quinta-feira, 19 de janeiro de 2017

Claudio Costa: PHILOSOPHICAL TEXTS - TEXTOS DE FILOSOFIA


THIS "BLOG" IS THOUGHT AS A WAY TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE TO A WIDE PUBLICUM. THERE ARE MORE THAN 100 TEXTS, MOST OF THEM IN DRAFT FORM. MANY ARE INTRODUCTORY TEXTS. THE TEXTS MARKED WITH ONE OR MORE # ARE THOSE THAT CAN BE OF SOME INTEREST FOR THE SPECIALISTS. I HOPE IT IS USEFUL.

ESSE "BLOG" FOI PENSADO COMO UMA MANEIRA DE TORNAR MEU TRABALHO EM FILOSOFIA ACESSÍVEL A UM PÚBLICO MAIS AMPLO. SÃO MAIS DE 100 TEXTOS, A MAIORIA EM FORMA DE DRAFT. AQUELES MARCADOS COM UM OU MAIS # SÃO OS QUE PODEM SER DE ALGUM INTERESSE PARA A PESQUISA. OS TRABALHOS MAIS ANTIGOS E INTRODUTÓRIOS ESTÃO EM PORTUGUÊS. ESPERO QUE SEJAM ÚTEIS.

On my CV:
After a study of medicine I made my M.S. in philosophy at the UFRJ (Rio de Janeiro) with prof. Raul Landin (1981). My PhD I made at the University of Konstanz (Germany) with Gottfried Gabriel and Friedrich Kambartel (1990). Afterwards there were very useful one year post-doctoral works in the Hochschule für Philosophie (with Friedo Ricken, 1995), at the University of Berkeley (with John Searle, 1999) at the University of Oxford (with Richard Swinburne, 2004), at the University of Konstanz (with Wolfgang Spohn, 2009-10) and now at the University of Göteborg (with Anna-Sofia Maurin, 2016) and in the Institut Jean Nicod (with François Recanati). There were also several short term stays in Germany, particularly in Konstanz with professor Peter Stemer. 
  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). I also developed 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, will be also published by CSP in 2017.

Presently I am full professor of philosophy and (often) a CNPq researcher at the UFRN, in Brazil.

I am diagnozed as having some light degree of autism. Although there is not much to recommend of my 'defective mind', autism forces me to work in the independence of the leading beliefs that must be shared by the community of ideas, what I believe to be necessary in order to make it cohesive enough to produce results. Nonetheless, I also believe that in philosophy this can be of some advantage!

Advertisement of some published books (see Amazon):









## SKETCH OF AN UNIFIED THEORY OF TRUTH (2) (the role of coherence)

Note that this is only an uncorrect draft of the last chapter of the book 'Philosophical Semantics' to be published by CSP in 2017.



12. The insufficiency of coherence
That truth has to do with coherence is out of doubt. If Mary says to us that she was breathing as she was asleep last night, we will see her statement as obviously true, not because of any verificational observation of Mary’s breathing, but because this statement is coherent with our accepted belief-system, which says to us that a human organism needs to burn oxygen in order to remain alive. If Mary says that she went to Mars as she was asleep, this statement will be seen by nearly all of us as false, again because it clashes against our generally accepted commonsensical and scientific system of beliefs. Coherence is obviously related to truth and according to most coherence theorists a belief is more true as far as it is more integrated in the system of beliefs, what also means that truth is a question of degree (Blanshard, Chap. 27).
   Bernard Bosanquet (2015: 24) gave once an interesting example aimed to show that a greater amount of information makes a statement more true, what seems to vindicate the idea that the integration of a statement with the system of beliefs is what makes the statement true. He notes that the sentence ‘Charles I died on the scaffold’ is quite indubitable when said by a leading historical authority and far less true when told by a schoolboy. The child has only a name and a picture in mind, while the historian has the context, the reasons, the succession of causing events, a wealth of meaning associated with the sentence (see Blanchard, Ch. 27, sec. 4-5). If this example does not show that the increase of the coherence of a statement increases its degree of truth, it at least shows, I think, that it makes the historian’s claim to know its truth (his truth-holding) more probable.
   Since countless possible systems of beliefs can be constructed, one basic objection against the coherence theory is that any proposition p could be true in one system and false in another, violating the principle of non-contradiction. This objection, however, does not seems to be felt as a great difficult for the theorists of coherence (e.g. Bradley 1914; Blanshard 1939, vol. II: 276 f.; Walker 1989: 25-40). One could, for instance, answer that what ultimately counts for the truth of a belief is its coherence with the system of all systems, namely, the most encompassing system of beliefs agreed upon by a community of ideas in the time t (preferably ‘the best informed community of our present time’),  which we may call the real-world system. This would neutralize the objection that some thought-content p can be true in one system and false in another in a way that leads to a contradiction. For instance, the roman Madame Bovary would be a fictional subsystem belonging to the all-encompassing real-world system, as much as the subsystem of the Marxism-Leninism and the subsystem of the Euclidean geometry. And some p could be seen as true in its coherence with one of these subsystems, but still ultimately false in its coherence with the all-encompassing real-world system, since these subsystems are held as false in their coherence with the last one.[1] Nonetheless, even after this or any other move, the coherence theory remains problematic, since the unsurpassable problem of this view stays elsewhere. One can call it as the problem of circularity.
   The problem of circularity arises when we try to define coherence. Traditionally coherence was approached to consistency. A set of propositions (thought-contents) is said to be consistent when the propositions belonging to the set do not generate contradiction. Consistence may be a necessary condition for coherence, but surely not sufficient. For instance, consider the elements of the consistent set {Shakespeare was a playwright, plumb is a heavy metal, 7 + 5 = 12}. Since they do not have anything in common, this set does not increase neither the coherence nor the truth of its elements; and we could build a huge set of this kind with ‘zero’ coherence. Moreover, any definition of truth based on consistence would be circular, since consistence, being defined as the absence of contradiction between the elements of a set of propositions, affirms that their conjunctions cannot be false, including the concept of truth-value in its own definiens.
   More than consistent, coherence must be defined as inferential. The coherence of a system of propositions is in fact determined by the dependence that this system has from the inductive and/or deductive relationships between its propositions; and 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 (see Bonjour 1985: 98-100). Indeed, we know that is true that Mary was breathing all the night because this claim is inductively reinforced by all that we practically and scientifically know about what is necessary to sustain a human organism alive.
   However, if we consider coherence as the only and proper mechanism able to generate truth, this definition also leads us to contradiction. For the concepts of inductive and deductive inferences are also defined by means of truth! A strong inductive inference is defined as an inference that makes a conclusion probably true, given the truth of its assumptions, while a valid deductive inference is defined as an inference that makes its conclusion necessarily true, given the truth of its assumptions. Consequently, the coherence account of truth can only generate the truth of any proposition of the system by assuming the truth of at least some other proposition of it, what makes the coherence view circular. Any form of pure coherence theory is victim of a petitio principii, assuming what it aims to explain.

13. Coherence as Mediator
The view of coherence that I wish to propose here enables us to circumvent this difficulty. The reason is that in my understanding coherence is a complementary dimension of the correspondence theory, namely, the condition that enables the transmission of truth in a network of thought-contents, usually beginning with those that are based on some empirical (sensory-perceptual) experience and/or some assumed formal evidence (a theorem or postulate). This condition allows us to finally accept some factual content that should make some proposition true without the need of reducing this factual content either to some correspondingly formal axiom or to an evident 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 a statement like that is true by corresponding to a fact as the result of coherence, that is, as the result of inferences derived from our system of beliefs. These inferences transmit what we may call the veritative force – which we may define as any positive probability of truth – from one proposition to the other. However, this veritative force cannot arise from the inferential transmission of propositions without truth-value, but from propositions ultimately based on a myriad of perceptual experiences that have provided our knowledge of biological laws, as much as our awareness that Mary is a living human being and self-experience.
   We begin to see that even if coherence cannot be seen as defining truth, it plays a role as a mediating procedure whereby correspondence is obtained. The modal proof of P → ◊P in our example does not come directly from AS1 and AS3 plus some rules of propositional logic. We have some deductive inferential steps, and these steps are what constitute the coherential dimension of the verificational procedure, which some coherence theorists erroneously saw as the proper criterion of truth for the formal sciences. In the present case, coherence is constituted by material implications transmitting the veritative force (here understood as material implication out of postulated truths), but, as it was already noticed, it inevitably contains inductive inferences in the case of the verification of empirical thoughts.
   This latter case can be better illustrated by two examples which make clearer the relationship between coherence and correspondence. First, suppose that a gift is anonymously sent to me; I open it and see that it is the book called The Cloven Viscount, of Italo Calvino. I wonder if a friend named Sylvia has sent it. I knew Sylvia in Rome as a literature student and in this time I presented her with an exemplar of the book The Invisible Cities from Calvino. However, the gift was mailed from Rio de Janeiro. Thus, I realised that this book could have been sent by someone else… But then, I remember that Sylvia could well be back in Rio de Janeiro, a city where she was born and lived most of her life. An advocate of the coherence theory of truth would say that the thought-content of the statement p = ‘My friend Sylvia has sent me an exemplar 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 gift the book The Cloven Viscount from Calvino. (r1)
2.     Sylvia was a literature student when I knew her in Rom.(r2)
3.     I gave to Sylvia as a gift an exemplar of The Invisible Cities from Calvino. (r3)
4.      (from 1, 2, 3) Hence: The book could be sent from Sylvia (s)
5.     But the book has been mailed from Rio de Janeiro (t)
6.     (from 4, 5) Hence: The book wasn’t sent from Sylvia, who I knew in Rom (u).
7.     However, Sylvia told me she lived all her previous life in Rio de Janeiro (v)
8.     (1, 2, 3, 5, 7) Sylvia has finished her study and has mailed me the book The Cloven Viscount from Rio de Janeiro.(w)
9.     (from 8) My friend Sylvia has sent me the exemplar of The Cloven Viscount.(q)

In the end, what we really have here is an indirect procedure by means of which correspondence is verified via coherence. To see this better we need only to revise the reasoning above, excluding s and rejecting the partial conclusion u in order to build the following coherent set of beliefs: {r1, r2, r3, t, v}. These beliefs reinforce inductively the conclusion w that implies q, making q very probable. This system makes me, starting with the guess ?p = ‘Was Sylvia who sent me the book?,’ see the identity of contents p = q and conclude with practical certainty ├p, according to which it was Sylvia who sent Calvino’s book to me.
   A pure coherence theory, as Stephen Walker has made plausible, is impossible (1989). Coherence could exist independently of correspondence if you think that thought-contents could acquire probability or formal certainty independently of any anchorage in the sensory-perceptual/self-sensory experience or in the postulates of a formal system. But this is not the case. The thought-contents expressed by the statements above either describe a perceptual thought (‘I knew her in Rom,’ ‘I gave her a book…,’) or a testimonial thought (‘She told me she lived all her earlier life in Rio’) or personal experience (‘I read the book…’) or an inference (‘She may be back in Rio…’) from testimony (She told me…) based again on sensible experience (She lived all her earlier life Rio…).
   What was given to me in the above example was an indirect product of the correspondence of thoughts-contents with their factual contents by means of perceptual experiences. And these experiences are the ones that guarantee to me q as the derived evidence representing the fact that Sylvia sent me the book. This guarantee of q, in turn, is what makes the thought-content of p true for me. In a summarized form, introducing the symbol ‘~>’ to represent 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

We understand now how coherence takes part in the processes of achieving truth. And we see why coherence of our empirical claims would have no force if it weren’t anchored on perceptual experience taken as evidence in the case of empirical truths, and on axioms or postulates in the case of formal truths. This is why a fictional writing can be perfectly coherent without in this way giving us any factual truth. Its anchors are only imaginarily true.
   This kind of reasoning invites us to think that correspondence comes first, since it is correspondence that creates truth. Moreover, there may be in this way correspondence without coherence, but not coherence without correspondence. However, this conclusion seems at first too hasty when we consider that all observation is conceptually charged, as Pierre Duhem, Karl Popper and many others have insisted, what requires coherence with at least parts of our belief-system to be conceptualized. We could reply that one should not confuse meaning with truth. It is the meaning of the experience that requires inferential relations with our belief system; but the veritative force is born out correspondence. This seems clear when we consider the retrograde correspondence process, since it begins with a kind of raw experience (!o) and in this regard does not demand even the inferential relations inherent to conceptualization. But the problem threatens to return with the conceptual recognition of ?p.
   I think that I can justify my point better by analysing the kind of input that our system of beliefs gives to a particular observation. Suppose that you go to walk in a neighbour field and you see a unicorn. You will distrust your own senses, since you know that unicorns do not exist. Later you are informed that it was a fake unicorn: a set of film has put a horn on the head of a horse in order to make a film and the animal was let free in the interval between the settings. The defender of the coherence theory would say that this is a proof that even the sense-perceptual observation can be made false by our system of beliefs. But wait a time! This argument is completely defeated when we consider that the responsible for your mistrust was not the system of beliefs as a whole, but the correspondence of other perceptual experiences. Indeed, you are informed that unicorns are mythological creatures, knowing that in the whole history no observation of unicorns or their skeletons has been really confirmed. Moreover, our evolutionary classifications of animals excludes unicorns. But these firm beliefs against the existence of unicorns were all gained with help of induction by means of a myriad of other sensory-perceptual testimonial observations that were historically and scientifically legated. This means that your sensory-perceptual observation that you were truly seen a unicorn was in the end of the day defeated, not by the system of beliefs as a whole, but by counter-evidences given by other direct correspondences also originated from perceptual observations. In other words: we agree that though sensory-perceptual is the spring of veritative force, that it can gain or lose veritative force by means of coherence. However, its confirming or rejecting coherence gains its force indirectly, from other sensory-perceptual observations, what leads us to the conclusion that the true origin of veritative force is always the sense-perception, letting to coherence the secondary though necessary role of transmitting veritative force. My conclusion is that the supposed counter-example only shows that correspondence comes first because it is the only true donator of truth. Thus, instead of defending an impure coherence theory, as Walker has attempted, I defend what he would call an impure correspondence theory.
   Risking to be exceeding boring I turn to a last and clearest example, this time concerning the verdict of a judge. As it is well known, judgments on crimes frequently cannot receive direct perceptual testimony from bystanders; because of this, they are often heavily sustained on coherence. This was the case of the American pastor David, who shortly after his marriage to Mrs. Rose, was admitted to a hospital with severe abdominal pain. Since the examinations showed a high level of arsenic in Reverend David’s blood, a thought-content that we abbreviate as r, the following suspicion appeared as the result of an abductive reasoning: ?p, which means: ‘Tried Mrs. Rose to poison Reverend David?.’ The following additional factual evidence later confirmed this suspicion:

s: Mrs. Rose had the habit of preparing bowls of soup for her husband, even taking them to 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, with the surprising discovery of a high level of arsenic in their hair.

We can now build the following retroanterograde verification process:

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

   Certainly, the conjunction of the statements r, s, t, and u add one another to form a strong inductive inference assuring us practical certainty that !q, which states an unobserved factual content (namely, that Mrs. Rose tried to poison her husband). This stated factual content confirms our initial suspicion expressed by !r. However, a crucial point to be noticed is that factual statements r, s, t, and u are all made true by corresponding with or deriving from publicly observable perceptual factual contents. Again, what is shown is that the coherence view of truth cannot stand alone. The plausibility of q is grounded by means of coherence on the conjunction of the observational statements r, s, t and u. But they are true because of their correspondence with observational contents, even if they also rest on empirically grounded theoretical assumptions, the last also in some way derived from perceptual experience. As we see, coherence alone cannot originate truth because inductive and deductive coherence relations are defined as ways of preserving and not of achieving truth.
   The conclusion is the same: coherence relations work like the wires of an electrical power grid: though they are not able to generate electricity, they are able to transmit it. Coherence is not an independent mechanism, but only an inferential network by means of which the correspondence makes its way. In other words: coherence only transfers the veritative force generated by the correspondence of contents of more basic beliefs with empirical or formal facts to the derived ones, those acting inside the belief system, in order to produce the content of thought expressed by the non-observed fact, which in the example is q. Here this content is accepted by us representing the factual content corresponding with the thought-content of p by having the same content, which means the same as making ?p true. This is why we can also say that statement p is true because it corresponds to the fact that Mrs. Rose poisoned the reverend, even if we know this fact not by observation, but indirectly, from the coherence of the hypothesis with other contents that correspond with observed facts.
   The thought-content q, as we will explain, has a kind of Janus face: on the one hand, it expresses a thought-content (a proposition), and on the other hand it expresses what we are sure to be an objective factual content, namely, the fact that Mrs. Rose tried to poison Reverend David. It is by being involved in the correspondence that coherence is involved with truth. In sum: coherence is just an interdoxal mechanism by means of which correspondence takes place.
   Now we return to a point already noticed as we analysed the first example. The veritative force of the observational experience, though not made of coherence, presupposes coeherence. As already noticed, all observation is embedded into theory as many philosophers of science have insisted. If someone affirms to have breathing all the night or to have seen a phantasm during the night, we will believe in the first statement and disbelieve in the second, since the first agrees with while the second clatches against our scientific system of beliefs. But this isn’t a point in favour of the idea that coeherence alone has no power to generate veritative force, since the veritative force that leads us to reject the truth of the observational experience was itself generated by a multitude of other observational experiences responsible for the building of our system of scientific beliefs.
   The important question that remains open is about the precise status of q. It is the expression of a thought-content, but it must be also seen as able to represent the factual content, the real or actual fact. Are these two possibilities conciliable?[2] This crucial question will be tackled in the following sections.

14. What about the truth of the truthmaker?
One of the most serious problems for the correspondence theory of truth concerns the infinite regress that treats the truthmakers, the factual evidences that verify the hypotheses. We can pose it in the form of a dilemma: Either the evidential fact or factual content is undoubtable or it can be doubted. Suppose (a) that it undoubtable. In this case, it seems that we fall into dogmatism, according to which our normal perceptual and even purely sensory truths are beyond any possibility of falsity. But this would not be in conformity with the fallibility of our empirically based knowledge; we cannot be absolutely sure about the evidence of any (maybe almost any) empirically given factual content; and even formal axioms have always a degree of arbitrariness in their choice and can have their applicability emptied after changes in our more extensive system of beliefs. Now, suppose (b) that the evidential content believed as a fact can be doubted. In this case, it seems that we need to search for new evidential content, which would warrant its truth; but, since this new factual content isn’t also beyond doubt, we should look for a further evidential content and so on indefinitely. If we cannot stop this regression, as it seems, we have no way to ground our suppositions because all grounds would lack the necessary solidity.
   Restricting myself here to empirical truths, I think that we can answer this dilemma when we consider the examples in sufficient detail. Consider the following example of an observational sentence !o: ‘There’s a dolphin swimming in the sea.’[3] Imagine that the truth of this sentence depends on the observation of a dolphin coming out of the water 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 the second person, already informed by the first and searching for 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 by reason of a lack of true dolphins and in order to entertain tourists, a diver swims under the surface with a rubber dolphin attached to his back, coming up from time to time in a way that produces in the bathers the illusion that they are seeing a real dolphin. In face of this, the factual content !o that should ground the verification of ?p is defeated. Those aware of the trickery could exclaim: ‘It is false that there is a dolphin swimming in the see.’
   However, the answer to the problem does not seem to be difficult. What we believe to be a factual content does not need to be seen as absolute. It is indeed only postulated or assumed as a factual content (as the real truthmaker) within the context of a practice that typically presupposes some informational background and lets aside the possibility of abnormal circumstances that if present would defeat the assumption. Thus, consider the language-game or practice (A), in which we recognize things under normal daylight, great enough and near enough, working in the context of a touristic beach where dolphins are supposed to appear… In this practice we are allowed to assume that the observational content ‘I am seeing a dolphin that has just emerged from the water’ as an unquestionable evidence expressible by !o, that is, as a matter of fact, a truthmaker or verifier that we consider as assuring us with practical certainty that there is a dolphin in the sea. Assuming the informational content and the context at disposition in this practice, and assuming that all other things remain the same, seeing a dolphin must be undoubtedly accepted as the truthmaker of the hypothesis ?p. Since o has also an internal phenomenal content (the psychologically given sensory impressions), we could say that in this case we are allowed to assume that the content of o, that is, o without ‘_’ (‘I am having the experience of seeing a dolphin emerging from the water’) can be seen as the vehicle of our experience of the real fact o given in the world (‘A real dolphin has just emerged from the water’). But this assumption of evidence in the practice can only be sustained under a ceteris paribus, namely: the assumption that the observation isn’t being defeated by some condition extraneous of the assumed informative contextual background.
   Now, the defeating extraneous condition is given because of a shortage of real dolphins in the region, and is constituted by a diver swimming under the water with a rubber dolphin on his back and rising sometimes to the surface in order to give tourists the impression that they are seeing a real dolphin… Assuming that some observer is aware of this information, what is given for him isn’t the practice (A) but a different observational practice that we may call (B), which includes the information about these specific abnormal background circumstances. In this (B) practice, we cannot postulate the observation of a real dolphin merely by experiencing the sight of a dolphin emerging from the water. Under the circumstances posed by (B), in which there are rubber dolphins being carried underwater, to observe a real dolphin would certainly require a closer and far more careful examination, for example, a near underwater inspection of a possibly fake rubber dolphin, which can be symbolized by o.’ In this new practice, the thought-content expressed by p would be falsified by o,’ as the following retroanterograde schema shows:

p ~> ?p, !o,’ p ≠ o’ /├ ~p

What this experiment shows is that our usual certainty regarding the experienced factual contents isn’t something absolute, but something that needs to be postulated as certain, i.e. as beyond a probable truth, under the assumption of the truth of the informational background that characterizes some linguistic practice, that is, under the assumption that there is no defeating evidence. If we get information indicating a different background circumstance able to discredit the assumed practice, as in the case above, the postulation of certainty vanishes.
   I give a second similar example only to reinforce the point. Yvonne is driving in a desert and has the experience of a mirage. At first, she believes that the lake she sees on the horizon is real. We can symbolize this through the following retrograde verification process:

!o, ?p, p = op

However, soon after it turns clear to her that it was a mistake; what she really sees is an inferior mirage originated by refraction of sunlight by the hot air near to the soil. She adds to the background circumstances the unusual circumstances that are able to defeat the normal perceptual evidence. As she has learned that unusual circumstances defeat the rules of the usual observational practice (A), instead of thinking !p: ‘I am seeing a lake’ she thinks ├ ~p ‘I am not seeing a lake,’ concluding:├q, ‘I am seeing a mirage.’  What was first seen as external evidence is now seen as a wrong interpretation of the data, being replaced by the new practice (B), which allows the falsification of what was at first assumed to be an inexpugnably truthmaker. We can state this change through the following anterograde verification process:
        
?p, !o’ , p ≠ !o’ ├ ~p

It is worth to notice that the phenomenal content of perception is in both cases the same. But the interpretation given to this content, when reading the factual content existing in the world, is very different, and it is different because the right awareness of the surrounding circumstances is able to defeat the natural interpretation of the visually-given content.

15. The objection of linguistic-cognitive circle
Probably the most relevant epistemic objection to the correspondence theory is the so-called problem of the linguistic-cognitive circle: propositions (thought-contents) can only be compared with propositions, and by comparing hypothetical propositions with the propositions expressed by evidential contents, even if these are taken as certain, we would remain trapped in our language and thought. Even if we find the strongest evidence, this evidence could only be considered in the form of linguistic expressions of propositions, thought-contents, s-thoughts, belief-contents… but in no way by direct comparison with actual facts, states of affairs or events in the world (Neurath 1931: 541; Hempel 1935: 50-51). Here again, we would be in danger of falling into an infinite regress with epistemic scepticism as corollary.
   A prima facie general reply to this objection is that in order to say that we are trapped into an intra-linguistic or intra-cognitive world, we are already assuming that we know the existence of an extra-linguistic external world – a knowledge that remains to be explained.
   Philosophers like Moritz Schlick (1936) and A. J. Ayer presented a more focused reply. Here is the well-known reply of A. J. Ayer:

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 be expected that they should? (Ayer 1963: 186)

Ayer’s words contain a strong appeal to common sense. Nevertheless, this appeal seems to contradict another persistent idea, which is also not alien to common sense, namely, that the content of the perceptual experience should be some kind of belief-content conceptually structured and therefore should be something mental by nature. Consequently, we could never direct and unquestionably access anything referred to by a perceptual thought, namely, the external facts as they are in themselves (see Blanchard 1939, vol. 2: 228).
   One reaction to this dilemma would be to accept the kind of last alternative called idealism. But idealism sounds today as a forbidden solution. It is the view according to which all reality is in some sense mental. However, this view runs against one of our most humble commonsense principles, namely, that there is an independent physical world outside us. Furthermore, it seems to be the other way round: our empirical knowledge (particularly the scientific one) says that the mental is in some sense a minuscule emergent portion of the physical (biological, biochemical) world, depending on it in order to exist, something as the phenotype depends on the genotype in order to exist. In other words, it seems that the mental supervenes the physical as far as our experience – scientific or not – has shown. Moreover, if we remain on the side of our principle of established knowledge (Ch. II, sec. 4), idealism remains an anathema, since it denies not only the modest commonsensical truth that the external world is non-mental, but also the scientific truth that almost the entire physical world has nothing to do with the mentality. In some sense of the word ‘emergency,’ mentality is an emergent property of life, which is an emergent property of organic chemistry, which as a carbon based chemic is an emergent property of the atomic physical world. Finally, idealism seems to find its appeal in the wishful thinking, as the philosophy of culture and human sciences, from Nietzsche to Freud, Dürkheim and Weber, has made plausible. It gives us the illusion to have some control upon an inevitably unpredictable and dangerous external world. The upshot is that we have today more than ever strong reasons to remain epistemic realists.

16. Answering the objection of linguistic-cognitive circle
Once accepting to preserve a categorial opposition between the mental and the physical in the sense that the first is cognitively-dependent and only first-personally experienced, while the second is (usually) cognitively-independent and third-personally experienced, I would like to defend direct realism, the view according to which our senses provide direct awareness of the external world pretty much as it is. Direct realism differs from indirect realism or representationalism, which is the view according to which we have direct experience only of our sensations (or sense data), which inform us about the external world, so that the last one is never directly experienced.[4]
   My defence of direct realism begins by the demonstration that all that is experienced in normal perception has a kind of Janus face. Non-metaphorically, what is given in our perceptual-factual experience are always two different entities: one psychological and the other physical, as follows:

(A) The psychological experience of the cognitively-dependent sensations or sensory impressions, also called sense data.

(B) The proper perceptual experience of the cognitively-independent, externally given physical content or entities (understood as singularized properties or tropes, objects as clusters of tropes, real facts as arrangements of them).

   The psychological experience (A) is of what we may call sensory impressions or contents (already called ideas, phenomena, representations, sense data, sensations, sensa, qualia…). It seems clear that beyond any doubt that sensory contents are always present in our perceptual experiences, as I intend to show later. But thesis (B) also seems beyond any doubt: it is the idea that in addition to the sensory experience, when we perceive something this something is given to us as an external entity. Indeed, it is also a commonsense truth to say that we usually perceive the external world as it really is, namely, as being minimally built up by cognitively-independent entities that are tropes (usually called properties), by clusters of compresent tropes with form and mass (mainly called material objects), and as arrangements of the first and second ones (rightly called facts).
   The clearest evidence favouring this double view is given by tactile experience (Searle 2015). Suppose that I touch with my hand on a warmed stove. I can say that I have the sensation of hotness: this sensory-impression is the psychological experience (A). Alternatively and with equal right, I can also say that I have perceived that the stove is hot; this is the proper perceptual experience of the externally given physical entity (B). The essential point to be noticed in this example is that in the normal case we cannot phenomenally distinguish the experience (A) from the experience of (B). Thus, for example, I can say based on the same tactile experience:

(A) [I feel that] the stove is hot.
(B)  The stove is hot.

In a similar way I can say:

(A) [I feel that] I am holding a tennis ball in my hand.
(B)  I am holding a tennis ball in my hand.

Now, from the auditory experience I can say:

(A) I [have the auditory impression that] I hear a thunder.
(B)  I hear a thunder.

And from the most common visual experience I can also say:

(A)    [I have the visual impression that] I am seeing a fisher boat entering into the mound of the Pirangi River.
(B)    I am seeing a fisher boat entering into the mound of the Pirangi River.

As you can see, the phenomenal descriptions outside the brackets are the same, but in the (A) cases, I speak of sensory contents going on in my head (sense data), while in the (B) cases I speak of independent physical contents – factual contents pre-existing in the external world. The real thing (B) is epistemically dependent on the sense impression (A), in the sense that without the sense impression (A) I couldn’t know (B). On the other hand, the sense impression (A) is ontologically dependent of (B), which causes (A).
   I can illustrate the harmlessness of the duplicity that I am pointing out by comparing it with the duplicity of the objects that we see through a looking glass. What we see in the looking glass can be interpreted as: (A’) a simple image of things, for instance, the image of a vase of flowers on a table. But it can also be seen as: (B’) the vase in itself that I am seeing through the looking glass. For instance, I can point to the object seen in the looking glass, 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 is made clear by contextual differences: the image isn’t said to be real, since we 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 definitely measured and shown to remain always the same, independently of the changeable apparent size of its image, etc. We can change the apparent size of the image by bringing the vase closer to the looking glass, this apparent distance doubles the real distance of the vase to the looking glass, and it remains limited to its frame... However, by looking at the mirror, we would not be able to see the vase on the table without the help of the image; and the elements and relations between both will coincide at least partially. Moreover, the access to the real vase is in the case dependent on the access to its image. As in the cases above (B’) is epistemically dependent of (A’) because without the image (A’) you couldn’t see (B’). Alternatively, (A’) is ontologically (causally) dependent of (B’). This is why, when through the looking glass you pay attention to the object you see it as perceptually dependent of its image, while when you pay attention to the image you see it as causally dependent of the real object. You can at easy say that you see the reality through the image. Moreover, you can also say (if you wish) that you are seeing the real vase directly through its image, if you compare it with the same vase seen in a photo. Finally, you can see either the image or the real thing – but not both together.
   As any other metaphor, this has its own limits, but I think that it 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 interpreted in two ways: (a) internally and psychologically, as a first-person sensory-perceptual thought-content, and (b) externally, as a third-person physical fact or factual content because as far as we are able to interpret the given content as an external factual content, we escape the linguistic-cognitive circle.
   A complementary but also fundamental point is that we almost never have a complete perceptual experience of the factual content. Our experience is typically perspectival. What we experience are facets, aspects, sub-facts. If I see the fisher boat entering the mound of the Pirangi River, from the point where I am, I experience only one side of the fisher boat. However, by means of this dynamic sub-fact (process) I am allowed not only to say that I am seeing one side of the ship – a sub-fact – but more often that I also see the whole ship and the whole process – the dynamic grounding fact: I see the real fisher boat entering into the mound of the Pirangi river (on facts, see chapter IV, sec. 20-25).
   These are the nearly commonsensical ideas that in my view allows us to break the linguistic-cognitive circle. However, the following arguments against direct realism are designed to show that these views must be misleading.

17. Answering some main arguments against direct realism
The view implicitly defended in what I wrote above is one form of direct realism. Against direct realism and favouring indirect realism or representationalism there are two famous traditional arguments: the argument of science and the argument of illusion. I will consider each of them separately.
   I begin with the famous argument of illusion. It usually concerns cases of perceptual illusions in which what we suppose that we perceive is not what we should perceive, particularly in the extreme case of hallucinations in which we only imagine to be perceiving. Although the hallucination can be phenomenally indistinguishable from the products of real perception, it isn’t real. There are many examples supporting the argument. They all intend to proof that in the best case our perception is indirect, since it always occurs through the ‘the veil of sensations.’ In what follows I summarily present several examples, some of them are considered since the antiquity:

1.     I go out without gloves, the temperature is of 26 degree minus. My hands are freezing. When I come back I wash my hands in water in room temperature. But my feeling now is that the cold water is warm! Thus, what I really feel is my feeling.
2.     A car passes in front of me with high speed and because of the Doppler Effect its sound changes the peach from high to lower. Thus, I do not hear the true sound but my auditory percept.
3.     A person with jaundice may in some rare cases see the world yellow due to the accumulation of bilirubin in the optical media of the eyes. Thus, why can we claim to see the world’s in its real colours?  
4.     If I press the side of my right eye with my right finger, I have the impression that things in front of me move in the opposite direction. Consequently, what I see directly are only images of things, that is, sensory impressions, and not the things as they are in themselves.
5.     If I raise my index finger fifty centimetres in front of my face and look at the end of the room, I see two images of index fingers. If I then focuses my eyes in the finger, the two images join themselves in one only image. Since they are not phenomenally different in the two cases, I conclude that what I really see are the sensory impressions of my index finger.
6.     I look at a coin. I know that it is round, but it seems to me elliptic. Indeed, only sometimes I see a coin in its real round form. So what I see are nearly always sensory impressions.
7.     I see a lake in the desert, but soon I perceive that it is a mirage caused by the hot air near to the sand. Since my sensory impressions are phenomenally the same, what I see are my sensory impressions of a lake.
8.     Suppose that I have the perfect hallucination of a white horse. I do not see any white horse, but the hallucinated image. Since this image made 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.

The main conclusion of the argument of illusion is the rejection of direct realism, which should then be replaced by indirect realism, already accepted by Descartes and mainly attributed to Locke. The suggestion is that the objectively real world is perceived indirectly, by means of the perception of sensory impressions or sense data, which form the veil of sensations.
   There is nowadays a convincing philosophical literature aiming to show that the argument of illusion is fallacious and that we are really able to perceive things around us directly as they really are.[5]
   To avoid misunderstanding, I do not wish to deny that there are sensory impressions or sense data. I do not wish even to deny that we perceive the world through a veil of sensations, since by accepting (A) I accepted these things. What I reject is that these things make our perception indirect. For we never say that we perceive our sensations; what we say is that we perceive the world directly through our sensations or sensory impressions. This suggests that the fact that we can show that we perceive the external world through one or even several veils of sensations doesn’t make our perception of the external world indirect. In clearer words: the central problem with the argument of illusion is that it is built upon a misunderstanding of the semantic of our concept of directicity.[6] Consider the three couples of sentences:

1. The package has been send directly to the receiver (by flight).
2. The package has been send indirectly to the receiver (by ship).

1. The travel is direct (the bus travels directly from Konstanz to Munich with a stop of thirty minutes for lunch).
2 The travel is indirect (first you take a bus from Konstanz to Lindau, then you must take the train to Munich).

1. The bullet reached the victim directly (after breaking the glazing).
2. The bullet reached the victim indirectly (after rebounding against the wall).

What these couples of examples show is that what makes some relation indirect is not necessarily the fact that we can find intermediaries between the relata – they very often exist and they can be more than one only. Directness/indirectness is an essentially conventional distinction that depends on the relevance of the intermediaries for what we are aiming to consider.
   In the case of perceiving, the language allows us to say that we perceive things outside us directly, even if by means of a causal process constituted by a number of intermediaries. And there is nothing wrong in accepting that we perceive things directly by means of sense data or through a veil of sensations, as much as there is nothing wrong in saying that the victim was reached direct by the bullet, though it has first to cross the glazing of the window.
   Having this in mind, if we consider again the examples of the argument of illusion one by one, we clearly see that perceiving through sensory impressions does not mean that we perceive indirectly:[7]

1.      I wash my freezing hands and the water feels warm, but I am fully aware that the water has a room temperature and I am perceiving the temperature directly, though in a deceptive way. If there was no room temperature to be perceived under normal conditions, I could not compare.
2.      The person may say, ‘I see things as if they were yellow, though I know that that isn’t their true colour.’ What we call the real colours of things are by convention those colours seen under normal conditions, what includes a normal vision, adequate illumination, etc.
3.      I hear the sound directly, though in deformed ways. If I could accompany the car in the same speed, I would hear the sound in a non-deformed way, which is taken as excluding Doppler Effect.
4.      Even if I show by pressing my eye that I see the things moving through my visual field, this does not mean that I am not seeing the things directly. In fact, I can even say, ‘I see the outside things directly as they are, though as if they were moving.’
5.      In the second example, as Searle has noted, I can instead say, ‘I do not see two fingers… I am directly seeing my only index finger as if it were duplicated.’
6.      About the form of the coin, it appears to me as elliptic, but I can say that I see directly a round coin that only ‘looks elliptic.’ – As A. J. Ayer noted, what we consider as the real form or the real colour is often a question of convention (see Ayer 1973, Ch. 4): we have the convention that the real form of a coin or of a table is the form we see when we look at these things from above. In the same way, we have the convention that the real form of a mountain is the form that we see when looking at it from the soil and at a sufficient distance, but not from above (e.g., Mattenhorn, Sugarloaf). The real colour of a tropical mountain is normally green, even if at a great distance it may seem blue, etc.
7.      In the case of the mirage, I see what looks like a lake, but I can say that I now know that what I really see is the image of the sky deflected by the warm air on the sand of the desert and I can say that I see this mirage directly.
8.      Finally, in the case of the hallucination, it is simply wrong to say that I would see the content of my hallucination. I would only believe to see, when in fact there is nothing there to be seen! Verbs like ‘seeing,’ ‘perceiving,’ ‘being aware of’ are primarily related to the factual, objective content, and not to the sensory content. Even if it is through the sensory content that we have perception of things, this does not makes our realism indirect; in a similar way, when we say that the bus made a stop of twenty minutes for lunch, this does not mean that the travel was indirect.

This kind of response is not as new as supposed. It was already present in the following remark of the direct realist philosopher Thomas Reid against his contemporary David Hume nearly three centuries ago testimonies:

…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 reflexion upon the signs or even perceiving that there is such thing. It is in a way something similar that the sound of a language after becoming familiar are overlooked and we attend only to the things signified by them. (Reid 1967: 135)

To my mind and to the mind of most philosophers today this is the correct answer, but the persistence of the concurrent doctrines is a demonstration of how slow, sundry and confused may be progress in philosophy.
   Summarizing my answer: we perceive things directly, even under misleading conditions like those of delusions, what justifies the direct realist view of whatever is given in really the perception; and this does not mean that there cannot be a veil of sensory impressions or sense data in-between. This justifies our psychological interpretation (A) of the given content as merely sensory data, without forcing us to reject the interpretation (B).
   Finally, one word about the argument of science. According to this argument, our perceptual experience depends on the stimulation of the distal neuronal cells that in the end lead to the stimulation of occipital cortical regions into the brain, so that our experience is in fact the experience of what is going on in our own brains, which is nothing but the experience of sensory impressions or sense data. Consequently, our direct experience can only be of these sensory impressions going on in our brains. From this follows that we cannot have a direct experience of the world outside us. From this also follows that we cannot be sure that the contents of experience reflect the way the external world really is. Worst yet, we may be lead to the incredible conclusion that, since brains also belong to the external world we cannot be even sure that our brains exists... What we can be sure is only that we have these internal sensory impressions!
   The answer to the argument of science is that there is nothing semantically wrong in saying that we experience directly the things given in external world, even if this experience demands the work of complex neuronal structures as intermediary means. In the case of visual perception, we have simulacra of things seeing, first in the activation of photoreceptor cells of the retina by the light-waves and in the end in a corresponding activation of the striate cortex (region V1) in the occipital region, which would be then analysed through the visual-association cortex. The relevant point is that the sentence ‘we see directly the object’ belongs to our ordinary language, while expressions like ‘by means of…’ or ‘through…’ indicate that there are underlying intermediating neurobiological processes responsible for this direct experience. As far as I am informed, it seems that what we call sensory impressions or sense data in the visual case has to do with the activation of the striate cortex, since the irritation of this region without the activation of the photoreceptors of the retina is apt to produce hallucinatory phenomena (Teeple, Caplan, Stern 2009: 26-32). However, this fact alone does not make the visual perception indirect, once it isn’t caught by our semantic conventions.








[1] Surely, this suggestion would relativize truth to a time and a community of ideas, what would make this truth-theory a theory of our taking to be true (das Fürwahrhalten). But in the end this would not be a problem if we agree that absolute truth is nothing but a kind of normative ideal that helps us to evaluate our taking to be true by comparison of claims, but has nothing to do with what we normally accept as true or false. That is, when we say that p is true, we only suppose that p is the final truth until we find a reason to falsify p (if p is empirical) or abandon p (if p is a formal statement). A theory of truth is a theory of what leads us to take something to be true rather than a theory of absolute truth.
[2]  If q is nothing but the direct expression of a factual content we fall into a kind of strong externalism that admits that part of our content-thought-meaning is a directly given fact in the word (the ‘structured proposition’ or something of the kind). However, without more qualifications this view requires too much of our epistemic powers, letting not only the possibility of falsity unexplained, but also the inevitable fallibility of our supposed knowledge of truth.
[3] A story about a rubber dolphin I read many years ago, but I am unable to remember where.
[4][4] The third traditional position is phenomenalism, according to which, since we can have experiencial access only to our sensations or sense data, there is no reason to postulate an external world independent of these sensations. This view leads us usually to epistemic idealism, which rejects the existence of a non-mental external world (see chap. IV, sec. 18).
[5] One could complain that it is how outside things really are for us and not by themselves. But what they really are for us is only a way to tell how they really are by themselves. For an admirably vivid contemporary defence of direct realism, see John Searle 2015.
[6] For similar lines of defense see Cornman 1975, Ch. 2, 6; Dancy 1985, ch. 10; Lowe 1992; Huemer 2001, Ch. VII. As Huemer notices, we need to distinguish sharply the object of perception from its vehicle, and as Lowe notices, the veil of sensation must be seen as bridge or a window to the real world.
[7] In what follows, I am indebted to John Searle (see Searle 2002, Ch. X).

sexta-feira, 13 de janeiro de 2017

## SKETCH OF AN UNIFIED THEORY OF TRUTH (1) ('static' and 'dynamic' correspondentialism)

Uncorrected draft for the book PHILOSOPHICAL SEMANTICS to be published in 2017 by CSP.


– 6 –
SKETCH OF A UNIFIED THEORY OF TRUTH


Das wahre Bild des Fehlers ist das indirekte Bild der Wahrheit; das wahre Bild der Wahrheit ist der einzig wahr.
[The veridical picture of the error is the indirect picture of truth; the veridical picture of truth is the only true one.]
Novalis

We have drawn some conclusions from the last chapters: the cognitive meaning of an assertive sentence is its verifiability rule, which is the same as an s-thought or though-content or proposition – the primary truth-bearer. On the other hand, the truthmaker or verifier of the proposition is the fact referred to by it, a fact composed by arrangements of tropes. Moreover, by symmetry to our conclusion that the effective applicability of a conceptual rule is the same as the existence of the trope or cluster of tropes denoted by it, we can expect that the effective applicability of the verifiability rule in its proper context should be the same as the existence of the fact in the world that satisfies it. Finally, since the property of a verifiability rule of being effectively applicable in the right context also makes such a rule-thought-sense true, it at least seems that the existence of the fact referred to by it should also be the same as its truth.
   However, this suggestion is at odds with another view, namely, the correspondence theory of truth, according to which the truth of a thought-content is its correspondence with a fact and not the existence of the fact referred to by it. As already noted, we have the best methodological reasons for hanging on the correspondence theory, since it expresses a modest (even lexicalized) commonsensical view with a long tradition (Ch. 2, sec. 4), being historically the standard truth-theory from Plato to the XIX century (Mosteller 2014, Ch. 2) and still today largely accepted. Moreover, existence and truth, like applicability and correspondence, seems to have clearly different meanings.
   Despite this, there is an easy way to get rid of the difficulty. The way out consists simply in remembering that the word ‘truth’ has in the natural language two very distinct main bearers. Dictionaries distinguish clearly between (a) thought-truth, which is the truth in the correspondence sense, as consisting in things being as we believe that they are, as conformity with reality (the property of a thought-content to correspond with the fact), and (b) fact-truth, the truth as the actual, real or existing thing or fact. Thus, my suggestion is that in the last sense of fact-truth, truth can be identified with existence – the existence of the fact or the applicability of the thought-content. But the truth in the privileged sense of thought-truth remains reserved to the property of correspondence with the fact, which we will be able to explain only later (sec. 20) in this chapter.
   Based on what we have learned until now, the purpose of this last chapter is to sketch what I believe to be a much more detailed and plausible correspondence analysis of truth, able not only to better clarify the above distinction, but also to unify some conflicting views.

1. Compatibility between verification and correspondence
Some think that the adoption of verificationism leads us to the rejection of the correspondence theory of truth. One apparently compelling argument is the following: a statement can be verified in many different ways, even insofar as it may be satisfied by an undetermined multiplicity of diversified criterial compositions of tropes serving as verifiers or truthmakers, while the fact corresponding to the true statement seems to remain univocally related to it as being one and the same. Consequently, according to the verificationism it does not seem possible that what verifies the statement is its corresponding fact…
   My view is that this is reasoning, as others of the kind, is deeply misleading and that one only reaches this conclusion by searching for correspondence in the wrong way and place. As we will see, in the normal sense correspondence is not between the thought-content and the multiple external criterial arrangement of tropes (the many possible aspectual sub-facts) that can be given directly in the sense-perception, being held as sufficient to verify the thought (Ch. IV, sec. 24-26). Correspondence must be between the thought-content and some grounding fact that because of sufficient satisfaction of such criterial arrangements (sub-facts) is usually only in a mediated form apprehended by us (for instance: I say that I see the grounding fact that the book is on the table, though I see this grounding fact always partially and perspectivelly, by means of specific arrangements of tropes that I’ve called sub-facts.); thus, the apprehension of a grounding fact is nearly always more or less indirect and inferential. Moreover, the correspondence must be not only (indirectly) between the thought-content of the grounding fact with the real grounding fact, but also between the intermediating thought-content of the sub-fact with the real sub-fact, both normally belonging to the external world. Nonetheless, in order to make these ideas clearer we need to dive more deeply in the waters of the correspondence view of truth.
   Such worries leads us to consider a first objection against the correspondence theory of truth. It is the claim that the theory is nothing but a trivial, empty truism. According to this view, to say that truth is agreement with the facts is a too obvious platitude to deserve philosophical attention (Davidson 1969; Blackburn 1984, Ch. 7). The problem with this objection resides in the fact that in philosophy what at first seems a trivial truism after adequate careful analysis often reveals unexpectedly hidden complexities. One impressing example of this is the causal theory of action. Who could at first view expect that after analysis such a simple thing like the human action would show such a variety of often complicated processes? In what follows I intend to show that with the correspondence view of truth we have the same. The supposed simplicity of the correspondence relation is only apparent, betraying lack of awareness of what we really do when rising our truth-claims.
   Methodologically, my strategy consists in reconsidering the best insights about correspondence theory and in asking as far they can be developed and combined in order to lead us to a full-blooded analysis of the correspondence relation. This, as will be seen, ultimately requires a pragmatic investigation of the dynamic constitution of correspondence, which in the end exposes its relationship with verifiability and what some have rather misleadingly called a criteriology of truth (Rescher 1973, Ch. 1). To begin with, however, I need to make clear the definition of truth handed to us by the tradition, which is nothing but an abstract description of the general form of the correspondence relation.

2. The nature of correspondence
Assuming that truth in a privileged sense is the correspondence (agreement, adequation, matching, fitting…) between the thought-content and the fact it refers to, we need first to clarify each term of this definition. We have already clarified the concept of thought-content or s-thought (as inherently conceived by means of psychological p-thoughts) as the archetypical truth-bearer in our discussion of Frege’s semantics (IV, sec. 28). We did this along with a detailed defence of the idea that a fact in its most interesting sense is a cognitively independent arrangement of elements, which are tropes and clusters of tropes. In this sense, as we saw, fact is an all-embracing term that includes static facts (situations, states of affairs…) and dynamic facts (events, processes…), serving in this way as the universal truth-makers, the most proper verifiers of statements (IV, sec. 4 f., sec. 21-22). What we are now missing is an explanation of the concept of correspondence in its relevant sense.
   Wittgenstein, as it is well-known, defended a correspondence theory of truth in his Tractatus Logico-Philosophicus (1984g, sec. 2.21). I prefer to ignore the implausible atomist metaphysics of this work, though not its deep insights. And a deep insight of the Tractatus is to me the idea that a fundamental condition of representation is a pictorial relationship between the analysed sentence or what he calls thought (Gedanke) and the possible fact, the state of affairs (Sachverhalt), or the given fact (Tatsache).[1] This idea was resourcefully explored by E. G. Stenius in his book (1960) and several articles (particularly that of 1981) by applying to it the mathematical concept of structural isomorphism.
   Applied to the correspondence theory of truth the structural isomorphism between thought-content and fact is, as I understand it, properly formed by three conditions, which are partially explanatory of the idea of correspondence:

(i)                A biunivocal relation: the semantic elements composing the thought-content (or its corresponding sentence) and elements composing the possible or actual fact must have a relation of one-to-one.
(ii)              A concatenation: the elements of the thought-content (or sentence) must be combined in the same form (e.g. ‘S-P’) and order (e.g. ‘S then P’) as that of the elements composing the possible or actual the fact.
(iii)            A correlation: the thought-content as a whole must be biunivocally related to the possible or actual (real) fact, making it its correlate.

Now, a necessary (though non-sufficient) condition for the truth of a thought-content is that it is structurally isomorphic with an actual fact in the world. And a necessary (non-sufficient) condition for the falsity of a thought-content is that it is structurally isomorphic, not with an actual fact, but only with a possible fact, that is, with a conceivable or imaginable fact.
   Notice that we do not need to believe that the possible fact inhabits any Platonic realm in order to accept this suggestion: to conceive or imagine a possible fact is simply a psychological event and you do not need to imagine it in all details that it would have if it were the actual fact. In other words, a true thought-content is correlated to a fact in the world, while a false thought-content is correlated only to a possible (conceivable, imaginable) fact by mean of which we know that it could be correlated with an actual fact.
   The natural way to apply this view to real statements is to begin with singular predicative or relational statements in their linguistic practices, taking their logically analysed components of sense as the elements that must be biunivocally related to the elements of the possible or actual facts. Thus, we begin with thought-contents expressed by sentences of the form Fa (e.g., ‘John is easy going’) or aRb (e.g., ‘John is father of Mary’) or Rabc (e.g., ‘John gives Mary a flower’) or Rabcd (John gives Mary a flower to please Jane’)… In order to be true, these statements must at least satisfy the following elaborated conditions of structural isomorphism:

(i)                Each sense or semantic rule of each of the nominative and predicative expressions must correspond biunivocally to the respective elements constitutive of the respective facts in the world. These facts are arrangements made up by simple or complex tropes (like being easy going, being father of, given something to someone, given something to someone to please someone other) and objects, which are made out at least of tropes like those of form, solidity, mass… displaying compresence, (John, Mary, Jane, the flower, etc.) (Cf. Ch. IV, sec. 5)
(ii)              The concatenation, i.e., what we called order and form of connexion between the elements, must be preserved. Regarding the order of connexion, Fa cannot be exchanged by aF (‘John is easy going’ cannot be exchanged by ‘Easy going is John’), the sentence aRb cannot represent the fact bRa (‘John is father of Mary’ cannot be exchanged to ‘Mary is father of John’). Regarding the form of connection, I would say that the predicates along with their references are relatively dependent of the nominal terms and their references (being easy going depends of John’s existence, being a father depends for its existence of the existence of John and Mary). (Cf. Ch. IV, sec. 6-9)
(iii)            the whole thought-content must be biunivocally related with its possible or actual corresponding fact.[2]

This view should apply even to complex and vague predicates. Take, for instance, statements like ‘Céline had a strange personality’ and ‘The 5th Symphony is more complex than Für Elise’. As far as these expressed thought-contents are able to be objectively-interpersonally verified, they are in order (though it is surely not very easy to explain what is to have a strange personality or what is to be more complex than, these things are possible to do). If you think differently it may be that you are suffering from vagueness phobia.
   Nonetheless, it is important to see that structural isomorphism as explained by the conditions (i), (ii) and (iii), being restricted to logical structures, though necessary, is still far from being sufficient to explain correspondence. Consider, for example, the following three assertive sentences:

1.     The book is on the table.
2.     Kitty is in the kitchen.
3.     John is father of Mary.

Structurally, the thought-contents expressed by these three sentences have the same two places relational form aRb. If their components are (i) bi-univocally related with the elements of the corresponding facts, (ii) the elements of each of them are similarly concatenated (in form and order), and (iii) each statement is correlated with one fact, they can be said to be structurally isomorphic with the fact they represent. But, if this is all that is required, then statement (1) could have as truthmaker the fact that the Kitty is in the kitchen or that John is father of Mary, the same plurality of facts being isomorphic with (2) and (3). Moreover, any one of these sentences, having a similar intransitive logical structure aRb, is able to hold structural isomorphism with the unlimited number of facts with this same structure. This leads us to the conclusion that structural isomorphism, though necessary, is in no way sufficient to explain correspondence, since sharing the same logical structure isn’t enough. As Erik Stenius also saw, there must be a condition (iv) demanding some kind of categorial similarity between each biunivocally related par of elements; in other words, the elements of the thought-content must be indices of the elements of the fact they are representing.
   Since ‘indice’ is too vague a word, it is advisable to search for something better. As we have already noticed (Ch. 4, sec. 3), Kant wrote about schemata. For him, a concept is a rule to be associated with a schema 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. (Kant 1988, A 141)

Although Kant’s full exposition is conceptually obscure, it seems to me that it anticipates what we have previously learned in our readings of Wittgenstein and Frege, suggesting us to look for an answer in terms of the individualizing power of semantic-cognitive rules. Restricting ourselves to the simplest case of the singular predicative statement, what we have is the following. First, what we have are the conceptual senses expressed by the singular and general terms, namely, the identifying and the ascription rules, along with their combination in the formation of a verifiability rule. Each of these rules is able to establish a variety of internal criterial configurations, whose satisfaction is nothing but their matching with external criterial configurations or simple/complex tropes (s-properties) or clusters of tropes (objects) or tropes-arrangements (facts). Once all these internal criterial configurations are adequately satisfied by the suitable tropes-arrangements or actual facts in the proper context, the verifiability rule is considered as effectively applicable. Since this rule is nothing but the thought-content, once effectively applicable this thought-content will be called true. 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, namely, to individualise the isomorphic elements.
   Indeed, what we need to add to our understanding of correspondence as structural isomorphism are the individualized senses of the component expressions, that is, the semantic-cognitive criterial rules by means of whose application constituting the thought-content or verifiability rule we may identify the corresponding (grounding-) fact through its many variable aspects (sub-facts). We must do this by means of structural isomorphism, relating in this way senses of different interpretations of a statement with different aspectual (actual or possible) sub-fact the sense of the standard interpretation of this statement with its (actual or possible) grounding fact. For instance, the correspondence of ‘The morning star is different from the evening star’, describing the sub-fact that being the morning star isn’t the same as being the evening star is one thing. But this thing is different from the sense of ‘Venus [as the morning star] is the same as Venus [as the evening star]’ corresponding the grounding fact that ‘Venus [in full] is Venus [in full]. (Ch. IV, sec. 25).
   Furthermore, we must remember that these rules can be made explicit by means of definitions, as we once have made with the concept chair. In the aforementioned examples we can do the same by means of, first, the (semantic-cognitive) criterial definitions of the nominal terms ‘the book’, ‘the table’, ‘Kitty’, ‘kitchen’, ‘John’, ‘Mary’. Second, by definitions of the relational predicative expressions ‘…is on…’, ‘…in the…’, ‘…is the father of…’, since these definitions will also show how the elements can and cannot be adequately concatenated (the table isn’t on the book, the kitchen not in Kitty, Mary isn’t father of John).
   These explanations entitle us to suggest that when two thought-contents p and q show structural isomorphism and the (semantic-cognitive) criterial rules that form the elements of p are the same as the (semantic-cognitive) criterial rules that form the elements of q, then both thought-contents are the same, that is, p and q express the same thought-content. This is a point that will be useful later.
   At this point I would like to point to a deep insight related to Wittgenstein’s view of correspondence that seems to be related with the last condition is that of logical form (1984g, 2.18 f.). For him, a representation, in order to be a representation, must have something in common with what it represents. A naturalist picture and the landscape it depicts must have in common at least the two-dimensional space; a melody and its score (when it is read) must have in common the dimension of time. But according to his doctrine, there must be something common between the thought-content and the fact represented by it, something unsayable that must be common to any representation and what it represents, which is the logical form. He sees logical form as the possibility of structure, or rather obscurely as the possibilities of the occurrence of an object in a state of affairs.[3] Without logical form a sentence cannot be meaningful. The idea of logical form should settle what can be seen as the ultimate bridge between the thought and the world, which must be logical. For in its fundamentals, logic is ubiquitous: no cognition and therefore no cognoscible reality can remain outside its reach; and since there is no non-cognoscible sense for what can be meant as real, there is simply nothing outside its reach.
   I think that we can understand Wittgenstein’s concept of logical form in a way that makes it at least complementary with the idea that each sense or concept or semantic-cognitive rule requires a proper corresponding factual reference. Suppose that we define logical form a necessary identity between the logical possibilities of combination under the elements of the representation and the logical possibilities of combination under those biunivocally related elements represented (either the possible or the actual). In this case, elements of atomic thought-contents with forms like Fa, aRb… molecular thought-contents of the forms ~Fa, Fa & Fb, Fa Fb, Fa → Fb… general thought-contents of the forms (x)(Fx) and Ǝx(Fx)… in order to have a truth-value, must not only contain structural isomorphism with respectively represented possible or actual facts, but must be able to share the same logical possibilities of combination with others semantic items, as a condition for meaningfulness. This suggests that speaking about logical form in this way amounts to something at least very near to speaking about the multiplicity of ways of satisfaction of semantic-cognitive rules by means of a diversity of criteria, corresponding to a particular multiplicity of tropes and combinations of tropes constituting the possible or actual facts able to satisfy them.
   Finally, there is a fifth factor that I believe that we need in order to complete our analysis of correspondence: (v) intentionality. By judging something true we must be aware that we are applying the verifiability rule to a fact, we need to have a ‘directionality’ that leads to conceptual rules to the criteria that satisfy them, from the thought-content to the fact that it is intended to represent..[4] One could say that the intentionality gives to the semantic-cognitive rule a word-to-world direction of fit, requiring the broader structure of our consciousness.
   On the other hand, from the opposite direction what we may find in the case of true thought-contents will be (vi) a suitable causal relation by means of which the actual fact may make us recognise the truth of its thought-content. Causality has a world-to-word direction of fit. We can here speak of the effective applicability of its verifiability procedure and, in the case of indexicals, even of the original building of such a rule in the given context. Intentionality and causality are the responsible for the asymmetry proper of the correspondence relation.  
   To summarize, I consider now a final example of a composite thought-content that I adapt from Stenius. When someone says: ‘John (j) is father (F) of Peter (p) and of Mary (m), who is a writer (W)’, the logical structure of the thought-content expressed by the statement is:

1.     ‘jFp & jFm & Wm’.

Assuming that we know the identification rules for John, Peter and Mary, along with the ascription rules of the predicates ‘…is the father of…’ and ‘…is a writer’, along with the semantic rule of application of the logical operator ‘&’ (which is provided by its 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 thought-content, giving to the statement, if not truth, at least a full meaning. If the statement is false the achieved correspondence stops here, as a correspondence with a possible but non-actual fact. Now, suppose that the statement (1) is true. In this case we have:

(i)                a biunivocal relation between each of the non-logical (and supposedly logical) components of the composed thought-content expressed by (1).
(ii)              the same concatenation (order and form of connexion) between the semantic cognitive rules of the three singular thought-contents and the biunivocally related elements of the three represented facts.
(iii)            a biunivocal relation between each singular thought-content and its represented fact (the same regarding the composed thought-content).
(iv)            a satisfaction of the criteria built by each semantic-cognitive rule by its proper objective correlate, assuring us the proper individuation of the correlated entities.
(v)              the intentionality of the rules leading us to distinguish what is representing – a composite thought-content – from what is being represented – the actual corresponding complex fact.[5]
(vi)            We assume that ‘jFp & jFm & Wm’ is true because it is suitably caused.

On the other hand, for a disjunction like ‘jFp jFm Wm’ at least one of the disjuncts must present correspondence with the elements not only of a possible fact but also of an actual fact, though any false disjunct must correspond to only a possible, conceivable or imaginable fact if we wish that the statement as a whole remains meaningful.

3. Formalizing the correspondence relation
Assuming the suggested analysis of correspondence, we can express symbolically what could be called a formal definition of truth: the logic structure by means of which the predicate ‘…is true’ is identified with the predicate ‘…it 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’ serves 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, and by means of this secondarily also to the real historical fact. According to this view, for any thought or content of belief p, to say that p is true is the same as to say that p corresponds to a real fact. We can express this symbolically, calling the thought p, the predicate ‘…is true’ T, and the predicate ‘... corresponds to a real fact’ C. The predicates T and C are semantic metapredicates belonging to a semantic metalanguage by means of which they refer to the thought-content expressed by p, which can be shown by placing p under quotation marks. Here is my first formal definition of truth:

(1)   Tp’ = Cp[6]

According to this identification, truth is the property of a thought-content expressed by a sentence p, namely, the property of corresponding to a fact.
   This formulation depends on the application of the monadic predicates ‘...is true’ and ‘...corresponds to a fact’. However, monadic predicates can often be unfolded into non-monadic predicates such as, for instance, ‘…is a father’ into the more discernible ‘…is the father of…’ The same can be said of the predicates ‘…is true’ and ‘…corresponds to a fact’, which can be unfolded as relational predicates of a semantic metalanguage relating the thought expressed by p with the fact or factual content that q as ‘…is true for…’ and ‘…corresponds to the fact that…’ (Cf. Künne 2003: 74). Illustrating by means of an example, one could say ‘“Themistocles was the winner of the battle of Salamis” expresses the same historical occurrence as “The battle of Salamis has been won by Themistocles”’, where ‘…expresses the same historical occurrence as…’ is a relational semantic metapredicate primarily applied to the thought-content of the two object-sentences.
   This means that the definition above can be explained more thoroughly as stating that for a given thought-content p, to say that p is true for the actual fact q is the same as to say that the thought-content p corresponds to or is adequate to the actual fact q. For this 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 the q in order to show that the content of the later, though also interpretable as an s-thought, is preferably interpretable as a real fact in the world.[7]) Giving a simple observational example: suppose that the thought expressed by ‘The Moon is white’ is true. We only say this because of the factual content understood as the real fact that the Moon is white. And this is the same as saying that the thought-content expressed by ‘The Moon is white’ corresponds to contents of observation that the white Moon, which are really factual.
   Now, replacing the semantically metalinguistic predicate ‘…is true for the fact that...’ for T*, and replacing the also semantically metalinguistic predicate ‘...corresponds to the fact that…’ for C*, we have the following formalised version of a more complete formal definition of truth. In this definition, the thought-content expressed by p and the factual content expressed by q are metalinguistically related by the metapredicates T* and C* as follows:

(2)   ‘pT*‘q’ = ‘pC*‘q

   More than an unpacking of (1), the formal definition (2) individualizes the corresponding fact in a more complete formulation. According to (2), the assignment of truth is the same thing as the assignment of the relational property of correspondence, that is, of the qualitative identity of content between thought-content and real factual content. (As we saw, this identity of content is to be analysed in terms of structural isomorphism, also satisfying criteria for the application of the component terms and the directionality from p to its suitable cause q).
   Finally, accepting that thought-contents are verifiability rules we can add that saying that a thought-content corresponds to a fact should be the same as to say that the verification procedure applies to the fact. Symbolizing the semantic metapredicate ‘…is a verification procedure that applies to a fact’ with P, we have:

(3) T‘p’ = C‘p’ = P‘p’

More precisely, symbolyzing the dyadic semantic metapredicate ‘giving … the verifiability procedure applies effectively to the fact …’ as P*, we have:

(4) ‘p’T*‘q’ = ‘p’C*‘q’ = ‘p’P*‘q

These are, I believe, the best ways to present formally the general identifications between attributions of truth, correspondence and the verifiability procedure.

4. Negative truths
Now, consider a false singular predicative or relational statement p. Since it is false, such statement does not correspond to any fact in the world. But to say that p is false is the same as to deny that p is true, saying that the statement ~p is true. Here arises a problem. If ~p is true and we accept the correspondence theory, it seems that ~p must correspond to a fact. However, suppose that we replace p with the false statement (i) ‘Teetetus flies.’ In this case ~p is (ii) ‘Teetetus does not fly.’ Then, at the first view it seems that we have a true statement that does not correspond to any fact in the world! This brought some to the suspicion that sentence (ii) is true because it refers to a ghostly negative fact: the unworldly fact that Teetetus isn’t flying.
   With help of our preceding formulations, it is easy to reach a more plausible answer. The statement ~p is true does not correspond to any actual fact in the world, since Teetetus is sitting. As ~p means the same as ‘p is false’, by saying that p is false one denies correspondence with the real fact in the world.  However, as we have insisted, by considering the false idea that Teetetus is flying we already accept its correspondence with a possible fact, namely, with our imaginary state of affairs of Teetetus flying. However, this imaginable, conceivable fact, is no negative fact in a metaphysical sense; it is something that is placed somewhere in our brains when we imagine it, and that is all. Moreover, ‘p is false’ means that p expresses a verifiability rule that although applicable to an only conceivable or imaginary state of affairs, a possible fact, does not apply to a real fact in the world.
   Now, consider the negation of the following general statement: ‘There is no cat with three heads’. It means the same as, ‘It is false that there is a cat with three heads’, which simply affirms that, though there is a corresponding conceivable fact-object that is a cat with three heads, there is not any actual fact-object that is a cat with three heads in the world. One could still 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 with three heads in the world (Searle 1998: 393). However, here I am on the side of the logician. It is more reasonable to think that this is a mere façon de parler allowed by the flexibility of our natural language.[8]

5. 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:

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 it is true, then it is false. On the opposite assumption, if the statement is false, then what it states is not the case, what means that it is true. Consequently, if the statement is true, it is false and if it is false, it is true. This is one example of a semantic paradox of self-referentiality involving the concept of truth in its most clear and direct form, though there are many variations.
   One of these variation is the case of indirect self-reference in which the statement refers to itself by means of other statement, generating the same paradox. Consider one 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) is true…
   Having in mind our formal definitions of truth as correspondence, the general answer is that self-referential statements like these are incorrectly constructed because in all these cases the predicate ‘…is true’ does not work as a semantically metalinguistic predicate referring to a complete thought-content, but as a normal predicate inbuilt within the thought-content, belonging forcefully also to the object language. Being incorrectly constructed, these statements have no real cognitive meaning beyond their grammatical form. They might seem to be meaningful on their surface, suggesting us to treat then as we would treat a statement with the form ‘p is true’ or ‘p is false.’ Once we have fallen into this trap, the paradoxical consequences follow.
   Normally a statement does not need the addition that it is true in order to be understood as expressing a verifying rule that is effectively applicable – a truth. Usually the truth-claim is already implicit (consider, for instance, the statement ‘The sky is blue’). Because of this the statement ‘This sentence is false’, though affirming its lack of applicability, naturally generates its truth, since what it affirms is naturally seen as true. The statement ‘This sentence is true’, on the contrary, affirming the applicability of itself, 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 or falsity.
   Now, consider the sentence ‘It is true that this sentence has nine words.’  This is a perfectly normal true sentence referring to itself. But why? The reason is that the metapredication of truth is applied to the thought-content that the sentence in question has nine words without belonging to this thought-content. One could unpack what is compressed in this sentence as: ‘The thought expressed by the sentence “It is true that this sentence has nine words” is true’, what makes clear that the attribution of truth is not inbuilt in the relevant thought-content.
   Furthermore, we can predicate truth of a metalinguistic thought-content as far as this semantic predication is meta-metalinguistic and so on, since the s-thought, as an arrangement of apparently disembodied mental tropes, is also a fact.


6. The pragmatics of the correspondence relation
What we have seen until now was the frozen logical structure of truth as correspondence. Now we will see how it works in the practice of truth-attributions that provides us to what some have called the criteria of truth. The view I wish to defend here is inspired in Moritz Schlick’s short defence of the correspondence theory of truth (Schlick 1910), though in my view this is an interpretation of a fundamental insight due to Edmund Husserl (1900, vol. 2/II, VI). The idea is that correspondence has a pragmatic or dynamic dimension that deserves to be explored – an idea that should not sound strange to those who wish to integrate verificationism with correspondentialism. We can begin by considering that very often we can establish an idealised sequence of four successive temporal moments, which we may call: (1) suppositional, (2) evidential (3) confrontational and (4) judgmental or conclusive. Together they form a very usual form of verification procedure.[9]
   The best way to introduce the idea is by means of examples. Schlick used the example of Le Verrier’s prediction of the existence of Neptun based on the orbital perturbations of Saturn: he first made a hypothesis that was later confirmed by observation, what made the hypothesis true, since the content of both is identical. I choose a much more trivial example. Suppose that it is rain season and that I ask to myself p: ‘Will it rain in Natal tomorrow?’ This is the suppositional moment. Now, tomorrow comes, I open the door of my home and see that it is in fact raining 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, seen 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 (satisfying the conditions (i) to (vi) of correspondence) I conclude that my hypothesis p was true, since it is raining today in Natal. This is the judgmental or conclusive moment.
   Examples like the former can be multiplied and a similar procedure, as we will see, applies to non-observational truths. But for now, restricting myself to perceptual judgments, I can say that at least regarding cases like the considered above we can formulate the following action-schema with four steps:

1)     The suppositional moment: a consideration, hypothesis, conjecture, guess, question... In this moment we ask ourselves whether some thought-content is true, that is, if the verifiability rule that constitutes it is not only imaginatively, but also effectively applicable in its proper context. We can express this as ‘I suppose that p’, ‘It is possible that p’, ‘I guess that p’, where p expresses a content that can be perceived. This step can be formalised as ‘?p’ (call ‘?’ the operator for supposition). This supposition is always made within some linguistic practice, within some context and its domain.
2)     What follows is the evidential or perceptual moment: the realization of a perceptual experience under already specified observa­tional circumstances, which may 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 thought-content that, in an adequate context, we simply read as a verifier (truthmaker), which can be rendered as ‘I perceive the fact o’, call it ‘!o’ (where ‘!’ is the evidential operator). Phenomenologists have called this moment registration or fulfilment (Sokolowski 1974, Ch. 9). As we will see, there can be no question about the truth-value of o: it must be seen as ‘evidence’ or ‘certainty’. In fact it is stipulated as evidence within the context or practice or language-game in which it occurs; otherwise we would be daunted by the question of the truth of o!, which should also need to be grounded, leading us to a regress.
3)     Confrontational moment: it is simply the comparison between the suppositional content and the factual content of the perceptual experience, which makes possible the verification or falsification of the supposition’s content.
Here we ask whether the supposition matches the evidential result of the perceptual experience. In the case I have considered, I asked myself whether the thought-content of the hypothesis were sufficient similar to the content directly given to me in the perceptual experience (categorically isomorphic, etc.). In the case of a perceptual experience the positive answer can be summarised as p = o (where the ‘=’ expresses qualitative identity). As will be explained and justified later, the underscored o can be read either as the thought-content or as the actual factual content given in the contextually expected sense experience. If this similarity of content is lacking, we have that p o. (In its concrete details it is more complicated: usually the experienced fact o is only partially and aspectually experienced, what does not prevents me say, for example, that I see that it is raining in Natal. Moreover, in practice often occurs that more than one perceptual experience must be carried out, 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 correspondence and the conclusion is an affirmative judgement that can be symbolised as ├p. In the case in which p ≠ o, that is, in the absence with the expected correspondence, the thought is false; this can be expressed by the negative judgement symbolised as ├ ~p.

Now we can summarise the four moments of this whole verifiability process regarding the achievement of observational 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 reaches correspondence between some suppositional thought-content (which is only a considered or imagined verifying rule in its possible application) and some perceptual content (given by the effectively applied verifying rule) that within the linguistic practice in which it is given is stipulated as beyond doubt.
   It is also worth noticing that the standard statement of ├p (a judgment), has the form of the report of an assertion that is settled and finished. However, this assertion can be always questioned again. In this case, new verifying procedures can reconfirm the judgment or detect some inadequacy in an at least virtually interpersonal way (for similar remarks, see Sokolowsky 1974, Ch. 9).[10]
   Now how to understand the correspondence relation as qualitative identity of content (structural isomorphism, identity of rules in their connection, intentionality…) for the example ‘It is raining in Natal now’ in terms of application of verifiability rules? The indexical phrase ‘in Natal now’ expresses the building of an identifying rule of a spatio-temporal region to which it adds the predicate ‘is raining’ (‘Now in Natal is raining’), expressing an ascription rule that effectively applies to the region by the satisfaction of configurations of tropes building nothing less than an uncountable multitude of drops of water falling from the sky. This combination of satisfactions gives me the arrangement that constitutes the sub-fact that is the verifier that allows me to infer the content building the grounding fact that it is raining in natal today, which (Ch. IV, sec. 19) supposedly has the same structure of its verifiability rule inversely projected in the outside world.

7. Anterograde versus retrograde procedures
Now, what was presented above is what we may call an anterograde way to reach the truth, since we went there temporally from the hypothesis to the perceptual evidence that confirms the hypothesis by having a qualitatively identical content. However, the move in the opposite direction is equally feasible. We can have a truth-value attribution that has its origin in the own perceptual experience, progressing from the evidence to the hypothesis – a way to achieve truth that we may call retrograde.[11]
   Here is a simple example of retrograde verifiability process. I open the door of my home with the intention to going out and unexpectedly I see that it is raining. Then I come back to look for an umbrella after reaching the obvious conclusion that it is raining... In this case, the perceptual evidence comes first. But it seems clear that the recognition of truth does not comes from the sensory experience as a direct product of it, since I could see the rain without taking account of it. This means that the sensory-perceptual state that comes first is different from the state of conscious awareness that follows, namely, that it is raining (suppose I open the door to get fresh air and do not even pay any attention to the fact that it is raining outside; if someone then asks me if it is raining I will recall the conceptual rule for raining, compare with the perceptual data and answer in the affirmative). Thus, it seems that here we can explain the process of getting the truth included in the judgment of the given example in the following way: First, I have the observational experience o! Then (still during or after it) I rescue in my mind the ascription rule for raining, which is like to consider the supposition ?p. Finally, I compare the content of my observation with the content of this recalled idea of raining; once I see that o = p, I am lead to the conclusion that it is true that it is raining or ├p. We could summarize this process of retrograde achievement of truth in the following sequential formulation:

!o, ?p, o = p /├p

Clearer cases of retrograde awareness of truth take place when someone has one unexpected sensation. If I awake in the middle of the night with a strange feeling in my right leg, it may at first not be identified as pain, and we may call it !s. Then I unconsciously recall in my mind the idea of pain putting it under consideration: ?p (it can be that I take some time to identify the pain as a pain, first misidentifying it as a cram). Since now I clearly identify s with p, I see that I have pain in my right leg, say, I reach the conclusion ├p. A similar example is when someone gives me to drink a suit beverage without telling me what it is. Since I do not know its precedence, I may need some minutes to bring to my memory the obvious answer: it is a juice of pressed sugar cane.

   The cases I have considered until now are the simplest sensory-perceptual cases. However, the pragmatics of correspondence can be extended to the truth of non-observational thoughts, which I will call here mediated thought-contents. Suppose that Lucy is in the Charles de Gaulle airport in Paris, ready to board a flight to Dakar. The flight time is of approximately five hours. She calls her daughter, who lives on a farm in the Senegal and asks her how is the weather in the city of Dakar, that is, if it is good; this is ?p. Suppose that after a while her daughter answers that the weather in Dakar is and will remain good and warm enough. There is no significant reason for doubting this information, which she takes as giving her the appropriate evidence. The thought-content !q that she had after she heard about the weather in Dakar is the same as the thought-content belonging to her wishful question ?p. Consequently, since p = q, she concludes that p is true, that the weather in Dakar is and will remain good. But the thought-content expressed by !q is not an observational thought! It is the result of testimonial inferences that are unknown to Lucy. Suppose that her daughter had this information from her man, who read in the internet about the weather, and that this information has its origin in meteorological observations of the weather conditions around Dakar. In this case, putting ‘>>>’ in the place of some chain of reasoning unknown to Lucy that leads to !q, and putting ‘!o’ in the place of the observational meteorological thought-contents that in some way have originated !q (which is 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 preserved in the supposed inferential chain that leads to !q (I put the process under parenthesis 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; then !q is compared with the guess expressed by ?p. So, against our most natural expectation of how correspondence should work, the truth of ?p isn’t directly made by the observational fact !o, but by something derived from it, namely, by !q understood as also referring to a fact, a state of affairs in the world. The correspondence is between unfulfilled and fulfilled thought-content-rules, the last one also interpreted as being fulfilled by a factual content composed by trope-based arrangements with an inversely similar structure.
   The foregoing example is one of an anterograde verifiability procedure, beginning with one supposition and ending with the comparison between the supposition and a derived evidential thought-content. However, we may also have a retrograde procedure with a chain of reasons that ends with the match of a derived piece of evidence with a supposition. So, imagine that at the beginning of the flight to Dakar the pilot informs to the passengers that the weather in Dakar will be good and warm enough. Any passenger will be led to the conclusion that the weather in Dakar will be in fact good by means of another indirect and for them unknown evidential chain. However, in this case it is the evidence that recalls the question regarding the weather conditions, what is answered by means of a comparison of contents from which results the final judgment that the weather in Dakar will remain good. This process can be summarised in the following temporal sequence:

 (!o >>> !q), !q, ?p, q = p /├p

We see that the difference between anterograde and retrograde verification repeats in its 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 on its truth, depends on the unconscious noticing that the knowledge of some factual content expressed by !q might be derived from evidential observations or postulates.

8. General statements
The general thought-contents – universal and existential – can also be in this way explained as the identity between the contents of the hypotheses and the contents of sets formed by the respective conjunctions and disjunctions of factual contents, often resulting from inductive inferences ultimately based on observational facts. So, suppose that ├p is the silly assertion: ‘All the books in this shelf are in English.’ Suppose that I reach this generalisation casually in a retrograde form from the casual observations o1, o2… on, of each book on the shelf, as follows:

{!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 each of them, concluding that this hypothesis is true in an anterograde procedure:

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

Now, suppose that ├p means: ‘There is at least one book in Italian in this other shelf’. First, I asked myself if there is a book in Italian in that shelf and after search I find only one: Princìpi di scienza nuova from Giambattista Vico, which I never tried to read. I call it !o1. This entitles me to affirm that there is at least one book in Italian in the second shelf, what has been done by means of an anterograde procedure:

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

As the formers, this example is of a deductive general conclusion, but it is easy to see that inductive generalisations should also have similar structures, given that they are also restricted within some more or less vague domain (Appendix to Chapter V, sec. 3).
   The next point is the old question of knowing if there must be general facts over and above singular facts (Russell 1918; Armstrong 2004, Ch. 6). Bertrand Russell, who 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).

In my view, this is a much more earthly question then supposed, since what Russell calls general fact is a singular fact neither over nor above any other. In the examples above what is need is an additional limiting fact restricting the extension of the generality first to the books belonging to the first shelf and then to the books belonging to the second shelf. I agree that the 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 the affirmation ‘those are all’ can be inferred as a consequence of the addition of the conjunction or disjunction of the singular facts and the corresponding singular limiting facts. Moreover, the only difference between the examples given above and a fact like ‘All men are mortal’ is that the delimitation of the last domain is the whole earth and adjacencies in the whole time of existence of the species homo sapiens, what is a much larger and vaguely determined domain. This is how the mysterious ‘general fact’ disappears.

9. Some funny facts
There are many questionable cases and I wish only select some of them to give an indicative solution. One of these is that of self-psychic truths. It is easy to know the truth-value of the thought p: ‘I am in pain.’ I believe that also here there is correspondence and that it is as follows. First, we learn interpersonally how to identify the location of pain. Them, simply by inductive exclusion (helped by many others concomitant observable occurrences…) we learn an ascription rule to identify the kind of feeling that we have when we have a pain, applying this rule to verify our headaches. Even if we cannot have interpersonal access to pain, we can make our identification highly plausible and the logic possibility of this interpersonal access isn’t excluded.[12] Second, suppose that I have a headache. The first thing I have is the feeling of pain: !s. Then comes ?p: the actualisation of the memory of what means the feeling of headache that I associate with the word; this is followed by the identification s = p, and the conclusion ├p:

!s, ?p, s = p /├p

I reach the truth that I have a headache in a retrograde way. An anterograde way to reach the same would be the case of a person who knows that she would have headache because she drink red wine and she always has headache after drinking red wine.
   Wittgenstein had, as it 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 correspondence. It is possible. But I find 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 and analogy concerning the hetero-psychic (see Costa 2011, Ch. 4).
   A funny case is that of true counterfactual conditionals. As it is known (p q) ↔ ~(p & ~q),  that is, the material conditional is true if and only if it is not the case that the antecedent is true and the consequent is false. Now, consider the statement (i) ‘If Evelyn were the queen of England she would be famous’. The objection is that there is no fact that can make this sentence true, since the truth-value of the antecedent is false: she isn’t the queen of England. However, statement (i) seems to be a true! The answer is also easy. Although there is no actual fact that can make the statement 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 conceivable fact that makes the statement true is that if it were the case that the antecedent were true, if Evelyn   actually were the queen of England, the truth of the consequent would be nearly unavoidable, that is, in that case she would be famous. The truthmaker of (i) is a modal fact that we could also express using the vocabulary of possible worlds. We can say that there is a near possible world We in which Evelyn is in fact the queen of England. Since in our world all queens of England are famous, we can infer that in We, if someone is the queen of England, this person will be also famous. Assuming that Evelyn is the queen of England in We, she is famous in We. We conclude that it is true that if Evelyn were the queen of England she would be famous because the expressed thought-content corresponds with a fact belonging to conceived counterfactual circumstance given in We. Another example: (ii) ‘Gandhi never killed anyone, but he could have’ (Wrenn: 178). It is true because it means the same as ‘Though Gandhi never killed anyone in the actual world, there is a possible world Wg where Gandhi killed someone’. This is a true statement, since it corresponds the conjunction of an actual and a possible (imaginary) fact, both existing, the first as an actuality and the second as a mere possibility.
   One could still also ask about ethical truths. Consider the statement (iii) ‘Dennis should help the drowning child’. Suppose that Dennis didn’t help because he is a sadist. We would not say that is true, but that it is right. It is right in a similar way as an illocutionary act like ‘I promise to go to your anniversary’ can be felicitous. Statement is morally right because it is in conformity with a rule, say, the rule according to which ‘One should help another person in danger of life, as far as one does not put himself in a great danger’. What is in question here is not truth, but normative correction – correspondence with a norm, if you will. Finally, there is still the case of ethical norms and principles like (iv) ‘A morally correct rule is that which, when applied (ceteris paribus) brings the greatest amount of happiness to all’. If it is a fact that when people act in accordance with this principle the well-being of their whole community increases, then this principle is true. The truthmaker of statement (iv) is a fact in the world.
   The greatest problem with ethical statements, however, is the same as with any other philosophical statement; they belong to speculative domains wherein we are only able to make the truth of our statements more or less plausible. Differently from science, philosophy belongs to all that we are still unable to know for sure.

10. Expansion to formal sciences
Analogous logical structures and dynamic procedures can be found in the formal sciences, allowing us to generalise the correspondence theory to a domain traditionally occupied by coherence theories of truth. The important difference is that while for the empirical truths the inferences are typically inductive, for the formal truths they are deductive. Suppose that we want to demonstrate that the sum of the angles of any Euclidean triangle is 180°. We can do this by first suspecting that this could be the case: ?p. Then we search for a proof. We can do it tracing a straight line that touches 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 triangle are the same as the internal angles of two opposed vertices of the triangle plus the angle of the first vertex, and their sum is evidently 180°, we conclude that the sum of the internal angles of this and indeed of any Euclidean triangle must be of 180°. This deductive conclusion is the evidence !q – the truthmaker as a geometrical fact.  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 form of this anterograde procedure can be rendered as:

?p, !as >>> !q, p = q, /├ p

Important is to see that !q, stating the fact that makes the thought-content p true, as in the case of Lucy’s question, is not in the beginning, but in the end of a chain of reasoning. But differently from Lucy, the geometer can be aware of the whole procedure.
   Now, one example from arithmetic: we can prove the statement (i) ‘2 + 2 = 4’ in a Leibnizian manner. We begin with definitions (which are here equivalent to the basic perceptual experiences in the 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 the statement (i) the numbers 2 and 4 by their definiens, we get (ii) ‘(1 + 1) + (1 + 1) = (3 + 1)’. Since 3 is defined as 2 + 1, and 2 as 1 + 1, 3 can be replaced by (1 + 1) + 1. Replacing now the number 3 by these results in (ii), we get the arithmetical fact (iii) ‘(1 + 1) + (1 + 1) = ((1 + 1) + 1) + 1)’, which is the same as ‘2 + 2 = 4’. In this way, we have derived the confirmatory evidence for the hypothesis ?p, which is the factual content !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 verification:

?p, !d  >>> !q,  p = q /├p

Once more we see that the factual content expressed by !q, which serves to check the hypothesis ?p that 2 + 2 = 4, is not the same as the definitions of 2, 3 or 4 as it may be initially thought. It is the result of a deductive reasoning process based on them, a reasoning process deductively derived from its definitional premises. This result represented by !q is the arithmetical fact that has the same content as the supposition ?p, so that p = q, what 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 making use of the axioms AS1, ‘◊P ↔ ~□~P’ and AS3, ‘□~P → ~P’ as assumptions. Taking these axioms and some rules of propositional logic as the evidences ‘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 ‘(P → ◊P)’ is !q, which represents the derived logical fact that serves as verifier for ?p, and since p = q, we conclude that p is true, that is, ├p. Using our abbreviation, we get the following anterograde verifiability process:

?p, !as >>> !q, p = q, /├ p

Since the logical fact represented by !q, which carries with it the evidences derived from the axioms (assumptions), expresses the same thought-content as the hypothesis ?p, we conclude that there is a correspondence. We conclude that p is true or ├p. (Also relevant is to note that in the case of logical facts we do not need to underline statement letters like a or q: there is no need to distinguish between the conceived and the real fact, since both are here the same.)
   Of course, one could also find a retrograde form regarding any of the three above exemplified cases. Considering only the first one, suppose that someone, having the strong intuition that the sum of the internal angles of an Euclidian triangle makes 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 Euclidian triangle would have 180° as the sum of its internal angles. In this case, we would have the following retrograde verification procedure:

!q, !as >>> !q, ?p, q = p, /├p

The !q would work here as the in-sight in the truth of a conjecture for a geometer, something equivalent to an unexpected observation.
   The upshot is that the procedures with which we demonstrate the correspondence of formal truths are structurally analogous to the procedures with which we demonstrate the correspondence of empirical truths. Even so there are some differences. The most obvious is that formal truths are deductively inferred while empirical truths are in their essence inductively inferred.

11. 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 correspondence, 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 ‘Singles are not married’ are true because they correspond to the respective facts that necessarily either it is raining or not, and that it isn’t possible that a single person can be married. But to what extent are we entitled to say this?
   Assume first, as we have made in our objections to Quine’s argument against analyticity, that the analytic statements are those that are true by means of a proper combination of the component senses of their expressions. In this case our question is:  are there facts that make analytic thoughts true? In the case in which these facts exist, how are they? Consider the following analytic statements:

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

   Surely, these sentences are all true by definition: 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 conceptual or logic-conceptual facts. Sentence (1) is made true by the logical fact that ‘j ˅ ~j’ (the law of the excluded middle) that it instantiates. Sentence (2) is made true by the logic-conceptual fact that the brother-sister relation is reflexive. Sentence (3) is made true by the conceptual fact that a bachelor is conventionally defined as a non-married adult male. Sentence (4) is made true by the conceptual fact that a triangle can be defined in Euclidian geometry as a closed plane figure with three straight-line sides. And sentence (5) is made true by the conceptual fact that it is part of the definition of a material body that it has some spatial extension. These are facts belonging to our defined conceptual structures; facts constituted by mental tropes.
   Moreover, we can summarise the process of self-verification of the statements above in the same way as 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?’. Faced with this, we realise right away that the sentence instantiates the principle of the excluded middle or ‘j ˅ ~j’, and that this instantiation, as any other, can be symbolised as the instantiation of the logical truth or fact !p2, which can be proved to be true by means of a truth-table. This is enough to make ?p1 true because we can see that independently of the senses given to its constituents, its logical structure warrants its truth. We can summarise the self-verifying process in which we find the correspondence in the same anterograde way as in the first of all our examples:

?p1, !p2, p1 = p2 /├p

In other words: the thought-content is identical with an instantiation of a logical truth of the classical propositional logic that is incorporated in itself, being in this way self-verifying.
   In other cases some reasoning may be necessary. In the case (3) the suppositional moment ?p1 is: ‘Are all Bachelors males?’ To verify this, we first need to look at the definition of a bachelor as a point of departure: !d = ‘A bachelor is an unmarried adult male’. From !d we can infer !p2 = ‘All bachelors are males’. Summarising the steps of this anterograde verification procedure, we get:

 ?p1, !d → !p2, p1 = p2 /├p1

We see that even if analytical thought-contents are true by courtesy, since they cannot be false, it is not senseless to speak of their being true by correspondence with facts. The reason is clearer in cases like the last one. For being these cases of self-verification, the procedure is not always direct and transparent, often demanding some degree of reasoning.




[1] Instead of call the thought what the completely analysed sentence expresses, as in the very implausible atomism of the Tractatus, I suggest that we simply call the thought what is expressed by a sentence as it is normally and completely analysed in accordance with the context (in the widest sense) of the practice in which it is inserted.
[2] We could certainly not go further, requiring that there must be some R1 relating F with a in Fa, etc. as explained in the Appendix to Chapter III, sec. 3)
[3]Die Möglichkeit seines Vorkommens in Sachverhalten, ist die Form des Gegenstandes.’ (1984g 2.0141)
[4] We can intentionally produce factual contents that are true, for instance, by acting in the world in order to change it, as constructivist philosophers since Giambattista Vico have noted, but even in this case it is the final fact in the world, as the product of human effort that is the truthmaker of the proposition, and not the opposite. That is: we can make the fact that makes the truth, but not the fact as truth.
[5] It is the sense determining (bestimmend) the reference in Frege’s way of speaking, or the meaning-fulfilling intention (Bedeutungserfühlende Intention) in Husserl’s way of speaking.
[6] 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 having properly emphasized the metalinguistic character of the truth-assignments in a formal language. However, his formula does not overcome the philosophical problems concerning correspondence. If you replace the sentence p by Fa, Tarsky’s theory does not provides criteria by means of which we apply F to a instead to any other object. Moreover, it does not considers the necessity of criteria for the reference of the name a, as if it were evident. For reasons like these I think that the formal definitions presented here are more adequate, particularly regarding our natural language. (See Tarski 1944: 341-375).
[7] How is this possible will be explained later (sec. 15 f.)
[8] This points to one easy way to analyse composite statements of the forms p & q, p q, p q and p q. As it is well known, we can use negation together with the conjunction to respectively the following descriptions of facts:  p & q, ~(~p & ~q), ~(p & ~q) and ~(p & ~q) & ~(~p & q). The negation means always that the thought-content is false, what also means that the verifiability rule that constitutes this thought-content has proved not to be effectively applicable in its proper context, that there is no corresponding actual fact.
[9] More often only three moments are considered, since the third and the fourth moments are normally seen as a unity. I distinguish them only because verifying identity of content seems to me distinguishable from attributing truth.
[10] It seems that consensual theories of truth, demanding that the truth ultimately satisfies an interpersonal consensus made authentic by being achieved through adequate agreement within a critical or ideale Sprachsituation explore this point in regard to the collective acceptance of truth (see Habermas 1983).
[11] The anterograde procedure brings what in Husserl’s phenomenology would be called ‘truth of correctness’ (Wahrheit als Richtigkeit), while the retrograde procedure is what may be called ‘truth of disclosure’ (Wahrheit als Entdeckheit) (see Sokolowski 2000: 158).
[12] See my objections to the private language argument in the chapter III, sec. 13 of the present book.