’ applies to Phobos and Deimos, what means that this applied number is located presently and in the surroundings of Mars and not in a distant Galaxy in a remote future or in a Platonic heaven. Our only moon exists circling the earth and this existence is not in Andromeda. Finally, there are the 0 moons of Venus, in the sense that the conceptual rule of ‘moon of Venus’ isn’t effectively applicable to its surroundings as expected.
  After identifying the applied natural number with the dispositional tropical property of the enumeration as an idealized counting of the effective application (existence) of dispositional tropical conceptual rules, what we need to do is to separate (or abstract) the numerical trope from the dispositional tropical conceptual rules in question and the dispositional application of them as attributions of existence. I suggest we can represent in a separated form these numerical tropes as spatiotemporally located dispositional sets-tropes of applications that in this way represent applied numbers separated from their associated conceptual rules. So, we can represent the numerical property of not being locally applied of the conceptual rule of ‘Venus moons’ using a set containing as its only member the lack of the applicability of an attribution of existence or {~a} (= 0). We can represent the numerical property of being locally applied only once, using the set that contains only one application of some conceptual rule or: {a} (= 1). We can represent the property of being applied twice using the set that contains a double trope of application or {a, {a}} (= 2). We can represent the property of being applied three times as the set {a, {a}, {{a}}} (= 3), and so on. Since {a, {a}, {{a}}} (=3) contains {a, {a}} (=2) that contains {a} (=1), each new representation shows the right kind of complexity, containing its antecedents. Moreover, it is essential to see that although we are here distinguishing applied numbers by means of sets, these are not pure sets! (We are not trying to build natural numbers from nothing, as do mathematician like von Neumann or Zermelo, beginning with the null set.) We are dealing with spatiotemporally located sets of higher-order trope-properties of ideally countable applications of conceptual-rules (I say ideally countable because great natural numbers are not countable to human beings). The two members set-trope of Mars moons is spatiotemporally located around Mars, the one member set-trope of earth moons is spatiotemporally located around the earth, and the null member set of Venus moons is a set of non-applicability, since there isn’t any moon spatiotemporally located in the surroundings of Venus, as expected – no numerical tropes are to be found.
At this point, a mathematician could object that we have explained only applied, not abstract numbers. Mathematicians are not interested in counting the number of fingers on their hands. When they perform the addition 7 + 5 = 12, they are considering numbers in abstraction from conceptual divisions of the world. What really matters, they say, are the numbers of abstract arithmetic, the universals, the numbers-in-themselves, independently of their satisfaction by ideally countable material objects. Reducing numbers to numerical sets of located applications, we explain an applied number but not what is common to all equinumerous applied numbers. The natural number 3, formulated as {a, {a}, {{a}}} is a triad, but not what is common to all triads, namely, the universal three, the three-in-itself.
   The proper way to represent what is common to all triads seems to be the appeal to things like a Russellian set of all sets of the same kind. However, this seems to lead us to his conclusion that the universe has an infinite number of objects (1919, Ch. XIII), which is too demanding, considering how infinite an actual infinite must be. Moreover, without assuming tropes, these sets seem to be abstract objects. In any chosen way, we seem to overpopulate our world with an infinite number of abstract objects.
  However, in the same way as we have constructed universal quality-tropes without appealing to sets, we can also construct universal numerical tropes without appealing to sets. As we have seen, an applied natural number can be understood as a trope, since it is spatiotemporally localizable as a second-order numerical property of a dispositional conceptual rule resulting from its (ideally countable) applications. Consequently, in order to account for the universal as the number-in-itself, we can also appeal to our disjunctive device.
  In this case, for instance, it is conceivable that the number 2 in itself would be a disjunction between a set instantiated by a chosen located higher-order set-trope of enumerable dispositional applications used as a model (e.g., the number 2 in the statement ‘I have 2 hands’) or any other strictly similar (equinumerous) located set-trope. Now, in order to get the number 2 as the ‘abstract universal’, the ‘2-in-itself’, all we need to do is to apply the same procedure we have applied to get universals from our usual quality-tropes to a numerical set-trope of located applications {a, {a}} understood as a selected model. For instance:

Number 2 (Df.) = a selected model understood as a higher-order set-trope of located countable applications {a, {a}}*, or any further higher-order set-trope of located countable dispositional applications strictly similar (equinumerous) to {a, {a}}*.

 In this sense, the natural number as a universal (or ‘abstract object’) can be defined as:
A higher-order located (ideally) countable set-trope taken as a model or of any higher-order located (ideally) countable set-trope strictly similar (equinumerous) to the model.

Note that such a universal or abstract object remains empirical since it is a higher-order disjunctive numerical set-trope of located dispositional applications that can be found as something dispersed across our whole spatiotemporal world.
  Assuming a definition like that, we neither stumble over controversial pure or infinite sets nor seem to remain limited to particular instances or directly committed to any empirical constituent of material objects. The foreseeable conclusion is that even the abstract world of mathematics is built of thin higher-order tropes. Such tropes, like some others, would be situated at the peak of a building whose originating genetic-epistemic foundations are our more feasible perceptually given quality-tropes, although retaining the distinctive property of being spatiotemporally located, even if in an extremely diffuse way. A final advantage of the proposed view is that it is consonant with the applicability of mathematics to the empirical world. Mathematical entities are applicable because, like our world, they are made up of tropes.

Berkeley, G. (1975). Of the Principles of Human Knowledge (1710), Philosophical Works Including the Work on Vision, (ed.) M. R. Ayers. London: Everyman.
Campbell, K. (1990). Abstract Particulars. Oxford: Blackwell.
- (1981). ‘The Metaphysics of Abstract Particulars.’ Midwest Studies in Philosophy 6, 477-486.  
Frege, G. (1996). Die Grundlagen der Arithmetik: Eine Logisch Mathematische Untersuchung über den Begriff des Zahls (1884)Stuttgart: Reclam.
Locke, J. (1975). Essay Concerning Human Understanding (1690), (ed.) P. H. Nidditch. Oxford: Oxford University Press.
Maddy, P. (1990). Realism in Mathematics. Oxford: Oxford University Press.
Russell, B. (1929). Introduction to Mathematical Philosophy (1919)London: George Allen & Unwin.

Williams, D. C. (1953). ‘The Elements of Being.’ Review of Metaphysics, vol. 7 (2), 3-18, 171-192.


ESBOÇO sobre um assunto sobre o qual sou um quase leigo. Trata-se de uma tentativa de salvar a distinção.


Se você acredita que eu penso que é preciso fazer uma opção entre ser de direita ou de esquerda, devo decepcioná-lo. No que se segue quero defender que é desejável a existência de uma saudável dialética entre direita e esquerda e que ela é intrínseca a um sistema político verdadeiramente democrático.
   Para começar, quero tirar de foco aquilo que foge ao escopo de nossa discussão, que são os sistemas totalitários ditos de esquerda ou de direita, que não deveriam ao menos pertencer à contemporaneidade. Quero também excluir deformações sociais populistas, como esquerda e direita regressivas, que não são o que aparentam ser, apontam para uma deformação manipuladora do processo democrático e portanto possuem um elemento totalitário. Suponho, como base necessária ao meu argumento, uma sociedade bem formada, na qual as leis sejam cumpridas e onde exista transparência e ‘fairness’ na atividade política.[1]
   Dito isso, minha intenção é procurar esclarecer os verdadeiros papéis da esquerda e da direita em uma sociedade legitimamente democrática. Escolho usar esses termos semanticamente carregados e ambíguos ao invés dos termos mais neutros, que poderiam ser libertarismo (libertarianism) versus liberalismo igualitarista (liberal igualitarism), ou conservadorismo versus liberalismo, pois quero desafiar concepções arraigadas nas mentes de muitos e que me parecem claramente errôneas.
A tese é simples:

Esquerda e direita, em um sistema legitimamente democrático e sem deformações, são opostos dialéticos interdependentes que podem e mesmo devem alternar-se em uma enriquecedora dinâmica interna.

Ou seja: faz parte da dinâmica de um estado democrático um possível revezamento entre governos mais voltados para a direita e outros mais voltados para a esquerda, pois ambos se complementam no intento de maximizar o bem comum e a justiça social.
Essa tese, naturalmente, demanda esclarecimentos. Primeiro é preciso definir com mínima precisão o que estamos entendendo por direita e esquerda, de modo a expor a razão mesma dessa dicotomia. Depois é necessário esclarecer por que considero ambas as posições legítimas. Depois preciso explicar por que uma alternância entre ambas, em um sistema sócio-político suficientemente desenvolvido costuma ser desejável. Finalmente, quero testar minhas considerações aplicando o critério de estado justo de John Rawls de maneira a mostrar que ele pode se aplicar positivamente a ambos os casos, uma vez dado o contexto adequado.

Vejamos primeiro como podemos definir o espectro político que vai da esquerda à direita de forma que espero não ser ideologicamente comprometida. Os termos surgiram no período da revolução francesa, a direita se referindo aos defensores da monarquia e a esquerda se referindo aos que a ela se opunham. Mais tarde a oposição passou a constituir um espectro que vai da estrema esquerda à esquerda moderada, ao centrismo moderado, à direita moderada e à estrema direita. Desse espectro quero considerar apenas a esquerda e a direita moderadas, uma vez que somente elas são compatíveis com um sistema democrático desenvolvido e capazes de um diálogo mútuo, diversamente de posições extremadas. Começo com uma breve caracterização contrastando as duas posições, começando com a direita democrática:
Tese A1. O ponto essencial é o de que a direita deve, por definição, representar as classes sociais ditas mais favorecidas ou dominantes. Claro que sob essa perspectiva a direita democrática por consequência defende a maximização do capitalismo privado. Ela defende a livre competição da parte da economia privada e a minimização do papel do estado. A diminuição das taxações decorrentes da minimização do papel do estado auxilia no crescimento econômico porque em um sistema livre de monopólios no qual o estado é pequeno e taxa minimamente as empresas se tornam muito mais capazes de competir umas com as outras. A livre competição, por sua vez, faz com que as empresas mais eficazes e criativas predominem, enquanto as menos competitivas vão à falência, o que no final serve como o principal instrumento no enriquecimento de uma nação.[2] Trata-se de uma espécie de inegável darwinismo econômico. O melhor exemplo disso pode ter sido o do desenvolvimento dos Estados Unidos na última metade do século XIX, notado pelo economista Newton Friedman. O governo taxava os cidadãos em menos de 5%, restringindo-se ao papel de manter a lei e a ordem, além da defesa. Praticamente tudo era privado. Como havia, por exemplo, competição entre as companhias ferroviárias, o preço das viagens era minimizado, facilitando a vida do cidadão. O resultado dessa política econômica foi um crescimento econômico exponencial que já no início do século XX fazia os Estados Unidos ultrapassarem a Europa em termos de riqueza.[3]
   Mas essa forma radical de capitalismo não acontece sem um preço, pois os perdedores da competição pelo capital caem na miséria, seja por incapacidade ou por simples má-sorte, passando a depender simplesmente da caridade dos mais afortunados. Há também a ansiedade social gerada pela competição. A própria mentalidade competitiva não parece em si mesma algo saudável. A palavra perdedor (loser) é tipicamente Americana. O pecado capital da direita, visível no que tem sido apelidado de “capitalismo selvagem”, é o da ganância.
   Vejamos agora, como contraste, características econômicas da esquerda:
Tese A2. Aqui o ponto essencial é o de que a esquerda deve representar as classes menos favorecidas, ou, para usar um vocabulário mais neutro, classes subordinadas na ordem social. Economicamente, a esquerda moderada tende a defender um socialismo democrático. Ela tende a defender uma maior intervenção estatal na economia, pois geralmente o estado é quem é capaz de redistribuir riquezas que tendem a se acumular nas mãos de alguns poucos, uma inevitável tendência da economia privada: dinheiro gera dinheiro. Um exemplo trivial evidencia isso: um fazendeiro que possui 20 alqueires pode investir suas economias comprando o dobro do que tem. Nesse caso conseguirá ter 40 alqueires. Já se um pequeno produtor que possui 2 alqueires investir suas economias comprando o dobro do que possui, conseguirá no final ter 4 alqueires. Na comparação o primeiro ganhará 20 alqueires a mais, enquanto o segundo apenas 2, ou seja, dez vezes mais do que o segundo. Assim, é evidente que o capital tende a se acumular nas mãos de poucos. Isso pode não ser mal do ponto de vista meramente econômico, mas os poucos possuidores de mais dinheiro facilmente possuem maior poder introduzindo distorções a seu favor, distorções no mercado capazes de produzir danos colaterais indesejáveis.
 Considerando o compromisso moral de auxiliar as classes menos favorecidas, a esquerda deve buscar diminuir essas desigualdades. É aí que entra o papel redistributivista do estado. Uma maneira de assegurar a redistribuição é agregar valor humano às pessoas, o que se faz pela educação, a começar pela educação básica. O próprio Marx acreditava que um engenheiro deve ganhar mais, uma vez que (segundo o seu raciocínio) foi investido trabalho na sua formação, o que o valoriza. Certamente, apenas isso não basta. O estado do bem estar social (o welfaire state) é uma conquista da civilização, protegendo os mais desfavorecidos. Que as pessoas possam de forma gratuita ter educação básica de qualidade, saúde, alimentação garantida em caso de desemprego, deveria passar à condição de direito humano. Mas não podemos nos esquecer que esses direitos só existem sob o pressuposto de uma estrutura econômica suficientemente robusta. Se a economia regredir à Idade Média esses direitos deixarão de existir. Eles são dependentes da realidade econômica.
   O óbvio problema causado pela introdução de medidas de auxílio social é que elas causam um aumento na taxação, diminuindo a competitividade da economia privada. A economia privada – o livre mercado – é o grande motor do desenvolvimento. Essa tese propagada por Adam Smith vale ainda hoje. O que enriquece uma nação é a livre competição entre os agentes econômicos; uma livre competição sem monopólios ou cartéis ou ajuda do estado e com base em leis igualmente aplicáveis a todos. Trata-se aqui do que Smith chamou de a “mão invisível” do mercado através da qual cada agente financeiro, movido pelo interesse pessoal busca vencer na competição do mercado, acabando por produzir mercadorias melhores e mais baratas, o que acaba por promover o enriquecimento de todos. Por isso, há riscos envolvidos na busca do estado do bem estar social, como erros estratégicos conduzidos pelo estado ou (no caso do Brasil) o crescimento excessivo do estado a ponto de esmagar a economia privada produzindo estagnação ao matar o “espírito animal” do empreendedorismo. O estado, como todos sabem, não tem competidores e é por essa razão pouco eficiente. A falência de sistemas totalitários de esquerda como a URSS e a China de Mao, para citar dois exemplos entre muitos, é uma prova disso. Esses sistemas de capitalismo de estado só funcionaram sob as mãos de ferro de ditadores e na medida em que eram capazes de dar algum espaço oculto à economia privada. O pecado capital da esquerda, claramente visível em sistemas comunistas, tem sido o da inveja.
Tese B1. A direita deve ou deveria estar comprometida com a defesa das classes dominantes sob uma justificação meritocrática. Segundo Rawls os membros dessas classes merecerão mais na medida em que forem capazes de produzir um bem comum maior (Digamos, Henry Ford ao produzir carros populares na década de 20).
B2. A esquerda deve estar comprometida com o redistributivismo com relação às classes menos favorecidas e com a minimização de desigualdades econômicas que podem facilmente se tornar injustas.
Tese A3. A direita costuma estar comprometida com a conservação dos valores tradicionais, com a resistência à velocidade da transformação ou mesmo com o retorno à ordem antes estabelecida. Mas qual a razão disso?
Tese B3. A esquerda deve estar mais comprometida com a mudança social sob o suposto de um contínuo progresso econômico. A razão da oposição entre A3 e B3 é simples: uma sociedade é um todo dinâmico geralmente em desenvolvimento, necessitando acomodações nas relações entre classes. O aumento da riqueza é o que permite uma melhoria na condição econômica das classes ditas subordinadas. Assim, é a esquerda que costuma demandar mudanças, até o limite onde essas mudanças possam se tornar excessivas. Um exemplo claro foi a revolução francesa antes da vinda de Napoleão, de sua degradação absolutista, seguida da reação que conservadora que veio depois de sua derrota.

Muitos pensaram, influenciados pelo marxismo, que a direita e a esquerda devessem ser posições políticas incompatíveis, a primeira delas defendendo a justiça social e a outra não. Para a esquerda influenciada pelo marxismo-leninismo, as classes menos favorecidas são socialmente exploradas e injustiçadas. Esse ponto valeu certamente para certos momentos da história, como os abusos da revolução industrial, mas não vale para todo e qualquer caso. Já a direita, influenciada por conservadores como Edmund Burke, defende que os mais abastados formam uma elite preservadora da tradição conquistada pela experiência de séculos, sendo no final das contas aqueles que se demonstraram os mais capazes e que por isso merecem preservar o que conquistaram, preservando assim o que foi bem sucedido em uma sociedade. Em termos individuais isso é claramente falacioso. Mas se considerarmos a maneira como o estado funciona, há uma certa lógica em se pensar assim. Por exemplo: os que pertencem à classe dominante tem mais acesso à educação, tem meios de conhecer os mecanismos concretos do poder e são capazes de passar sua experiência para os que pertencem ao mesmo grupamento social. Em princípio, ao menos – pressupondo legalidade e a ausência de corrupção – seriam mais capazes de gerir o estado de modo a produzir o bem comum.
   Quero defender aqui algo diverso disso, pois penso que ao menos quando consideramos formas moderadas de esquerda e direita representadas em um sistema verdadeiramente democrático de governo em que a corrupção é minimizada e as leis são reconhecidas e seguidas, ambas as posições são complementares e capazes de uma interação enriquecedora capaz de beneficiar a todos. John Searle devia ter algo assim em mente quando notou que o bipartidarismo americano é uma forma de sabedoria política.
   Quero considerar a questão da justiça social, mas antes disso pretendo considerar a questão das classes sociais. A existência de diferentes classes sociais é algo inevitável, absolutamente necessário a sociedades desenvolvidas. Ela praticamente não existe em tribos indígenas onde mais ou menos tudo é de todos, existindo em geral duas classes equiparadas. A dos homens, dedicados à caça e eventualmente a guerra, e a das mulheres, dedicadas aos afazeres domésticos e ao cuidado dos filhos. Mas desde os impérios da antiguidade a existência de classes sociais se tornou um fato social cuja necessidade é indiscutível. A existência de classes sociais não significa, inevitavelmente, injustiça social, como pensava Marx. A história não é a história das lutas de classe, mas dos compromissos entre as classes. Basta considerar estados social-democráticos muito desenvolvidos para que isso se torne claro. Uma pessoa rica na Finlândia tem encargos sociais muito elevados, estabelecidos pelo estado do bem estar social e a sua maior riqueza e maior status social deve ser justificada por maiores deveres e responsabilidades sociais, ou seja, pelo que ela é capaz de retornar para a sociedade. Isso nos faz passar à questão da justiça social.
   Quero notar que tanto um estado de esquerda quanto um estado de direita pode ser socialmente injusto. Não é somente a classe dominante que pode ser injusta com a classe subordinada, mas o contrário também é possível. Considerando o estado de direita, quero exemplificar meu ponto considerando o estado francês pouco antes da revolução francesa. Os custos do governo monárquico absolutista eram imensos, junto às suas dívidas, enquanto o povo passava fome. Aqui temos um exemplo da direita injusta e exploradora. Passemos agora ao caso oposto, o do comunismo soviético da época de Stalin. Nesse tempo uma pessoa que tivesse pertencido à nobreza corria risco de vida. Seu próprio modo de falar poderia denunciá-la, fazendo com que fosse acusada de traição ao regime por qualquer razão banal ou inventada, sendo então julgada e executada.[4] Esse é um exemplo de injustiça da esquerda. Ainda outro exemplo é o dos exageros que se seguiram à revolução francesa, como a indiscriminada condenação à morte de parte do clero.
   É difícil aplicar esse argumento nos casos de totalitarismos de extrema esquerda ou direita, pois eles deixam de representar realmente a população, uma vez que a oligarquia dominante passa a ter sobre ela controle físico e mental. Considere a anomalia trágica que foi o Kmehr Vermelho que liderou o Cambodja de 1975 a 1979. A ideia absurda que conduzia seus líderes era a de que o estado ideal seria o de camponeses auto-suficientes, que decidiu esvaziar uma cidade de mais de um milhão de habitantes em menos de um mês fez com que muitos, talvez quase um terço da população do país, mais de dois milhões de pessoas, foi morta em um período de pouco mais de três anos, de fome, de doenças ou condenados à morte por suspeita. Qualquer pessoa que fosse educada, não tivesse calos nas mãos, ou conhecesse outro idioma, era executada. A capital Pohn Penh, de um milhão e meio de habitantes foi esvaziada em poucas semanas e seus habitantes – mesmo os velhos e doentes – precisaram marchar a pé para os campos para trabalharem em grandes fazendas coletivas, quem não sobrevivesse não sendo digno do novo sistema. A mesma coisa ocorreu com a extrema esquerda da Coréia do Norte. Lá o povo camponês vive em extrema miséria. Comer grama não e coisa rara, dada a escassez de alimentos. Estima-se em 150 mil o número de prisioneiros em campos de concentração. Kim Jong-un, no entanto, vive na opulência junto aos que se deixaram corromper de modo a poderem pertencer ao governo. Não sei se é possível classificar essa anomalia como sendo um governo de esquerda ou a sua degradação final pela manipulação totalitária, mas esse como os outros – da URSS à Cuba – é extraordinariamente injusto para o povo a quem deveria beneficiar. O nazismo era uma ditadura com objetivos socialistas mas que ao mesmo tempo admitia o livre mercado capitalista, o que não nos permite considerarmos um regime de esquerda, mas também não de propriamente de direita no sentido em que estamos considerando, que tem como principal elemento caracterizador a classe representada pelos dirigentes do estado representam. Essas aberrações totalitária fogem, pois, à nossa tentativa de classificação.

Quero aplicar agora o teste de John Rawls para a justiça social.[5] A sua ideia é importante. Para Rawls existe um teste para se saber qual é o estado justo. Trata-se de se perguntar em que sistema político você preferiria viver se você caísse nele sob o véu da ignorância. O véu da ignorância é aquele no qual uma pessoa, embora sabendo como funcionam os estados, devendo escolher um deles, não sabe se nele cairá sendo rico ou pobre, homem ou mulher, saudável ou doente, heterossexual ou não, hábil ou inábil, etc. Sob tais condições a pessoa tenderá a escolher o estado justo, pois é nele que ela terá mais chances de ser tratada de forma justa.
   Rawls estava pensando em um sistema de bem estar social ao formular a sua teoria. Mas é interessante perceber que a melhor escolha pode se dar tanto com relação a um sistema de esquerda quanto em relação a um sistema de direita. Por exemplo: um sistema direitista justo como o da Singapura, que é governado por um único partido desde a sua libertação da Inglaterra (o Partido da Ação Popular) e possui características autoritárias, mas privilegia a meritocracia, é mesmo assim um lugar ao qual preferiríamos pertencer, pois está próximo de um sistema social justo. Um sistema com viés de esquerda, mas democrático, como o da Finlândia, também é algo que sob o véu da ignorância seria de nossa escolha. Não escolheríamos anomalias econômico-sociais como Rússia ou Brasil, e muito menos Cuba ou a Coréia do Norte. Assim, tanto um governo de direita quanto um governo de esquerda podem ser aproximar de um sistema socialmente justo.
  Finalmente, as circunstâncias de uma sociedade são mutáveis. Um sistema esquerdista moderado pode levar longe demais suas intenções, tornando-se injusto. Mais do que isso, pode aplicar suas políticas de forma inadequada. Esse me parece o caso da Suécia contemporânea. A admissão descontrolada de imigrantes acabou por formar mais de trinta “no go zones”, algo parecido com as favelas brasileiras, onde as pessoas, embora recebendo auxílio governamental, não tem qualquer disposição a se integrar culturalmente e mesmo economicamente ao país onde se encontram, passando à criminalidade. Com isso um estado social-democrático exemplar corre o risco de se perder. O exemplo contrário é o de uma direita como a mexicana atual, que privilegia uma minoria de governantes que certamente não conquistaram o poder por méritos próprios, dificultando a mobilidade social. Pelo que soube, o governo mexicano secretamente dirige o narcotráfico e privatizou empresas entre amigos. Não pode haver muito lugar para um livre mercado não distorcido e para a meritocracia em um governo dessa espécie.
  Vejamos finalmente as vantagens da alternância de poder entre esquerda e direita. Aqui outra vez os Estados Unidos servem como exemplo: em princípio o partido democrata exemplifica a esquerda moderada (igualitarismo libertarista), enquanto em princípio o partido republicano exemplifica a direita moderada (libertarianism). O governo republicano de George Bush cometeu um grave erro tático e humanitário na política externa, que foi a invasão do Iraque. Já na época especialistas advertiam que o preço dessa intervenção militar seria a guerra civil, pois o Iraque era uma colcha de retalhos cultural, herança do colonialismo, mantido unificado apenas pelas mãos de ferro de Sadam Hussein. O resultado da ação americana foi um conflito com um preço humano alto demais: fala-se em mais de duzentas mil vítimas civis.
   O contraponto disso foi o governo esquerdista liberal de Barack Obama. Ele conseguiu conter a crise econômica, mas foi muito além do razoável, do possível e mesmo do justo na implementação de políticas de auxílios sociais com secretas intenções populistas. Dessa maneira foram cometidos erros memoráveis, como a aceitação indiscriminada de imigrantes, o aumento na taxação de indústrias produzindo fuga de capital, a desastrosa Obamacare, a suspensão do embargo a uma ditadura sanguinária como a de Cuba... Um exemplo de apoio ingênuo a ditaduras foi o acordo para a utilização pacífica da energia nuclear, que liberou o estado totalitário que é o Iran para após dez anos produzir uma bomba nuclear, o que induzirá a uma corrida armamentista no oriente médio. Finalmente, como é frequente nas esquerdas, Obama gastou mais do que podia: a dívida Norte Americana saltou de 8 trilhões de dólares para mais de 20 trilhões, pondo em risco a estabilidade econômica do país. A continuação dessa política significaria um debacle econômico. Ou seja: a esquerda foi longe demais e em suas políticas cometeu tantos erros quanto a direita havia antes dela.
   O contraponto disso está sendo agora o governo conservador de Donald Trump cujo programa é de direita: organizar a imigração, diminuir os gastos do estado, aumentar o papel da iniciativa privada taxando menos e com isso criando mais oportunidades de emprego, além de combater a corrupção. Vemos aqui um bom exemplo do zig-zag político em um país desenvolvido, o que entendo como sendo responsável pelo equilíbrio dinâmico constitutivo da forma como um sistema democrático é capaz de auto organizar as relações entre classes sem recurso à violência do totalitarismo. Os programas de esquerda e de direita se corrigem um ao outro, como se poderia dizer, “dialeticamente”.  
   Tudo isso me faz concluir que tanto a esquerda – fazendo ouvir as classes subordinadas – como a direita – privilegiando as classes dominantes – tem o seu lugar, e que uma alternância de poder entre uma e outra pode ser algo saudável e plenamente compatível com uma sociedade legitimamente democrática.

[1] Isso é sempre um ideal. Mas uma democracia só possui autenticidade na medida em que se aproxima desse ideal.
[2] Adam Smith: An Inquiry into the Nature and Causes of the Wealth of Nations, Book
[3] Newton Freedman: Free to Choose: A Personal Statement
[4] Stalin chegou a fazer listas de pessoas que eram escolhidas pelos nomes para serem acusadas e executadas com o objetivo de manter a população aterrorizada.
[5] John Rawls: A Theory of Justice

domingo, 20 de maio de 2018


DRAFT for the book 'Philosophical Semantics'. Final version will be published by CSP in july 2018.


He who thinks the separated to be separated and the combined to be combined has the truth, while he whose thought is in a state contrary to that of the objects is in error.

1. Deceptive simplicity of correspondence
I begin by addressing the shallowest objection against the correspondence theory of truth. It is the claim that the theory is nothing but a trivial, empty truism. According to this widespread objection, to say that truth is agreement with facts is a too obvious platitude to deserve philosophical attention (Blackburn 1984, Ch. 7.1; Davidson 1969).
     The illusion that feeds this objection emerges from the fact that all too often in philosophy careful scrutiny has shown that what initially seems to be a plain, uncomplicated meaning conceals unexpected complexities. One impressive example of this was the causal theory of action. Who could at first glance foresee that analysis would show that such an apparently simple thing as the concept of human action could involve a variety of sometimes very complex processes, like the formation of reasons (made from desires and beliefs) producing previous intentions that at the right time produce the intention-in-action (the trying) directly causing the right bodily movements, which should produce as final outcome the intended effects? In what follows, I hope to convince you that the correspondence theory of truth is no exception to this rule. The supposed simplicity of the correspondence relation is only apparent, revealing our lack of awareness of what we really do when making truth-claims.
     Methodologically, my strategy consists in reconsidering the best insights that we have inherited on the correspondence theory and in asking how far they can be developed and plausibly combined in order to lead us to a full-blooded philosophical analysis of the correspondence relation. As you will see, this endeavor ultimately requires a pragmatic investigation of the dynamic constitution of correspondence, which in the end exposes its intrinsic relationship with verifiability, coherence, criteria of truth and even its dependence on an adequate answer to the problem of perception.
     Consequently, in order to bring clarity to our views, what we need is to delve more deeply into the waters of the above suggested approach to the correspondence theory of truth.
2. Analysis of correspondence (1): structural isomorphism
Suppose that truth in a privileged sense is indeed correspondence (adequation, agreement, match…) between a verifiability e-thought-content rule and the fact it represents. In this case, we must first specify each term of this definition. We have already clarified the concept of thought as an e-thought – an extensible thought-content properly built upon psychological p-thought-rules, as the archetypical truth-bearer in our discussion of Frege’s semantics (Ch. IV, sec. 34). We did this along with a detailed defense of the idea that an elementary real fact is a cognitively independent arrangement of elements, which are tropical properties and clusters of compresent tropes corresponding to a proper singular statement. And as we also saw, ‘fact’ is an umbrella-term that includes actual static facts (situations, states of affairs…) and dynamic facts (events, processes…), serving in this way as universal truth-makers – the most proper verifiers of statements (Ch. IV, sec. 23). What is now in need of analysis is the concept of correspondence in its relevant sense.
     The early Wittgenstein, as is well known, insightfully defended a correspondence or adequation theory of truth in the form of a pictorial theory of representation in his Tractatus Logico-Philosophicus (1984g, sec. 2.21). I prefer to ignore the implausible atomistic metaphysics of this work, later rejected by him, though not its deeper insights (Cf. Stenius: 1981[1]); and one profound insight of the Tractatus is that a fundamental condition of representation is a pictorial relationship between the logically analyzed sentence (Satz), expressing what he calls a thought (Gedanke),[2] and the possible fact, called a state of affairs (Sachverhalt), which can be actualized as the real fact (called by him a Tatsache[3]), the fundamental verifier able to make the thought true. The idea was resourcefully explored by E. G. Stenius in his important monograph on the Tractatus (1960) and several later articles (particularly that of 1981) by applying to it the mathematical concept of structural isomorphism.
     Applied to the correspondence view of truth, a true thought-content must have at least structural isomorphism with a possible (conceivable) or actual (real) fact. As I understand it, the structural isomorphism is constituted by three conditions, which are at least partially explanatory of the idea of correspondence:

(i)    A bi-univocal relation: each semantic component of a verifiability e-thought-content rule (or of the sentence adequately expressing it) and each corresponding element constituting the possible or actual fact (understood as something epistemically objective[4]) must have a biunivocal relation.
(ii)   A concatenation: the component rules of a verifiability e-thought-content rule (or of an analyzed sentence) must be combined in the same manner as are the elements composing the possible or actual fact.
(iii) A correlation: a verifiability e-thought-content rule as a whole must be biunivocally related to the possible or actual (real) fact, making it its correlate. (This condition presupposes the satisfaction of (i) and (ii), though it goes beyond them.)

Now, a necessary condition for the truth of an e-thought-content-rule is that it must be structurally isomorphic with an actual fact in the world. And a necessary condition for its falsity is that although it is structurally isomorphic with a possible fact – that is, a conceivable or imaginable fact – it is not structurally isomorphic with any expected contrastively real fact. Structural isomorphism is a necessary condition, because a supposed proposition, an e-thought-content-rule, must be at least possibly classifiable as true or false in order to have any cognitive function and deserve its name.
     Notice that we do not need to believe that possible facts exist in some Platonic realm in order to accept the requirement of conceivability. To conceive or imagine a possible fact is simply a psychological phenomenon, and it is clear that we don’t need to conceive or imagine it in all the details we would be forced to consider if it were a real-actual fact. In other words, a true verifiability e-thought rule must be isomorphic with a fact in the world, while a false e-thought-rule, though not isomorphic with a fact in the world, must at least be isomorphic with a possible (conceivable, imaginable) fact, because it is by means of this ‘projection’ that we know that in principle it could be correlated with an actual fact in the world.
     The natural way to apply this view to real statements is to begin with singular predicative or relational statements in their actual linguistic practices, taking the logically analyzed sense-components of their sentences as the elements that must be biunivocally related to the elements of the possible or actual facts. Thus, we begin with e-thought-contents expressed by singular statements of the form Fa (ex.: ‘John is easygoing’) or aRb (ex.: ‘John is the father of Mary’) or Rabc (ex.: ‘John gives Mary a flower’) or Rabcd (ex.: ‘John gives Mary a flower to please Jane’)… In order to be true, these statements must at least satisfy the same already explained conditions of structural isomorphism:

(i)    Each component sense or semantic-cognitive rule expressed by each nominative and predicative expression must correspond biunivocally to the respective elements constitutive of the respective fact in the world. This fact is an arrangement made up of simple or complex property-tropes (like being easygoing, being the father of, giving something to someone, giving something to someone to please someone else) and tropical objects, made up at least of tropes like those of form, solidity, mass… and possibly mental states like feelings… all of them displaying compresence (John, Mary, Jane, the flower…) (See Ch. IV, sec. 5)
(ii)   The concatenation, i.e., what we called a manner of connection between the component rules of the e-thought-rule and the fact, must be preserved. Because of the manner of connection, a sentence with the form Fa cannot be replaced by aF (e.g., ‘John is easygoing’ cannot be replaced by ‘Easygoing is John’), and a sentence with the form aRb cannot represent the fact represented by bRa (e.g., ‘John is the father of Mary’ cannot be replaced by ‘Mary is the father of John’). Regarding these forms and orders of connection, they emphasize that properties are relatively dependent on objects in the context of the facts they belong to (being easygoing depends on John’s existence, being a father depends of the existence of John and Mary…); the concatenation can be already read in the components. [5] (See Ch. IV, sec. 7-9)
(iii) the whole thought-content must be biunivocally related with its possible or actual corresponding fact.

This view should apply even to complex and vague expressions. Take, for instance, statements like ‘Céline had a strange personality’ and ‘The Irish potato famine was caused by late blight.’ Insofar as these expressed thought-content-rules can be objectively-interpersonally verified, they are acceptable. Although it is surely not so easy to explain Céline’s strange personality or how the late blight caused the Irish potato famine, these concepts remain open to investigation and reducible to complex associations of tropes.
3. Analysis of correspondence (2): categorial match
According to Stenius, sharing the same ordered logical structure isn’t enough. He was aware of this difficulty when he suggested that there must be what we could classify as a condition (iv), demanding some kind of categorial match between each biunivocally related pair of elements. Using his own words, we could say that the components of the e-thought-rule must be indices of the elements of the fact they biunivocally represent.
     Since words like ‘categorial match’ and ‘indices’ are not very informative, one could search for something less metaphorical. As I have already noted (Ch. IV, sec. 3), Kant wrote about schemata. For him, a concept is a rule able to produce figure-types or patterns (Gestalten) that we can correlate with the objectively given in order to recognize it. As he wrote:
The concept of dog means a rule according to which my imagination in general delineates the figure [pattern] of a four footed animal, without being limited to any particular figure offered by experience or by any possible image that I can represent in concreto. (1988, A 141)
Although Kant’s full exposition of this topic is frustratingly obscure, it seems clear that it anticipates what we have previously learned in our readings of Wittgenstein, Frege and later philosophers (particularly Michael Dummett and Ernst Tugendhat), suggesting that we look for an answer in terms of the specifying power of semantic-cognitive rules. Restricting ourselves to the simplest case of the singular predicative statement, what we have is the following. First, consider the conceptual senses expressed by singular and general terms, namely, the identifying and ascription rules along with their joint formation of a verifiability rule. Each of these semantic-cognitive rules is able to establish an undetermined variety of dependent criterial configurations, whose satisfaction is nothing but their matching with independent or external criterial tropes or configurations of tropes (properties), clusters of selected compresent tropes (objects), arrangements of such configurations of tropes and such clusters (facts). Once all these dependent criterial configurations are seens as satisfied by suitable tropical arrangements or actual facts in the appropriate context, the verifiability rule is considered effectively applicable. Since this rule is nothing but the e-thought, once definitely applicable this verifiability e-thought-content rule will be called true and said to represent a fact. This shows that Stenius’ indices, Kant’s schematized patterns, and our Wittgensteinian criteria or criterial configurations are only increasingly detailed attempts to do the same thing, namely, to isolate, to distinguish in their uniqueness the isomorphic elements constitutive of the represented facts, in order to justify the applicability of their verifiability rules.
     Since these semantic-cognitive rules are also senses in a Fregean conception of ‘modes of presentation,’ what we first need to add to our understanding of correspondence as structural isomorphism are the individualizing senses of the component expressions, that is, the semantic-cognitive criterial rules constitutive of the verifiability e-thought rule. As explained in Chapter IV, we typically identify the grounding fact corresponding to the basal e-thought by means of some variable criterial aspect: a sub-fact. In order to achieve this, what we usually do is the following. By means of the partial structural isomorphism between the criteria demanded by the derived verifiability e-thought rules and sub-facts as independent criteria, we usually infer the isomorphism between the cognitive rules constitutive of the basal e-thought (e.g., an identification rule and an ascription rule building the verifiability rule) and the grounding fact, if the e-thought-rule is true, or merely a conceivable grounding fact, if the e-thought-rule is false.
     Furthermore, we must remember that we can make any of these rules explicit by means of definitions able to bring their criteria of application to the surface, as I have initially shown using the concept of chair as an example (Ch. II, sec. 7). In the aforementioned examples, we can do something similar. Concerning names, in examples like (1) ‘The book is on the table,’ (2) ‘Kitty is in the kitchen,’ and (3) ‘John is father of Mary,’ this would be done by means of the (semantic-cognitive) criterial definitions given by the identification rules of the nominal terms ‘the book,’ ‘the table,’ ‘Kitty,’ ‘the kitchen,’ ‘John,’ ‘Mary’ (See Appendix Ch. I). Concerning predicative expressions in examples (1), (2) and (3) this would be done by means of definitions of the relational predicative expressions ‘…is on…’, ‘…is in the…’, ‘…is the father of…’ Such definitions will also show how the elements can or cannot be adequately concatenated one with another (the table cannot be on the book, the kitchen cannot be in Kitty, Mary cannot be the father of John) and, mainly, how they can be applied to the tropical elements constitutive of the corresponding grounding fact. The condition (iv) of categorial match is also the condition that the e-thought and its elements can be made explicit as semantic-criterial rules able to match their proper references, distinguishing each statement by its proper semantic content.
     These explanations entitle us to suggest that when two e-thoughts p and q display structural isomorphism and the (semantic-cognitive) criterial rules that form the required elements of p are the same as the (semantic-cognitive) criterial rules that form the required elements of q, then both e-thoughts are at least qualitatively the same. That is, since the cognitive verifiability rules are the same, p and q express what we may call the same senses, the same verifiability e-thought rules or, as we can also say, the same contents. We will return to this point later, when we arrive at the pragmatics of the correspondence relation.
4. Analysis of correspondence (3):
intentionality and causality
There are two additional elements that we need to consider in order to complete our analysis of correspondence: (v) intentionality and (vi) causality. In judging something to be true, we must be aware that we are applying a verifiability rule to a fact, we need to have a referential directionality that leads us from semantic-cognitive rules to the tropical criteria that should satisfy them, from an e-thought to the real-actual fact it aims to represent in judgment.[6] One could say that intentionality gives to the correspondence a ‘mind-to-world direction of fit,’ defining the direction of fit of a mental state as what John Searle would call its ‘responsibility’ to fit an independently existing reality, that is, as its ‘mind-to-world responsibility of fit’ (2004: 167-9). Intentionality isn’t a condition on the same level as the others. It is added to the above explained conditions of correspondence as something belonging to the broader structure of our consciousness, since it requires some kind of conscious attention on the speaker’s side. The upshot is that correspondence restricted to isomorphism is symmetrical, while correspondence cum intentionality is asymmetrical. Since correspondence (as agreement, accordance, congruence, conformity, matching) is symmetrical (if A corresponds to B, then B must correspond to A) – correspondence can be the best word for distinguishing isomorphism, but not as well isomorphism regarding categorical match and still less isomorphism regarding intentionality. Less neutral words would be ‘picturing,’ ‘adjustment’ and ‘adequation,’ since these relations are less forcefully symmetrical (if A pictures B, B does not literally picture A, if A is adequate to B, B isn’t necessarily adequate to A…). Because of this I will give preference to the word ‘adequation,’ meaning by it correspondence cum intentionality.
     Finally, from the opposite direction, what we may find in the case of true e-thoughts will be (vi) a suitable causal relation by means of which an actual fact may make us recognize the truth of its e-thought. However, it seems that in the real world the causal network is so extremely complex that we are led to see that the causal relation we are considering in no way needs to be a direct one. In fact, it can be very and even extremely indirect, easily misleading us to the belief that it does not exist.
     Causality has a ‘world-to-mind direction of fit’ or a ‘world-to-mind responsibility of fit’ in the sense that it is what causes thought-content to match reality. We can speak here of the effective applicability of its verifiability procedure and, in the case of some unintentional perceptual indexical e-thought-rule, even of the causal transient construction of such a rule in a given context – a rule that once constructed is intentionally applied.
5. Exemplifying adequation
For reasons of clarity, I will consider a final example of a composite thought-content adapted from Stenius, which allows us to summarize what we have learned about adequation. If someone says: ‘John (j) is the father (F) of Peter (p) and of Mary (m), who is a violinist (V)’, the logical structure of the e-thought-content expressed by the statement is:

1.     jFp & jFm & Vm.

Assuming that we know the identification rules for John, Peter, and Mary, and with the ascription rules of the predicates ‘…is the father of…’ and ‘…is a violinist,’ along with the semantic rule of application of the logical operator ‘&’ (which can be provided by a truth-table), we know that this statement might be true. In other words, we know that we can combine these semantic-cognitive rules, applying them imaginatively in order to conceive a possible state of affairs corresponding to the e-thought-content, giving to the statement at least a meaning. If the statement is false, the correspondence stops here, as a mere adequation with a possible but non-actual fact. Now, suppose that statement (1) is true. In this case, we have the five conditions of correspondence satisfied by a complex real fact. The satisfaction of these five conditions can be presented at least as follows:

(i)    The bi-univocal relation between each of the non-logical and logical components rules of the composed verifying e-thought-content rule expressed by (1) and each corresponding factual tropical element.
(ii)   The same concatenation between the semantic-cognitive rules constituting the verifiability rule of each singular e-thought-content, including the relations of conjunction among them and among the biunivocally related elements of the three represented elementary facts.
(iii) The bi-univocal relation between each singular verifiability e-thought-content rule and its represented elementary fact (the same regarding the composed e-thought-rule and composed fact).
(iv) Concerning each verifiability e-thought-content rule, the matching (or satisfaction) of the dependent criteria formed by each component semantic-cognitive rule (identification plus ascription rule) regarding its proper objective correlate – a tropical criterial correlate – together with the two rules of conjunction, assuring us the proper individuation of the rules working as meaning unities.
(v)  The intentionality (directionality) we link to the rules, leading us to distinguish what is representing – a composite e-thought-content rule – from what is being represented – the actual corresponding composite fact – building a mind-to-world direction of fit.[7]
(vi) The assumption that ‘jFp & jFm & Wm’ is true because we have reasons to believe that it is, even if in some very indirect way, causaly determined by the facts, the causation having a world-to-mind direction of fit.

As we know, for a disjunctive statement with the form ‘jFp jFm Vm’ to be true, one of the disjuncts, at least, must represent not only a possible fact, but also the actual fact, by having criterial configurations of its verificational rule matched by the external tropical structure of its represented fact. Finally, all false disjuncts must at least correspond to possible (conceivable or imaginable) facts, if we want the statement as a whole to remain cognitively meaningful.
6. Compatibility between verification and correspondence
Against the correspondence view of truth, there is also the objection that it is incompatible with verificationism. The objection can be as follows: a statement can be verified in many different ways, insofar as its verifiability rule may be satisfied by an indeterminate range of diversified sub-facts, which are tropical arrangements acting as verifiers. By contrast, correspondence should be a one-to-one relation: the fact corresponding to a true proposition should be univocally related to the proposition stated by the assertoric sentence. Consequently, it does not seem possible that what verifies the stated proposition is a corresponding fact, as claimed by traditional correspondence theory. (e.g., Hallett 1988: 29)
     As you have probably already noted, the above argument is deeply misleading and it only reaches its conclusion by searching for correspondence in the wrong place. Usually, correspondence requires more than a match between an e-thought-rule and a fact in the world. The verifiability e-thought rule might accept multiple correlative independent criterial tropical arrangements for its application, as it was already clear as we distinguished correspondence with sub-facts from correspondence with the grounding fact (Ch. IV, sec. 26) and later, as we considered Wittgenstein’s examples (See Ch. V, sec. 3, his example of the Cambridge boat race).
     Correspondence is here, we can say, often a relation between an immediately-derived verifiability e-thought rule and its sub-fact belonging to a more encompassing relation between a mediated-basal verifiability e-thought rule and its grounding fact. And what interests us most here is the last case: the correspondence between the basal verifiability e-thought rule as a typically ramified verifiability rule and the grounding fact with its many different sub-factual manifestations. Concerning this, the central point is that our resulting awareness of the grounding-fact can be inferred from the satisfaction of this or that isomorphic sub-fact, viewed as a partial independent external criterial tropical arrangement, often the only one immediately experienced. For instance: I say that I see the grounding fact that there is a ship in the bay, even though I can see this grounding fact only from one side and at a certain distance, that is, by visualizing the specific tropical arrangement constitutive of a sub-fact I already have enough criteria for the inference of the grounding fact. Hence, the comprehension of a grounding fact is typically indirect and inferential. Summarizing, correspondence often occur on two different levels:

1)     Immediate-derived level: as the matching between the dependent criterial configuration generated by some derived verifiability e-thought rule and the independent criterial configuration formed by some tropical arrangement constitutive of the appropriated sub-fact (e.g., ‘I see the side of a ship’).
2)      Mediated-basal level: as the match between a basal verifiability e-thought rule with its many ramifications (i.e., encompassing a great variety of probably true albeit non-verified e-thoughts) and the grounding fact to which the many tropical arrangements constitutive of its derived sub-facts very probably belong. Normally it is the satisfaction of a suitable criterial configuration by means of a sub-fact that enables us to indirectly infer[8] the correspondence between the basal e-thought-rule and the grounding fact (e.g., ‘I see a ship because I see the side of the ship’).

These two levels of correspondence work in the same way, requiring what can be called a two level structural isomorphism, first between the derived though and the sub-fact, second between the basal thought and the grounding fact.
     In more detail, the intrinsic relation between verification and correspondence can be explained as follows. First, concerning the immediate-derived level of correspondence, we have a derived e-thought constituted by its own verifiability rule that can be expressed by a sentence of the form Fa, for instance,

(a)     A ship-bow is rising,

when a ship is approaching the pier. This rule is satisfied by the sub-fact that a ship-bow is rising, which requires the satisfaction of the criteria for an identification rule for the singular term ‘a ship-bow there,’ added by the satisfaction of the criteria for application of the ascription rule of the predicate ‘…is rising.’ Clearly, the relation between this derived e-thought-rule and the criterial configurations requires structural isomorphism with the independent external criterial tropical arrangements. But in this case and in many others, the immediate-derived level of correspondence can ground the inference of a mediated-basal level of correspondence. In this case, by means of the experience of sub-facts as independent criteria, we may indirectly infer that overall a main verifiability e-thought rule with its wider divisions corresponds to a whole grounding fact. Consider for instance the e-thought-rule expressed by the following statement of the form Fa: ‘That ship is approaching.’ We may conclude the truth of this statement simply by means of the already verified criterial dynamic sub-fact of the form of a ship-bow rising up before our eyes. That is, using the identified sub-object of a ship-bow as a criterion, we are able to infer that the identification rule for the concrete object expressible by the singular term ‘There is a ship there’ is applicable to the object and that based on this the ascription rule for the predicate ‘…is approaching’ applies to the property of approaching, which belongs to the same whole object, both rules building the verifiability rule expressed by the statement

(b)     That ship there is approaching.

Since this verifiability rule proves to be effectively applicable, it can be seen to have the higher-order property of being true, since a verifiability rule is the same as an e-thought-content. We see that based on the awareness of the dynamic sub-fact of a ship-bow rising we conclude that the dynamic grounding fact of the ship approaching is also real, that there is also a correspondence between the elements of the verifiability e-thought rule and those belonging to the grounding fact.
     This is why we can still say that a thought expressed by p, its cognitive meaning, corresponds to the factual content q, even if it is a rule and its verifications are very often variable, partial and perspectivistic, relying on sub-facts. The sub-facts and their corresponding verifiability rules are like the branches of a tree that has a trunk, the grounding-fact, and its corresponding basal e-thought, its verifiability rule. Having access to some identifiable branches you can reach the tree. And a similar metaphor could be applied to the basal thought as a trunk and the derived e-thought-rules as the branches specularly corresponding to the first suitable external branches, the sub-facts, the last belonging to an external grounding fact, the external trunk. We will come back to this point in the end.
7. Formal definitions of truth
Assuming the suggested analysis of correspondence, we can symbolically express what could be called a formal definition of truth, giving us the logical structure by means of which we can identify the predicate ‘…is true’ with the predicate ‘…corresponds with a fact.’ As with the predication of existence, the predication of truth is of a higher-order. It is a semantically metalinguistic predicate applicable to thought-contents. We call a predicate semantically metalinguistic when it refers primarily to the content of the object language, contrasting it with a syntactically metalinguistic predicate, which refers only to the symbolic dimension of the object language. The statement

 ‘“Themistocles won the battle of Salamis” is a historical statement’

can serve as an illustration. The semantic metapredicate ‘…is a historical statement’ refers metalinguistically primarily to the semantic content of its object-sentence, that is, to its thought-content-rule, and by means of this, secondarily, also to the real historical fact (acknowledging it as real). According to this view, for any e-thought or content of belief p, to say that p is true is the same as to say that p adequates to an objectively real or actual factual content. We can express this symbolically, using p to express the e-thought, replacing the predicate expression ‘…is true’ with T and the predicative expression ‘... adequates to an actual fact’ with A. The symbols T and A stand for semantic metapredicates belonging to a semantic metalanguage, by means of which they refer to the e-thought-content-rule expressed by p, which can be shown by placing p in quotation marks. Using ‘=’ to express something like a (numerical) identity, here is a first identification of truth with adequation:

(1)    Tp’ = Ap[9]

According to this identification, truth is the property of a thought-content expressed by a sentence p of adequating to some real-actual fact.
     This formulation depends on the application of the monadic predicates ‘ true’ and ‘...adequates to a fact.’ However, monadic predicates can often be unfolded into non-monadic predicates such as, for instance, ‘…is a father’ into the more specific ‘…is the father of…’ The same can be said of the predicates ‘…is true’ and ‘…adequates to a fact,’ which can be unfolded as more complete relational predications of a semantic metalanguage relating the thought expressed by p to the fact or factual content that q as ‘…is true for…’ and ‘…corresponds to the fact that…’ (Cf. Künne 2003: 74). We can also illustrate this point using an example. One could say

‘“Themistocles was the victor at the Battle of Salamis” expresses the same historical occurrence as “The Battle of Salamis was won by Themistocles”,’

 where ‘…expresses the same historical occurrence as…’ is a relational semantic metapredicate primarily applied to the e-thought-content-rules expressed by the two object-sentences and only secondarily to the facts represented by them.
     This means that the definition (1) can be more completely explained as stating that for a given thought-content p, to say that p is true for the actual factual content q is the same as to say that the thought-content p adequates to the actual factual content q. For this explanation, one can understand correspondence as a relation of identity of contents expressed by p and q, so that we can say that p = q. (I underscore q in order to show that its content, though also interpretable as an e-thought, is preferably interpretable as an actual or real fact in the world; how this is possible will be explained later…) To offer a simple observational example: suppose that the thought expressed by ‘The Moon is white’ is true. We only say this because of the real-actual fact that the Moon is white. And this is the same as saying that the e-thought-rule expressed by ‘The Moon is white’ corresponds to contents of observations of the white Moon understood as really factual.
     Now, replacing the semantically metalinguistic relational predicate ‘…is true for the fact that...’ for T*, and replacing the also semantically metalinguistic relational predicate ‘...adequates to the fact that…’ for A*, we have the following more telling formalized version of a so-called formal definition of truth as adequation. In this definition, the e-thought-rule expressed by p and the actual factual content expressed by q are metalinguistically related by the metapredicates T* and A* as follows:

(2)    ‘pT*‘q’ = ‘pA*‘q

More than an unpacking of (1), the identity (2) is a more complete formulation that individualizes the corresponding fact to be represented by any instance of q. According to (2), the assignment of truth is the same thing as the assignment of the relational property of correspondence, which can be viewed as the assignment of a qualitative identity of content between an e-thought-content-rule and an actual corresponding factual content. (As we saw, this identity of content should be analyzed in terms of structural isomorphism, added to the satisfaction of criteria for applying each component term of p…)
     Finally, assuming that e-thoughts are verifiability rules, we can add that to say that an e-thought corresponds to a fact should be the same as saying that the verification procedure constitutive of the e-thought applies to a fact. Symbolizing the semantic metapredicate ‘…is a verification procedure that applies to a fact’ with V, we have:

(3) T‘p’ = A‘p’ = V‘p’

More completely, symbolizing the dyadic semantic metapredicate ‘given… the verifiability procedure effectively applies to the fact …’ as V*, we have:

(4) ‘p’T*‘q’ = ‘p’A*‘q’ = ‘p’V*‘q

These are, I believe, the best ways to represent in an abstract formal way the general identifications between attributions of truth, adequation and verifiability.
8. Negative truths
Now, consider a false singular predicative or relational statement p. Since it is false, such a statement does not correspond to any epistemologically objective real fact in the world. However, to say that p is false is the same as to refute the attribution of truth to p, which means to say that the statement ~p is true. Here the problem arises. If ~p is true and we accept adequation theory, it seems that ~p must correspond to some fact. However, suppose that we replace p with the false statement (i) ‘Theaetetus is flying.’ In this case ~p is to be instantiated by (ii) ‘Theaetetus is not flying.’ Then, at first glance it seems that we have in (ii) a true statement that does not correspond to any fact in the world! This would lead some to suspect that (ii) is true because it refers to a ghostly negative fact: the unworldly fact that Theaetetus isn’t flying.
     With the help of the preceding formulations, it is easy to reach a more plausible answer. That the statement that ~p is true does not correspond to any actual fact in the world, even if it is instantiated by ‘Theaetetus is not flying’ and we know that Theaetetus is in fact sitting, since according to ~p he could also be standing, lying down, running, etc. However, since ~p means the same as ‘p is false,’ and by saying that p is false one denies correspondence with an objective real-actual fact in the world, one denies that the verifiability rule has effective applicability in its proper context, and that is all. Despite this, as I have insisted, by imagining the false idea that Theaetetus is flying (that I symbolize as ‘f’), we already accept that f corresponds with a possible fact, namely, with our imaginary dynamic fact of Theaetetus flying, which although epistemically objective in Searle’s sense isn’t actually real in the sense of belonging to the external world. However, a possible fact can be no real external fact in any metaphysical sense; it is something that is located somewhere in the mind (-brain) when we imagine it. In summary, ~p and ‘p is false’ only mean that p expresses a verifiability rule that although applicable to an only conceivable or imaginary state of affairs – a possible fact – does not effectively apply to any actual, objectively real fact.
     Summarizing, if you consider a general statement like ‘There is no cat with three heads,’ it means the same thing as ‘It is false that there is a cat with three heads.’ And what this statement says is that although there is a corresponding conceivable factual-object that is a cat with three heads, there is no externally real fact-object in the world that is a cat with three heads. Still, one could argue that the statement that there is no cat with three heads is true because it agrees with the fact that there is indeed no cat in the world with three heads (Searle 1998: 393). However, here I must disagree. It seems more reasonable to think that this is a mere façon de parler, allowed by the flexibility of our natural language. The statement ‘There is no cat with three heads’ is true because it means ‘It is false that there is a cat with three heads,’ which says that there is no real fact constituted by a cat with three heads living somewhere in the outside world – only an imaginary one.
9. Self-referentiality
As expected, the identifications we have made until now also enable us to develop a kind of Tarskian answer to the so-called liar paradoxes of self-referentiality. Consider the following standard self-referential statement:

(i) This statement is false.

If this statement is true, what it states must be the case. But it states that it is itself false. Thus, if the statement is true, then it is false. On the opposite assumption, that the statement is false, then what it states is not the case, which means that the statement is true. Consequently, if the statement is true, it is false, and if it is false, it is true. This is the simplest example of a semantic paradox of self-referentiality involving the concept of truth, although there are many variations.
     One of these variations is the indirect self-reference in which a statement refers to itself by means of another statement, generating the same paradox. Consider an example (Haack 1978: 135):

(1)     The next statement is true…     (2) The previous statement is false.

If statement (1) is true, then (2) is true; but if (2) is true, then (1) must be false... On the other hand, if statement (1) is false, then (2) must be false; but if (2) is false, then (1) must be true.
     Having in mind our previous formal definitions of truth as correspondence, the general answer is that self-referential statements like these are mistakenly constructed because in all these cases the predicate ‘…is true’ does not work as a semantically metalinguistic predicate referring to a complete thought-content. Rather, ‘…is true’ functions as a normal predicate built into the thought-content, in this way belonging to the object language. Being mistakenly constructed, these state­ments have no proper cognitive meaning beyond their grammatical form. They might seem meaningful on the surface, suggesting that we should treat them as we would treat a statement with the form ‘p is true’ or ‘p is false.’ Once we have fallen into this trap, paradoxical consequences follow.
     Now, why doesn’t an affirmation like (ii) ‘This sentence is true’ generate a paradox? Consider the statement ‘The sky is blue.’ The truth-claim is here unnecessary, since implicit. For reasons of parsimony, a statement usually does not need the addition that it is true in order to be understood as expressing a truth. Because of this, the statement (i), though affirming its lack of effective applicability, naturally generates its truth-claim, since what it affirms (its falsity) is seen as though ‘This statement is false’ should be additionally true. The statement (ii), to the contrary, affirming its own effective applicability, though also devoid of content, resists a paradox-generating interpretation because the affirmation of its own applicability does not generate a statement that implicitly affirms its lack of applicability, adding to it its falsity.
     Now, consider the sentence (iii) ‘It is true that this sentence has nine words.’ This is a perfectly normal true sentence referring to itself. Why? The reason is that the metapredication of truth is applied to the thought-content (verifiability rule) that the sentence in question has nine words without really belonging to this thought-content. For the same economical reason that assertions do not demand the explicit attribution of truth, (iii) is in fact understood as (iv) ‘“it is true that this sentence has nine words” is true’, and this can be made more completely explicit as (iv) ‘The thought expressed by the sentence “It is true that this sentence has nine words” is true.’ This makes it clear that the relevant attribution of truth is not built into the relevant thought-content.
     Furthermore, we can predicate the truth of a metalinguistic thought-content insofar as this semantic predication is meta-metalinguistic and so on, since the e-thought, as an arrangement of apparently disembodied mental tropes, is also a fact.
10. Pragmatics of the correspondence relation
What we have seen up to this point was the frozen logical-conceptual structure of truth as correspondence. Now we will see how it works in the practice of truth-attributions, as a process occurring in time. The view I wish to defend here was inspired by Moritz Schlick’s brief defense of the correspondence theory of truth (1910), though in my judgment this could be regarded as an empiricist revision of a relevant insight attributable to Edmund Husserl (cf sec. 31 of the present chapter). The idea is that correspondence has a pragmatic or dynamic dimension that deserves to be explored and cannot be captured in static formal definitions – an idea that should not sound strange to those who wish to combine correspondentialism with verificationism. We can begin by considering that very often we can establish an idealized sequence of (I choose) four successive moments, which we may call: (1) suppositional, (2) evidential (3) confrontational and (4) judgmental or conclusive. Together they constitute a very common form of verification procedure.
     The best way to introduce the idea is by means of examples. Schlick used the example of Le Verrier’s prediction of the planet Neptune’s existence based on orbital perturbations of Saturn: Le Verrier first developed a hypothesis, which was later confirmed by observation, since the contents of both were the same. I next offer a more trivial example. Suppose that it is the rainy season in Northeastern Brazil, where I normally live, and that I ask myself: ‘Will it rain in Natal tomorrow?’ This is a suppositional moment. Now, when tomorrow comes, I open the door of my house and see that, in fact, it is raining heavily outside. This is the second, the evidential moment. Once I do this, I compare my earlier question with the observational evidence that it is in fact raining and see that the content of the question is like the content of my observation. This is the confrontational moment. Finally, considering that these contents are qualitatively identical (in fact, satisfying conditions (i) to (vi) of adequation), I conclude that the thought-content of my earlier hypothesis is true by adequation with the fact that today it is raining in Natal. This is the judgmental or conclusive moment. Now, if instead of seeing rain outside I see a very blue sky, the content of my observation contradicts that of my supposition. Seeing that the content of my observation in this proper context diverges from the content of the supposition, I conclude that p must be false: it is not raining in Natal today.
     Examples like these are common, and an analogous procedure, as we will see, applies to non-perceptual truths. But for now, restricting myself to perceptual judgments, I can say that at least regarding cases like those considered above, we can formulate the following action-schema with four moments:

1)     The suppositional moment: what I call ‘supposition’ can be a thesis, a hypothesis, a conjecture, a suspicion, a guess, a question, a doubt... In this first step we ask ourselves whether some thought-content-rule is true, that is, if the verifiability rule that constitutes it is not only imaginatively, but also definitely applicable in its proper context. We can express this as ‘I suppose that p,’ ‘It is possible that p,’ ‘I guess that p,’ ‘Is it the case that p?,’ where p expresses a content that can be perceived. This moment can be formalized as ‘?p’ (call ‘?’ the operator for supposition). This supposition is always made in the context of some linguistic practice.
2)     What follows is the evidential or perceptual moment: the realization of a perceptual experience in an already more or less specified observational context gives us a perceptual content, which may or may not correspond to the content of the supposition.

Here we try to verify the truth of the supposition by finding a perceptual content that is identical to the content of the supposition. In the case of observational truths, this step is very simple. We look for an expected adequate perceptually reached content of thought that, in a suitable context, we simply read as a truth-maker (verifier), which can be rendered as ‘I perceive the fact o,’ call it ‘!o’ (where ‘!’ is the evidence operator). Phenomenologists have called this moment registration or fulfillment (Cf. Sokolowski 1974, Ch. 9). As we will see, there can be no question about the truth-value of o: it must be assumed as ‘evidence’ or ‘certainty’. In fact, it must be stipulated as indisputable within the context of the practice, the language game in which it occurs; otherwise we would be daunted by the question of the truth of o! which would also need to be grounded, leading us to an infinite regress. (The ontological problems concerning o! will be discussed only at the end of this chapter.)

3)     Confrontational moment: it is the comparison between the sup­posi­tion­al content and the factual content of the perceptual experience which makes possible the verification or falsification of the suppositional content.

Here we ask whether the supposition matches the evidential result of the perceptual experience. In the case I considered, I asked myself whether the thought-content-rule of the hypothesis was sufficiently similar to the factual content directly given to me in the perceptual experience (satisfying conditions (i) to (vi) of adequation). In the case of a perceptual experience, the positive answer can be summarized as p = o. As will be better explained and justified later, here also we underscore o as o, so that it can be read as either the thought-content-rule (a proposition) (o) or the actual factual content (presented by o) fulfilling it, which involves an arrangement of external tropical criteria given in the contextually expected sensory experience. If the expected similarity of content between p and o is lacking, we have p o. (In its concrete details it is more complicated: as we already noted, usually the fact presented by o is only partially and aspectually experienced, which does not prevent me from saying, for example, that I see that it is raining all over Natal. Moreover, in practice it is often the case that we must have more than only one perceptual experience and in more than one way...)

4)     Judgmental or conclusive moment: Finally, in the case in which p = o, the thought expressed in the supposition will be accepted as true, otherwise it will be rejected as false. When p = o, there is adequation and the conclusion is an affirmative judgment that can be symbolized as ├p. In the case in which p ≠ o, that is, in the absence of the expected adequation, the thought p is false. This can be expressed by the negative judgment symbolized as ├ ~p.

Now we can summarize the four steps of this whole verifiability process regarding the discovery of perceptual truths of the simple kind considered above in the following temporal sequence:

?p, !o, p = o /├ p

This analysis shows that in many cases one finds adequation (particularly as identity of content) between some suppositional e-thought-content-rule ?p (which is only a considered or imagined verifiability rule in its possible application) and some perceptual e-thought-content-rule !o (given by the definitely applied verifiability rule) that within the linguistic practice in which it is stipulated is regarded as indisputable. In other cases, the adequation is only between the supposition and an imagined, non-actualized fact, being therefore distinct from what can be found in the observation. In these cases, the statement must be false.
     It is also worth noting that the standard statement of ├p (a judgment) has the form of the report of an assertion that is settled. However, this assertion can always be questioned again. In this case, new verifying procedures can reconfirm the judgment or detect some inadequacy refuting it in an at least virtually interpersonal way (Cf. Sokolowski 1974, Ch. 9).[10]
     Now, how can we understand the adequation relation as a qualitative identity of content (structural isomorphism, identity of cognitive rules, intentionality…) in terms of the application of verifiability rules? Here is my suggestion. When I first perceive that it is raining in Natal, the indexical phrase ‘now in Natal’ expresses the building and application of an indexical identification rule of a spatiotemporal region to which the predicate ‘…is raining’ is applied. This predicate expresses an ascription rule definitely applicable to the region by the satisfaction of configurations of tropes constituted by the countless drops of water falling from the sky above. This combination of satisfactions gives me the arrangement that constitutes the sub-fact that is the truthmaker which allows me to infer the content building the grounding fact o! that it is raining in (all parts of) Natal today. Now, p = o means that the contents of both e-thought-rules are identical. In more detail, there is an adequation between both e-thought-content-rules or, in still more detail, the identification rule of p has a one-to-one relation with the identification rule of o, the ascription rule of p has a one-to-one relation with the ascription rule of o, the concatenation between the rules of p and of o is the same, there is categorical match, intentionality and causality; p is intended to fit o, and o has a causal direction of fit concerning p, since it makes p true. Consequently, the verifiability e-thought-content rule p adequates to the verifiability e-thought-content rule o, even if in details this can occurs by means of the most diverse sub-factual isomorphic matches of criterial configurations.
      Now one could object: must we have a qualitative identity between p and o? It is true that between the ?p of yesterday and even the ?p that I made to myself as I awakened today and the !o there is indeed qualitative identity. However, I cannot believe that at the moment when I perceive that it is raining, p and o are qualitatively distinct. It seems to me more plausible that the identity p = o in the perceptual moment have a numerical identity, which means that Husserl was in his own way right in understanding correspondence as a form of identity (See sec. 31 of this chapter). Moreover, it is always possible to interpret o as a real external fact and not propositionally, as we can do with the mere identification p = o.
11. Retrograde procedures
Now, what was presented above is what we may call an anterograde way to achieve truth. I call it so because we went in a temporal sequence from the supposition containing a conceivable e-thought-content-rule to the perceptual evidence that confirms the supposition by the application of a perceptual e-thought-content-rule that is qualitatively identical with the supposition. However, a move in the opposite direction is equally feasible. We can have a truth-value attribution that has its origin in perceptual experience, progressing from evidence to the affirmation of a supposition – a way to discover truth that I call retrograde.[11]
     Here is a simple example of a retrograde verification procedure. I open the door of my home in Natal with the intention of going out and unexpectedly see that it is raining. Since I need to go out, I go back inside to look for an umbrella, aware that it is raining… In this case, the perceptual evidence comes first. However, it seems clear that the recognition of truth does not occur as a direct product of sensory experience since I could see rain without consciously perceiving it. This suggests that the initial rough and pre-conscious sensory-perceptual state was different from the state of awareness that immediately followed, namely, the conscious awareness that it is raining. (Suppose I open the door to get some fresh air although I see I do not even pay attention to the fact that it is raining outside. If someone then asks me if it is raining, I will pay attention to the already non-reflexively roughly applied conceptual rule for rain, compare it with a similar now fully conscious application of this rule and answer in the affirmative). Thus, it seems that we can explain the process of arriving at the truth included in the judgment of the given example in the following way: First, I have the rough, non-reflected observational experience ‘o!’ of rain. This momentary experience makes me immediately recall the fully conceptualized ascription rule for ‘it is raining,’ which together with the identification rule for ‘the city of Natal today’ forms the supposition ‘?p.’ Finally, I compare the content of my first observation with the content of this recalled e-thought-rule of raining in Natal today. Once I see that o = p, I am led to the conclusion that it is true that it is raining or ├p. If I am right, then this process is normally completed very quickly, which accounts for our lack of awareness of its different steps. Anyway, this is a retrograde discovery of truth, which I believe that can be summarized in the following sequential formulation:

!o, ?p, o = p /├ p

Clearer cases of retrograde awareness of truth occur when we have an unexpected sensation or perception that we only slowly come to be aware of in its true conceptualized nature. To illustrate I give two examples. The first is related by Paul Feyerabend in his auto-biography. He writes that once when he was sleeping he at first mistakenly identified a feeling with a cramp, and only when he woke up did he see what he was really feeling: a severe pain in his leg. We may call the first sensation ‘!s,’ mistakenly taken as a cramp or s’. In the process of waking up, he must have been led to recall the most appropriate conceptual rule for pain as ‘?p.’ As he clearly identified s with p, he realized that he was feeling pain in his leg, reaching the conclusion ├p.
    The second example is of an experience that I myself once had. A nice woman gave me a teacup at her home containing a sweet beverage, without saying what it was. I was sure I knew the taste, though I could not identify it. Hence, I must have applied a mugh ascription rule, which I call !t. However, since the context gave me no clue as to what the liquid in the cup was, I needed about a minute to recall the taste of juice from pressed sugarcane, that is, ‘?p.’ Then, by comparing this conceptual memory ?p with the taste of the liquid !t in the cup and seeing that t = p, I came to the obvious conclusion: the liquid was pressed sugar-cane juice. Here the action-schema is:

!t, ?p, t = p /├p.

The retrograde procedure seems to be the inverse of the anterograde, also because the first moment of both seems loose, unsettled, insufficiently determined.
12. A more complex case
The cases I have considered until now are the simplest sensory-perceptual ones. However, the pragmatics of adequation can be extended to the truth of non-observational e-thought-rules, which I will here call mediated thought-contents. Suppose that Lucy is at Charles de Gaulle Airport in Paris, waiting to board a flight to Dakar. The flight lasts approximately five hours. She calls her daughter, who lives on a farm in Senegal and asks her how the weather is in the city of Dakar. She wonders if it is sunny. This is supposition ?p. Suppose that after a while her daughter answers that the weather in Dakar is and will remain mild and warm enough. There is no significant reason for doubting this information, which she takes as providing adequate evidence. The factual thought-content expressed by ‘!q’ that she had after she heard about the weather in Dakar is the same as the thought-content belonging to her hopeful question ‘?p.’ Consequently, since p = q, she concludes that p is true, that the weather in Dakar is and will remain mild. But the thought-content-rule expressed by !q is not observational! It is the result of testimonial inferences that are unknown to Lucy. Suppose that her daughter got this information from her husband, who had read a weather report, and that this information had its origin in meteorological observations of weather conditions around Dakar. In this case, putting ‘>>>’ in the place of some chain of reasoning unknown to Lucy that led to the factual judgment expressed with !q, and putting ‘!o’ in the place of the observational meteorological thought-contents that in some way led to !q (which will probably be similar to those that she will have when she arrives in Dakar five hours later), we can formally structure the verification process in which p is presently made true for Lucy as follows:

?p, (!o >>> !q), !q, p = q /├ p

Important to note is that the evidential character of the observation !o is taken as preserved in the supposed inferential chain that leads to !q (I put the process in parentheses in order to show that it is unknown to Lucy and even to her daughter). The informational content is transmitted from thought-content to thought-content up to the conclusion !q, which inherits the evidential character of !o, and then !q is compared with the question expressed by ?p. Thus, contrary to our most natural expectation of how adequation should work, the truth of ?p isn’t directly confirmed by the observational fact represented by !o, but by something derived from it, namely, by !q, understood as also representing a fact, a personally non-experienced state of affairs in the world. The adequation is between unfulfilled and fulfilled thought-content rules, the last ones also understood as being fulfilled by a factual content composed of external tropical arrangements.
     The foregoing example is one of an anterograde verifiability procedure, beginning with one supposition (the question) and ending with a comparison between the supposition and a derived evidential thought-content of an unexperienced fact. However, we may also have a retrograde procedure with a chain of reasons that ends by matching a derived piece of evidence with a supposition. So, imagine that at the beginning of the flight to Dakar the pilot informs the passengers that the weather in Dakar will be mild and warm enough. Each passenger will be led to the conclusion that the weather in Dakar will, in fact, be mild by means of another indirect and for them also unknown evidential chain. However, in this case, it is the evidence that recalls the concern regarding weather conditions. This concern is satisfied by means of a comparison of contents from which the final judgment results that the weather in Dakar will be mild. This retrograde process can be summarized in the following temporal sequence:

 (!o >>> !q), !q, ?p, q = p /├ p

We see that the opposition between anterograde and retrograde verification repeats on mediated levels. We may guess whether the intuitions of some researcher who still does not know how to prove some hypothesis, though having a glimpse of its truth, depends on unconsciously noticing that the knowledge of some factual content expressed by !q might be derived from evidential observations or postulates.
13. General statements
General statements of e-thought-contents – universal and existential – are also involved in the pragmatic process of adequation, as an identity between the contents of the hypotheses and contents of sets formed by the respective conjunctions and disjunctions, often resulting from inductive inferences ultimately based on observational facts. So, suppose that ├p is the assertion: ‘All the books on this shelf are in English.’ Further, suppose that I reach this generalization casually in a retrograde form from earlier observations ‘!o1, !o2… !on,’ of each book on the shelf. The action-schema is the following:

{!o1 & !o2 &… & !on } → !q, ?p, q = p /├ p

Of course, it can be different. It can be that I first ask myself if all the books on the shelf are in English. Then I look at each of them, concluding in an anterograde procedure that this hypothesis is true:

?p, {!o1 & !o2 &… & !on } → !q, p = q /├ p

Now, suppose that for another Mrs. Hildish asks: ‘Is there at least one book in Italian on my shelf?’ Now, after searching, she finds just one. We call it ‘!o1.’ This enables her to affirm that there is at least one book in Italian on her shelf, concluding by means of an anterograde procedure:

?p, {!o1 ˅ !~o2 ˅… ˅ !~on } → !q, p = q /├ p

As in the previous cases, this example deals with a general deductive conclusion, but it is easy to see that inductive generalizations should also have similar structures, given that they are also restricted to some more or less vague domain (See Appendix to Chapter V, sec. 3).
     Now we return to the old question of knowing if there must be general facts – the all facts – over and above singular facts (Russell 1918; Armstrong 1997, Ch. 13; 2004, Ch. VI). Bertrand Russell, who seems to have discovered the problem, defended their existence as follows:
I think that when you have enumerated all the atomic facts in the world, it is a further fact about the world that those are all the atomic facts there are about the world, and that is just as much an objective fact about the world as any of them are. It is clear, I think, that you must admit general facts as distinct from and over and above particular facts (Russell 1956: 236, my italics).
It seems to me that this is much more a worldly question than Russell supposed, since it can be shown that his all fact is not a fact hanging over any other. In the examples above, all that is needed to get the totality of facts is an additional limiting fact restricting the extension of the generality, first to books belonging to my first shelf and then to books belonging to Mrs. Hildish shelf. I agree that descriptions of such limiting facts need to be added to the given sequences of particular conjunctions or disjunctions in order to close their domain. But these limiting facts are nothing but ordinary empirical ones. And the harmless affirmation ‘those are all’, meaning ‘there is nothing beyond these’ can be inferred as a consequence of adding the conjunction or disjunction of the singular facts to the corresponding empirical singular limiting facts, in the given case the facts established by the spaces the shelves have for their books! Using a still simpler example, if I say that I have only three coins in my pocket, the ‘all fact’ is given by the domain established by the fact that there is a pocket in my pants that I use to carry coins. Moreover, the only difference between the examples given above and an extensive fact like ‘All men are mortal’ is that the delimitation of the last domain is probably the whole earth during the whole existence of the species Homo sapiens, which is a much larger and more vaguely delimited domain. This is how Russell’s mysterious and inconvenient all fact disappears.
14. Some funny facts
There are a variety of puzzling ‘funny’ facts, and I will only select a few to give some indicative explanations. One of these is that of self-psychic (self-reported) truths. It is easy to know the truth-value of the thought p: ‘I am in pain.’ I believe that here as well there is adequation. But first, I need to learn the rule. A first step to this is that I interpersonally learn to identify the location of pain. Then, helped by a considerable network of other concomitant, previously and later observable occurrences, along with the fact that I am told by others that pain is none of these, I discover, by means of induction by exclusion, that pain must be an invisible but physically located feeling of intense discomfort… Even if others cannot have interpersonal access to the subjective feeling of my pain in order to confirm it, I am able to make my verifiability rule for pain highly plausible, even if the logical possibility of interpersonal access to my pain itself cannot be excluded.[12] Now, suppose that I have a headache. The first thing I have is an unamed feeling of pain: ‘!s.’ Then comes ‘?p’: the actualization of the memory of what the feeling of having a headache means (the conceptual rule), which is what I associate with the word. Then I make the identification s = p, being led to the conclusion ├p:

!s, ?p, s = p /├ p

Here I discovered the truth that I have a headache in a retrograde way. An anterograde way to reach the same truth would be the case of a woman who guesses that she will have a headache because she has drunk red wine, and she knows she always has a headache after drinking red wine.
     Wittgenstein offered, as is well known, an expressivist explanation for such cases. For him the utterance ‘I am in pain’ is nothing more than an extension of natural expressions of pain like ‘Ouch!’ (Wittgenstein 1984c, I, sec. 244). In this case, our schema would be something like ‘!s ├ p’ without adequation. I do not reject this possibility. But I find it easier to believe that this could be the expression of a more direct reaction that turns out to be seen as true only after the exercise of the previous, more elaborate cognitive process of induction by exclusion concerning auto-psychic states and induction by analogy concerning the hetero-psychic states (Costa 2011, Ch. 4).
     Another odd case is that of true counterfactual conditionals. Consider the statement (i) ‘If Evelyn were the queen of England, she would be a public figure.’ The objection is that there appears to be no fact that can make this sentence true, since Evelyn isn’t the queen of England. However, statement (i) seems to be true! Nevertheless, the solution is easy. Although there is no actual fact that can make statement (i) true, this is not what the conditional requires. What statement (i) requires as its verifier is not an actual fact, but only a possible fact. The possible or conceivable fact that makes the statement true is that under the assumption that the antecedent were true, namely, that Evelyn is in fact the queen of England, the truth of the consequent will be unavoidable, that is, she will surely be a public figure. That is, the truthmaker of (i) is a modal fact that could also be expressed using the vocabulary of possible worlds. In other words, suppose that We is any nearby possible world where Evelyn is in fact the queen of England. Since in our world all queens of England are public figures, we can infer that if someone is the queen of England in We, this person will also certainly be a public figure. Assuming that Evelyn is the queen of England in We, she is also (certainly) a public figure in We. We conclude that it is certainly true that if Evelyn were the queen of England she would (certainly) be a public figure, because the expressed thought-content certainly corresponds with the expected fact belonging to a conceived counterfactual circumstance given in We. Understanding (i) as the supposition ?p, and calling the certainty that in any nearby possible world Evelyn would be the queen and therefore a public figure q, we can summarize the anterograde process as follows:

?p, (We)q, p = q, / ├p

A second similar example is, (ii) ‘The Dalai Lama never slept with a woman, but he could have.’ This is certainly true because it means the same thing as (iii) ‘Although the Dalai Lama never slept with a woman in the actual world, there is a nearby possible world Wd (our world with some differences) where he slept with a woman.’ The statement (iii) is true, since it corresponds to the conjunction of an actual and a possible (conceivable) fact, this conjunctive fact being conceivable as a highly probable physical possibility (ontologically, an association of actual and possible tropical arrangements).
     One could also ask about ethical truths. Consider the statement (iv) ‘Dennis should help the drowning child.’ Suppose that despite being a very good swimmer, Dennis didn’t even try to help the drowning child, because he is a sadist. We would not be inclined to say that (iv) is true, but rather that (iv) is right. It is right in a similar way as an illocutionary act like ‘I promise to go to your anniversary celebration’ can be felicitous. The statement about Dennis would be morally right because it is in conformity with a utilitarian norm, let us say, the rule according to which:

UR: One should help another person in mortal danger, insofar as one does not put oneself in real danger.

Note that what counts in this case is not truth, but normative correctness – adequation with a norm, though the mechanism of validation is similar. Statement (iv) is validated by what could be called the moral norm UR (an equivalent to the fact regarding truth). Finally, there is still the case of the validity of such utilitarian norms. In an attempt to achieve this, consider the following utilitarian normative principle:

UP: A morally correct rule is one that when applied under normal circumstances brings the greatest possible amount of happiness to all participants, without significant unhappiness to anyone.[13]

Suppose it is a fact that when people act in accordance with this principle the well-being of their whole community increases. Assuming that this is our ultimate goal, this principle can be considered correct or true, and we can say that UP validates UR, which validates (iv). (Note that the normative principle UP as much as the norm UR are moral facts that should be also instantiated as arrangements of tropes.)
     Obviously, this is just an illustration. The greatest problem faced by ethical statements is the same as with any other philosophical statement. Unlike the statements of natural sciences, they belong to those speculative domains wherein we are only able to make the truth of our statements more or less plausible.
15. Expansion to formal sciences
Analogous logical structures and dynamic procedures can be found in the formal sciences, allowing us to generalize adequation theory to a domain traditionally claimed by coherence theories of truth. The main difference is that while for empirical truths inferences are mainly inductive, for formal truths they are normally understood as deductive. Suppose we want to demonstrate that the sum of the angles of any Euclidean triangle is 180°. We can do this by first proposing that this could be the case: ‘?p’ and then searching for proof. One proof would proceed by drawing a straight line through one of the vertices of the triangle, so that this line is parallel to the side opposite to this vertex. Since the three juxtaposed angles formed by the parallel and the vertex of the triangle are the same as the internal angles of the two opposed vertices of the triangle plus the angle of the first vertex, and their sum is obviously 180°, we conclude that the sum of the internal angles of this and indeed of any Euclidean triangle must be 180°. This deductive conclusion is the evidence ‘!q’ – the truthmaker as a geometrical fact constituted, I suppose, by geometrical tropes (Cf. Appendix of Chapter III, sec. 4). Since we see that the content of !q is the same as the content of the hypothesis ?p, we conclude ├p. Using ‘as’ for the axioms or assumptions (the formal data), the form of this anterograde procedure can be summarized as:

?p, !as >>> !q, p = q, /├ p

It is important to see that !q, stating the fact that makes the thought-content p true, as in the case of Lucy’s question, should not be placed at the beginning, but at the end of a chain of reasoning. Unlike Lucy, a geometrician can (and should) go through the whole procedure.
     Now, an example from mathematics: we can prove the arithmetical identity statement (i) ‘2 + 2 = 4’ in a Leibnizian manner.[14] We begin with definitions (which here correspond to basic perceptual experiences in empirical sciences). First, we define 2 as 1 + 1, 3 as 2 + 1 and 4 as 3 + 1. We call this set of definitions ‘d. Replacing in statement (i) the numbers 2 and 4 with their definiens, we get (ii) ‘(1 + 1) + (1 + 1) = (3 + 1).’ Since 3 is defined as 2 + 1, and 2 as 1 + 1, we see that 3 can be replaced by (1 + 1) + 1. Now, replacing the number 3 in its analyzed formulation in (ii), we get the arithmetical fact represented by (iii) ‘(1 + 1) + (1 + 1) = (((1 + 1) + 1) + 1),’ which is the same e-thought-content as ‘2 + 2 = 4.’ In this way, we have derived confirmatory evidence for the hypothesis ‘?p’ posed by statement (i), which is the (supposedly tropical) factual content of ‘!q’ described in (iii). This confirmatory evidence serves to check the hypothesis ‘?p’ that 2 + 2 = 4. Again, abbreviating the definitions as ‘d,’ we have the following anterograde verificational action-schema:

?p, !d >>> !q, p = q /├ p

Once more we see that the factual content expressed by the identity !q, which serves to check the hypothesis ?p that 2 + 2 = 4, is not the same as the definitions of 1, 2, 3 or 4, as might be initially assumed. It is the result of a deductive reasoning process based on these definitions, a reasoning process deductively derived from its definitional premises. This result, expressed by !q, represents the arithmetical fact represented by the supposition ?p, so that p = q, which makes p true.
     Finally, we can give examples involving logic. Consider the following theorem of modal logic: P → ◊P. This can be seen as our hypothesis ?p. How do we prove it? In the S5 modal system, we can do this by using as assumptions the axioms AS1, ◊P ↔ ~□~P, and AS3, □~P → ~P. Taking these axioms and a few rules of propositional logic as the evidence ‘as’ we construct the following anterograde proof of the theorem:

      The hypothesis is: ‘?p,’ where p = P → ◊P

      The proof:
1         □~P → ~P                              (AS3)
2         ~~P → ~□~P                         (1TRANS)
3         P → ~□~P                              (2~E)
4         ◊P ↔ ~□~P                            (AS1)
5         ~□~P → ◊P                            (4 ↔E)
6         P → ◊P                                   (3,5 SD)

Now, the conclusion (6), P → ◊P, is the ‘!q,’ which represents the derived logical fact that serves as a verifier for ?p, and since p = q, we conclude that p is true, that is, ├ p. Using our abbreviation, we get the following anterograde verificational action-schema:

?p, !as >>> !q, p = q, /├ p

Since the logical fact represented by !q, which carries with it evidence derived from the assumed axioms, is presented by the same e-thought-content-rule as the hypothesis ?p, we conclude that we have adequation. We conclude that p is true, or ├ p. – Also relevant is to note that in the case of formal facts we do not need to underline statement letters like a or d or q: there is no need to distinguish between the conceived and the real-actual facts, since here both can be regarded as the same.
     Of course, one could also find a retrograde form regarding any of the three above exemplified cases. Considering only the first, suppose that someone, having the strong intuition that the sum of the internal angles of an Euclidean triangle is 180°, decides to draw a straight line that touches the vertex of a triangle, this line being parallel to the opposite side. This person could then easily prove that this triangle and in fact any Euclidean triangle would have 180° as the sum of its internal angles. But in this case, the person would have the following retrograde verification procedure:

!q, !as >>> !q, ?p, q = p, /├ p

The !q would work here as the insight into the truth of a conjecture, something to be compared with an unexpected observation.
     The upshot is that the procedures with which we demonstrate the adequation of formal truths are structurally analogous to the procedures with which we demonstrate the adequation of empirical truths. Even so, there are some differences. The most obvious is that formal truths are deductively inferred, while empirical truths unavoidably include inductive inferences.
16. Why can analytic truths be called true?
Finally, we can apply a similar procedure to analytic-conceptual statements, showing that they are also called true because of adequation, even if this is a limiting-case. It is possible to say, for instance, that the analytic statements ‘It is raining or it is not raining’ and ‘Bachelors are not married’ are true because they correspond to the respective facts that assuming the principle of the third excluded it must be either raining or not, and that by definition it isn’t possible for a bachelor not to be unmarried. But to what extent are we entitled to say this?
     Assume first, as we did in our objections to Quine’s argument against analyticity, that analytic statements are true due to the proper combination of the component senses of their expressions. In this case, our question is: are there facts that make analytic statements true? And if they exist, how do they make these statements true? To find an answer, consider the following analytic statements:

(1)      Either it is raining or it is not raining.
(2)      If John is the brother of Mary, then Mary is the sister of John.
(3)      Bachelors are males.
(4)      A triangle has three sides.
(5)      A material body must have some extension.

Surely, these statements are all true in themselves: if there is a fact making them true, it is not a fact in the world. However, we are still allowed to say that they are made true by logico-conceptual, conventionalized facts. Thus, statement (1) is made true by the logical fact that ‘j ˅ ~j’ (the law of the excluded middle), which it instantiates. Statement (2) is made true by the conceptual fact that the brother-sister relation is reflexive. Statement (3) is made true by the conceptual fact that a bachelor is conventionally defined as an unmarried adult male. Statement (4) is made true in Euclidean geometry by the conceptual fact that a triangle can be defined as a closed plane figure with three straight-line sides. And statement (5) is made true by the conceptual fact that part of the definition of a material body must include the requirement of some spatial extension. These are conceptual facts supposedly instantiated by arrangements of our mental tropes and their combinations.
     In all these cases the statements are self-verifiable, that is, the intertwining of rules that constitutes the verifiability rule of an analytic statement is verified not by its application to the world, but by means of an application of one rule to the result of the application of the other in a way that makes the whole true independently of any state of the world. For instance, ~(P & ~P) is tautologically verified by its truth-table, in which we combine the rules for the application of the negation and the conjunction in ways that always gives as a result the value true.
     Moreover, we can summarize this process of self-verification of the above statements by applying the same action-schemata we did with the statements considered in the last section. Thus, in case (1) we can begin with the question ?p1 = ‘is it the case that it is raining or not raining?’ Faced with this, we immediately realize that the sentence instantiates the principle of the excluded middle or ‘j ˅ ~j’, and that this instantiation, like any other, can be symbolized as the instantiation of the logical truth or fact represented by ‘!p2,’ which is proved true by the application of a truth-table to the sentence. This suffices to make ?p1 true, because we can see that independently of any sense given to its constituent parts, its logical structure warrants its truth. We can summarize the self-verifying action in which we find the adequation in the same anterograde way as in the first of our examples:

?p1, !p2, p1 = p2 /├ p

Putting differently: in this case, the thought-content is identical with an instantiation of a logical truth of propositional logic, a logical fact that makes (1) true by self-verification.
     In other cases, reasoning may be necessary. In case (3) the suppositional moment ‘?p1’ is: ‘Are all bachelors males?’ To verify this, we first need to take the definition of a bachelor as our point of departure: ‘!d’ (Df.) = ‘A bachelor is an unmarried adult male.’ From !d we can infer the conceptual fact !p2 = ‘All bachelors are males.’ Summarizing the steps of this anterograde self-verificational procedure, we get:

 ?p1, !d → !p2, p1 = p2 /├ p1

It is correct to say that analytical thought-contents are true by courtesy, since they cannot be false. But despite this, it is not senseless to speak of their truth as correspondence or adequation with facts. The reason is clearer in cases like the last one. For even if these cases are all ones of self-verification, the procedure is not always direct and transparent, often requiring a reasoning process.
     Finally, what about contradictions like (6) ‘It is raining and it is not raining’? Suppose we call the statement of this contradiction the supposition ‘?p,’ which is shown to be opposed to the true statement ‘~p,’ asserting the factual content that it cannot be the case that it is raining and simultaneously not raining at the same time and place, which is derived from the principle ‘!q’ of non-contradiction: ~(j & ~j). In this simple case, the anterograde verifying procedure will be:

?p, !q, q → ~p, p ≠ ~p, ├ ~p

The conclusion is that p is false, since the principle of non-contradiction shows that p cannot be the case and that strictly speaking there can be no fact in the world able to verify p. The verifying procedure that falsifies p is the self-falsifying cognitive action that gives the contradiction its contradictory meaning.
17. The insufficiency of coherence
That truth has something to do with coherence is beyond doubt. If Mary says that she was breathing while she was asleep last night, we accept her statement as obviously true. We believe Mary, even if we did not watch her sleeping last night, because her statement is coherent with our accepted belief-system. We are certain that people will die within a few minutes if they cannot continuously breathe oxygen. If Mary tells us that she visited the Moon while asleep last night, almost everyone would consider this statement to be false, because it clashes with the generally accepted commonsense understanding of what is possible or impossible under ordinary life circumstances, together with our system of scientifically confirmed beliefs. Coherence is obviously related to truth, and according to most coherence theorists, a belief is truer the more it is integrated into our system of beliefs, which also means that truth is a question of degree (e.g., Blanshard, 1939, Ch. XXVII).
     Bernard Bosanquet (2015: 24) once gave an interesting example intended to show that a greater amount of supporting information makes a statement more true, which seems to vindicate the idea that some kind of integration of a statement within a system of beliefs is what makes it true. He noted that the sentence ‘Charles I died on the scaffold’ seems quite true when said by a leading historian and far less true when said by a mere schoolboy. The child has at most a name and a picture in his mind, while the historian knows from documents and historical studies a wealth of meanings associated with the sentence (Cf. also Blanchard 1939, Ch. XXVII, sec. 4-5). The aim of this example is to show that increasing the coherence of a statement increases its degree of truth.
     Nevertheless, there is an alternative interpretation. We can say that the example only shows that the historian’s claim to know the truth has a better chance to be confirmed. In other words, it is his truth-holding (Fürwahrhalten) that has a higher chance of achieve truth. This alternative is better, since there is no indication that our ordinary view of truth has degrees. Hence, the example only confuses the degrees of probability that a person knows the truth – the probability of truth-holding that can be attributed to the person – with an illusory degree of truth in itself.
     The best known objection to the coherence theory of truth is the following. Since countless possible belief-systems can be constructed, any proposition p could be true in one system and false in another, violating the non-contradiction principle. This objection, however, was never regarded as a major difficulty by coherence theorists (e.g. Bradley 1914; Blanshard 1939, vol. 2: 276 f.; Walker 1989: 25-40).
     One could, for instance, answer the objection that some thought-content p can be true in one system and false in another in a way that eliminates the contradiction. One can introduce the idea of the system of all systems, namely, the most encompassing system of beliefs agreed upon by a community of ideas at time t (preferably the best informed and trained community that we are able to consider…). To this can be added the fundamental subsystem contained in the system of all systems, which is the real-world belief-system, so that this system generates all the other derived sub-systems that might fall under the epithet ‘fictional.’ The novel Madame Bovary, for instance, is for us a fictional subsystem belonging to the all-encompassing system of systems. That at the end of the novel Charles says, ‘C’est la faute de la fatalité,’ is true in the context of the novel, but false for the real-world system, because in our real world there was never any Charles Bovary married to Emma Bovary and able to say this sentence regarding the series of events that led up to her suicide. The admission that Charles made this comment is thus true in the novel and false in the real world, which does not lead to a contradiction, not only because these are two belief-systems, but also because they do not conflict, as what counts is the real-world system, where this sentence was never uttered in a proper context.
     Consider now a second example, the statement that the sum of the angles of a triangle is 180°. This is true in the system of Euclidean geometry, but false in Lobachevsky’s and Riemann’s systems. And it is in the end false regarding the physical real-world system. Consider, finally, the statement that the value of a good is determined by the importance people assign to it as a means to achieve their desired ends. It is considered true in the subjective economic theory of value and false in the labor theory of value, since for the latter the value of a good is determined by the amount of labor required to produce the good... Nonetheless, regarding the real-world system, the first theory seems to be (according to the great majority of economists) more probably true.
     Surely, this view relativizes truth to a certain extent, by limiting it to a time and a community of ideas, making truth-theory to a certain extent subordinate to our taking things to be true (das Fürwahrhalten).[15] However, in the end this would not be a problem if we agree that ‘the truth,’ that is, absolute truth, is actually nothing but a kind of directive idea that helps us evaluate our holding something to be true, but has no decisive identity with what we normally accept as true or false. – As already noted (Ch. IV, sec. 30), even if by chance we were to discover an absolute truth, we would not be able to know with any certainty that we had really found it (See Popper 1972, Ch. 2). That is, when we say that p is true, we only assume that p is the final truth until we find some sufficiently good reason to falsify p (if p is empirical) or abandon p (if p is a formal statement). Because of this, a true theory of truth is a theory of what leads us to take something to be true rather than a theory of absolute truth. The same can be said regarding the concept of knowledge. We pragmatically treat our truths and knowledge of truths as if they were the ultimate ones, simply postulating or assuming we have achieved final truths and knowledge. But concepts like those of final, ultimate or absolute truth and knowledge can serve only as directive ideas. They are ‘as if’ concepts since they cannot possibly have experienceable objects that allow us to see if we have achieved them.[16]
     A strategy like that of admitting a system of all systems that includes a real-world system as the most fundamental seems to overcome the objection of contradiction. Nonetheless, even so coherence theory remains problematic, since the insurmountable problem of this view is located elsewhere. I call it the problem of circularity.
     The problem of circularity arises when we try to define coherence. Traditionally coherence has been conflated with consistency. A set of propositions (thought-contents) is said to be consistent when the conjunctions of propositions belonging to it do not generate a contradiction. Consistency may be a necessary condition for coherence, but it is surely not sufficient. For instance, consider the elements of the consistent set {Shakespeare was a playwright, lead is a heavy metal, 7 + 5 = 12}. They do not contradict one another. But since they do not have anything in common, taken together the elements of this set increase neither the coherence nor the truth of its elements; and we could create a set of this kind as large as we wish with ‘zero’ coherence. Consistency may be a necessary, but it is not a sufficient condition of truth. And worst than this is when we perceive that any definition of truth based on consistency alone would be circular, since consistency, being defined as the absence of contradictions generated by the elements of a set of propositions, assumes that their conjunctions cannot be false, in this way requiring the concept of truth-value in its own definiens.
     More than just being consistent, coherence must be defined as inferential. The coherence of a belief system, of a system of propositions, is in fact determined by the dependence of this system on the inductive and/or deductive relationships among its propositions. This means that the degree of coherence of a proposition p should be determined by its inductive and/or deductive relationships with the system to which it belongs (Cf. Bonjour 1985: 98-100). Indeed, we know it is true that Mary was breathing the whole night long, because this is inductively supported by everything we practically and scientifically know about human metabolism and behavior, and this is a truth concerning our system of reality.
     However, if we consider coherence as the only and proper mechanism able to generate truth, this last definition also leads to circularity, since the concepts of inductive and deductive inference used in the definiens of coherence are also defined by means of truth! A strong inductive inference is defined as an argument (or reasoning) that makes a conclusion probably true, given the truth of its premises, while a valid deductive inference is defined as an argument (or reasoning) that makes its conclusion necessarily true, given the truth of its premises. Consequently, the coherence account of truth can only generate the truth of any proposition of the system by assuming the independent truth of at least some of its other propositions, which makes the coherence view clearly circular. Any form of pure coherence theory is the victim of a petitio principii, as it simply assumes what it aims to explain.
18. Coherence as mediator
The view of coherence that I wish to propose here enables us to circumvent the difficulty. The reason is that in my understanding, coherence must be seen as a complementary dimension of adequation theory, namely, the condition that enables the transmission of truth in a network of thought-contents, usually beginning with those that are based on empirical (sensory-perceptual) experiences and/or some assumed formal evidence/assumptions (axioms or postulates).
     Such view allows us to accept some factual content that should make some proposition true without the need for reducing this factual content either to some corresponding formal axiom or to an obvious perceptual or self-psychic thought-content. For instance, we know that the statement ‘Mary was breathing when she was asleep last night’ is true, and it is true because it corresponds to the factual content that Mary was breathing during her sleep. But usually we reach our belief that such a statement is true by adequation to a fact, not by means of direct observation, but by means of coherence, that is, by means of inferences derived from our system of beliefs. These inferences transmit what we may call veritative force – which we may define as any probability of truth higher than 0.5 – from one proposition to another. However, this veritative force cannot arise from propositions without truth-value, but instead is derived from propositions whose truth-value is ultimately based on (in Mary’s case) a myriad of past judgments. These correspond to perceptual experiences that are the ultimate sources of our knowledge of biological laws, as well as our common awareness that Mary is a living human being like us and subject to the same natural constraints.
     We begin to see that even if coherence cannot be regarded as defining truth, it plays an important role as a mediating procedure whereby adequation is an indispensable ground. For example: the modal proof of P → ◊P in our formal example does not come directly from AS1 and AS3 plus some rules of propositional logic. We first take a series of deductive inferential steps, and these steps are already constitutive of a linear coherential dimension of the verification procedure, which some coherence theorists erroneously saw as the proper criterion of truth for the formal sciences. In this modal proof coherence is constituted by implications transmitting veritative force – here understood as material implications from logical-conceptual, self-verifying truths postulated as axioms – but, as already noted, inevitably containing inductive inferences in the case of the verification of empirical thought-contents.
19. Roles of empirical coherence
The trouble with the coherence of empirical truth can be better illustrated by examples able to make clearer the relationship between coherence and correspondence or adequation.
     First, suppose that someone anonymously sent me a package per post. I open it and see that it contains a book called The Cloven Viscount by Italo Calvino. I wonder if a friend named Sylvia sent it to me. I once knew Sylvia as a literature student in Rome, and at that time I gave her a copy of Calvino’s book The Invisible Cities. However, the package was mailed from Rio de Janeiro. Thus, I realize that this book could have been sent to me by someone else. But then, I remember that Sylvia told me that she was born and lived most of her life in Rio de Janeiro. Hence, she could well be back at home in Brazil. An advocate of the coherence theory of truth would say that the thought-content of the statement ‘p,’ understood as abbreviating ‘My friend Sylvia sent me a copy of The Cloven Viscount,’ is made true by its coherence with other thought-contents, which can be ordered in the following way:

1.     I received as a present the book The Cloven Viscount by Calvino. (r1)
2.     Sylvia was a literature student when I knew her in Rome. (r2)
3.     I gave Sylvia as a present a copy of Invisible Cities by Calvino. (r3)
4.      (from 1, 2, 3) The book could have been sent by Sylvia. (s)
5.     But the book was mailed from Rio de Janeiro. (t)
6.     (from 4, 5) The book wasn’t sent by Sylvia. (u)
7.     Sylvia told me she had lived most of her previous life in Rio de Janeiro. (v)
8.     (2, 7) Sylvia finished her studies in Rome and returned to Rio de Janeiro. (w)
9.     (1, 2, 3, 5, 8) My friend Sylvia sent me a copy of The Cloven Viscount. (q)

What we really have here is an indirect procedure by means of which adequation is verified via coherence. To see this better, we need only revise the above reasoning, rejecting the partial conclusion u because of v. As a result, I can build the following coherent set of beliefs: {r1, r2, r3, t, v, w}. Together, these belief-contents inductively make the conclusion q very probable. This anterograde set of reinforcing premises makes me – starting with the guess ‘?p’ (‘Was it Sylvia who sent me the book?’) – see the identity of thought-contents p = q and conclude with practical certainty ├ p, affirming that it was Sylvia who sent me Calvino’s book. However, each element of the coherent set of beliefs {r1, r2, r3, t, v, w} has its truth directly or indirectly based on correspondence.
     To sum up, I agree with Stephen Walker’s argument that a pure coherence theory is impossible (1989). Coherence could only exist independently of adequation if we were able to assume that e-thoughts could acquire probability or formal certainty independently of any anchorage in sensory-perceptual/self-sensory experience or in the axioms or postulates of a formal system. But, as our examination of the nature of coherence has shown, this would be circular. Moreover, consider again the example offered above. The thought-contents expressed by the statements that by means of coherence make the correspondence between p and q probable are all in some way observationally anchored. Either they describe a perceptual thought (‘I knew her in Rome,’ ‘I gave her a book…,’) or report testimonial information (‘She told me she lived all her earlier life in Rio’) or describe a personal experience (‘I read the book…’) or an inference (‘She may be back home in Rio…’) from testimony (‘She told me…’) based again on the sensory experience of others.
     What was given to me as a fact in the above example was an indirect product of correspondences of other thought-contents with their own factual contents. And the increase of the veritative forces resulting from these experiences is what inductively warrants q to me as the derived proposition representing the fact that Sylvia sent me the book. The assumed warrant of q, in turn, is what makes the e-thought-content of p true for me. In summarized form, introducing the symbol ‘~>’ to represent strong inductive and/or deductive inference, the anterograde reasoning that leads to this attribution of truth can be symbolized as:

?p, {r1, r2, r3, t, v, w}~> !q, p = q, / ├ p

This helps us to understand better how coherence plays a role in the truth-discovery process. And it shows us why the coherence of our claims would have no force if it weren’t anchored in perceptual experiences taken as evidence in the case of empirical truths, and in axioms or postulates in the case of formal truths. This is also why a fictional text can be perfectly coherent without in this way representing any factual truth concerning the real world: its anchors are only imaginary ones.
     This kind of reasoning invites us to think that adequation comes first, since this kind of correspondence is what reveals truth. Moreover, in cases like, say, sensory-perceptual knowledge, we can in a sense have correspondence without coherence, while there is no coherence without correspondence. However, this conclusion can be considered simplistic for the following reason. Correspondence without coherence must be impossible because of the fact emphasized by philosophers of science that all observation is conceptually charged or theory impregnated (Duhem, 1906, Ch. 6, sec. II; Popper, 1972, Ch. 2, sec. 18). In order to be conceptualized, experience already requires coherence with at least one sub-domain of our belief-system.
     Nonetheless, I think that I can give a stronger justification for the indispensability of correspondence as the origin of veritative force by considering the real origins of the own input that a particular sensory-perceptual observation receives from our belief system. Suppose you go for a walk in a beautiful nearby field and you cannot believe what you see there: you think you are seeing a live unicorn! Soon you will begin to distrust your own senses, since you have learned that unicorns do not exist. Later the mystery is solved. You hear that it was actually a fake unicorn: a film production team had attached a horn to the forehead of a small white horse to create the illusion of a real live unicorn. Between scenes, the make-believe unicorn is allowed to graze in the field. The defender of coherence theory would say this proves that even sensory-perceptual observation can be falsified by our system of beliefs alone. But this argument is completely refuted when we consider that what was really responsible for your mistrust was not our system of beliefs alone, but the adequation of other perceptual experiences belonging to this same system or sub-system of beliefs. Indeed, we all know that unicorns are mytho­logical creatures, and there have been no scientifically confirmed observations of unicorns or their physical remains, such as bones, fossils, tissue, etc. Nor have we found depictions of unicorns in cave paintings from prehistoric times, while we have found paintings of aurochs, for example. Moreover, we also know that evolutionary classifications of animals like horses and goats rule out the possible existence of unicorns. But these firm convictions against the existence of unicorns were all reached with the aid of induction by means of a multiplicity of other testimonial sensory-perceptual observations that were historically and scientifically made and passed on to us! This means that your sensory-perceptual observation of a unicorn was in the end discredited not by your system of beliefs independently of adequation, but by counter-evidence derived from the veritative force of other beliefs, all of them anchored in their proper adequation to perceptual observation.
     Now, suppose we call ‘!u’ the factual statement ‘I am looking at a unicorn’ and ‘~u,’ its denial, based on the firm belief that there are no unicorns, which is grounded on the accepted zoological system of beliefs that is in its essentials based on a multiplicity of observational experiences ‘e,’ questioning the possibility of !u, and we call ‘i’ the supplementary information given to you regarding the make-believe unicorn. We can symbolize the procedure that leads you to conclude the obvious falsity of u in two steps that jointly form a retroanterograde verification procedure:

(1)    !u, (e ~> ~u), ~u, u ≠ ~u / ├ ?~u,
(2)    ?~u, i ~> ~u , ~u = ~u / ├ ~u    

Putting my argument in other terms: I certainly agree that sensory-perception is the immediate origin of the veritative force of a perceptual judgment, and this judgment can gain or lose veritative force due to greater or lesser coherence with our system of beliefs. However, this confirming or rejecting coherence acquires its own veritative force only by means of other sensory-perceptual observations whose truth is based on adequation. And reflection on this leads us to the inevitable conclusion that in one way or another the real ultimate origin of the veritative force of empirical judgments is always sense-perception, giving coherence the second­ary, even if indispensable role of transmitting the veritative force gained by means of sensory-perceptual experiences of adequation. My conclusion is that under closer scrutiny the supposed counter-example shows that correspondence comes first, simply because it is the only real source of truth. Thus, instead of defending an impure coherence theory, as Walker endeavored to do, I defend what he would probably classify as an ‘impure’ adequation theory – what I more accurately prefer to call an adequation theory that incorporates coherence.
20. Reverend David’s case
To reinforce my point, I now offer a second, more distinctive empirical example of the incorporation of coherence in correspondence/adequation. It concerns a judge’s verdict. It is well known that court rulings in criminal trials frequently cannot rely on direct perceptual evidence supplied by witnesses. Because of this, they are often heavily dependent on coherence, on proof by means of circumstantial evidence. This was the case with an American minister named Reverend David, who shortly after marrying a certain Mrs. Rose was admitted to a hospital suffering from severe abdominal pain. Since examination showed a high level of arsenic in Reverend David’s blood, a thought-content that we abbreviate as ‘!r, the following suspicion arose as the result of abductive reasoning: ‘Did Mrs. Rose try to poison Reverend David?’ in short, ‘?p.’ The following additional factual evidence later confirmed this suspicion:

s: Mrs. Rose had the habit of preparing bowls of soup for her husband, even bringing them to him in the hospital.
t: Traces of arsenic were found in the pantry of Mrs. Rose’s house.
u: The bodies of Mrs. Rose’s first three husbands, who all died of unknown causes, were exhumed, and it was not so surprising that high levels of arsenic were found in their hair.

We can now construct the following retroanterograde verification procedure:

!r ~> ?p, {!r & !s & !t & !u} ~> !q, p = q, /├ p

Certainly, the conjunction of the statements r, s, t, and u gives us a strong inductive inference assuring us practical certainty that !q, which states an unobserved dynamic fact (namely, that Mrs. Rose did indeed try to poison her husband). This inferred factual content confirms our initial suspicion ?p derived from !r. However, a crucial point to be noticed is that factual statements r, s, t, and u are all considered true either by direct adequation with public factual observation or by derivation from publicly observable perceptual factual contents. Again, what is shown is that the element of coherence cannot stand alone. The plausibility of q is grounded on the conjunction of the observational statements r, s, t and u by means of coherence. But these statements are all true because of their direct or indirect adequation with perceptual contents, even if they may also rest on empirically grounded theoretical assumptions, the latter in some way also derived from other perceptual experiences. As we see, coherence alone cannot prove truth, because inductive and deductive coherence relations are ways of preserving and not of finding truth.
     The conclusion is the same: coherence relations work like the high voltage power lines of an electrical power grid: though they are not able to generate electricity, they are able to transmit it over long distances. A plausible coherent system is not an independent mechanism, but only an inferential network over which the truth arrived at by means of originary adequation is transmitted. In other words: coherence only transfers the veritative force generated by the adequation of the contents of more basic beliefs concerning empirical or formal facts to derived beliefs or thought-contents. This transference of veritative force within a belief-system can act to produce an e-thought-rule that we believe corresponds to a non-observed fact, which in my present example is q: the attempted murder using poison. The thought-content p is accepted by us as representing the factual content q, because both have the same content (structural isomorphism, etc.) which makes p true. Because in various ways q is reinforced in its application, we accept it as factual evidence of p’s truth. And statement p is true because it corresponds to the fact that Mrs. Rose poisoned her husband, Reverend David, even if we know this fact not by observation, but only indirectly, from its coherence with other thought-contents that are observational and match their facts in a direct way. The thought-content q, the truthmaker of p, as I intend to explain, has a kind of Janus face: on the one hand, it expresses here a basal thought-content (an e-thought-rule or proposition), and on the other hand, it represents what we by indirect means are sure is an objective factual content, namely, the fact that Mrs. Rose tried to poison Reverend David. All this shows that coeherence is nothing but an interdoxal mechanism by means of which adequation can transfer its veritative force. It is by this means that coherence helps in confirming the truth of statements.
     Now, concerning the truth of the observational statements r, s, t, u, we return to the point already made when we analyzed our first example. Each of these obser­vations is embedded in at least some subsystem of beliefs. Although a given observa­tion r makes its own contribution to truth by means of direct adequation with a fact (the high level of arsenic in the blood), it can be reinforced by its coherence with the accepted subsystem of beliefs in which it is embedded (like s, t, u together with the hypothesis p), or even be refuted by other beliefs of this same system. But here again, the consideration of this network of giving and taking among sensory-perceptual and derivative beliefs leaves no room for a veritative force arising from coherence.
     The important question that remains open is about the precise status of the statements of factual evidence (like of q) in our examples. It is the expression of an e-thought-content-rule, but it must also be seen as able to represent the actual factual content, namely, a cognitively independent external criterial tropical arrangement. Are these two possibilities reconcilable?[17] This crucial question will be tackled in the following sections.
21. What about the truth of the truthmaker?
One of the most serious problems for the adequation theory of truth concerns the infinite regress that arises from factual evidence that verifies suppositions, that is, verifiers or truthmakers. We can pose the problem in the form of a dilemma: Either the truthmaker – the evidential fact, the real or actual factual content – is unquestionable, or it can be doubted. Suppose (a) that the evidential fact is unquestionably true. In this case, we seem to be guilty of dogmatism, because we treat our normal perceptual truths and even purely self-sensory truths[18] as if they were beyond any possibility of being false. But this would be to deny the fallibility of sensory-perceptual knowledge. We cannot be absolutely certain about the evidence for any (or maybe almost any) empirically given factual content. Even formal axioms always have a degree of arbitrariness in their choice and can lose their applicability after changes in our broader system of reality. Now, suppose (b) that we consider the evidential content believed to be a fact (which shows itself as a thought-content) as open to doubt. In this case, it seems that we need to search for new evidential content (another thought-content) that would warrant its truth. Since this new factual content will likewise not be beyond doubt, we would have to look for further evidential content and so on endlessly. Since we cannot stop this regress, we have no way to ground our suppositions, because any ground we find will lack the necessary solidity. The upshot is that neither alternative (a) nor alternative (b) is satisfactory.
     Restricting myself here to the cases of external empirical truths, I think we can solve the dilemma if we consider examples in sufficient detail.[19] Consider the following example of an observational statement !o: ‘There’s a dolphin swimming in the sea.’ Imagine that the truth of this sentence depends on the observation of a dolphin surfacing from time to time – an observation that can be interpersonally shared. For the first person who sees the dolphin, the procedure has a retrograde form:

!o, ?p, o = p /├ p

For a second person, already informed by the first and trying to locate the dolphin in the sea, it will have a retroanterograde form:

p ~> ?p, !o, p = o /├ p

But this does not mean that !o, the given evidence, is absolutely warranted! It can be defeated. Suppose that due to a scarcity of real dolphins and in order to entertain tourists, a diver is hired who swims just below the surface with a rubber dolphin mounted on his back, surfacing from time to time in a way that gives dolphin watchers the illusion that they are seeing a real dolphin.[20] In face of this, the factual content !o that should ground the verification of ?p is defeated. Those aware of the deception could correctly point out: ‘It is false that there is a dolphin swimming in the sea.’
     However, it should not be hard to find a solution to the problem. What we believe to be factual content need not be regarded as absolute. It can be seen as a thought-content assumed to unquestionably represent an actual factual content (the ultimate truthmaker) within the context of a practice that typically assumes that we do not have atypical circumstances that if present would defeat the assumption. Thus, consider the linguistic practice (A), in which we recognize things in normal daylight that are large enough and near enough to be identified as dolphins, and they are employed in the context of a tourist beach where people expect to see dolphins swimming in the water offshore… In this practice we are allowed to assume that the observational content ‘I am watching a dolphin that has just emerged from the sea’ can be taken as unquestionable evidence expressible by !o. It is thereby a real-actual fact, a truthmaker or verifier that we accept as giving practical certainty to the thought-content that there is a dolphin in the sea near where the observer is standing. Assuming the information content and the context at our disposal in this practice, and assuming that all other things remain the same, seeing a dolphin must undoubtedly be accepted as the truthmaker of the hypothesis ?p. Assuming that o also has internal phenomenal content (with psychologically given sensory impressions), we could say that in this case we are allowed to assume that the e-thought-content-rule of o, that is, o without the underline (expressible as: ‘I am having visual impressions of a dolphin emerging from the sea’) can be considered the vehicle of the experience of the real-actual fact o given in the world (representable as: ‘Being a real dolphin that has just emerged from the sea’). Summarizing: in practice, our willingness to accept evidence is dependent on a ceteris paribus, namely, on the assumption that the observation isn’t being defeated by some condition extraneous to all that is expected for the working of the given practice.
     Now, in the given case there is a defeating extraneous condition, which begins with the scarcity of real dolphins in the vicinity and ends in the training of a diver to swim just below the surface with a rubber dolphin mounted on his back, sometimes rising to the surface in a way that gives people on the shore impressions of seeing a real dolphin… Assuming that some observer S is aware of this information, what is given to him isn’t the practice (A) but a different observational practice that we can call (B), which includes information about the very unusual background circum­stances. In this (B) practice, we cannot postulate the observation of a real dolphin merely because we see what appears to be a dolphin emerging from the sea. Under the circumstances presented by (B), in which a rubber dolphin is often carried on the back of a diver swimming just below the surface, to know with certainty that one is observing a real dolphin would require closer and far more careful examination. Closer underwater inspection, for instance, might reveal factual evidence of a fake rubber dolphin, which can be symbolized by o’. In this new practice, the thought-content expressed by p could not be verified by the fact able to be represented by !o, because !o isn’t really given to S, since we already know that in its context !o cannot be trusted to be a real dolphin. However, ?p could be falsified by the more careful observation provided by o’, as the following retroanterograde schema shows:

p ~> ?p, !o’, po’ /├ ~p

What this example shows is that our usual certainty regarding experienced factual content, despite not being absolute, must be postulated as certain or irrefutable! This is assumed as a practical certainty and must be treated as beyond the level of a merely probable truth, under the assumption that the factual context does not involve unknown evidence able to defeat the linguistic practice in the context of which the perceptual judgment is made. If we obtain information indicating different background circum­stances able to discredit the practice sustaining the perceptual judgment, as in the case above, the assumed evidence vanishes.
     I can offer a second, similar example, only to reinforce the point. Yvonne is driving a car through a desert, and she thinks she sees a lake, but it is really only a mirage. At first, she believes the lake she sees on the horizon is real. We can symbolize this through the following retrograde verification procedure:

!o, ?p, o = p / ├ p

However, it soon becomes clear to her that she has made a naïve mistake; what she really sees is nothing but a so-called inferior mirage. This is caused by the refraction of sunlight passing through a layer of hot air near the ground. In this way, she adds to the background conditions the easy graspable unusual circumstances able to invalidate normal perceptual evidence. As she has learned that these unusual circumstances defeat the rules of normal observational practice (A). Instead of thinking !p, ‘I see a lake’, she thinks ├ ~p ‘I do not see a lake,’ eventually concluding:├ q, which asserts the sentence ‘I see an inferior mirage’ (or ‘I see the refracted blue of the sky’), which represent a different factual content that can be represented as o.’[21] Consequently, what was at first accepted as external evidence is now viewed as an erroneous interpretation of phenomenally given data, since practice (A) was replaced by the new practice (B). The gained awareness of the context allows the invalidation and replacement of what was at first assumed as an unassailable truthmaker. We can symbolize this change through a sequence of the two following anterograde verification procedures belonging to practice (B):
?p, !o’, p ≠ !o’├ ~p,
?q, !o’, q = !o’├   q

It is worth noting that in both interpretations the phenomenal content of perception remains the same: an impression of seeing the color blue near the horizon. But the interpretation of this content is very different, once o’ is read as a new factual content: a mirage existing in the world. And Yvonne understands what she sees differently because a more complete awareness of the background information given by the surrounding circumstances (including the fact that the blue band always keeps the same distance to the car) is able to defeat the seemingly reasonable initial interpretation of the visually-given content as o.
22. Objection of the linguistic-cognitive circle
Probably the most influential epistemic objection to the correspondence theory of truth is the so-called problem of the linguistic-cognitive circle: Propositions can only be compared with propositions. If we compare hypothetical propositions with propositions representing evidential contents, even if these are taken as irrefutable, we remain trapped in our language and thought. Even if we find the strongest factual evidence, this evidence could only be considered in the form of linguistic expressions of propositions, but in no way do we find evidence by direct comparison of propositions (even if understood, as we do, as e-thought-rules) with real facts, states of affairs or events in the world (Neurath 1931: 541; Hempel 1935: 50-51). Here again, we would be in danger of ending up in an infinite regress with epistemic skepticism as a corollary.
     A prima facie general reply to this objection is that saying we are trapped in an intra-linguistic or intra-cognitive world already assumes we know there exists an extra-linguistic and extra-cognitive external world – a knowledge that remains unexplained.
     Philosophers like Moritz Schlick (1936) and A. J. Ayer presented a more focused reply. Here is A. J. Ayer’s well-known reply:
We break the circle by using our senses, by actually making the observations as a result of which we accept one statement and reject another. Of course, we use language to describe these observations. Facts do not figure in discourse except as true statements. But how could it be expected that they should? (1963: 186)
Ayer’s argument contains a strong appeal to common sense. Nevertheless, this appeal seems to contradict another enduring idea, which is also not alien to common sense. It is the idea that the whole content of our usual perceptual experience should be some kind of conceptually articulated belief-content and therefore should be mental in nature. Consequently, it remains not entirely unreasonable to think that we could never have direct and unquestionable access to anything referred to by a perceptual thought, even if considered as e-thought-rules, namely, external facts as they are in themselves (Cf. Blanchard 1939, vol. 2: 228).
     One reaction to this dilemma would be to accept the kind of last resort solution called idealism (e.g., Foster 2000). But today idealism seems to be an almost forbidden solution. According to idealism, all reality is in some sense mental. This view conflicts with one of our chief modest commonsense principles, namely, that we are surrounded by a cognitively independent external material world. In fact, our empirical knowledge (particularly our scientific knowledge) has told us that the mental is in some sense a minuscule emergent portion of the physical world, dependent on it to exist, just as the phenotype is dependent on the genotype. In other words, the mental appears to supervene the physical insofar as experience – scientific or otherwise – has shown. Moreover, if we stay on the side of our principle of established knowledge (Ch. II, sec. 5), idealism will remain anathema, since it denies not only the modest commonsense truth that the external world is non-mental, but also the scientific truth that the external world as a whole is overwhelmingly non-mental. In some non-mystical sense of the word ‘emergent,’ science has shown that mind is an emergent property of life, which is an emergent property of organic chemistry, a rare carbon-based chemistry emergent from our atomic and sub-atomic physical world. And all our astronomical knowledge conspires to show that this minuscule accidental phenomenon of the emergence of the mental is destined to disappear with the unavoidable process of death of the universe, which is foreseen by the laws of thermodynamics. Finally, from an anthropological perspective, idealism is very often motivated by wishful thinking, as is argued in the philosophy of culture and the humanities by authors ranging from Nietzsche to Freud and from Hume to Marx and Durkheim. It seems that human beings pay a high price for having acquired consciousness. In some way, it recalls the price paid by Prometheus for his theft of fire to benefit Mankind. Even if consciousness makes us better able to survive, it also gives us an increasing awareness that we live in an unpredictable and dangerous world, along with a clear sense of our own physical vulnerability and finitude. Idealism, by making the external world in some way mind-dependent, can be helpful in supporting those illusions of control over the external world that could give us some hope of beating the odds, a thought that is made explicit in Berkeley’s writings. Summing up, due to all the knowledge we have at our disposal today about the physical world and ourselves, more than ever before we have strong external reasons to reject idealism in favor of epistemic realism. (The internal reason is what I intend to expose later.)
23. Answering the objection of the linguistic-cognitive circle
Epistemic realism concerning the external world can be understood as the view that preserves the natural opposition between the mental and the material worlds in the sense that we can roughly characterize the internal mental world as only experienceable in the first-person, while the external physico-material world can be mainly characterized as able to be experienced in the third-person.
     Assuming epistemic realism, in what follows I will defend direct realism as able to give us the kind of epistemological framework that will make it possible to break the linguistic-cognitive circle. Direct realism is the view that our senses provide direct awareness of the external world, showing it pretty much as it is. Direct realism differs from indirect or representational realism, which is the view that we have direct experience only of our own sensations, which inform us about the external world, so that the latter is never directly experienced. Both, direct and indirect realisms, differ from a third traditional epistemological position, called phenomenalism. According to this last view, we can have experiential access only to our sensations or sense-data, since there is no sufficient reason to postulate an external world independent of actual or possible sensations. This view leads almost inevitably to idealism and to rejection of a really existing non-mental external world (Cf. Ch. IV, sec. 20).
     My defense of direct realism begins with the suggestion that everything experienced in real perception has a kind of Janus face, able to explain the double nature of !o, as the thought o and as a fact in the world underlining o. What I mean is that what is given to us in proper sensory-perceptual experience of the external world can always be understood as two different types of interrelated entities: one psychological and the other physical, as follows:

(A) The merely psychological experience of cognitively-dependent internally given sensory content, the so-called sense-data.

(B) The proper, physically understood cognitively-independent, externally given perceived content (that is, the external real entities understood as physically particularized property-tropes, material objects as clusters of tropes, simple or complex facts as tropical arrangements…).

Psychological experience (A) gives us what we may call sensory impressions or sensory contents (also called sensations, sensa, sense-data, percepts, phenomena, representations, ideas…). It seems commonsensical that sensory contents are always present in perceptual internal tropical experience (even if we are usually unaware of them) as I intend to show later. But experience (B) also seems beyond doubt: it is the view that in addition to sensory experience, when we really perceive something, this something is given to us as an external, physico-material kind of entity. Indeed, it is also commonsense knowledge to say that we usually perceive the external world directly and as it really is. And this external world, as we have shown, is originarily accessible as constituted by physical, external tropes (properties) relatively dependent of clusters of relatively independent compresent external tropes with some form and mass, most of them called material objects, and by arrangements of both, also called facts.
     The clearest evidence favoring this double view is given by tactile experience. Suppose I touch a hot stove with my hand. I can say I have a sensation of heat: this sensory-impression is the psychological (criterial) sensory-content of experience (A). Alternatively, I can also say that I have perceived that the stove is hot; this is the correct perceptual experience of the (criterial) perceptual content, that is, an externally given physical tropical state of a material object (B). The most important point is that in the normal case we cannot phenomenally and descriptively distinguish experience (A) from experience (B) (Cf. Searle 2015: 24). In spite of this, we can always conceptually distinguish the two cases, as the following examples of tactile experience show:

(A)  [I have the feeling that] the stove is hot.
(B)   The stove [I am touching] is hot.

In a similar way, I can say:

(A)  [I have the feeling that] I am holding a tennis ball in my hand.
(B)   I [am aware that] I am holding a tennis ball in my hand.

Now, from auditory experience, I can say:

(A)  I [have the auditory impression that] I hear thunder.
(B)   I hear thunder [outside and over there].

And of the most common visual experience, I can also say:

(A) [I have the visual impression that] I am watching a fishing boat entering the mouth of Pirangi River.
(B)  [I am aware that] I am watching a fishing boat entering the mouth of Pirangi River.

As you can see, although what we could call linguistic descriptions of contents outside the brackets are the same in cases (A) and (B),[22] in (A) cases I speak of merely sensory (criterial) contents occurring in my head, while in (B) cases I speak of objectively real physico-material external contentsperceived factual (independent criterial) contents pre-existing in the external world. Note that in cases of perceptual contents, I speak of contents such as the distinguishable objects found in a drawer, that is, of objectively real tropical entities given to experience, which should not be confused with semantic contents understood as rules whose dependent criteria should be satisfied by the first ones). Furthermore, on the one hand, the real perceptual content (B) is epistemically dependent on mere sensory content (A), because without sense impressions (A), one couldn’t know (B); on the other hand, sensory content (A) is ontologically dependent on the real external things constituting perceptual content (B), since (B) causes (A).
     Accepting the above dual understanding of perceptual experience is not hard and does not compromise direct realism. I can illustrate how harmless the duplicity is by comparing it with our interpretation of objects that I see in a mirror. What I see in a mirror can be understood as: (A’) a simple image of things, for instance, the image of a vase of flowers on a table. But it can also be understood as (B’) the vase in itself that I am looking at in a mirror. For instance, I can point to the object I see in a mirror, and you can ask me if I am pointing to the reflected image of the vase of flowers or to the real vase of flowers. That they belong to different domains of experience is made clear by contextual differences: the image isn’t considered real, because I cannot touch or smell it. The real vase of flowers, on the other hand, can be touched, smelled, directly seen from all sides, manipulated, broken; its weight and its size can be accurately measured and shown to remain constant, independently of the changeable apparent size of its image… Alternatively, I can change the apparent size of the image by bringing the vase closer to the mirror. And this apparent size always doubles the real distance of the vase from the mirror… Nevertheless, to a reasonable extent, qualitative properties and relations of both image and reality will be alike or correlated. Moreover and unavoidably, looking in the mirror I would not be able to see and locate the vase on the table without the help of its image.
     In fact, access to the real vase is dependent on access to its image. As in cases like (B) above, (B’) is epistemically dependent on (A’), because without the image (A’) I could not see (B’). Alternatively, (A’) is ontologically (causally) dependent on (B’). This is why when I pay attention to an object in a mirror I interpret it as perceptually dependent on its image, but when I pay attention to the image I see it as causally dependent on the real object. I can easily say I see the reality by means of the image. But I will never say that I cannot see the actual object only because what I really see is just its image.
     Like all analogies, the mirror-image analogy has its limits. For instance, I can always be aware of the image in the mirror as an image, but I am normally unaware of my own sense-data (except, for instance, in cases like those of lucid dreams). However, even here we find something similar: I am aware of the image qua image externally, mainly through conditions like the restriction to visual access and the relations to other things, not due to the image itself. Anyway, the mirror-analogy reinforces the idea that we can answer the objection of the linguistic-cognitive circle by saying that the content of any real experience can be understood in two ways:

(A) Internally and psychologically, as a first-person sensory-based e-thought-content-rule (a sensory-perceptual e-thought-content-rule with its internally fulfilled criteria).
(B) Externally as a third-person physico-material fact (the referred non-semantic factual content constituted by arrangements of external tropical criteria).

Now, insofar as we are also able to read in the given phenomenal content an external factual content, we should be able to escape the linguistic-cognitive circle.
     A complementary but also indispensable point that I have dealt with many times already is that we almost never have a complete sensory-perceptual experience of external factual content. Our perceptual experience is typically perspectival. We experience only facets, aspects, sub-facts. If from a position on shore I see a fishing boat entering the mouth of Pirangi River, I may experience (see) only one side of the fishing boat. However, based on this dynamic tropical sub-fact (an aspect of a process), I am able to say not only that I see one side of the boat – the sub-fact – but also that I see the whole boat and that I am following the whole process of the real fishing boat entering the mouth of Pirangi River – a dynamic grounding fact (See Ch. IV, sec. 25-27; Ch. VI, sec. 6). All these descriptions might be true and their truth derives equally from adequation.
     Another complementary point is the unavoidable admission that sensory content (sense-data) really accompany all our perceptions. That this purely sensory content exists can be illustrated by a phantom pain from a missing limb, after-images, and lucid dreams. A person can feel pain in an amputated limb as if the limb were still there. An after-image appears when someone closes his eyes after looking briefly at the sun. A lucid dream is a dream controlled by a person who is aware that she is dreaming. Furthermore, for those still skeptical of the existence of internal sense-data in normal perception, experiments with vision reconstruction, which involve computationally reconstructed brain experiences of scanned moving images by means of fMRI (e.g., Nishimoto et al. 2011), are more than proof that these sensory contents in the brain really exist, as in these experiments subjects experience their own sensory images and interpersonally compare them with what they see in the external world![23] The dichotomy considered above is also important because it is a necessary condition for the already noted defeasibility of observational evidence: under perceived anomalous conditions we can reinterpret experience by withdrawing from what we believed to be real perceptual content to mere sensory content reinterpreting the lost one.
24. The argument of illusion
Against the kind of direct realism explicated above and favoring indirect realism or even idealism, there are two well-known traditional arguments: the argument of illusion and the argument of science. As almost too much has been written against these arguments,[24] I will emphasize only the essentials. I think that answering these arguments strengthens my own moderate direct realist view.
     I begin with the argument of illusion. It usually concerns cases of perceptual illusions in which we seem to perceive something that should not be perceived, particularly in the extreme case of hallucinations. There are many examples that support this argument. They all aim to prove that in the best case perception is indirect, since it always occurs through the ‘veil of sensations.’ In what follows, I summarily present several examples, some of which were already known in antiquity:

1.     I go outside in mid-winter without wearing gloves, although the temperature is minus 26 degrees. When I come back inside, my hands are stiff from the cold and I cannot feel them. I soak my hands in water that is only at room temperature and yet feels warm! Generalizing, what I directly feel are my sensations, and only through them can I gain information about external temperatures…
2.     I am near a speedway. A car passes me driving at a very high speed. Because of the Doppler Effect, its sound changes pitch from high to low. Hence, I do not hear the true sound, but only experience my own auditory perception, which gives me information about external sounds.
3.     A person with jaundice may in some rare cases see the world as yellow due to an accumulation of bilirubin in his eyes. Now, what allows us to claim that people who do not have jaundice see the world as it really is, in its true colors?    
4.     If I press the side of my right eye with my right finger, I have the impression that things in front of me are moving in the opposite direction. Since these things are not moving, I conclude that I can directly see only my images of things, that is, my sensory impressions, my sense-data, and not things as they are in themselves.
5.     If I hold my index finger fifty centimeters from my face and focus on the far end of the room, I see two images of index fingers. If I then focus my eyes on the finger, the two images merge into a single one. Since they are not phenomenally different in the two cases, I conclude that what I really see are only sensory impressions of my index finger, even if I can secondarily locate my finger through these sensory impressions.
6.     I look at a coin I am holding at an angle to my line of vision. I am convinced it is round, even though it appears elliptical. Indeed, only occasionally do I see a coin in what I consider to be its true round shape. Hence, what I primarily experience are my own sensory impressions of elliptical forms that I think of as different views of its true round form.
7.     I walk around a table looking at it from different perspectives. Then I look at the same table from different distances. The visual impressions are always different. Consequently, what I see is not the table, but only my own changing visual impressions.
8.     I see a lake in the desert, but soon I perceive that it is an inferior mirage caused by layers of hot air above the sand which refract the blue light from the sky. My visual impressions of a lake and a mirage are phenomenally the same, hence what I primarily see are my visual sensory impressions of a blue lake that is not really there.
9.     Suppose I have a perfect hallucination of a white horse. What I see is not a real white horse, but only a hallucinatory image. Since this image made up of sense-data isn’t different from what I see when I see a real white horse, the primary object of perception must be my sensory impressions or sense-data.

If the argument of illusion applies to cases (1) to (9), why not to all cases? Why not, as Bertrand Russell once suggested, be democratic and admit that in all cases we first need to perceive our sensory contents – the sense-data – in order to get information about the external world?
     The conclusion suggested by the argument of illusion seems to refute direct realism, which should then be replaced by indirect realism – a view already accepted by Descartes and mainly attributed to Locke. The suggestion is that the objectively real world is always perceived indirectly through the veil of sensations, which is formed by sensory impressions or sense-data. To this one could add, using a Kantian argument, that we experience how external things are for us and never how they really are in themselves.[25] Nonetheless, against this one could also sustain that, since what external things are for us is the only way to tell meaningfully what they can be in themselves, what they are for us must also in some way be what they really are in themselves.[26]
25 Answering the argument of illusion
In my understanding of direct realism, I do not wish to deny that there are sensory impressions or sense-data; I do not even wish to deny that we perceive the world by means of a veil of sensations formed by sensory impressions, since by accepting (A) I accept these assumptions. What I reject is the claim that these things make our perception indirect. For as is well known, we never say we perceive our sensations; what we might say is only that we normally perceive the external world directly through our sensations or sensory impressions. This means that just because we can show that we perceive the external world by means of one or even several veils of sensations doesn’t make our perception of the external world indirect, since it is a category mistake to defend this view. Put simply: the main problem with the argument of illusion can be seen as resulting from a misunderstanding of the semantics of our concept of directness.[27] Consider the following four sentence pairs:

1.   I saw the Sun directly, through my green glasses.
2.   I saw the Sun indirectly, in a dark room projected on a screen by means of a telescope.

1.   The trip was direct (the bus traveled directly through Germany from Constance to Munich, with a lunch stop of thirty minutes).
2.   The trip was indirect (it started with a bus trip from Constance to Lindau, where passengers completed their journey on a direct train to Munich).

1.   The bullet struck the victim directly (after piercing a windowpane).
2. The bullet struck the victim indirectly (after ricocheting off a wall).

These examples show that what makes some relations direct is not necessarily the fact that we cannot find intermediaries between the relata – they very often exist and are more than just one. Directness/indirectness is to a great extent a conventional distinction that depends on the relevance of the intermediaries for what we aim to consider.
     In the case of perception, language conventions allow us to say that we perceive things around us directly, even if by means of a causal process involving a number of intermediaries. Because of this, there is nothing wrong in accepting the view that we perceive things directly by means of our percepts or sensory data or through a veil of sensations, just as much as there is nothing wrong in saying that a victim was struck directly by a bullet, even though it first had to pass through a windowpane.
     Having this in mind, if we again consider the examples of the argument of illusion one by one, it becomes clear that perceiving things through sensory impressions does not mean that we must perceive them indirectly:

1.     I soak my cold, stiff hands in water that feels as if is warm. I am fully aware, however, that the water is actually at room temperature, and although I perceive the temperature directly, I know my perception is deceptive. I know very well that if my hands were not cold, I would feel the water in its room temperature. Then I would feel it in a non-deceptive way because the normal functioning of our perceptual organs is an expected condition for adequate perception.
2.     I hear the car’s motor directly, though in distorted ways. If I could drive alongside the car at the same speed, I would hear it in an undistorted way; I would hear it directly as it is assumed to really sound, that is, free from the distorting Doppler Effect.
3.     A person can say, ‘I see things directly as if they were yellow, though I know that isn’t their true color,’ because he knows he has jaundice. – What we call the true colors of things are by convention the colors I see under what are considered to be normal conditions. This presupposes the right distance from them, having normal vision, seeing things in adequate illumination with a neutral white balance, etc.
4.     Even if I show by pressing my eye that I see things as if they were moving through my visual field, this does not mean that I am not seeing them directly. In fact, I can even say, ‘I see external things directly and precisely as they are, though having a false impression that they are moving.’
5.     In this example, as Searle has noted, one can instead say, ‘I do not see two fingers… In fact, I am directly seeing my own index finger as if it were doubled.’
6.     Concerning the form of the coin, it appears elliptical, but I can say that I directly see a round coin that only ‘looks elliptical’ because it is being held at an angle. – As A. J. Ayer pointed out, what we consider to be the true form or the real color is partially a matter of conventions (Cf. 1973, Ch. 4). Here we have the convention that the real form of a coin or a table is the form we see when we look down on them from above. In the same way, we have a convention that the real form of a mountain is the form we see when looking at it on the level of the base at a certain distance, but not an aerial view from above (e.g., the Matterhorn, the Sugarloaf). Based on conventions defining the perception of things as they are (our normal perception), we say that the real color of a tropical mountain is green, even if it may seem blue when viewed from a great distance...
7.     In the case of the different sensory images of the table, you always assume that you are seeing a table that is always one and the same. This shows that the different perspectives and distances are only variations in the way the same table ‘looks like.’ And these different perspectives and distances are said to be different ways in which you directly see the same table.[28]
8.     In the case of mirages, I see what looks like a lake, but usually I can say that I am aware that what I really see is the image of the sky refracted by layers of hot air on and above the desert sand, and I say that I see this mirage directly.
9.     Finally, in the case of a hallucination, it is simply incorrect to say that I see the content of my hallucination. As Searle emphasized, I only believe I see it, when in fact there is nothing there to be seen! Verbs like ‘seeing,’ ‘perceiving,’ ‘being aware of’ are here primarily related to factual, external content, and not to merely internal sensory content. Even if we agree that it is by means of sensory content that we have perceptions of things, this does not make our realism indirect. In a similar way, when we say that a bullet struck a victim after piercing a windowpane, we do not mean that the bullet struck the victim indirectly.

This kind of answer is not as new as it might seem. It was already present in the following comment by the direct realist philosopher Thomas Reid targeting his contemporary David Hume, almost three centuries ago:
…visible appearances of objects are intended by the nature only as signs or indications and the mind passes constantly to the things signified without making the least reflection upon the signs or even perceiving that there is such a thing. It is in a way something similar that the sounds of a language after becoming familiar are overlooked and we attend only to the things signified by them. (Reid 1967: 135)
To most present-day philosophers, including myself, direct realism is the most proper answer, and we can see the persistence of competing doctrines as a testimony to how slow and uneven progress can be in philosophy.
     Summarizing: we perceive things directly, even under misleading conditions like those of delusions. This justifies the direct realist view of whatever is given in perception. And this does not mean that we do not perceive the world inevitably by means of a veil of sensory impressions or sense-data, just as seeing an object in a mirror does not mean that we do not perceive the object as it is by means of its mirror-image. This justifies our psychological interpretation (A) of a given content as based on sensory data, without forcing us to reject interpretation (B). This reinforces the idea that a phenomenal content can be interpreted as psychological (constituted by sense-data), but also as physical (constituted by material things, their tropical properties, etc.)
26. The argument of science and its answer
Finally, a word about the argument of science. According to this argument, perceptual experience depends on causal physical stimulation of distal neuronal cells that through synaptic activation ultimately lead to the stimulation of cortical regions in the brain, which produces in us an awareness of the objects of experience. Thus, our experience is in fact the experience of something occurring in our brain, which is nothing but the experience of sensory impressions. Consequently, our direct experience can only be of sensory impressions occurring in our brain. From this it follows that we cannot have direct experience of the world around us and that we cannot be sure that our contents of experience reflect how the external world really is or even provide a warrant of its existence. Worse yet, we may be led to the incredible conclusion that since our brains also belong to the external world, we cannot even be sure that our brains exist... All we can be sure of is that there are sensory impressions!
     The answer to the argument of science is that there is nothing semantically wrong in saying that we directly experience things given in the external world, even if this experience demands the underlying work of complex neuronal structures as intermediary means. In the case of visual perception, we have simulacra of things seen, first in the projected image of the object causing the activation of photo-receptor cells in the retina and then in a corresponding activation of the striate cortex in the occipital region, which is analyzed by the visual-association cortex...
     In my view, the decisive point is that the sentence ‘we directly see the objects’ belongs to the conceptual schema expressed by our natural language, while expressions like ‘by means of…’ or ‘through…’ used in the argument of science belong to a physical-neurobiological language concerning the underlying intermediating physical processes responsible for neuronal activation-patterns that in our natural psychological language we use to refer to direct experience of the world around us. Each language – each conceptual system – works well in its proper field, and each language has its own way of segmenting or not the process of perception. Mixing both languages is what leads to fallacious reasoning. In the present case, the fallacy arises when we use the semantics of the physical-neurobiological language – which has discovered complex causal processes at the physical and neuronal levels – to deny the semantics of our natural language – which establishes a direct relation of seeing or being aware of things in the outside world. This confusion is again a clear case of equivocity (Ch. III, sec. 11).
     Finally, as far as I know, what we call sense-data in the visual case has much to do with the activation of the striate cortex, since the stimulation of this region without the activation of photoreceptors in the retina is apt to produce hallucinatory phenomena (Teeple, Caplan, Stern 2009: 26-32). However, this fact alone does not make visual perception indirect, since it isn’t captured by the semantic conventions governing what we are used to call the directly perceived objects around us; and it is this psychological-natural language that is responsible for what we understand with the ordinary word ‘perceiving.’
27. Question: How do we warrant the perception
 of external content?
Even agreeing with all these commonsense arguments made to show that we are able to have direct access to entities belonging to the external world by means of the veil of perception, that is, by means of sensory contents or sense-data, the phenomenalist can still pose the question: why are you so sure that the externally given tropical entities that you say your semantic-cognitive rules apply to really belong to a non-mental physico-material world? After all, as we learned from our discussion of Berkeley’s and Mill’s phenomenalism (Ch. IV, sec. 20), it does not seem inconceivable that the objects that satisfy these rules are only actual or dispositional configurations of mental or psychological sensations… which seems to lead us back to idealism.
     However, for the already given external reasons (related to what science and culture presently have to say or suggest about the world and ourselves), idealism seems to be far from a plausible option. In what follows, I expect to give internal epistemological reasons to think that idealism is a philosophically equivocal solution. This means I need to give reasons for our commonsensical assumption that the external fact that we believe to satisfy the dependent criterial configurations demanded for the application of the verifiability rule must be able to be seen as belonging to a physico-material external world. These reasons must justify not only the externality of an inferentially reached grounding fact constituted by arrangements of physical tropes and their combinations but also (more directly) the externality of its aspectual sub-facts as partial arrangements of physical tropes and their combinations (Ch. IV, sec. 25). In other words: the kind of commonsense direct realism defended in the last sections, though intuitively correct, still does not seem to justify the way the magic trick is performed of interpreting (reading, understanding, projecting, displacing… it is hard to find the right word) our internal sensory psychological contents as external physico-material contents perceived by our senses in a way similar to the way we interpret a mirror image as a reflection of something external. That is, even by accepting that we perceive the external world directly by means of the veil of perception after answering the arguments of illusion and science, we still seem unable to explain what we do in order to rid ourselves of what is internally mental when speaking of the external entities that are objects of perception.
     In my view, a more complete answer begins to appear when we press the question further. Suppose we ask: under what conditions are semantic-cognitive rules like the verifiability rule not only conceivable, but also effectively applicable to entities belonging to the so-called real external world? In other words: what are the conditions responsible for our awareness of the effective applicability of the rule to what we are allowed to call mind-independent physico-material entities really existing in the external world? In still other words: when do those phenomenal entities that we could otherwise be able to recognize as mere sensory contents (sensations, sense-data) become likely to be recognized as directly experienced external tropical contents beyond our actual or dispositional mental states? (– I primarily mean their recognition as perceived external properties, that is, as simple or complex external tropes… material objects as clusters of external tropes displaying compresence… and real factual contents as external tropical arrangements.)
     My suggestion is that what makes semantic-cognitive rules effectively applicable to mind-independent third-person physico-material tropical entities in the external world is the satisfaction of suitable conditions of external reality in the absence of any verified skeptical scenario. I hold that the adequate satisfaction of these conditions is ultimately responsible for the ‘magic’ of using our internal phenomenal sensory data as a way to reach external reality. That is, like the changes of our reading of mirror-images, our reading of what is phenomenally given in indexical thought-contents supported by sensory-impressions (internal criteria) can be changed into our reading of them as real factual contents belonging to the external world and constituted by what might be called physical external tropes (independent external criteria). More specifically, I wish to show that by definition, once the conditions for external reality are adequately and sufficiently satisfied, they constitute the proper, independent, externally given criterion for the external reality of the contents of experience that fall under the scope of those rules. These conditions act somewhat like the conditions that, once considered, allow us to understand what we see in a mirror as the objects reflected and not as mere images of objects. (A skeptical scenario verified as a simulacrum of reality would be like a second mirror interposed between us and the object. The question is if the doubt whether there is not a second mirror makes any sense when there is no evidence for the existence of a second mirror.)
     However, are there such conditions? In my view, these general conditions certainly exist, and their adequate satisfaction always constitutes what we implicitly assume in our attributions of external reality. The point was already touched on in the explanation of Mill’s complementary conditions for external reality in Chapter IV. In fact, conditions for external reality were (within a diversity of metaphysical frameworks) already largely suggested by modern philosophers, beginning with Descartes and continuing with analytical philosophers, from G. E. Moore to J. R. Searle.
     I can summarize the most fundamental conditions to warrant external reality proposed by modern philosophers, beginning with Locke. According to Locke, our opinions about physical objects are justified by the properties associated with our ideas of sensations, such as their involuntary character, order, coherent agreement reflecting law-governance, and interpersonal accessibility (1690, Book IV, Ch. 11). The immaterialist Berkeley concluded that the ideas constituting so-called external reality are very strong, distinct and independent of the will (1710, III). For Hume the impressions of a real thing are those that ‘enter into the soul with the most force and violence’ (1738, Book I, sec. 1). Kant held that conformity with laws (Gesetzmäβigkeit) is what defines the formal aspect of nature (1783, § 16). J. S. Mill, as we have already considered in some detail, said the external world consists not only in continuous or guaranteed or certified possibilities of sensations, but also in their independence of our will and their conformity with the regularities of nature, such as the causal laws of physics (1889, Ch. XI). According to Frege – already an analytic philosopher – the externally objective realm (his erstes Reich) has as a criterion of objectivity its interpersonal accessibility and independence of will, while its reality has as a criterion its spatiotemporal location (1918b). A direct realist analytic philosopher of the early 20th century, G. E. Moore, summarized the main conditions of external reality in the following passage:
The real is something independent of the mind that is verifiable by others, continuously connected with other things, and in this way has certain causes, effects and accompaniments with the highest degree of reality. (1953)
Such explanatory efforts have continued up to the present. To give an example, in a recent study John Searle pointed to some characteristics of the object or state of affairs really perceived, such as presentation (instead of representation), causation, non-detachability, indexicality (things are presented here and now), continuity and determinacy (Searle 2015: 60-70; See also Huemer 2001, Ch. 4).
     Finally, a genetic account of our awareness of external reality proposed by Sigmund Freud (1911) could be mentioned. He suggested that we begin our lives under the governance of the pleasure principle (Lustprinzip), which seeks immediate gratification of desires and avoidance of pain. Since the external world does not grant us painless immediate gratification, we gradually learn the reality principle (Realitätsprinzip), according to which we need to act rationally toward the external world, postponing the immediate satisfaction of our desires in order to assure continuing lower levels of gratification accompanied by a foreseeably lower level of pain. For Freud, it is by means of this slow and difficult transition to the reality principle that we learn to distinguish an external material world with its own constraints.
     It is true that when considered in isolation none of these conditions warrants that the contents of perceptual experience are externally real ‘material’ contents constructed from tropes. Indeed, criticizing Locke, Laurence BonJour correctly noted that none of the conditions of reality given by Locke is sufficient to warrant the external reality of anything (BonJour 2002: 130-135).
     Examples easily confirm BonJours objection: A mere content of sensation can have the highest degree of intensity and determinacy and yet be hallucinatory, as may occur in some rare cases. A perfectly realistic dream could be in strict conformity with all the expected regularities of our physical and social world. Although many mental acts are dependent on our will, dreams, obsessive thoughts, along with most feelings, are typically independent of our will. Even interpersonal agreement about states of affairs can occur without their real existence, as in the case of a dream in which we find other persons who agree or disagree with our experiences, or in the rare case of a collective hallucination (suppose that several people with similar beliefs take a hallucinogenic drug and, motivated by suggestion, share similar pseudo-perceptions…). Finally, external occurrences can possibly be directly dependent on our will (as in the case where someone has a brain-reader connected with his motor cortex, enabling him to move objects in the outside world using his mind alone).
28. Answer: a definitional criterion of external reality
Notwithstanding, I think there is a way to surmount the problem identified by BonJour. The mere conditions of externality can be transformed into a definitional criterion for the existence or reality of the external world outside us, that is, into a sufficient condition for the ascription of external reality in the typical realist sense of the word. This suitable definitional criterion consists simply in the demand that the most relevant of these conditions should be satisfied together, in accordance with conventional peculiarities of the expected kind of entity (property, object, fact…). Hereby we find a decisively subsumed criterion that, once given, allows the perceptual contents that satisfy a semantic-cognitive rule to be projected onto the physical world outside us, as externally existing tropes or constructions made up of them, which are by definition external, material and free of any psychological element, among a complete system of external entities also able to satisfy the same kind of rule in a similar way.
     We can better establish this point by proposing that the entities that can be seen as externally real are those that suitably satisfy all the main conditions of reality. And when these conditions are put together in such a way that we could in the proper sense of the word speak of them as constituting a definitional criterion of external reality, they work as what could be called axioms of externality. Here is how this view can be explicated concerning perceptible entities surrounding us:

In order for some content of belief to satisfy an e-thought-content-rule as an externally real entity (as a factual content minimally constituted by an object and a property) belonging to the physico-material world, it must satisfy the basic axioms of externality. In the standard case, the axioms that the entity must satisfy in order to be considered externally real must be the following:

(i)    The entity must be able to be given to the senses of cognitive subjects in its most intense degree and detail. In many cases, it must also be co-sensorially given in the most intense degree.
(ii)   The entity must (usually) be independent of the will.
(iii) While existing, the entity must always be an object of perceptual experience and possible interpersonal agreement insofar as the adequate conditions are given (namely, it must be the subject of what Mill called ‘continuous, guaranteed or certified possibilities of sensations’) – here we could also speak of, if not actual, at least interpersonally possible perceptual experience.
(iv) The entity must obey the laws of nature, displaying expected regularities within a larger context (one would not be restricted to physical laws; biological, psychological and even social regularities could be included…).
(v)  The entity must be able to be seen as in some (even if indirect or extremely indirect) way causally related to any cognitive subject who applies the rule.

I am not sure that this list cannot be improved, and I am unable to order the axioms hierarchically. But I believe they are the most relevant ones. Moreover, my thesis is that once all these conditions are suitably satisfied, there is nothing in the world that can defeat the kind of external reality that we intend to attribute by means of them. Together they are sufficient for the attribution of external reality in the most proper sense of the word, which I call the inherent sense, although it can be contrasted and easily confused with what will later be called the adherent sense of external reality, applicable in skeptical scenarios.
     I will use the following example to make clear that the axioms of externality constitute together a sufficient condition of external reality. Right now I am working with my notebook computer. I am very sure that what I am experiencing of this device is presented to me as a complex of mental images and sensations (as variable contents of sensations or ‘sense-data’). But I am also very aware that this device is also given to me as a corresponding physico-material object existing externally (an interpersonally perceivable and independently existing combination of material or external tropes of solidity, volume, form and… inertial mass, displaying compresence). Now, how do I know that I effectively apply my notebook’s identification rule in its proper context, so that I am entitled to say that it exists externally? What warrants my understanding of the perceptual content as that of a real physico-material object in the outside world to which I might definitely apply its identification rule? The answer is clear: the suitable satisfaction of the above listed axioms of externality in the application of my notebook’s semantic-cognitive identification rule. That is:

(i) The device must be able to be given to my senses in the most intense degree and detail. It is in this way also co-sensorially given (I can see, touch and hear it).
(ii) The device must exist and be constituted independently of my will.
(iii) The device must be continuously able to be given to sensory-perception under suitable conditions (I have seen this notebook computer intermittently in my home for many months and some other persons have also seen it). And (because of similar past experiences of material objects) I am sure that other persons would agree that this notebook computer is here in front of me now if they were here to see it; so I can be sure that my experience is at least interpersonally possible.
(iv) The device must obey expected physical regularities (it functions as described in the instructions, sometimes I have to recharge or replace its battery, I can download and install new programs from the internet, etc.)
(v) The device must satisfy its identification rule in a causal way (very often I am causally interacting with my notebook computer, and I am aware of this).

The interesting point is that even if the whole world were just an incredible dream – including my body and my notebook computer – I would still be entitled to affirm that my notebook computer is indeed very real, that it exists in an external world (even if in the end only a fictional one) and behaves externally as a material object in the sense that it suitably meets the criterion of reality by satisfying the axioms of externality from (i) to (v), that is, it is fully real in the inherent sense of the word. Indeed, if a dream has all the features of reality, then it is real in the relevant sense of the word.
     A second point is that the satisfaction of the axioms may be incomplete and more or less constrained by conventions. A rainbow does not completely satisfy axiom (i): Although it is seen in its greatest expected intensity, it cannot be touched or heard. But probably for the same reason we aren’t inclined to say that a rainbow is the most real thing in the world. New technology for brain-computer interfaces (BCI) enables us to move objects with willpower alone, which shows that some external things are to a certain extent dependent on our will and do not satisfy axiom (ii). Anyway, it is not our will that sustains their existence – not yet. And the real form of a mountain is conventionalized as satisfying the axioms of externality when viewed from its base and at a certain distance, which is a contextually dependent addition to the axioms.
     On the other hand, internal sensory-contents, even those of a hallucination, typically do not satisfy, or only barely satisfy, the criterion of inherent reality. Indeed, if they sufficiently satisfy all externality axioms, they satisfy the criterion of external reality and must be considered in a sense externally real. It must be so because the totality of the partial conditions constituting the axioms of externality simply form a definitional criterion, grammatically or logico-conceptually warranting that the object of perception – in this case, the notebook computer in front of me – can be said to be an externally real material object belonging to what I am allowed to call a material physical world around me, and not just something merely mental.
     Another point is that, although taken together the axioms of externality are a sufficient condition for attributions of external reality, their satisfaction is not a necessary condition. For instance, a person can be under the influence of some drug or suffer from some perceptual deficiency… so that although she is indeed experiencing a state of affairs that is externally real, several of these conditions are not being satisfied for her (e.g., some people take drugs to ameliorate the harsh reality of the external world).
     Anyway, it seems clear that it is the satisfaction of the externality axioms from (i) to (v) that for conceptual reasons alone warrants to me that my notebook computer’s identification rule is effectively applicable to a real material object in the external world. Together these axioms establish the criterion for the application of our usual concept of the inherent reality or existence of things belonging to the external material world: a pre-condition that must be satisfied for the effective applicability of semantic-cognitive rules to inherently real things belonging to the domain of external physico-material reality. Their satisfaction warrants to me that a physico-material object like my computer is real, that it exists externally in a very concrete sense of the word, as a compresent cluster of stable tropes of solidity, density, volume, form, colors… effectively satisfying its identification rule and being constituted in conformity with it – and it must be so as a derivative of the cognitive senses we give to our words.
     At this point a Berkeleyan immaterialist can object that even if the semantic-cognitive rule, along with the sensory content that satisfies it, demonstrates itself to be effectively applicable and consistent with all the axioms of externality, these sensory contents still belong to a mental order, so that although we believe that we grasp the material world, we remain in the domain of idealism. The answer I can give is that the sensory content that satisfies all these conditions must be a perceptual content belonging by definition to an external physico-material world, insofar as we let out of consideration radical skeptical doubts. My personal computer, by satisfying the axioms of reality, must satisfy the physical laws, it must satisfy the conditions for a material object (inertial mass inclusive) within the context of a physico-material world, at least insofar as no skeptical scenario has been found. The psycho-phenomenal content of sense data is now read as a physico-phenomenic content of material properties and objects. (I think that this point is made easier to understand when we remember that science has unmistakably proven that the mental is also physico-material, though as such only internally accessible.)
     Skeptics will certainly object to this conclusion. They will point out that they can imagine skeptical hypotheses like those of a brain in a vat, a Cartesian soul or a dreaming subject… who are continuously and systematically being misled about a whole world that perfectly satisfies all the usual axioms of externality without having the least bit of external reality or the expected kind of physico-materiality. But as will be made clear below, the concept of external existence or reality applied in a skeptical scenario has an adherent sense, which is very different from the inherent sense of reality analyzed until now and, as we will see, cannot be applied in the absence of skeptical scenarios.
     Now we already know how what to do in order to warrant perceptual content, which as I noted is physical, like the content of a drawer. First, it is important to remember that the sensory-experience of mere sensory content is usually also a cognitive experience. If I have the feeling that a stove is hot or that I am holding a tennis ball, if I seem to hear a thunderclap or become aware of my sensory experience of my personal computer, these are all indexical thought-contents with their own verifiability rules satisfied through internal sensory experiences or sense-data. The point to be emphasized is that these sensory data will be read as internal only insofar as they are not seen as satisfying the criterion of external reality constituted by the axioms of externality (I may simply be hallucinating my notebook), while they will be read as external when they do satisfy these axioms (I have worked with this notebook computer for a long time, others have confirmed this). In the first case, I am considering the merely psychological experience (A) of sensory-psychological contents. In the second case, the applicability of the axioms of externality to what is given to me as sensory-psychological phenomenal contents (A) is only a transitive necessary condition for something further, namely, the proper perceptual experience (B) of external perceptual contents understood as physico-material tropical arrangements.
     Furthermore, in case (B) we might suppose there to be something external unifying the variety of aggregates of sensory experience which make the real, actual external entity (a property, an object, a fact) in the world (for instance, my personal computer). Indeed, it seems reasonable to think that this actual external entity should have a unifying structure that could be captured through the effective applicability of rule’s many diverse criterial ramifications.
     A final point is that in perceptual experience, when sub-facts sufficiently satisfy the verifiability rule, and this rule is accepted as effectively applicable because it satisfies the axioms of externality, we have at least a necessary condition for accepting the aspectual match between some derived indexical thought-content and the corresponding external sub-factual content. However, this satisfaction of the inherent sense of external reality also indirectly applies to the grounding fact represented by the basal thought, whatever it is. Consequently, for its effective application to facts belonging to the outside world, the verifiability rule must be applied in a way that also satisfy the axioms of externality. Only in such ways can ambiguous sensory-perceptual contents be understood as not merely mental, but as belonging to the inherently real external physical world, as physico-material constituents of the sub-facts belonging to a grounding fact, and because of this also to the grounding fact itself.
29. Proving the external world
Before we consider expected objections suggested by the consideration of skeptical scenarios, it is important to note that the application of the axioms of externality can be inductively extended to contents that can be experienced only indirectly or potentially or both. Thus, calling ‘(A)’ the genetically originated trivial case of the external reality of perceived entities surrounding us, like the case of the personal computer I am writing on now, we also have other cases like:

(A*) All the things we cannot experience directly with the unaided senses but can experience indirectly, such as viruses, atoms, magnetic fields, gravitational fields (one can indirectly verify the existence of atoms using scanning tunneling microscopy, and one can indirectly verify the existence of electromagnetic forces by manipulating magnetized material). These things can be considered externally real because the complexes of causes and effects that are associated with them satisfy axioms (i) to (v). Consequently, using a well-known mechanism of semantic extension already suggested by Aristotle, we are also justified in attributing external reality to them.[29]

Another form of semantic extension is case (B) of application of the concept of external reality to entities beyond the reach of our actual spatiotemporal possibilities of experience. This case (B) can easily be subdivided into three subcases:

(B1) Past things. Everything I know to satisfy the criterion of external reality because I remember having experienced it as satisfying the criterion, but that is not present now (like my grandfather’s house, which I visited only in my early childhood, or a former childhood friend).
(B2) Testimonial things. The great number of things that I know satisfy the criterion of external reality by means of testimony or any reliable informative source (from the city of Angkor to Napoleon’s coronation or the extinction of dinosaurs). I would also include as ‘testimony’ photos, videos, historical documents, archaeological remains, etc.
(B3) Unknown things. This is finally the case of my inductive belief that because I have always had new experiences of real external things in the past, the world is full of other real external things that I have never experienced but that are directly or indirectly able to satisfy the criterion of external reality – let us call this ‘the openness of the world.’

Finally, this allows us to inductively prove the inherent reality of the external world, since what we understand by our whole world is nothing more than the sum of all the entities that we reasonably believe to satisfy (A), (A*), (B) as (B1), (B1*), (B2), (B2*) and (B3) (B3*), understanding B1*, B2* and B3* as things indirectly experienced or able to be experienced in the corresponding domains.[30] In this way, we use the inherent criterion of reality in its extended forms to prove the existence or reality or actuality of the external world in the usual sense of the word.[31] It is because all of us have unconsciously engaged in similar reasoning at some point of our childhood that we all believe that the external world self-evidently exists, and that only philosophers and madmen can doubt its existence or reality.
     These extensions also explain how we can make ordinary attributions of truth to statements based on adequation with inferentially derived statements of facts that aren’t presently given to our senses. Consider as an example the judgment ‘It is true that Mrs. Rose tried to poison Reverend David with arsenic,’ symbolized as ├p, which is true by adequation with the inductively reached statement of fact symbolized by q. We know that q expresses a verifiability e-thought-content rule that can be read as representing an external factual content. But what entitles us to give the status of a fact to something that no person (with the exception of Mrs. Rose) has ever observed? The answer is that we are inductively aware that this dynamic fact occurred, satisfying the axioms of externality from (i) to (v) by the indirect means of the more direct satisfaction of the criteria of reality of the perceptual or perceptually based e-thought-contents r, s, t, and u, corresponding to their respective external facts. This entitles us to conclude that the verifiability rule of q would have been effectively applicable in its proper context if someone able to apply it were there, that is, that the fact-event of Mrs. Rose’s attempt to murder her husband occurred as something inherently real.
30. Skeptical scenarios
Now, what about extreme skeptical scenarios or experiments with artificial reality? The challenge to our view is that in these cases the satisfaction of the definitional criterion of external existence considered above can (in principle) be in part or, it seems, even totally emulated. Thus, the brain in a vat (pace Putnam[32]) has experiences that seem as real to it as experiences we have in our actual world, though it is on the very different planet Omega, interacting only with the program of a supercomputer... However, curiously enough, if this were the case and, for instance, the brain were removed from the vat and implanted in a living organism, so that it could experience the world of the planet Omega as it really is, his past normal attributions of reality would in an important sense not be denied. The same would be the case if someone comes to know he has been the object of a flawlessly executed virtual reality experiment. That is, happenings belonging to the life of the brain in a vat were very real indeed, since the axioms (i) to (v) were all satisfied, even if everyone should agree that this solid reality was in a sense unreal, since it was a sub-product of the present world, here treated as if it were the ‘ultimately real’ world. Now, it seems that the world presented to the brain in a vat could be simultaneously real and unreal, which would be contradictory.
     We can solve this dilemma by simply accepting that there are two different senses of external reality, which should not be confused:

(a) the inherent sense of external reality
(b) the adherent sense of external reality

The inherent sense of external reality (a) is the foregoing, demanding the suitable satisfaction of externality axioms from (i) to (v). We are all very well acquainted with the inherent sense, since it is the sense of reality that we apply on a daily basis. The brain in a vat (or the dreamer of a totally realistic dream) also experiences the criterion of inherent reality as being perfectly satisfied, and it is in this sense that the brain in a vat is right when it thinks that the experiences of the world given to it are perfectly real: they are still real in the usual inherent sense.
     Nonetheless, the external world experienced by the brain in a vat before its liberation was unreal in the adherent sense, the sense (b) of external reality. The adherent sense is reserved for skeptical scenarios and circumstances of virtual reality. It forms a different sense of ‘external reality,’ because the criterial conditions for satisfying or non-satisfying the adherent sense of reality are very different from the criterial conditions for satisfying the inherent sense. The criteria for the adherent sense are more properly coherential. We would be able to reject the adherent reality of something experienced, based on the fact that we now know (or always knew) that we have been subjects of an experiment in virtual reality, since the coherence of that experience with actual and past surrounding circumstances is lacking.
     Examples make the point clear. Consider an experiment with artificial reality in which we use special digital gloves that give us a sensation of touching holographic images of objects. You see the holographic image of a cup of tea, you touch the cup, you feel it, others can see it, but when you try to firmly grip it, your fingers go through the cup. Here to some extent the conditions of inherent reality are satisfied, though this does not suffice to endow the cup with reality. Moreover, we know from the start that the criteria of adherent reality are not being satisfied, since we are aware that the artificial reality is a counterfeit one made from material of our own real external world. We can even admit that the holographic image has some limited degree of inherent reality acquired by the satisfaction of some conditions of external reality, but surely no adherent reality and the reason for this last conclusion is that this evaluation fits much better with our more complete informational background.
     Now, it is of utmost importance to see that when effectively applied in experience the concept of adherent reality is relative. Relative concepts are used only comparatively. For instance, the attribution of size in the sentence ‘A small baby elephant is large relative to a mouse.’ (Copi) Thus, we cannot effectively attribute or disattribute adherent reality independently of a given basis of comparison. Because of this, the idea that we can in a justified way know the ultimate or absolute adherent reality of things is an empty one because it is devoid of criteria; we do not have and do not need to have a verifiability procedure assuring us that we and our actual world cannot be victims of a skeptical scenario. Because the concept of adherent reality is relative we cannot prove the adherent reality of our world and we cannot disprove it. Consequently, to ask about the adherent reality or unreality of our world outside of any skeptical scenario is senseless. It is an illusion of reason invented by philosophers. We can ask only about its inherent reality and get a positive answer. That is all.
     To further exemplify the relative or comparative character of the application of the concept of adherent reality, suppose now that you are a brain in a vat. Let us suppose that you fall asleep one night, and when you wake up you find yourself in completely different surroundings with a new, unfamiliar bodily form. You see around you creatures that look quite strange and alien, and what is worse, you also look like them. They claim that you are now on the Planet Omega and tell you your brain was removed from the vat and implanted in the head of a creature belonging to their species. The creatures give you coherential reasons to think that the world you are now living in is adherently real, compared with the world where you lived in the past, even if both are equally inherently real (they can show you the vat and the supercomputer. They tell you that the reason for the experiment is a pedagogical intention to increase the mental diversity on Planet Omega. They acquaint you with their wonderful new world, inhabited by the most fascinating creatures…). In the end (if you don’t go insane) you may come to believe they are right, since this is the best way to give coherence to the relation between your present experiences and your memories. But it is important to remember that the application of the concept of adherent reality is here only comparative, since outside of the relation to a skeptical scenario you cannot have any workable criterion to judge whether or not the present world is the ultimately real world. This impossibility is shown by the fact that even in a radical skeptical scenario where you have such a criterion it may be that you have been deceived again. Perhaps your brain was only moved to another vat, where the program ‘Awaking on the planet Omega’ is running, so that you are deceived again and will be only able to gain a new relative awareness of it if you are awakened once more…
     On the other hand, the conditions of inherent reality are or have been equally well satisfied in any of these worlds, and in this sense they are all sufficiently real worlds. Thus, the earth-world was adherently unreal relatively to the present Omega-world, while the present Omega-world is adherently real relatively to the earth-world, even though both worlds are inherently real, and both worlds can turn out to be adherently unreal relative to a third adherently and inherently real world within a further skeptical scenario (e.g., being awakened from the program ‘Awaking on Planet Omega’) and so on.
     These remarks are already sufficient to allow us to answer the radical skeptic, since it seems clear that for lack of semantic discernment the skeptic, as much as the anti-skeptic, confuses inherent attributions/disattributions of reality with relative adherent ones, producing equivocal arguments. According to the modus tollens skeptical argument for ignorance, because I cannot be absolutely sure that I am really not a brain in a vat, I cannot be sure that I have two real hands… However, the skeptic makes here a mistake, since the concept of reality (usually implicit in the argument) should occur first in the adherent sense and then in the inherent sense. The anti-skeptic is victimized by the opposite confusion in his modus ponens argument for knowledge, according to which because I know that I have two real hands, I can know that the world where I now am is the real one and not a vat-world… since the (usually implicit) concept of reality here occurs first in the inherent sense and then should occur in the adherent sense.[33]
     It is also important to note that the inherent reality of the external world experienced by the brain in a vat could not be one of a physico-material world obeying the laws of physics as we understand them! Indeed, being aware of a skeptical context, someone would be able to agree with the lack of adherent reality of the vat-world – made up only of electronic patterns in the supercomputer configured by a computer program – or the adherent unreality of the content of the world as a dream – constituted only by neuronal activity and not real material things surrounding the person who dreams. In a skeptical scenario, the attribution of adherent reality comes to the fore and makes sense, since there are reasons to make a comparison. But normally there is no reason. As we have already noted, this is why it is normally senseless to pose radical skeptical or anti-skeptical questions without offering a skeptical scenario, and this is why it is senseless to doubt or affirm that our world is a dream in the ultimate adherent sense. That is:

The question ‘Is our external world the ultimate, absolutely (adherently) real?’ is empty. It is a senseless transgression of the limits of meaningful language because it is an attempt to treat the relative concept of adherent reality as if it were an absolute (non-relative) concept.

     Nonetheless, a question arises here: why are we so naturally disposed to accept the external world as not only inherently real, but also as the authentic physico-material world filled with the material objects we see around us, that is, as well as an adherently real world? Why is the assumption of the physical materiality of the external world part of our common knowledge? The answer is that people who ask this question have not differentiated between the inherent and adherent senses of external reality. Because of this, they perceive that we can prove that the external world is real in the inherent sense, but they believe we are in this way also affirming that the external world is ultimately real in the adherent sense of reality. But they feel there is something excessive in this affirmation, which leads them to treat skeptical riddles as if they were more than mere semantic pseudo-problems. The question of adherent reality only arises because we are able to comparatively imagine skeptical scenarios in which the question would make sense. Inherent reality is all that we know on earth and all we need to know.[34]
     The main point of this section was to reaffirm that adequate satisfaction of the axioms of externality is what essentially performs the magic trick of allowing us to interpret phenomenally given sensory contents as belonging to external physico-material entities independent of us, which by definition aren’t mental or psychological. In this way, idealism is ruled out insofar as we find no evidence of a skeptical scenario providing us with relative criteria to pose the question of whether our world does or does not adherently exist and leading us to reject its physico-material reality. Once we feel ourselves free not only to interpret phenomenal contents as mind-independent, third-personally accessible, but also as obeying the real laws of nature, and therefore being physico-material in all their aspects, we have no meaningful reason to pose the question of whether or not our world has adherent reality, simply because we lack verificational resources to answer that question, and a question without a possible answer is a question without meaning. Aside from skeptical scenarios, the satisfaction of the criterion of inherent reality by our phenomenal content is all that is needed to support the kind of displacement that puts content within what is called the non-mental external physico-material world.
31. Verification and intentionality: Husserl
At this point, it can be helpful to recall some of Edmund Husserl’s views on truth in his Sixth Logical Investigation. I believe that he offers there his deepest insight, even if his insistent attempts to develop it might have entangled him in a speculative maze. As we saw, Frege spoke of senses as meanings and thoughts, understanding them as abstract entities. The work of Wittgenstein, Michael Dummett, Ernst Tugendhat and others leads us instead to the suggestion that what Frege identified as senses or meanings are in fact semantic-cognitive rules or adequate associations of these rules considered in a particularist way a coming into being only through their effective or only merely rehearsed application. These rules can be applied either effectively (to the real world) or at least to some extent only imaginatively (as a possibility) if they do not remain mere psychological dispositions. Against this, Husserl spoke of intentional acts as ephemeral instantiations of meanings, supporting the Platonist view that meanings in themselves should remain abstract entities, as Frege and others have also held.
     Nevertheless, it is important to see that Frege, Wittgenstein, and Husserl were all struggling with the very same issue, although using different strategies and starting from different perspectives and assumptions. As we saw, Fregean senses must be semantic-cognitive rules or associations of such rules. But similar reasoning should be applicable to Husserl’s intentional acts: they should unavoidably include – in accordance with our view of semantics as always psychologically embodied – cognitive instantiations of semantic rules or associations of rules, which can be expressed in a cognitivist (psychological) and/or in a semanticist (logico-linguistic) fashion. As you might remember, in our analysis of adequation we considered an intention with a mind-to-world direction (responsibility) of fit added to its proper structural isomorphism as constitutive of a verifiability rule, which seems to a large extent a good way to understand Husserl’s view of intentional acts.
     In what follows, I will first present a short summary of Husserl’s theory of intentionality in its relation to his adequation theory of truth. Then I will try to translate his main insights into my own conceptual framework.
     As already noted, according to Husserl’s view, the meaning (sense) of a linguistic expression is an ideal, an abstract (Platonic) object, as it was for Frege and others. However, for him the meaning of an expression can be instantiated by two fundamental kinds of ephemeral intentional acts:

(a)   A meaning-conferring intentional act (bedeutungsverleihende Akt or Bedeutungsintention), which relates to an ideal object, abstracting its application to reality and disregarding truth-value (for example, I think that my sunglasses could be in the drawer);
(b)  A meaning-fulfilling intentional act (bedeutungserfüllende Akt), which relates itself to the object actually given (for example, while looking for my sunglasses I open a drawer, where I find them).

In case (b) the object of the act is not only intended, it is also given to us ‘in person,’ even if always in perspectival ways, by means of distinct intuitions that can successively reinforce one another. Finally, there is a third act, an act (c) of synthesis, through which we make ourselves aware that the object intended in the meaning-giving intentional act is the same as the object intended as actually given in the meaning-fulfilling intentional act. For Husserl, with this last act we achieve awareness of truth and knowledge. Consequently, according to him, truth is correspondence because it is the identity of the object intended by the meaning-conferring act and the object intended by the meaning-fulfilling act. As he writes, truth is ‘the complete agreement of what is intended with what is given as such.’ (1980 vol. II/2, VI sec. 38) Knowing that there can be an unlimited variety of perspectival acts of fulfillment, which can be added to one another in order to warrant our knowledge of the object by giving the experience increasing evidential value, he also writes:
When a presentative intention finds its ultimate fulfillment, the genuine adaequatio rei et intellectus is realized. The object is really presented as intended. So is the idea of all signitive fulfillment. The intellect is the intention of thought, the intention of meaning. Correspondence is realized when the intended object in the strict sense is given to us as it is thought. (1980 II/2 VI, sec. 37)
This ‘correspondence’ as the identity between the ‘objects’ of two intentions seems to me to be Husserl’s chief insight on the nature of truth, since the process he describes is clearly at the origin of the pragmatics of adequation, as developed in the present chapter.[35]
     Now, we can read meaning-conferring and meaning-fulfilling intentional acts as involving the instantiations of two verifiability rules. What Husserl identifies as the meaning-conferring intentional act can be approximated to the intention related to the verifiability rule that isn’t effectively applied, but only taken into consideration – conceived as applicable. In other words, we see that it is possible for this rule to be definitely satisfied or applied, because we know by means of rehearsal that we can to a greater or lesser extent imaginatively apply it, as in the case of ?p. On the other hand, what Husserl identifies as the meaning-fulfilling intentional act can be approximated to the intention related to a verifiability rule in its effective satisfaction or application within some actually given context. In the case where it is expressed by an assertoric sentence, this verifiability rule is a semantic-cognitive rule that can be said to be true or false in the sense that it can be shown to be effectively applicable or not. In the case in which we effectively apply a verifiability rule of the kind that can be expressed by an assertoric sentence, we are considering the act of synthesis by means of which the verifiability rule ?p, due to its identity of content with q, is considered effectively applicable in its proper context, which also confers truth on p (├ p), making us aware of an actual fact that satisfies it.
32. Solving two Husserlian Problems
Now, comparing the kind of empiricist approach defended here with Husserl’s theory of truth, we see that we are able to overcome two main drawbacks pointed out by his critics.
     The first and more serious one is that working only with intentional-phenomenal material, Husserl was unable to explain the linkage of the object ‘in person’ with the object in itself, since this would require him to go beyond the phenomena. As Günter Patzig concluded:
…the daring bridge called evidence intended to connect the judgment with the fact had the drawback, rather unfortunate in a bridge that it ended on the same side of the river from which it began. (1977: 194)
Our understanding of adequation offers us a non-idealist way to overcome this limitation. As already noted, the e-thought-rule expressed by ?p can be approximated with what Husserl calls a meaning-conferring intention. And the e-thought-rule expressed by !o can be approximated to what Husserl called the meaning-fulfilling intentional act. Finally, the awareness of the qualitative identity of content represented by ‘p = o,’ which brings us to the conclusion ├p, can be approximated to Husserl’s synthesis by means of which we reach truth by seeing that the objects of the two acts are the same.
     However, in doing this we do not need to follow Husserl in assuming some kind of idealism, because according to our analysis existence is the effective applicability of a conceptual rule, while the object of its application should only be conceived as what satisfies the criteria that could be generated by the rule, and its ‘having existence or reality’ is only its potentiality of having its conceptual rule effectively applied to it. The same holds for the verifiability rule; this rule demands for its effective application the satisfaction of criterial configurations by isomorphically matching criterial configurations of the factual content belonging to the external world as it presents itself to us. These external criterial tropical configurations, in contrast, are manifestations of the empirical fact and are here not interpreted internally as psychological configurations of sensory impressions, but externally, as real aspects of external facts (that is, as tropes and constructions from tropes), insofar as they suitably satisfy the definitional criterion of external reality in its inherent sense. These are at least external aspects of what Husserl called the ‘object in person,’ but in our case, even if being sub-factual contents, they are externally real non-mental physico-material entities by definition. We can say that a fact is externally real because:

(1)     this fact has the second-order dispositional property of having its first-order verifiability rule effectively applicable to it, even if this rule was never conceived or applied by any cognitive being.
(2)     Insofar as the effective applicability of the verifiability rule to the external fact implies the satisfaction of the inherent criterion of reality that defines what is externally real in the most natural sense of the word (maximal intensity, independence of the will, interpersonal access, conforming to expected regularities, possible causal interaction…).

This fact will with right be called a physico-material external fact, insofar as there is no skeptical scenario in view, for in the absence of a skeptical scenario there is no sense in questioning whether this external fact is not just inherently real, but also adherently real. It would be senseless, simply because the concept of adherent reality is a relative one and the attempt to apply it in the absence of a skeptical scenario would be an attempt to transform it into an absolute concept – which can easily happen when the philosopher hasn’t yet learned to distinguish inherent from adherent reality.
     The second objection to Husserl’s view is that the object is never given to us in its entirety. Since what we experience is always part of the object, it can never really be given to us ‘in person.’ Husserl saw this problem and suggested that the object could still be seen as a pure or empty X of ideal nature (1976, sec. 52).[36]
     Here I partially agree with him. Also, in the proposed view, it was assumed that neither the object nor the fact are perceptually given to us in their entirety, with the consequence that we can never be absolutely sure that what is given to our experience is the real object or fact. However, we can infer that the object or fact is given with enough probability, with practical certainty, assuming or postulating as warranted the evidence provided by the factually interpreted !o and, consequently, the corresponding truth of p in the context of an adequate linguistic practice, assuming that all other things remain the same. As we saw, we can infer that we have seen a dolphin and not just a rubber dolphin gliding over the water, and we can postulate what is given to our experience as indisputable evidence, insofar as we assume that the context of the expected observational practice is undefeated by unaccessed information.
     Anyway, I agree that the compresent clusters of tropes that constitute the objects, as much as the linked property-tropes and the resulting facts, are in themselves inexhaustible. And this means that we can never be absolutely certain that any of our semantic-cognitive criterial rules is able to match such objects, properties or facts in order to warrant their existence in an unchallengeable sense. However, the fact that we cannot be absolutely sure of the external reality of what we have accepted as an external entity isn’t sufficient to justify concluding that this entity must be something belonging to a purely mental realm. Indeed, there is a world of difference between the internal mentally-phenomenal (the ‘phenomenological’ of philosophy) and the external materially-phenomenal (the ‘natural phenomena’ of empirical science), which is conceptually warranted by satisfaction of the axioms of externality, insofar as there is no relativizing skeptical scenario in sight.
33. Truth and factual existence again
Now we return to the problem posed at the beginning of this chapter. There we asked whether the existence of a fact isn’t the same thing as its truth, since truth is also a property of a verifiability e-thought-content rule of being effectively applicable to a fact, which we have also understood as a correspondence with a fact, as was expressed by the formal identities (3) T‘p’ = C‘p’ = V‘p’ and (4) ‘p’T*‘q’ = ‘p’C*‘q’ = ‘p’V*‘q.
     Nonetheless, we have also seen how to recognize here a false dilemma. ‘Truth’ in its proper sense of correspondence, as an e-thought-truth (propositional truth), can exist only as the result of the direct or indirect awareness of the effective applicability of a verifiability rule by at least one cognitive being, as we have clearly shown in our many examples of the dynamic processes that lead us to regard a verifiability e-thought rule as true or false. This amounts to the same thing as to say that the e-thought-rule represents its corresponding fact. Consequently, the variables V and V* should be understood as abbreviations of such verifiability procedures. On the other hand, what we call a fact-truth, the existence of a fact, requires the effective applicability of its verifiability rule independently of our awareness of it, and thus even independently of the very instantiation of the rule in some mind (Ch. IV, sec. 34-35).
     As we also saw, this means that real or true facts do not require the existence of epistemic subjects, existing without requiring anything beyond the dispositional property of being the object of application of possible verifiability rules, while e-thought-rules cannot be true without consisting of verifiability rules that are effectively applicable because at least one epistemic subject exists in the awareness that they were or could at some point be effectively applied to the corresponding facts. Because of this, ‘truth’ is an epistemic term, while ‘existence’ is an ontological term. The ontological (fact-truth) exists independently of the epistemic, while the epistemic (thought-truth) requires the ontological (fact-truth) in order to exist, necessitating for this at least one epistemic subject as a thought-bearer. This is why, despite similarities, we attribute truth to e-thought-content-rules and existence in the sense of reality to the facts that can be represented by them, while we do not attribute reality to the e-thought-rules in order to replace truth.
     The distinction considered here helps us to better understand the difference between the truth of a thought-content (thought-truth) and the existence of a fact (fact-truth) in the verification procedure. Consider the identity of contents verified in p = q. The existence or reality of the fact is assumed by q (representing a fact-truth), and the truth of the thought-content is expressed by ├ p (expressing only a thought-truth). Even if p and q have qualitatively identical semantic contents (express identical verifiability rules) in the case of a true statement, the fact that they are differently identified on the symbolic level points to the already indicated more substantial difference.
     The role of the thought-true can be grasped in a more detailed way if we consider again the truth-making procedure described in the case of Mrs. Rose’s unfortunate husband:

!r     ~> ?p, {!r & !s & !t & !u} ~> !q, p = q /├p

This whole action-schema presents a verification procedure constitutive of the e-thought-content-rule of p endowed with truth. That is, the verifiability e-thought rules expressed by r, s, t, u… are at least partial constituents of the thought-content of p – of its whole cognitive meaning. And I say ‘partial constituents’ because there are certainly many other ways to verify p, many other possible ramifications of the verifiability procedure. Moreover, r, s, t, u also have their own separable verification procedures constitutive of their own e-thought-content-rules besides the indispensable central e-thought-content-rule of p, which would be the direct verification of Mrs. Rose’s attempts to poison her husband, which isn’t available to us. Meaning comes to be an extended, gradually fading rule-complex, but since the above procedure is dependent on the direct verifiability of Mrs. Rose’s attempts, the conceivability of the last one comes to be an indispensable meaning-condition. Finally, if Mrs. Rose confesses her attempts to murder her husband, we have added something considerably relevant for p’s truth.
34. The rule’s structural mirroring of the world
Let us recall that for J. S. Mill material substance was the ‘permanent or warranted possibility of sensations’ (Chap. IV, sec. 20). We have corrected this idea. Not the matter or substance, but the existence of the material object should be approximated to its permanent possibility of sensations, since permanence is always the same property, while objects can be endlessly diverse. Or, in our paraphrase, external existence is the effective applicability of the semantic-cognitive rule to entities of its proper domain or context, this effective applicability being measured by the assumed satisfaction of a criterion of inherent reality. This suggests a question: shouldn’t for Mill matter or substance most properly be the multiple and variable configurations of ‘sensations,’ insofar as they are permanently accessible to our experience? Or, in our more qualified direct realist paraphrase, aren’t the material entities (objects, their properties, the facts composed by them) constituted by the countless variable objective configurations of external physical property-tropes able to suitably satisfy the axioms of externality necessarily required for the effective applicability of their semantic-cognitive rules in the external world?
     The answer to this question seems to be: ‘yes, but not only.’ Indeed, dependent criterial configurations demand their isomorphic match with independent external criterial configurations enabling the application of semantic-cognitive rules, that is, mainly physico-material external quality-tropes and constructions from them (objects, facts) that are able to satisfy the rules, along with the expected satisfaction of the axioms of externality, since this allows us to classify such tropes and combinations of independent tropes as belonging to the external, material world.
     This we already know. However, if it were only this, how could these multiple and diversified configurations of tropes that satisfy the criteria for the application of semantic-cognitive rules be conceived as belonging to only one entity (a complex property, a material object, a fact)? What is the glue that holds them together? How could they be unified instead of remaining inevitably dispersed? The plausible answer has been already suggested:

What unifies all the aspects of an objective entity (property-tropes, individuals, facts) should be logically structured in a way that mirrors the logical structure of the semantic-cognitive rule.

Only in this inverted way would external structures be able to unify the multitude of external criteria. They are the totality of external criterial configurations, only a few of them being the configurations of tropes used to satisfy – that is, isomorphically match – dependent criterial configurations, though understood as belonging to the domain of the external world by satisfying the criterion of inherent reality.
     In more detail: an objective external entity, be it (i) only a trope (complex or not, monadic or n-adic), be it (ii) a nuclear cluster of tropes displaying compresence and having the specific tropical properties constitutive of a material object, or be it (iii) any fact primarily conceived as a tropical arrangement (in the given case inevitably including (i) and (ii))… they should respectively mirror the same logical structure of the semantic-cognitive rules by means of which we ascribe predicative terms to (i), identify (ii) with nominal terms, and represent (iii) with statements.
     This is why we can apply semantic-cognitive rules to a number of facets or aspects of an external entity and by these means identify the same entity as a whole; this is why a basal e-thought-rule can by means of its component rules be isomorphic with the elements of a grounding fact. This is only possible because we assume that the perceived facets or aspects are associated with unperceived facets or aspects in ways that are structurally similar to those of the corresponding semantic-cognitive rules. In Chapter IV we used the rough metaphor of two identical trees that touch one another at the tips of their ramifications: on the one side, the dependent criterial configurations generated by the rule, on the other, the external ones – the structured configurations of material/external tropes (possibly complemented by mental/internal tropes, as in many complex physico-social states of affairs).
     A trivial example can show the plausibility of the idea that a semantic-cognitive rule’s logical structure should mirror the logical structure of the entity to which it applies, which on its side should be mirrored in the structure of the rule. Suppose I start driving to the university, where I intend to hold a class. As I drive onto the freeway, I see that there is less traffic than usual. I begin to ask myself if today is a holiday.[37] I do not have with me any smartphone to check whether today is a holiday. However, some minutes later I arrive at the university where I find that it is closed, and a security guard tells me that today is a national holiday. Now, I have used ramifications of the verifiability rule to confirm the truth of (I) ‘Today is a holiday.’ This is confirmed by three facts: the symptom (a) that there is less traffic than usual on the freeway, the secondary criterion (b) that the university is closed; and the (less) secondary criterion (c) that when asked, a security guard informs me that it is, in fact, a national holiday. From the thought-content of (i), I derived ramifications of the verifiability rule which were the thought-contents of (a), (b) and (c). But on the other hand, I can say that from the corresponding institutional fact that it is a holiday, more completely stated as the grounding fact that today is a national holiday, which was declared to be one by Congress and was institutionalized as a law by publication in the official legal gazette... From this grounding fact (I*) inductively follow sub-facts that can be used as symptoms or secondary criteria, such as (a*) there are fewer cars than usual on the roads, (b*) the university is closed, and (c*) if one asks a security guard, he will certainly say that today is a holiday. That is: the same things that inferentially follow from statement (I) as its verifying criteria or symptoms also follow from the institutional grounding fact (I*) that today is a holiday, allowing a corresponding multiplicity of matches. And this makes it sufficiently clear that the ramified logical structure of the applied verifiability rule mirrors similarly ramified structural relations of sub-facts derived from the grounding fact that today has been declared a legal national holiday.
     Nonetheless, it is also fundamental to perceive that usually our awareness of most of these mirrored structures is merely putative. The structure of objective reality is often more complex or is only approximately similar to that of our semantic-cognitive rules. Indeed, we usually assume that our semantic-cognitive rules are inevitably fallible, insofar as they are directed at the open world of experience. That is, we only assume as probable that the structures of the internal semantic-cognitive rules mirror the structures of their external unifying references, which can in principle be corrected or even refuted by new experiences, leading us to expansions or disavowals regarding the structures of the semantic-cognitive rules. This can be the case with ascription rules, identification rules, and verification rules, and is more explicitly shown by rules stated as laws of nature.
     Summarizing: material objects, complex property-tropes and facts must have proper unifying logical structures that explain why the entities in question remain the same, even when experienced in different ways; and these structures are thought to be mirrored by the many variable structures of the semantic-cognitive rules that allow us to refer to them in unified ways.
35. Conclusion
The conclusion of this chapter can be extended to the whole book. It was an attempt to restore and unify some unjustly undervalued but intuitively fundamental ideas of the linguistic-analytic tradition. Once their acceptability is exposed, it is easier to see where they can be related to one another, building in this way what seems a plausible systematic overview. If the arguments presented here are essentially correct and well-grounded, then analytic philosophy of language must follow a somewhat different orbit and the right method to learn could be that of ‘successive approximations’ (Haack 2016), instead of almost gratuitous counter-intuitive challenging – going further by correcting and detailing the rough sketches presented here.

[1] E. G. Stenius suggested that although rejecting the logical atomism of the Tractatus, Wittgenstein withholds the pictorial view in his later book, Philosophical Investigations, what is shown in his suggestion that the photo of a boxer in a particular stance is a sentence-radical (Satzradical) susceptible to different interpretations (like the varied possible illocutionary forces of an utterance) (Cf. 1984c, sec. 22, note). The sentence-radical must possibly express an e-thought representing a real person in a pictorial way.
[2] In a letter to Russell from 1919 Wittgenstein explained that for him a thought consisted of psychical elements (Wittgenstein 1974). This liberates him from Frege’s Platonist commitment.
[3] I follow here Stenius interpretation of the Sachverhalt/Tatsache distinction (1964: 31).
[4] I will use the phrase ‘actual fact’ in the sense of an epistemically objective real fact, understanding the word ‘objective’ in John Searle’s sense of epistemically objective, which includes not only external but also internal (psychological) facts, insofar as they are intersubjectively sharable. (Cf. chapter IV, sec. 34)
[5] The analysis could certainly not go further, requiring that there must be some R1 relating F with a in Fa, etc. (Cf. Appendix to Chapter III, sec. 1)
[6] We can intentionally produce factual contents that we call true by acting in the world in order to change it in accordance with our views. For this reason, constructivist philosophers followed Giambattista Vico in the attempt to reverse the direction of fit of the correspondence: we are the ultimate truthmakers. However, this is not correct. Even in this case the truthmaker of the proposition, as the product of human action, is the final fact in the world and not the idea that has produced human action. That is: we can make the fact that makes the truth, but not the fact as truth.
[7] In my view, the addition of intentionality, the sense determines (bestimmt) the reference in Frege’s way of speaking, or turns into a meaning-fulfilling intention (Bedeutungserfüllende Intention) in Husserl’s way of speaking.
[8] To review the considered kind of inference, see Ch. II, sec. 9; Ch. III, sec. 10.
[9] We remember here Alfred Tarski’s disquotational formula, according to which ‘“p” is true in L ≡ p.’ Tarski’s approach has the great merit of properly emphasizing the meta­linguistic character of the truth-assignments in a formal language (Cf. Tarski 1944: 341-375). However, his formula does not overcome the philosophical problems of correspondence. If we replace sentence p with Fa, Tarski’s theory does not provide criteria that tell us why we should apply F to the object referred to by a instead of to any other object, and it does not consider the necessity of criteria for the reference of the name a, which natural language requires. The task here is to review his insight in order to integrate it in our maximalist approach.
[10] An at least virtual interpersonal confirmation is here important. In my view, truth must be able to ultimately satisfy an interpersonal consensus made authentic by its achievement through adequate agreement within a critical community of ideas (a community with equally competent members, with the same rights of interaction, etc.), a point particularly relevant in regard to the collective acceptance of complex law-like generalizations (Cf. Habermas 1983).
[11] I believe the anterograde and retrograde procedures are a more explicit version of a distinction already present in Husserlian phenomenology: the distinction between ‘truth as correctness’ (Wahrheit als Richtigkeit) and ‘truth as discoveredness’ (Wahrheit als Entdecktheit) respectively (See Sokolowski 2000, Ch. 11).
[12] See my objections to the private language argument in Chapter III, sec. 13 of the present book.
[13] My preferred moral theory is two-tiered utilitarianism. According to this view, we should apply rule-utilitarianism in ordinary situations, although in extreme situations, utilitarian rules are defeated and we must turn to act-utilitarianism. (Hare 1981, Ch. 2)
[14] Leibniz’ original proof can be found in his 1765, liv. IV, Ch. 7, Sec. 10.
[15] I say ‘to a certain extent’ because different communities of ideas are not incommensurable, as the relativist philosopher would like us to believe. As Searle once noted, the Inuits’ historical origins as told by anthropologists (crossing the Bering Strait circa 13,000 years ago) is nearer to the truth than the Inuits’ own creation myth (thrown out of a great crater that opened up in the earth…). And this is obvious to anyone who knows both belief-systems, just as it would be to an Inuit who had studied anthropology at Harvard.
[16] Popper treated absolute truth as a directive concept in Chapter 10 of his Conjectures and Refutations. Kant originated the view that there are directive concepts which lack a possible basis in our experience, but are still able to perform the pragmatic function of guiding our intellect in the direction of further syntheses. This was the case of his ideas of reason. According to the Critique of Pure Reason, they are concepts that reason uses in its striving to unify our knowledge, though unable to find satisfaction in sensory intuitions (1787, A 484, B 612).
[17] If q were only the direct expression of a factual content, we would fall into a kind of strong externalism that admits that part of our content-thought-meaning is a directly given fact in the world (a ‘structured proposition’ or something of the kind). However, without further qualification this view would demand too much from our epistemic powers, leaving unexplained not only the possibility of falsity, but also the inevitable fallibility of our supposed knowledge of truth.
[18] When I write of purely sensory truths, I am thinking of cases covering false sensations and feelings, such as imaginary pain induced by hypnosis or an emotion that someone defensively substitutes for the true one.
[19] A deeper understanding will demand a response to the problem of perception that will be attempted later in this chapter.
[20] I read this story many years ago, although I am unable to find the source.
[21] Even though the phenomenal contents of o and oare similar, the whole factual context must be very different, since at least the dispositional properties of ‘the blue there’ must be completely different.
[22] Searle uses the expression ‘phenomenal appearance,’ but then we should distinguish the psychological phenomenal appearance from its correlative physical phenomenal appearance.
[23] It is true that fMRI measures brain activity by detecting changes in blood flow, but blood flow and neuronal activation are coupled.
[24] For an admirably intelligent and vivid defense of direct realism, rejecting the argument of illusion, see John Searle 2015.
[25] Kant defended a minimalist form of direct realism: all that we are able to know is a multiplicity of in some way cognitively dependent phenomena resting on an unknowable thing in itself (Ding an sich).
[26] There is no view from outside. One can use different conceptual schemas (or languages) to say what something is for us. For example, I can say that this computer is made of metallic and plastic pieces, and I can also say that it is made of atoms. The macrophysical and microphysical schemas are complementary ones, and they both inevitably explain how something is for us.
[27] For similar lines of defense, see Austin 1962, Ch. 2; Cornman 1975, Ch. 2 and 6; Dancy 1985, Ch. 10; Lowe 1992; Huemer 2001, Ch. VII. Huemer proposes that we should sharply distinguish the object of perception from its vehicle, and Lowe points out that the veil of sensations must be seen as a bridge or a window to the real world.
[28] Searle’s conclusion goes to the point: ‘The whole discussion presupposes that I am actually seeing the table throughout, for there is no way that the table could continue to present to me different appearances from different points of view, if I were not actually seeing the table.’ (2004: 273) See also Huemer 2001: 119-124.
[29] It is the same mechanism of semantic derivation that explains the archetypal truth-bearer considered in Chapter IV, sec. 30 of this book. See also Aristotle, Metaphysics 1003a, 33-37.
[30] For a more complete exposition of this point, see Costa 2014: 145-157.
[31] This is where Lewisanism – suggesting an infinite number of possible real worlds and accepting only our own world as real and actual – fails. We know that our existent, real, actual world, is distinct from merely possible non-real worlds, because we know that the verifiability rules of the facts of our world are (or could be) effectively applicable through the satisfaction of axioms of externality. In my view, D. K. Lewis’ distinction between reality (inherent) and actuality (1986, Ch. 1) is a distinction without a difference that loses its teeth when we pay sufficient attention to the ways we can effectively attribute reality to a world.
[32] Hilary Putnam rejects the skeptical possibility that one could be a brain in a vat, hallucinating an unreal virtual reality produced by a supercomputer on the planet Omega or simply by chance (1981, Ch. 1). However, his objection is controversial, to say the least. According to Putnam’s externalist point of view, if I am a brain in a vat, in order to have thoughts like those of brain, vat, water, etc., I need to be in causal contact with these things; hence, once I have these thoughts, I cannot be a brain in a vat. The problem with Putnam’s argument, as some have noted, is that it ignores the flexibility of language. Unless you are a staunch externalist on meaning, there is no good reason to believe that electrical patterns in the brain cannot misleadingly appear to us as brains, vats, water, etc. They could be falsely represented and intended as such, assuming that various outside factors (like the supercomputer on the planet Omega or anything belonging to a comparatively real external world) could systematically produce these patterns. Anyway, if you still believe in Putnam’s argument you can choose another skeptical hypothesis like that of a realistic dream or appeal to ‘recently envatted brains.’ (See DeRose & Warfield, eds., 1999, Preface)
[33] Calling p any trivial proposition on the external world, s a person, h a skeptical hypothesis, and K the knowledge operator, the modus tollens skeptical argument has the form 1. ~sKh, 2. sKp → sKh, 3. Hence ~sKp. The modus ponens anti-skeptical argument has the form 1. sKp, 2. sKp → sK~h, 3. sK~h. (Cf. Costa 2014, Ch. 6.)
[34] One example of this kind of confusion is offered by Rudolf Carnap’s conclusion that his external question about the existence of the external ‘thing-world’ in its totality must be answered by means of an irrational decision to accept the system, a pragmatic fiat (1947). For us, either this is an inherent question to be answered affirmatively or it is an adherent meaningless pseudo-question.
[35] Husserl in fact distinguished four different concepts of truth. However, the question of their justification is controversial. (Husserl 1980, II, VI, sec. 39; Cf. Tugendhat 1970: 91 f.)
[36] Peter Simons summarized Husserl’s view of intentional objects as follows: ‘In particular, each noema has a kernel or nucleus which consists of three elements: a substratum, a set of qualitative moments, and modes of fulfillment of these qualities. What he calls a pure or empty X is the subject of predicates that are intended in the nucleus and which are more or less intuitively fulfilled. …this X is not a further concrete constituent in the noema; it is an abstract form occurring in it.’ (Simons 1995: 127)
[37] I do not consider the many ways I have to verify this hypothesis; but I know very well the implications of its falsification. One of them is that I will not hold any class today; another is that I am wasting my time going to the university. As we have seen (Ch. V, sec. 1), these inferences are more or less derived from my awareness of the meaning of the supposition that today is a holiday, though they do not belong to its meaning.