quarta-feira, 17 de setembro de 2014

CLAUDIO COSTA: PHILOSOPHICAL TEXTS






DEAR READER!
THE AIM OF THIS PAGE IS TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE.
SOME OF THE 67 TEXTS WERE ORIGINALLY WRITTEN IN ENGLISH.
TEXTS WITH SOME INTEREST FOR RESEARCH ARE MARKED WITH "#". COMMENTS AND OBJECTIONS WILL BE WELCOMEN. MANY TEXTS ARE ONLY DRAFTS WITHOUT RELEVANCE, USED FOR DISCUSSION WITH STUDENTS.

PREZADO LEITOR!
O OBJETIVO DESSA PÁGINA É TORNAR ACESSÍVEIS MEUS TRABALHOS EM FILOSOFIA E ÁREAS AFINS PARA ESTUDANTES E INTERESSADOS. SÃO 71 TEXTOS POSTADOS DESDE 2012. O MEMORIAL CONTÉM RESUMOS DE QUASE TUDO O QUE É IMPORTANTE. TRABALHOS COM # PODEM TER ALGUM INTERESSE EM TERMOS DE PESQUISA. MUITOS TEXTOS SÃO ESBOÇOS USADOS PARA DISCUSSÃO EM SALA DE AULA, SEM MAIOR INTERESSE.
 AGRADEÇO POR COMENTÁRIOS E OBJEÇÕES.



CURRICULUM:
Associate professor of philosophy at the UFRNJ (Brazil). M.S. in philosophy at the IFCS (Rio de Janeiro, 1982). Ph.D. at the university of Konstanz (1990). Sabbatical stages of one year as a visiting scholar in the Hochschule fuer Philosophie, Muenchen (1995), University of California at Berkeley (1999), University of Oxford (2004) and university of Konstanz (2009-10).
Areas of interest: all the central questions of philosophy.
Main published work: The Philosophical Inquiry (UPA: Langham 2002), "Free Will and the Soft Constraints of Reason" (Ratio 2006), "The Sceptical Deal with our Concept of External Reality" (Abstracta 2009), "A Perspectival Definition of Knowledge" (Ratio 2010) and "A Metadescriptivist Theory of Proper Names" (Ratio 2011); a corrected version of the ideas of the last paper are here presented under the title "Outline of a Theory of Proper Names". The best selection of papers in portuguiesih is Paisagens Conceituais (Rio de Janeiro: Tempo Brasileiro).
More developed versions of the papers listed above, among others, were recently published in the book called Lines of Thought: Rethinking Philosophical Assumptions (Cambridge: Cambridge Scholars Publishing, 2014). This book I find groundbreaking in its methodology and relevance. But I have found my attempts to convince others of the obvious truth of its ideas very frustrating.
My presernt research is an attempt to reestablish the internalist and cognitivist-descriptivist tradition concerning theories of reference. I believe that this is possible if we develop these theories is a sufficiently sophisticated form, able to answer the important challenges presented mainly by Kripke, Putnam and Kaplan. Moreover, I believe that contemporary philosophy of language has challenged our commonsensical intuitions too much. Hence, I would like to reestablish some old plausibilities, and show that they can be linked together in a sistematic way.




#####

terça-feira, 16 de setembro de 2014

ADVERTISING FOR MY BOOK "LINES OF THOUGHT: RETHINKING PHILOSOPHICAL ASSUMPTIONS




ADVERTISEMENT FOR THE BOOK 'LINES OF THOUGHT: RETHINKING PHILOSOPHICAL ASSUMPTIONS' (CAMBRIDGE: CAMBRIDGE SCHOLARS PUBLISHING, 2014).








Lines of Thought: Rethinking Philosophical Assumptions is a highly innovative and powerfully argued book. According to the author, noted Brazilian philosopher Claudio Costa, many philosophical ideas that today are widely seen as old-fashioned suggests replacing the causal-historical view of proper names with a much more sophisticated form of descriptive-internalist theory able to meet Kripke’s challenges. In epistemology, he argues convincingly that we should return to the old traditional tripartite definition of knowledge, reformulated in a much more complex form in which Gettier’s problem disappear. The correct response to skepticism about the external world should not be to adopt new and more fanciful views, but rather to carefully analyze the different kinds of reality attributions implied by the argument and responsible for its equivocal character. In metaphysics, he argues for a more complex reformulation of the traditional compatibilist approach of free will, relating it intrinsically with the causal theory of action and making it powerful enough to assimilate the best elements of hierarchical views. Finally, according to the author, contemporary analytic philosophy suffers from a lack of comprehensiveness. In response to this, the papers in this collection aim to restore something of the broader perspective, salvaging isolated insights by integrating them into more comprehensive views. The text is written in a clear and accessible style that meets the needs of not only professional philosophers, but also of contemporary students and laypersons.



This is an impressive contribution to answering several important questions of analytic philosophy. Few philosophers have written on such difficult questions with comparable lucidity and originality.
Guido Antônio de Almeida - Emeritus professor of philosophy - Federal University of Rio de Janeiro

Claudio Costa's collection of philosophical essays covers many of the central problems of philosophy - the nature of philosophy and of knowledge, how names refers to individuals, frewill and consciousness. He reminds us of some of the major insights on these issues from the early years of 'linguistic philosophy' and develops important objections to some more recent views about them".
Richard Swinburne - Emeritus Noloth professor of philosophy - Oxford University


(from the back-cover)





__________________________________________________________________________________________________________________________________________________________________







ADVERTISEMENTS FOR MYSELF: I CONFESS THAT I WAS IMPRESSED BY THE FACT THAT THIS BOOK DIDN'T RECEIVED ANY REVIEW. THIS IS NO GOOD NEW FOR THE PHILOSOPHICAL COMMUNITY. TRYING TO HELP THEM I DECIDED TO MAKE SOME REVIEWS OF MY OWN:




I. SUMMARY OF THE MAIN IDEAS


"For me, contemporary analytic philosophy suffers from a lack of comprehensiveness due to the growing influence of related particular sciences, and this ‘scientism’ tends to transform philosophy into a handmaiden of science. Partially because of this, I defend the view that many philosophical ideas that today are widely considered old-fashioned and outdated should not be abandoned, but instead should be extensively reworked and reformulated.
An example is my sketch of a totally general correspondence theory of truth (published as the first chapter of the book Paisagens Conceituais). In my view the process by which we find correspondence usually incorporates coherence as an important element.
Usually we have a hypothesis p and a reverse chain of reasons that begins in criterial evidences and ends in q, and if q equals p, we have correspondence, otherwise not.
Even if the chain of reasons gains its ultimate certainty from observations, it is the element of coherence that sustains this certainty through the whole chain of reasoning.
 So understood, the view applies also to the formal sciences. For example: I have the hypothesis that the sum of the angles of a triangle is 180 degrees, this is p. And I make a reasoning that begins with evidential axioms and brings me to the same result, this is q. Since p equals q correspondence is warranted. The certainty of q is conventionally accepted as an evidence impossible to be false in the context of the particular linguistic praxis, the language-game, in which the truth-value is asked.
 The upshot is a totally general correspondence theory of truth that incorporates in it the coherence view.
  
The book Lines of Thought is a collection of published and unpublished papers, presented in a revised and expanded form:
 The most important paper in the collection is a long essay called ‘Outline of a Theory of Proper Names’, which is an expanded and corrected version of an earlier paper published under the titel ‘A Meta-Descriptivist Theory of Proper Names’ in the journal Ratio.
 In this essay, a new and much more sophisticated version of the cluster theory of proper names emerges. Thus, calling localizing description a description that expresses a rule for the spatio-temporal location of the reference, and calling a characterizing description a description that expresses the rule that is the proper reason for our choice of the name, we can state the following form of the identification rule for any proper name:

A proper name N refers to an object of a certain class C iff in a sufficient manner and more than in any other case, its localizing description applies and/or its characterizing description applies.

 Normal speakers do not need to know the identifying rule, but must know enough from it to be able to insert adequately the name in the discourse.
 The identifying rule, turned into a description, is a rigid designator, applicable in all possible worlds where the object to be referred can be found. This explains the rigidity of proper names.
 Since usual definite descriptions are loosely associated with the identifying rule of proper names of the objects they are usually designating, they are accidental designators.
   To show that this view is right we need only consider cases of definite descriptions that do not belong to the cluster of descriptions of any proper name, for example, ‘the third cavalry regiment of Cintra’. This description is rigid, since it will be applied in any possible world where there is a third cavalry regiment of Cintra.
 This theory not only gives descriptive paraphrases of actual discoveries of Kripke, but allows us to explain the most relevant classical counterexamples to descriptivism more precisely than Searle’s memorable attempt to do it in the chapter 9 of his book Intentionality.

   Since proper names is a touching stone to the theories of reference, a radical change of perspective in the direction of descriptivism should bring with it also a radical change in the way we understand the reference of others terms and expressions.

   Another relevant paper in the collection is the previously unpublished ‘On the Concept of Water’, proposing a neo-descriptivist analysis of this concept.
   For me the word ‘water’ has two nuclei of meaning: an old popular nucleus, and a new scientific nucleus. A complete descriptivist view must extend itself to the scientific meaning too, since ‘Water is made of H2O’ is a descriptive sentence that is found in the definition of water given by modern dictionaries.
   When sufficiently developed, this analysis allows us to give an internalist answer to Putnam’s twin earth experiment, as resulting from our projection of one of these senses in Oscar’s indexical use of the word. For according with the context of interests involved we can emphasize the popular meaning of the world ‘water’ or the scientific meaning of this world.
   Moreover, distinguishing several senses in which we can say that ‘Water is H2O’, our analysis shows more clearly than two-dimensinalist views why it is misleading to see this statement as being necessary a posteriori.  To make it clear: for me in the statement ‘Water is H2O’ the word ‘water’ can be understood as ‘watery liquid’ or as ‘dihydrogen monoxide’, according to the context. In the first case the statement will be read as contingent a posteriori. In the second it will be read as necessary a priori. Kripke simply mixed the contingence of the first statement with the necessity of the second, arriving in this way to the necessary a posteriori.
  As Wittgenstein would say, Kripke’s conclusion results from a metaphysical confusion caused by lack of attention to the ways in which language really works.

  Another relevant paper is called ‘Free Will and the Soft Constraints of Reason’ is a modern defense of compatibilism in which the causal theory of action is used to explain different levels of free will.
 According to that theory, reasoning causes volitions that cause actions. Freedom can be constrained, externally or internally, by pressure or limitation, under a reasonable range of alternatives, in these three levels: physical, motivational and rational, in the last case possibly without awareness of the agent, what makes it important and contestable and demands a detailed explanation.
 The upshot is a view potentially able to incorporate the results of modern hierarchical views.
   This paper is followed by a compatibilist analysis of our feeling that we can do otherwise, with consequences for the arguments of Van Inwagen and Harry Frankfurt.

 ‘A Perspectival Definition of Knowledge’ is a paper revising the old tripartite definition of knowledge in a way in which Gettiers problem disappears without creating new difficulties, since the internal link between the conditions of justification and truth is made fully explicit in a formal way. The basic intuition is that the adequate justification must be able to satisfy the condition of truth to the knowledge-evaluator in the moment of his evaluation. However, the details of the definition are partially formal and too complex to be explained in few words.

The most difficult paper is, I believe, ‘The Sceptical Deal With our Concept of External Reality’. This paper offers shows that both, the modus tollens skeptical argument about the reality of the external world, as much as the modus ponens anti-skeptical argument about the external world, are both equivocal and consequently falacious. The way to get this result is through an analysis of the concept of reality. I show that this concept is ambiguous; it has a sense in the usual contexts and another sense in the context of skeptical hypothesis. Since there is an implicit attribution or disattribution of reality in the different sentences of the skeptical and anti-skeptical arguments, the passages from the premises to the conclusion are implicitly equivocal and consequently fallacious.
   This paper contains an passant a developed proof of the external world. It is in my view in the whole philosophical literature the only proof that really works. It is able to explain why we are so sure that the external world is real.

   What these papers have in common is that they belong to the same program of restoring something from the traditional comprehensiveness of philosophy, often by reviving views that by many are, I believe, wrongly considered outdated."



 II. THE BURDEN OF OUR SCIENTIST "ZEITGEIST"
   
 "In my view this book contains a deep challenge to some results of contemporary philosophy and to the way theoretical philosophy is usually made – a challenge that can go unnoticed for several reasons.
 The brothers White were the first to put an airplane to flight. But since they were from the country-side, poor, not well related with the influential people of New York, only very few have noticed their invention until ten years later, when it was needed for the efforts of the war.
   In my case not only I am living in the most distant country-side, but I have a light degree of autism, what makes me not the most social being, to say the least. Moreover, I am challenging the mainstream philosophy, and since my challenge cannot be easily discarded, I guess that a serious discussion of the book will be simply avoided by it.
  Furthermore, I believe that at least some of the papers in this book have true philosophical deep with some fire of originality shining through them. And this is already something, since even this is very difficult to find in the wilderness of much of contemporary philosophy, severed as it is from the philosophical tradition.
  I can see the reasons why my arguments are independent. Because of my condition I am not really concerned about what my fellows think, and I don’t feel myself as a member of their community of ideas. Since during all these years I’ve been moved only by my curiosity and some sense of personal achievement, a different perspective was unavoidably developed, even if the last judgement, of course, does not belong to me.
 A distinctive feature of the perspective shown in this book is that it is, I would say, not reductively perspectival, like those build from a scientist or formalist or even from a purely commonsensical inspiration. Instead, it is "multiperspectivally" grounded, and this multi-perspectivalism makes justice to the true nature of philosophy, which should – as wisdom without a center - take into account the whole of our understanding.
  Moreover, since this multiperspectivally gronded view approaches to science as a consensualizable knowledge – as I also tried to show – I guess that it is also the true one."










 III. PERSONAL BLURB

"IN MY VIEW THIS BOOK IS GROUNDBREAKING BECAUSE IT IS A TOTALLY INDEPENDENT AND SERIOUS ARTISAN WORK, GROWN FROM AN CONSTANT AN PROBABLY MOSTLY UNCONSCIOUS SEARCH, IN WHICH SOME WAYS OF PHILOSOPHY ARE REINVENTED; THIS IS THE REASON OF ITS ORIGINALITY AND RELEVANCE. 
 IN MY VIEW THIS BOOK PUTS THE "DISCOVERY" OF KRIPKE IN THE RIGHT INTERNALIST SHOES. THIS BOOK PUTS PUTNAM’S BRILLIANT THEORY OF MEANING IN THE SHADE. IT TELLS US, FINALLY, WHAT KNOWLEDGE REALLY IS, EXORCISING GETTIER’S PROBLEM FOR EVER AND EVER. IT NOT ONLY GIVES THE ULTIMATE PROOF THAT THE EXTERNAL WORLD REALLY EXISTS, BUT SOLVES - ONCE AND FOR ALL - THE DIFFICULT PROBLEM POSED BY THE MODUS TOLLENS SKEPTICAL ARGUMENT. AND IT OFFERS THE MOST COMPLETE AND PLAUSIBLE COMPATIBILIST THEORY OF FREE WILL.
 ANYONE REASONABLY SMART AND COMPETENT, AND NOT YET TAIMED IN THE LATEST ART OF PHILOSOPHICAL SELF-DECEPTION, WILL SEE THESE THINGS. 
 SINCE I AM AN OUTSIDER, AND SINCE AN AUTHOR WRITES TO BE READ BY THE RIGHT READERS, I AM FORCED (SOMEWHAT AGAINST MY WILL) TO MAKE THIS ADVERTISEMENT."


  


sábado, 9 de agosto de 2014

# AN EXTRAVAGANT READING OF THE FREGEAN SEMANTICS


Work in progress: part of the draft for the book: 'PHILOSOPHICAL SEMANTICS", chapter 2, book I (Englsh uncorrected)





– 3 –
AN EXTRAVAGANT READING OF THE FREGEAN SEMANTIC


The importance of the Fregean semantics for the philosophy of language derives from its unique blend of theoretical simplicity, explanatory scope and philosophical relevance. I want here to reconstruct the essentials of the fregean semantic, making clear that the basic concept of sense can be paraphrased in terms of cognitive rule and that the concepts of existence and truth can be reinterpreted in terms of the effective applicability of specific cognitive rules. The first idea was in some way suggested by Michael Dummett, but I think that it can be more systematically explored. My aim here is not to achieve definitive results, but to test some ideas and to insert the insights explored in the last chapter in a more precise framework.
   As is well known, Frege explains the reference (Bedeutung) using a semantic intermediary link, which he called sense (Sinn). The schema (1) shows how Frege deals with these two levels in the case of a predicative singular sentence of the form Fa:

   singular term: a           general term: F                  sentence: Fa
   sense                            sense                                   thought
   reference                      concept > object                 truth-value

Although the fregean semantic has been a development of unparalleled importance for the philosophy of language, it is not free from well-known eccentricities. My reading of its main semantic elements in terms of semantic-cognitive rules will show a way to purge Frege’s semantic from its greatest oddities.

The reference of the singular term
Let’s start with the singular terms. The reference of a singular term is, for Frege, the object itself, taken in the broadest sense, which includes abstract objects. The reference of the name ‘Moon’, for example, is the Moon itself with its craters. To designate the reference he uses the German word ‘Bedeutung’, whose literal translation for the English is ‘meaning’. The lucid English translators have chosen words like ‘reference’, ‘denotation’, and ‘nominatum’, expressing in this way what Frege really had in mind. Other used terms like ‘semantic value’, ‘semantic role’ and ‘truth-value potential’, which underline the contribution of the references of the sentence’s components for the truth-value of the sentence as a whole. The literal translation of ‘Bedeutung’ as ‘meaning’ remains the most correct; but for the sake of clarity, I will keep using the word ‘reference’.[1]
   There is an interpreter’s discussion about the reason why Frege would have chosen the word ‘Bedeutung’. One of them would be that one of the meanings of ‘Bedeutung’ (as well as of ‘meaning’ or ‘signification’) is relevance or importance, since the reference is that which matters most.[2] The stronger reason, however, at least with regard to the reference of natural language terms, is that by introducing the term ‘Bedeutung’ Frege has substantivated the verb ‘bedeuten’, used to express, no longer the act of pointing at (deuten) or of designating (bezeichnen), but what is pointed at (die Bedeutung), what is designated (das Bezeichnete), that is, the reference itself.[3] In German this would look like:

Bedeutet ... → deutet ...   bezeichnet.      was gedeutet, bezeichnet wird/
(means)           (points ...  means ...)             (what is said)
                                                                                ↓
                                                                      die Bedeutung
                                                                      (meaning = reference)

This would have been the small semantic twist with which Frege turned the word ‘Bedeutung’ in a technical term – a twist that betrays without assuming the semantic-referentialist disposition.[4]

Sense of the singular term
Now we come to what Frege understands as the sense of a singular term. To introduce it, compare the following two sentences:

1.  The morning star has a dense atmosphere of CO2.
2.  The evening star has a dense atmosphere of CO2.

The sentences (1) and (2) refer to the same thing, which is the planet Venus. But despite that, a person can know the truth of (1) without knowing the truth of (2). The explanation of this is that although the singular terms (definite descriptions) ‘the morning star’ and ‘the evening star’ refer to the same planet Venus, they convey different informative content, they have different senses (Sinne). The sense is defined by Frege as the way in which the object gives itself to us (die Art des Gegebenseins des Gegenstandes), what is uselly translated as the mode of presentation of the objet. The senses of the natural terms ‘the morning star’ and ‘the evening star’ are different because the first singular term presents Venus as the brightest celestial body usually seen near the horizon just before sunrise, while the second singular term presents the same planet Venus as the brightest celestial body usually seen near the horizon shortly after the sun goes down…
   According to Frege, words express the sense (drücken den Sinn aus) while the sense determines (bestimmt) the reference, since the mode of presentation shows us the way to find the object. This determination of reference through the sense is given even in cases where the object of reference does not exist, what points to a flaw in Frege’s idea that the the sense is the way the object gives itself to us: in this cases it cannot be. This is why sense has been better undrestood as being the intended mode of presentation and not a given one[5]; the sense is the mode how we intentionally present to ourselves the object, whether it exists or not. Anyway, an expression can have sense without reference, but cannot have reference without its determination through sense.
   The notion of sense in Frege is comprehensive, and in the case of the meaning of the sentences he calls it epistemic value (Erkenntniswert). The expression is adequate. The Fregean sense has epistemological interest, for it involves the informative content of the linguistic expression. It is, in the words of Michael Dummett, what we understand when we understand an expression.[6] The philosophical importance of the fregean semantics results from this epistemological importance of the concept of sense.
   Frege is a Platonist about the senses. He conceives them as abstract entities, which he analyzes in terms of other senses as constituents. That is: he does not analyse senses in terms of other concepts. This analysis, however, is something that naturally imposes itself. For it seems very plausible to understand senses as semantic-cognitive criterial rules. Herein is the fundamental connection that can be made between the Frege’s semantics and the reflexions of the later Wittgenstein, who saw the senses as being determined by rules.[7] The plausibility of this identification is particularly clear when we take numeric expressions as examples. Consider the following expressions:

    ‘1 + 1’,
    ‘6/3’,
    ‘(7 + 3) – 8’,
    ‘2’.

   They all have the same reference, the number 2, but they have different Fregean senses. At the same time, they constitute procedures, methods, cognitive-semantic rules, through which we identify the same number 2 as a result.[8]
   By treating senses as semantic rules we contrast them with what Frege called colorations (Färbungen). Colorations is the name he has for what we today call expressive meanings, i.e. emotional states regularly associated with certain expressions. Thus, for example, the words ‘love’ and ‘hell’, in the sentence ‘Love is a dog from hell’ (Bukowski), associate contrastivelly specific emotions. As Frege realised, the similarity that the emotional colorations associated with words have to different people depend on the similarity between their human natures and not on conventions, as it is the case with the senses. This is why some people like some poems, while others do not. And this is why it is so difficult to translate poetry, which greatly depends on the colorations acquired by an expression in a particular language and culture. We can thus assume that the reason for the objectivity (intersubjectivity) and for the consequent communicability of the senses – in contrast with the relative lack of objectivity of the colorations – is that the senses are cognitive rules are usually agreed upon in a pre-reflexive manner, when they are not what the combinations of these rules constitute, a point we have also considered as we considered Wittgenstein’s views.
   Under the light of these assumptions, the sense of the singular term should be considered the same as a rule or method or procedure conventionally grounded, whose function is to serve as a way to identify the object. This rule is generally expressed by definite descriptions. Thus, the rule bound to the singular term ‘the morning star’ can be made more explicit by the description ‘the brightest celestial body usually seen near the horizon just before the Sun rises.’ And a name like ‘Aristotle’, as Frege noted, abbreviates a bunch of modes of presentation of the object expressed by definite descriptions like (i) ‘the disciple of Plato and the teacher of Alexander the great’ or (ii) ‘the person born in Stagira’.[9] If this is the case then (i) and (ii) express different meanings, different rules that in some way are able to help us to identify Aristotle, so that the sense in some ways determines the reference.
   Of course, there is a controversy about this issue rosen by Kripke’s arguments against descriptivist views of proper names like that suggested by Frege. However, in my view Kripke’s arguments can be countered if we find a more complex and sophisticated identification rule, able to establish what are the relevant descriptions and how much of them is sufficient for the application of the proper name. I offer a summary of my theory of proper names in the Appendix I of the present book.

Reference of a predicative expression
Frege has something to say about the reference of the general term used in a predicative function, which he calls a concept (Begriff) and may include relations. This is odd because it seems natural to call the concept something like the sense of the conceptual expression – the form of presentation of its reference – while the reference itself would be called a property (e.g. a red patch) or some kind of combination of properties (e.g. a rainbow). More than the proper name, the concept is in philosophy traditionally seen as a rule. In addition to belonging to the realm of reference, for Frege the concept is a function. The mathematical concept of function can be defined as a rule that has as input arguments and as output values (for example: ‘3 + x = ...’ is a function that takes as value the number 6 when the argument which replaces x is the number 2). For him a concept is a function whose argument is the object that ‘falls under it’ (fällt unter) and whose value is a truth-value, which can be two abstract objects named ‘the true’ (das Wahre) or ‘the false’ (das Falsche). Thus, the concept designated by the conceptual term ‘...is white’ has the value true when under it falls the object Moon and has the value false when under it falls the object Sun.
   A serious problem is that Frege never explained satisfactorily what are concepts understood as unsaturated abstract entities. Concepts cannot be for him objects, neither collections of objects or extensions[10] The reason is that an object, a collection of objects and an extension, are independent entities (unabhängig). That is, they are saturated entities, not needing anything to complete them. The concept, by contrast, being a function, is characterized by Frege as being open, that is, as an incomplete (unvollständig) or unsaturated (ungesätig) entity, needing to be always completed with arguments, which in this case are the objects falling under the concept. Only objects are, by contrast, complete (vollständig), saturated (gesättig) or independent (unabhängig).
   The relation saturation-insaturation accurs in the three levels: linguistic, semantic and referencial. For example: the predicate ‘…is a horse’ is an unsaturated expression (the insaturation being shown by the gap ‘…’ or by an ‘x’) expressing a supposedly unsaturated sense, which refers to an unsaturated concept, which is completed when some object falls under it, while the object is saturated or complet and is referred by a name, for example, ‘Bucephalus’.
   Incomplete predicate and complete singular term combine to form the complete sentence ‘Bucephalus is a horse’, which being complete must be the name of an object that for Frege is the truth-value. It was already argued that the complete sentence refers to an object is confirmed by the possibility that we have of nominalizing sentences in the form of definite descriptions, which are singular terms. Thus, the sentence ‘Bucephalus is a horse’ can be transformed into the description ‘the horse named Bucephalus’, which can appear in the sentence ‘The horse named Bucephalus belonged to Alexander’. However, the same can be made with general terms: ‘…is a horse’ can be nominalized as ‘the horse’, occuring in sentences like ‘The horse is a vegetarian animal’, what shows that the foregoing argument hasn’t much value.

The ontological level
The discussion regarding the unsaturated nature of the reference of predicative expressions leads us to the question of the ontological nature of what Frege meant by a concept. Freges has the wisdom of accepting that concepts can be empty. For him the predicate ‘... is a Unicorn’ refers to an empty concept, though under it does not fall any object. However, it is obvious that ‘...is an Unicorn’ does not have any reference, though obviously expresses what we ordinarily understand as a concept. This contrast shows clearly that the Fregean identification of the reference of a predicative expression with a concept is inconsistent with the ordinary meaning of the word, resulting from what has been called a contamination of the domain of sense (in which we should talk about concepts as modes of presentation) by the domain of reference (in which we should talk about properties).
   The question is: even if the Fregean concept has nothing to do with our normal understanding of what a concept is, is there a room for it? I doubt this possibility. It seems that Frege has been moved by some kind of Aristotelian ontological lead as he proposed that the reference of a predicate is a concept: his concepts, like Aristotelians universals, should be something covering the objectual level but without being confounded with the objects themselves, what so understood seems to be an inconsistent view.[11] If so, the best option seems to me be to forget about Fregean concepts as references of predicates and to admit that the concept is simply the sense of the predicative term in its predicative function. In other words, it is the method of presentation of the predicate, what can also be understood as a function, a rule. In this case the reference of the predicate is in fact something that may ‘falls under’ the concept expressed by it, even though it is not something like a full object or extension. But what this something could be?
   I propose the answer that seems to me the most feasible. I want to revise Frege interpreting the reference of a predictive expression in terms of what we now call tropes, which are nothing more than singularized spatio-temporal properties or s-properties (to simplify), such as the white that we see when we look at the Moon and which, in a way, is there (as the reflection of all wavelengths of the visible spectrum from our perspective). In its most coherent version, the modern ontology of tropes maintains that all reality must be constituted of tropes, which from an epistemological perspective are its building blocks.[12] In this sense, this smooth surface I am touching, the white I am seen, that sharp sound I just heard, and even (maybe) the rectangular shape of the the computer before me, are tropes. Non perceivable things like atoms, physical forces and even numbers could be someway explained as constructions inferred from tropes.
   It is easy to suggest that an universal could be in principle defined as the qualitative identity of tropes with some casualy chosen s-property model S*, assuming that what we take as S* may vary with the cognitive subject and even for the same cognitive subject in different occasions.[13] In this case the s-properties S1, S2… Sn are identified as instantiations of the universal only because they are similar to the s-property model S*. And material objects could be in principle understood as co-located co-temporal systems of s-properties, eventually containing a nucleus of more essential s-properties surrounded by more contingent ones.[14]
   Although the ontology of tropes (s-properties) is a very new acquisition and brings a range of unsolved problems with it, it does not produce more difficulties than the traditional universal doctrines of realism and nominalism. In return, it promises an extremely economical solution for the ontological problems, freeing us not only from oistrich nominalist solutions, which lack rationality, and also freeing us from questionable entities like the Platonic-Aristotelian universals multiplying the world, as much as from incognoscíble substances, which occupied the philosophical heads for more than two millennia without a progress able to make them more plausible. The only reason why these options are still in the foregroud is the weight of tradition.
   For reasons like these I accept the ontology of tropes as the most plausible one. But since the issue is controversial and the reader may have a different belief, I must say that the assumption of an ontology of tropes isn’t even necessary for my point here. All that you must assume is that the our empirical predicates refer to singularized properties or s-properties, i.e., tropes like the read of this coach and that sharp sound in the air, at least in the case of observational singular sentences like ‘This coach is read’ or ‘the music here is too noisy’ (I will use the term s-properties only because the philosophical tradition has hipostasied the word ‘property’ as referring to some scarcelly intelligible non-empirical entity, since in the ordinary language we use the word ‘property’ always referred to tropes.).
   According to the understanding of the reference of predicative terms that I am proposing, a predicative expression like ‘... is white’ in the sentence ‘the Moon is white’ is not a Fregean concept; it is a singularized property, namely, the s-property of the whiteness of the moon as it is given to the observers. Even here, the singularized property (a configuration of tropes) can be interpreted as a function if we wish to insist in maintaining Frege’s explanatory devices. It is a function whose argument in the case is the Moon, and whose value could be simply the whiteness of the Moon. In this case, the function referred to by the predicative term ‘... is white’ would not be satisfied by the object named ‘Moon’, but by the s-property of whiteness that, when considered in its relation to the object referred by the proper name ‘Moon’ is the whiteness of the moon in the sentence ‘The Moon is white’. Anyway, it is hard to see any advantage in this procedure.

Unsaturation as ontological dependence
A problem with the idea of incompleteness or insaturation is that it does not seem sufficient to distinguish a predicative function. Between the object and the property designated by the predicate there is a well-known asymmetry: the object that is typically referred to by the subject and the property is by the predicate (e.g. ‘Socrates is wise’); But while the property may somehow be referred to by the subject (e.g. ‘Wisdom is a virtue’), the object cannot be referenced by predicate (‘Wise is Socrates’ doesn't make sense, unless ‘wise is ...’ is understood as predicate). However, the distinction saturated/unsaturated really does nothing to explain this asymmetry, for it seems also possible to affirm that the singular term and, therefore, its reference, is unsaturated. After all, what is the difference between the ‘(Bucephalus, Silver, Pegasus ...) is a horse’ and ‘Bucephalus is ... (white, restless, fast ...)’? Both, the general term as the singular term, can be seen as expressing functions that can be supplemented by a myriad of other terms, and the same applies to their supposed references.
   However, the notion of unsaturation does not eshaures so easily. In chemistry a carbon compound is said unsaturated, when it contains carbon-carbon bonds removable by the addition of hydrogen atoms, which make it a saturated compound. Isn’t in the metaphor a hint of an answer that Frege didn’t explored sufficiently?
   I want to show a reading of the reference of a predicative expression in terms of tropes-functions that enables us to make a useful paraphrase of the Fregean distinction between saturation and insaturation. This paraphrase is inspired in one of the Aristotelian definitions of substance, that is, to be that which exists in the independence of other things.[15] Applied to objects as systems of tropes, the intuition is that some systems of s-properties are generally more stable than the associated s-properties; they exist in a manner relatively independent of the s-properties more or less loosely associated with them. Indeed, s-properties do not exist alone: an s-property of green, for example, does not exist in the complete independence of others s-properties, which need to be spatio-temporally related to other s-properties, etc.
   Admitting that isolated s-properties are the proper referent of predicative expressions, and they have their existence in the dependence of relatively independent and more stable systems of s-properties named by singular terms, we can paraphrase the dichotomy unsaturation/saturation or incompleteness/completeness by the dichotomy dependence/independence, only rarely used by Frege. After all, what distinguishes the reference of a general term, in the case of a predicative sentence or even a relational sentence, is that this reference is a trope (or a complex of tropes) whose existence depends on a whole which is the system of tropes establishing the private object referred to by the term. Thus, the predicate ‘... is quick’ in the sentence ‘Bucephalus is quick’ and the relationship ‘...belongs to...’ in the sentence ‘Bucephalus belongs to Alexander’ apply respectively to the combination of s-properties of quickness and the relational property of belonging to, which would not possibly exist if the horse and Alexander could not be identified as particulars. Their possibility of identification is indebted to the existence to the more stable and independent complex systems of s-properties building the objects Bucephalus and Alexandre. These systems of s-tropes are referred to by the names ‘Bucephalus’  and ‘Alexander’, which are objects that certainly exist in the independence of the existence of the constituent but unessential combinations of s-properties of ‘being quick’or ‘belonging to someone’.
   Understanding the unsaturation as dependence suggests, therefore, that the s-properties referred to by predicates have an inevitable relation of dependence vis-à-vis particulars, and that this fact gives us a better explanation, I guess the only one, for the relation between singular terms and predicative expressions.
   It should be noted that the relationship of dependence/independence wouldn’t be preserved if the references of predicative terms were extensions, understood as classes of objects to which the predicative terms apply. However, the relationship of dependence/independence is preserved if we understand the reference of the predicate in terms of singularized properties. Such a relationship has its origin in the ontological level of reference, but it is reflected in the two other levels, as Frege has defended regarding the relationship unsaturation/saturation. First, it is reflected in the epistemic level of sense by the fact that the sense, the mode of identification of the object referred to by its name, is independent of the mode of identification of its s-properties, while the sense, the mode of identification of its predicative expressions depends upon the prior identification of the object referred to by the term. And second, the relation is reflected in the linguistic distinction between subject and predicate.
   We should also note that the relationship of independence/dependence does not have to be restricted to empirical individuals. Even the formal objects considered by Frege seem to submit to it. Consider the predicate ‘... is an even number’ applied to the reference of the abstract name ‘6’. The application of the predicate depends on the recognition of the existence of the number 6. And the very concept of being an even number doesn’t seem to take place in the independence of the existence of particular numbers to which it can be attributed.
   This kind of solution seems finally viable by the fact that it gives a principled explanation to the asymmetry between private object and property. It explains the independence of the singular term’s reference. The name ‘Socrates’ cannot pass to the predicate position because what it refers to is something independent (and independently identifiable), that is, the system of s-properties which is essential to the abstract object. Even the name of an abstract object as the number ‘6’ cannot pass to the predicate position, since it refers to something relatively independent of its properties (allegedly not the definitory ones), being identifiable in the independence of many of its predicates, say ‘... is even’ or ‘…is greater than 1’.

Sense of a predicative term
Frege has nothing to say about the sense of the predicative expression. This is understandable, since he has no longer seen it as a concept… But the logic of our reconstruction leads us to think that this sense, this mode of presentation, is nothing else than what we might call a rule of characterization (or application), and that this rule is what should be investigated as what has been called the concept.[16]
   As with the singular sense of the word, the meaning of the predicative expression can also change without the change of its reference. Consider the sentences:

   1. the Moon is white.
   2. the Moon reflects all wavelengths of light.

The reference of the predicates of sentences (1) and (2) – the sets of arrangements of tropes that constitute the whiteness of the Moon – remains the same, while the senses or meanings of the predicates are different: a person may know that the Moon is white without knowing that its surface reflects all wavelengths of the visible spectrum. This means, in our understanding, that the concepts, modes of presentation, or criteriais rules of characterization-application of predicates of (1) and (2) are different.
   Another result of our understanding of predicative expressions contradicts the Fregean expectation that the same sense cannot have more than one reference. Consider the following sentences:

1.     The Moon is white.
2.     The Mont Blanc is white.

   The predicates ‘...is white’ in sentences (3) and (4) obviously have the same sense, for they express the the same rule of characterization. But the s-property of the whiteness (of reflecting all waves of the spectrum) of the Moon is located on the Moon itself, while the s-property of whiteness of Mont Blanc is located in its eternal snows. This is of course no isolated example: in the case of singular predicative or relational sentences (assuming that relations are s-tropes) the references are different according to the object referred to by the conceptual sense, since each object has (or is constituted) by its own s-properties.
   We could say that the predicative expression used in a singular sentence has an explicit role and two implicit ones. The explicit role is that trough its rule of application it refers to an s-property. The first implicit role is that this rule, applied in association with singular terms, alludes the object referred to by these singular terms, and that this is what distinguishes the role of the predicative sense in singular sentences (This fact is what could be rescued from Frege’s displaced speech of objects falling under incomplete concepts, seen as functions-rules that have as arguments objects and as values truth-values.) Finally, the second implicit role of the predicative expression in a singular sentence is that it also alludes the universal as the fact that we also know that the referred s-properties can be seen as strictly similar to other s-properties. I think that this is what we can mean when we apply a predicative expression in a singular sentence.
   But how is the predicative expression used in the case of general sentences? From the perspective I am investigating, a universal sentence is the abbreviated expression of a conjunction of singular sentences, each of them referring to s-properties of objects. For example, the universal sentence ‘All trees are made of wood’ would be analysed as ‘Tree 1 is made of wood, tree 2 is made of wood… tree n is made of wood’; thus, the strictly similar s-properties S1 of 1, S2 of 2… Sn of n, are conjoined and jointly referred to by the sentence, what also means that the rules of application able to characterize the s-properties belonging to the objects trees, which are the same rules, need also be conjoined in the sense that the universal sentence at least points to this conjunction of rules. A similar consideration can be made regarding existencial sentences, which abbreviate a disjunction of rules of characterization and refer to a disjunction of s-properties belonging to different trees as objects.
   We could say, I believe, that in the singular sentence the sense of the predicative expression refers to a s-property and alludes to the universal understood as a conjunction of s-properties similar to the s-property referred, and that in the case of general sentences the predicative expression refers generally to the s-properties belonging to its extension, though only alludes to the s-tropes of each individual thing belonging to its extension. By accepting this kind of explanation it seems that we can forget Frege’s technical use of the term ‘concept’ as superfluous.

Dependence of predicative terms
The ontological distinction between independence/dependence (saturation/unsaturation) is also reflected in the epistemic level. This is understandable when you consider the sense of the predicative term as a rule of application. The identification rule of the singular term applies to the object, which is considered as independent in relation to its contingently possessed singularized properties. Consequently, the rule of identification is also liable to be applied regardless of the application of rules of characterization, and can be itself alone conceivable in its application, and in that sense independent, complete, saturated. The same is not true, however, with the characterization rules expressed by predicative general terms. Being the tropes or sets of tropes to which they ultimately apply system-dependent constitutive tropes of the objects to which the rules of identification apply, characterisation rules of predicates require prior application of the rules for identification of objects in order to become applicable themselves, which makes them dependent on the rules for identification of singular terms in the same way that the properties are dependent on the objects possessing them.[17]
   The general sense of the word, which (diverging from Frege) we identify with the concept expressed by it, should be then a rule whose application to an object depends on the prior application of another rule. The rule of application of the predicative expression is dependent on and, accordingly, incomplete, unsaturated, in the sense that it demands the prior application of the identification rule of the singular. It is necessary to identify, that is, to find in space and time some particular object, to be able to characterize it. You need to apply the rule that allows us, for example, to find space-temporally the animal called Bucephalus in order to apply, on that basis, rules of characterization of predicative general terms like ‘... is a horse’, ‘... is white ', ' ... is docile’, and also the complex rules of application of more complexe predicates like ‘…a horse that belonged to the best tessalian strain’. And you need to apply the rule that allows us to identify mentally the number 6 to be able to apply to it the identification rule for numbers that are divisible by 2.
   It would be a naive objection to think that after all it is possible to say ‘That is a horse’ or ‘There is a white thing’, without identifying Bucephalus, because this would be an exagerated requirement. Singular terms indexicals as ‘it’ and ‘there’ already identify some particular in the form of something that is independently space-temporally localizable, to be made explicit by expressions such as ‘that object’, ‘that place’, ‘that beast’ and this is sufficient. Therefore, not only the reference of the predicate is dependent, but also its meaning. This is how the relation of semantic dependency – at the level of sense – mirrors the relation of ontological dependency – at the level of reference.
   If we accept this revision of Frege’s views, some problems of his theory can also be better understood and solved, like the so-called paradox of the concept horse. Based on his understanding of a concept as something insaturated, Frege is lead to the strange conclusion that one cannot name a concept. For him the sentence:

(1)   the concept horse is not a concept,

 is true.  After all, ‘the concept horse’ is a singular term, a definite description, and as such it must refer to something saturated, an object. The paradoxal point is that the denial of (1), the sentence

(2)   the concept of horse is a concept,

sounds like a true analytic sentence.
   In my view the answer to this paradox emerges when we distinguish between, say (i) being a reference of a nominalized general term and (ii) being the reference of a general term when it working in the predicative position. In the case where the entity referred to by the general term isn’t referred to as the entity referred to by a predicative expression working predicativelly, it ceases to be seen as unsaturated or incomplete.[18] If we make this distinction (3) can be understood as an ambiguous phrase. If interpreted as

(3)   the reference to the word ‘horse’ is in itself saturated as the reference of a nominalized general term,

it will be true. But if interpreted as

(4)   the reference of the word ‘horse’ is in itself unsaturated as the reference of a nominalized general term,

it becomes false. Under this understanding, what Frege is saying becomes harmless.
   Now, suppose that we drop the idea that a concept is some kind of abstract reference and see it as the sense of a predicate. Then our response to Frege’s paradox is still clearer. The sentence ‘The concept horse is not a concept’ is true when we wish to say that in its nominalized sense the concept horse isn’t working as a rule, a function, since it is being referred to by the definite description ‘the concept of horse’, which is a name and not a predicate. On the other hand, the sentence ‘The concept horse is a concept’ is also true when used to say that the dependent sense of the predicate, the rule or function in its role as a rule or function, can only work as a concept, namely as something in its predicative role.

The concept of existence
At this point we can consider Frege’s treatment of the concept of existence. Deepening an idea already present in Kant, Frege suggested that existence is a property (Eigenschaft) of a concept, namely, the property that it should not be empty but satisfied or fulfilled by at least one object.[19] A similar idea was later defended by Bertrand Russell in the suggestion that existence is the property of a propositional function of type ‘x(...)’ to be true for at least one instance.[20]
   I will not consider here the details of Frege’s view of existence. Following a more current terminology, I will consider the following example that I take from John Searle.[21] Consider the sentence ‘Horses exist’. This sentence lets to be analysed as:

There is at least one ... such that ... is a horse.

As Searle notes, this sentence contains two components. One of them is expressed by the predicate ‘…is a horse’, symbolically Hx (where x is in place of ‘...’ and H in place of ‘a horse’). The other component is the predicate of existence, the open sentence ‘there is at least one ... such that ...’, symbolically x(...) (where is in the place of ‘there is at least one’, and ‘...’ is the gap to be fulfilled by some concept. This means that the predication of existence x(...) is a concept of a concept, a higher-order concept, a metaconcept under which some other concept can fall. The sentence x(Cx) expresses a concept of second order applied to a concept of the first order. What this concept of higher order does, in the words of Frege, is to say that at least an object falls under the concept of the first order, that is, that this concept is satisfied, what means the same as to assign the application of this concept of first order to at least one object. All these are different ways to say the same.
   The last way of saying, namely, to say that existence is the applicability of conceptual rules is the most interesting to us. It interests us for allowing us to analyze concepts in terms of rules, once it is proper of rules to be applicable. Thus, when we say that the Moon exists, we mean that the concept expressed by the predicate ‘is the Moon’ is applicable, which means that the conceptual rule for the identification of the Moon is effectivelly applicable. With the term ‘effectively’ I want to emphasize that the conceptual rule does not apply only as a possibility entertained by our imagination, but that it is in fact applicable in the domain of actual physical objects (‘This rock exists’), followed by the psychological domain (‘My nausea exists’), belonging more properly to them. Summarizing, we can say that the existence is the property of a conceptual rule of being applicable in a choosen domain.
   The parallel between the concept of existence in Frege and the existence in our reconstruction of sense as conceptual rule is strict:

     Concept of existence (Frege) =
A higher order concept that demands to its satisfaction that a concept of lower order has at least one object that falls under it.

     Concept of existence (rebuilt) =
A higher order conceptual rule that demands for its application that a first order conceptual-criterial rule is effectively applicable to at least one object.

The advantage of this last form of analysis is in my view epistemic: we are able to better scrutinise the nature of our existence-assignments, as will be shown in the answer of objections.
   A first objection could be that the concept of applicability of a rule is an anthropomorphic one. However, this objection would only arise when we confuse the concept of effective applicability with the concept of aplication. The application of a cognitive rule is an act or a series of acts. The application of the cognitive rule for the identification of the Moon really demands the existence of cognitive beings able to apply it. The application of cognitive rules depends on actual cognitive actions, by which we make judgments. Our judgment that the Moon exists depends on the experience of application of a rule by ourselves or by someone who testify its applicability. However, the concept of effective applicability is not antropomorphic. Even if there were no human beings able to apply the identification rule for the Moon, the Moon would continue to exist, since the characterization-rule for the Moon would still be effectively applicable to this object. The rule would be still applicable, even if it weren’t ever conceived or applied, even though nobody was here to think that the Moon exists. Contrarily to the concept of effective applicabiliby, the concept of application of the rule is anthropomorphic.
   Another objection concerns empty concepts. When we say that horses exist we are applying a second-order concept, that of existence, which is nothing but the concept of effective application to at least one object, a metaconcept applied to a first order concept. A consequence of this is that the metaconcept of existence cannot, obviously, be applied to an empty concept, because such a concept cannot satisfy it, since it is not applicable to any object. That is why ‘There are unicorns’ is a false sentence: the first-order concept Unicorn does not satisfy the metaconcept of existence, because under it doesn’t fall any object.
   Based on these considerations, it is possible to rebut an objection that the proponents of the idea that existence is a property of things would easily arise, namely, that if existence is a property of concepts, then it has no more to do with the objects that fall under these concepts, which seems absurd because it leads us to think that existence doesn’t has anything to do with the real things.
   The answer to this objection lies in the consideration of the peculiarity of the conceptual property that we call existence. We not only can say that the concepts have the property of being applicable to objects, but also that the objects have the property of having concepts applicable to it. That is, when we say that an object exists, we also mean that the considered object has the property of having a conceptual rule applicable to it, and this property is also a property of the objects, even if secondary, which we could call its property of existence. Thus, the red of this couch only exists insofar as that object (the couch) has the property of falling under the concept of being red, according to Frege. But we can more satisfactorily say that the redness of this coach exists only to the extent that the rule of constitutive characterization of the concept of being red has the property of being effectively applicable to the s-property of this couch of being red; but this also means that the s-property of the couch of being red owns secondarily the property that the metarule applicable to its concept applies itself to the concept that applies to the s-property, so that the metarule applies secondarily to the s-property too. It is a peculiar feature of the concept of existence (and certainly to others) that, being owned by a first-order concept, it must also be owned by things belonging to the real world, though not being  a constitutive part of the object. Summarizing, if the existence of the s-property P is the conceptual rule CR (which constitutes its concept), which has the property A of being definitelly applicable to P, then the s-property P has also the property that the conceptual rule CR is applicable to itself.
   The idea that existence is a property of concepts concerns not only general terms, but also singular terms, since both express senses. Consider the case of proper names. As we have seen, they should have senses in the form of identifying rules. As the effective applicability of a cognitive-semantic rule, the existence of the object referred to by the name needs to be the applicability of its identifying rule.
   Although this issue cannot be properly addressed without a deeper inquisition on the nature of proper names,[22] we can give a suggestive defense of the foregoing idea by transforming the proper names in predicative expressions applied to one only particular: it will show that the senses of the proper names themselves can be reduced to conceptual senses of predicates. A first way to attempt this is to transform the proper name into a predicate. Thus, ‘Socrates’ in ‘Socrates exists’ can be predicated in the sentence ‘There is something that socratizes’, or ‘Ǝx(x socratizes)’, as W. V-O Quine has suggested. This is linguistically bizarre, as well as inappropriate, since it leaves open the possibility that there is more than one Socrates.
   Despite this, ‘Ǝx(x socratizes)’ points into the right direction by suggesting that the existence of the bearer of the name itself is referred to by conceptual senses of predicative terms, as the verb ‘socratize’ can be seen as an abbreviation of predicates that attend those descriptions resumed by the proper name ‘Socrates’, following the fregean suggestion, is short. To illustrate we can assume that the sentence ‘Ǝx(x socratizes)’ would be an abbreviation of what could be more extensivelly exposed as as:

Ǝx(x is the inventor of maieutics, x was the master of Plato... x was Xanthippe's husband).

   Of course, this is still insuficient, since it is lets open the possibility that these predicates could be applied to many objects and not only to Socrates. However, this can be easily remediated by means of the russellian device of restricting the number of objects of predication to one and nothing more than one:

Ǝx (x was inventor of maieutics and exactly one x was the inventor of maieutics, x was master of Plato and exactly one x was teacher of Plato… x was husband of Xanthippe and exactly one x was Xanthippe’s husband).

   Symbolizing the predicates ‘inventor of maieutics’ by P1, ‘Plato’s master’ for P2, and ‘husband of Xanthippe’ by Pn, and replacing the commas for disjunctions, the sentence above can be symbolically formulated as follows:

Ǝx (P1x ˅ P2x ... ˅ Pnx) & (y) ((P1y → (y = x)) & (P2y → (y = x)) ... & (Pnx → (y = x)))

   It is important to note that the meaning of the proper name is translated into conceptual-senses of predicative expressions as P1, P2 and Pn that in our analysis are nothing more than conceptual rules expressed by predicates, which are shown as applying to a single thing and the same thing. So analysed, the attribution of existence by a proper name in predicative position is msde by saying that its sense, its identifying rule, effectively applies. As this rule for the identification of the name was here analysed in terms of a set of rules for the characterization of predicates that must be applied to an individual, the existence of the bearer of the proper name becomes the effective applicability of rules of characterization of predicates to a same and unique individual. (I will pass here Russell’s criticism to the concept of meaning in Frege: until the point we have arrived Fregean senses and Russel’s descriptions remain compatible. Later we will return to this point).
   Of course, here some would object that all these descriptivist attempts to explain the meaning of the name are doomed to failure, because they amount to some version of the theory of aggregate, whith its well known difficulties already pointed by Kripke, Donnellan, Devitt and others. However, it should be pointed out that, unlike a current bias, these objections have few effect against more sophisticated versions of the descriptivist theories, having been most of them already answered by J.R. Searle.[23] In other words, the theory of the aggregate may not convince, but has not been refuted.[24] Moreover, even the analysis presented above is a simplification, since I have developed a more elaborate version of the theory of aggregate, which has (in my humble opinion) a greater explanatory power than any previous theory, allowing more complete answers to known counterexamples, although it cannot be exposed here demands a more sophisticated formal analysis than the proposed here.[25] (Although I cannot return to my theory in the present book, I present a summary of it in the Appendix I.)
   The great advantage of the way of conceiving the existence proposed by Frege it that we do not find problems with the denial of existence. Suppose that existence were a first order property of the object. In this case, in a sentence like ‘Vulcan does not exist’, the negation of the existence should be applied to the object itself, and we would have first to identify the object, in order to deny that it owns the property of existence. But since in order to identify the object we need to admit that it exists, we would fall into contradiction. That is, we would have to admit the existence of Vulcan in order to deny its existence. However, in our understanding of Frege’s discovery this is not necessary, because all that we do by denying the existence of Vulcan is to admit that the sense-concept expressed by the proper name ‘Vulcan’ does not fall within the concept of existence, since the rule of application hasn’t the property of being effectively applicable. Substituting the name ‘Vulcan’ by the predicate ‘vulcanizes’, the sentence vulcanizes is formally rendered as ‘~Ǝx (x vulcanizes)’, according to which the meaning of the name itself is the sense of a predicate – the sense of a conceptual rule of application.
   We have seen that this formulation is incorrect because the individual isn’t the bearer of the name as being one and the same. Thus, it is better to say that the meaning of the name can be expressed by defined descriptions, by conceptual rules expressed by them when they are transformed into predicates in a ‘russellian’ analysis. Thus, in the analysis suggested ‘Vulcan’ is a shorthand way of saying (to illustrate): ‘~  Ǝ x ((x is the planet that orbits between mercury and the Sun) & (y) (if y is a planet that orbits between mercury and the Sun, then y = x).’ What falls under the scope of ‘~Ǝ x’ here is the expression of the identification rule name, which consists of rules for characterization of predicates that must be applied to one and the same thing. What ‘~Ǝx’ does is just denying the effective applicability of this rule.
   The understanding of existence as the effective applicability of conceptual rules allows us to explain the nearly ilimited extensions in the application of this concept. Why, though the existence is primarily attributed to properties and objects from the outside world or psychological states, we can still say that imaginary objects exist. Some believe that even contradictory objects exist. We can somehow say even that everything exists, for there is nothing that does not exist. And even the very existence can be said that it exists. How is this possible?
   Well, beginning with the existence of imaginary objects: surelly, we can say that imaginary things – as imaginary things, of course – exist. This is no problem for the proposed view. For it is obvious that our conceptual-cognitive rules can also apply, partially or completely, only in the imagination – an unnefetive, ‘als ob’ aplication. If I imagine Vulcan orbiting the Sun, I apply the identification rule for that proper name in my imagination (even if in a vague and precarious way), but a scintist like Le Verrier hat den regel in ‘als ob’ mathematisch applied and concluded that Vulcan should be 21 million km distant from the Sun. Consider another, rather different example: Alice from the story The Wizard of Oz does not exist in the real world; but she exists in the small fictional world built in this story. She exists because we have a rule for her identification in this fictional world, which demonstrates itself appropriate, fulfilled, satisfied, applicable within that domain. Indeed, Alice is the subject of application of conceptual predicates such as the eight-year-old girl, who has a cat, who finds three friends, whose house was taken away by a typhoon and so on.
   What about the assignment of existence to contradictions as ‘the round square’? This is not so easy, because we cannot combine the rule of identification of the square with the rule of identification of a round thing, so that both things must be the same and only one. This we cannot do even in imagination. Because of this we must recognize that the round square does not exist: we cannot apply a combination of rules that we are unable to build. Since the characterizing rules of concepts are what makes their cognitive senses, this result agrees with our strongest intuition: contradictions do not exist, since they lack cognitive sense.[26]
   Finally, what about the existence? Can we say that the very existence exists? Surelly, we know that the existence exists in the sense that we know that the applicability of conceptual rules to the most diverse domains is applicable, that is, exist. It in my view exists in the sense that we can build a metameta-rule of existence, whose criterion of application is the effective applicability of meta-conceptual rules of existence. Since these last metarules are effectively applicable (since objects exist), the meta-meta-rule – which demands the applicability of meta-rules to their conceptual rules – also applies. Consequently, it is safe to conclude that the existence itself exists.

Reference of concepts again (a metaphysical excurse)
It is instructive to consider what happens when we compare the famous phenomenalist view from J.S. Mill, according to which ‘matter’ or ‘substance’ is nothing more than ‘permanent possibilities of sensation’ with our view of existence in terms of effective applicability of conceptual rules. The results will be no less speculative than Mill’s phenomenalism itself.
   Mill was aware that everything by means of which we gain knowledge about the external world are our own sensations. However, if all that is given to us are sensory phenomena, how to justify our belief in the existence of an outside world, an objective world constituted by substance or matter? Mill’s answer to this question was a development of Berkeley’s unofficial view, according to which things that exist when they are not perceived by us are nothing more than things that we know that they would be perceived by us under adequate circumstances.[27] As Berkeley writes:

The table I write on, I say, exists, that is, I see and feel it; and if I were out of my study I should say it existed – meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it.[28]

   According to this view, esse is not only percipi, but also percipi possi. In a more radical and explicit manner, Mill suggests that matter or substance is not made up of actual sensations, but of groups of permanent (or guaranteed or certified) possibilities of sensation.
   Mill justifies his identification of matter or substance with permanent possibilities of sensation in the following way. First, these possibilities of sensation are conditional certainties: they are not mere epistemic possibilities, but firm conditional expectations that are or could be based on experience. They are permanent because, given the adequate circunstances, they could be always experienced as far as they can be said to exist. And they are guaranteed or certified in the sense that we could form a firm expectation concerning they experience under the right circumstances. This does not mean that the groups of permanent possibilities of sensation would depend, for their existence, of our past experience of them, of our verification, because if it were so they could not exist without us as subjects of knowledge. This is not what Mill means. As he explains:

We mean… something which exists when we are not thinking of it; which existed before we have ever thought of it, and would exist if we were annihilated; and further that exist things that we never saw, touch or otherwise perceive, and things which never have been perceived by man.[29]

Thus, the permanent possibilities of sensations would exist even if beings able to perceive then never have been existed. However, we can acquire knowledge of them by having actually had sensations that were associated with others by repetition building groups of possible sensations, which we expect to be repeated when adequate circumstances are given to us.
   These permanent possibilities are for Mill objective, differing from our actual passing sensations, which are subjective. They are grounded in our common public world, what means that we can intersubjectivelly agree that these possiblities exist. Even if different persons cannot have access to the same sensation, they can have access to the same possibilities of sensation. As he writes:

The permanent possibilities are common to us and to our fellow creatures, the actual sensations are not… The world of possible sensations succeeding one another according to laws is as much in other beings as it is in me; it has therefore an existence outside me; it is an external world.[30]

This is in summary the deeply suggestive but controversial view of matter suggested by Mill.
   In my view there is clearly at least one important confusion that can be made clear when we compare with Mill’s view with Berkeley’s remarks. According to the berkeleyan non-official view, the outside world is constituted of sensations whose experience, if not present, is continually (permanently) as possible, even if not present. But if it is so, the material objects constituting the external world cannot be reduced to simple ‘groups of permanent possibilities of sensation’, since the possibility as such, permanent or not, is unique: it is always one and the same, while the things that constitute the external world are multiple and varied. The correct way to express the berkeleyan insight in Mill’s terms would be that the material objects are nothing more than groups of sensations whose effective experience is permanently possible. Indeed, this would satisfy the required multiplicity. But if the permanent possibility is not the object what is it?
   The answer emerges when we consider Mill’s view under the light of our reconstruction of the concept of existence in Frege, according to which existence is the effective applicability of a concept. If it is so, why the effective possibility of sensations would not be approximated to existence? Why could we not say that the expression ‘groups of effectively experienciable sensations’ means something like ‘groups of existing sensations?
   More precisely: According to our reconstruction of Frege, existence is the effective applicability of a conceptual rule. But what is the form of a conceptual rule? It is a cognitive rule, a rule that brings us to some cognition under the satisfaction of criterial configurations generated by the rule instantiated in it. For example, to be applied to a real object the conceptual rule for the concept chair demands as criterial configuration the satisfaction of the conditions that what is observed is a seat with a back made for only one person to seat on. Surelly, these criterial configurations are variable but they end up always in the requirement of sensations, like the sensation of colours or hardness. Now, the requirement that the conceptual rule should be effectivaly applicable implies the effective possibility that a multiplicity of criterial configurations as groups of sensations are given to experience. And this means that the effective possibility of having groups of sensations implies the existence of the object, since it implies the effective applicatility of the conceptual rule. In other words: if to say that a material object exist is to say that the characterization rule of its concept is effectively applicable, then to say that it exists is also to say that the sensory configurations that we have when we experience the object are guaranteed as effectively, permanently actualisable, whenever the appropriate conditions for its experience are given.
   Now, Mill’s insights can help us to expand our reconstruction of the concept of existence in Frege. An empirical object exists not only when its conceptual rule is effectivelly applicable, but also when sensory criteria for the application of this rule are in some way objectivelly given, that is, when they are intersubjectivelly acessible through more or less direct sensory experience, when they are independent of will, and when they follow causal rules regarded as typical of objects of the external world.
   There is, however, an important and in seemingly fatal objection to Mill’s view, which is reforced by the reparations we have made. It is that sensations or the sensory criteria that satisfy a conceptual rule are by definition psychological. Even the sensations that are effectively possible must be psychological. This means that if we follow this path we fall into some kind of idealism in which we have no objectivity to contrast with our subjective world of sensations or sensory criteria. It is true that they are given independently from us, that they follow regularities of nature, that they are intersubjectively accessible as something that has their experienciability warranted, but they remain nonetheless, as sensations, in the subjective side of the experience. An answer to this objection will only be given in the next chapter, when we will discuss the correspondence theory of truth.


The reference of the sentence as its truth-value
Now we come to the reference of the sentence (Satz) on Frege. He understands it as being that which remains the same when we change the senses of the components of the sentence without affecting their references. This happens when we replace ‘The evening star is illuminated by the Sun’ with ‘The morning star is illuminated by the Sun’. Here the references of the sentence-components do not change. Hence, the reference of the sense must also do not change. But what hasn’t changed? Frege’s reply is: the truth-value. Both sentences remain true. Indeed, the search of truth is what brings us from the sense to the reference, he notes. From this he concludes that in extensional languages the reference of sentences is their true-value. All true sentences have only one reference, which is for Frege the abstract object the True (das Wahre), while all false sentences have only one reference, which is the abstract object the False (das Falsche). Interpreters have noticed that the truth-value is decisive importance (Bedeutung) for the logic, because it is what must be preserved in valid arguments; the logician does not needs to know more than this about the referring function of the sentences he is dealing with.
   Nonetheless, in spite of any theoretical advantage that this suggestion can provide to the logician, it remains oddly implausible. To refute the acusation of oddness, Alonzo Church has shown that we can by means of intersubstitutivity create arguments from which it results that the most different sentences have the same reference. I will consider one of them:[31]

1.     The USA is the country with with worlds leading economy.
2.     The USA is the Nation comprising 50 states.
3.     The number of states that comprises USA is 50
4.     50 is the atomic number of tim (So).

   At first view seems that the five sentences have the same reference. Consequently, the reference of these so different sentences should be their truth value True. However, the argument let to be convincing when we consider that the first two sentences seems to refer to USA, while the fourth and fifth sentences seems to refer to the number 50. The sentences 2 and 3 seems to be replaceble, but they aren’t. For the sentence 2 refers to the property of USA of having 50 states, while the sentence 3 refers to the property of the number 50 of being the number of states that comprises USA. Formaly formulated, calling ‘The USA’ = b, ‘is (is the same as)’ = S, and ‘the nation constraining 50 states’ = n, the sentence 2 can be rendered as bSn; and calling ‘…is 50’ = ‘F’ (where we have an ‘is’ of predication), and ‘the number of states of USA’ = a, the sentence 3 can be rendered as Fa. However, there is no way to replace the relation of identity aSn with the predicative sentence Fa. The whole argument is based on the illusion that the ‘is’ of the sentence 3 is also an is of identity.
   After we have debunking Church’s argument, there are an amount of embaracing objections. A fisrt one is that there are substitutibility problems with Frege’s view on the reference of sentences. If all true sentences refer to an object called ‘the Truth’, the name ‘the Truth’ also refers to the Truth. If it is so, then in the conditional sentence ‘If it rains, than water falls from the sky’, we can replace ‘it rains’ by ‘the True’, getting the sentence ‘If the Truth, than water falls from the sky’, which should be true, though it is in fact uninteligible.[32] Moreover, runing against any healthy intuition, Frege’s proposal contradicts the meaning we give to the word ‘reference’. We would say that the sentence ‘Napoleon was born in Corsica’ has a reference, while the sentence ‘2 + 2 = 4’ refers to something very different, even if both are true. One could argue that science has discovered unexpected things, for example, that plants take their energy from the Sun and not from the soil… Why would Frege haven’t discovered something unexpected regarding the nature of reference? Indeed, empirical science can discover something unexpected about the intimate nature of things. But it would be ridiculous to conclude that Frege is discovering something about the intimate nature of the object of linguistic conventions that have been always with us. What he is doing is to use the word ‘reference’ in an ungrammatically new and equivocal sense. In addition, it should be expected that the reference of the components of our sentences should belong to the same ontological domain of their references. But this is not the case: the reference of the name ‘Napoleon’ is the Napoleon of flesh and blood, while the reference of the sentence ‘Napoleon was born in Corsica’ must be the abstract thing called the Truth. Finally, even from the perspective of the Fregean semantics, his solution sounds false because it violates a principle of compositionality, whereby the whole depends on the parts, so that a change in the part produces a change in the whole. If the reference of the sentence is its truth-value, it cannot be established by its parts, since the true-value is a simple object. The components of the sentence, however, have their own references, which vary enormously.

The reference of the sentence as a fact
The Fregean accout of the reference of sentences turns to be still less acceptable when we consider that there is a much more natural alternative at hand, which, as Anthony Kenny noted, was not even mentioned by Frege.[33] We can, as Wittgenstein, Russell and others did, suppose that the reference of a sentence may be understood as a fact, generally understood as a combination of elements given in the world. Facts would satisfy the Fregean condition that the referent of a sentence is an object: they are independent, complete, closed. Moreover, facts would satisfy the principle of compositionality: they could vary without limit according to the unlimited possible variations in the senses of the component parts of the sentences and, consequently, with the unlimited possible variations in the senses of different whole sentences.
   If we assume this answer, many questions arise. The first is the following: how to establish what fact the thought expressed by a sentence refer to? Consider the following sentences:

1.     The morning star is the morning star.
2.     The morning star is the evening star.
3.     The morning star is Venus.
4.     Venus is the second planet orbiting the sun.
5.     The morning star is the most briliant planet visible in the sky.

Since all components of these sentences have the same reference, these sentences should also have all the same references, just changing their ways of representation, dependent on the varying senses of their components. This shows us that the fact, understood as the Fregean reference of the sentence, cannot be what is immediately considered when we use the word ‘fact’ in the introduction of these sentences after a that-clause in the indirect speech. For example, when I say ‘It’s a fact that Venus is the morning star’, I'm considering a reference other than the one that I believe when I say ‘It is a fact that Venus is the second planet orbiting the Sun’, because the fact that Venus is the morning star is obviously not the same as this planet orbiting the Sun.  We conclude that the facts immediately set out by the sentences (1) to (5) cannot be the fact-reference, if we wish to preserve a Fregean way of identifying facts. We are looking for what we could call the grounding fact ultimately responsible for the truth-value of these five sentences and distinguishing it from mere perspectival facts.
   The question is: is there a privileged grounding fact able to be described that can be identified as the same truth-maker of all the identity sentences about the planet Venus, incluseve the five stated above? My suggestion is that this task can be accomplished by sentences of identity between proper names. Assuming for the sake of argument that the fundamental intuition view of proper names as abbreviations of aggregates of descriptions, first suggested by Frege, is correct, then the proper name ‘Venus’ shortens in its content all known modes of presentation of this word. This means descriptions such as ‘the morning star’, ‘the evening star’, ‘the second planet orbiting the Sun’, etc. Well, in that case there is a sentence that could describe the grounding fact, which is the ultimate truth-maker of any identity sentence concerning the planet Venus, including the sentences (1) to (5) above. Here is it:

1.      Venus is (the same as) Venus.

This sentence would be able to refer to the single grounding fact, which considered in its entirety, is able to work as truth maker to any identity sentences of the kind. Indeed, if the proper name ‘Venus’ is understod as an abbreviation of the descriptions that uniquely identify our object, then this proper name shortens the descriptions ‘the morning star’, ‘the evening star’, ‘the second planet orbiting the Sun’, etc. Well, in this case under the right circumstances the sentence ‘Venus is Venus’ is able to imply the sentence (3) ‘The morning star is Venus’ by replacing the first occurrence of the name ‘Venus’ with the description ‘the morning star’, and so with all other co-referencial identity sentences above.
   What I am considering can be more clearly expressed by numerical identities like the following ones:

1.     2 + 2 = 2 + 2
2.     2 + 2 = 1 + 1 + 1 + 1
3.     2 + 2 = 4
4.     4  = √16
5.     2 + 2 = (14 – 6) / 2

   Of course, the identity sentence expressing the grounding fact would be here:

6.      ‘4 = 4’

   But could the sub-fact expressed by the sentence (5) be derived from (6)? In this case the answer is surelly ‘yes’, because I made it as I wrote the five sentences above.
   But this is not so easy when we consider contingent facts, like the fact that Venus is the brightest planet in the sky (it could be not).
   Moreover, one could object that a sentence like ‘Venus is Venus’ is a tautology, which does not demand verification. ‘Venus is the same as Venus’ is a necessary truth. How could a necessary truth originate contingent truths like ‘Venus is the most briliant planet visible in the sky’?
   My only answer for both objections is that at least for someone who knows all facts about Venus, the fact expressed by the sentence ‘Venus is Venus’ must imply that Venus is the brightest planet in the sky.

The ontological status of the facts
If we accept that the reference of sentences and of sentence-meanings are facts, we also have to answer the well-known controversy between those who think that empirical facts are objective entities that may exist in the external world and those who, like Frege, who believed that the a would be an abstract entity, nothing more than a true thought.[34] In an influential article P. F. Strawson suggested that empirical facts – which certainly must include observational facts – are mere ‘pseudo-material correlates’ and not something in the world.[35] His most incisive argument is that the empirical facts are not spatio-temporally localizable, differently from the events. Thus, to give a classic example, the event of crossing the Rubicon by Cesar occurred in the year 47 BC, but that fact that he crossed the Rubicon did not occur in the year 47 BC, because facts simply do not occur.
   However, this argument is at least controversial. An easy way to get around it was proposed by John Searle. For him we need a word to describe the thing in the world that makes our thoughts true. The word fact is at hand. So, why not to use it estipulativelly in order to designate the truth-maker, whatever it is?[36]
   However, it seems clear to me that even this way out is unnecessary, and that it is at least curious that the postumously published arguments of J.L. Austin against Strawson’s view have been so little regarded.[37] To begin with, I’m of course not saying that everything we call ‘fact’ is objectively real. We can say that it is a fact that the Sun is not green, but that’s not exactly a State of affairs effectively given in the world. What I want to suggest is that the so-called empirical facts, particularly the so-called observational facts, should be considered objectively real. And I believe that I have the key-argument to regenerate the idea that the empirical facts are correlates of true thoughts, so that the empirical facts that we represent through affirmative sentences may be combinations of elements in the external world or in the world (external and/or internal) in general (supposedly, of more or less complex s-properties designated by predicates andqor relations and combinations of s-properties referred by proper names). This would be the case of facts as simple as those referred by the sentence ‘Frege used a beard’ or ‘The book is on the table’.
   My key-argument against Strawson’s opposition between non spatio-temporal facts and spatio-temporal events is that it is confused. It treats facts as if they were on the same level as the events. But this is incorrect because the word ‘fact’ is an umbrella term that encompasses events. In other words, events are sub-types of facts, that is, the word ‘event’ is an hyponimous of the word ‘facts’. To make this clear I suggest that facts are combinations of elements and that there are two great sub-classes of facts:

1.     STATIC FACTS: Can be formal or structural, but can be also, when located in space and time. The relationships between the elements constitutive of a fact do not change during the time of its existence. They are usually called ‘situations’, ‘circumstances’, ‘states of affairs, etc.
2.     DYNAMIC FACTS: Are always empirical. The relationships between the elements constitutive of them change during the time of its existence, so that they have a beginning, suffer some kind of development, and have an end. They are called ‘events’, ‘occurrences’, ‘processes’, etc.

Formal facts, like the fact that 7 × 5 = 12, are static, since they are beyond spatio-temporality. They are not our major concern here. Many facts are empirical and static, since the relationships between the elements constitutive of them do not change during their existence. This kind of statical facts are usually called ‘situations’, ‘circumstances’, ‘states of affairs’… with different nuances of meaning. For example, the situation that I am laying in the bed, the circumstance that Frege used beard, the states of affairs that Venice is a city crossed with channels and that the earth orbits the sun (which is an static fact, since the relationship of spinning around the sun remains the same – there are changes, but they repeat themselves ever and ever during the time of its existence...). The dynamic facts, on the other hand, are defined by irrevocable changes in the relations between their elements in the time of their existence. They are usually called events and occurences, when their duration is shorter, processes, when their duration is longer. Examples of events are a blitz in the dark clouds, the explosion of a bomb. Examples of occurences are the eruption of a Vulcan, the World War I and the slow process of global warming. We can predict the stages of many events and processes, though many are also unpredictable. All these things, however, are obviously facts, they are dynamic empirical facts. They can be called not only events, occurrences, processes, but also facts, since they are facts of a dynamic kind.
   We are now able to find the real reason why we can use that-clause regarding facts but not regarding events. When we speak of dynamic facts, we do not use a that-clause. So, we can speak about the event of the crossing of the Rubicon by Caesar, but not about the event that he crossed the Rubicon, about the process of climatic change but not about the process that the clima changed… The same isn’t the case regarding static facts, which can be referred by means of that-clause or not, indifferently. Thus, the that-clause is used to emphazise static facts. And since the hyperonimic term ‘fact’ can be applied to both, static and dynamic facts, it inherits the property of being used indifferently, with or without the that-clause: you can say ‘It is a fact that the Vesuv is near to Neaple’ (referring to a state of affairs) as much as ‘It is a fact that the Vesuv has erupted’ (referring to an event).
   Crossing the Rubicon by Caesar is in turn a special case. This is a very misleading expression: it is usually understood not as the description of an event, but as an illustrative way of referring to a social, static fact: the state of affairs established by the entrance to the army of Cesar in the Italian territory, violating the law that prohibited this action and forcing the Roman State to declare war against him. Rarely crossing the Rubicon will be understood in the literal sense, as the physical event of crossing the river, which comprises the Caesar locations in relation to the Rubicon from t1 to tn.
   Due to the nature of the dynamic facts like events and processes, we say that they not only are, but also occur in time, while of the static facts we say only that they are in time, while they exist. It seems, therefore, that because philosophers such as Strawson have not realized that events are subspecies of facts, realizing only that from events we may say that they occur in time, they hastily concluded that only events are in time, opposing them the timeless facts. But that this isn’t true can be shown even by intersubstitutivity salva veritate: it is not incorrect to say that the event, the occurrence of the crossing of the Rubicon by Cesar was a fact and that this fact occurred in 47 BC, as a dynamic concrete fact. On the other hand, the social state of affairs established by the crossing of the river was far more durable, because it was a static fact, the social situation that produced, as is well known, the fall of the Republic. However, it seems clear that the state of affairs instarred by the crossing of Rubicon was spatially circunscribed to the Roman Empire and to the time of Julius Caesar’s life.
   Because of its scope, the fact remains the ideal candidate for the role of truth-maker within the scope of the correspondencial theory of truth. In this case the fact given in the world will be seen as being composed of a static or of a dynamic configuration of elements, which can match the configuration of criteriais elements (properties or systems of s-properties) demanded by the verification rule, as it is conceived by the epistemic subject. And it doesn't seem implausible the suggestion that the match depends on finding some kind of structural isomorphism between criterial configurations designed and demanded by the rule, on one side, and the configurations of elements (combinations of s-properties) constituting or indicating the fact in the world, on the other.
   This suggestion, as others here presented, is such that it could be erected a wall of pigmean arguments against it, which could not be possibly answered in the present text. However, since what I am saying is intuitivelly plausible and since in philosophy there is no anounced truth, it is my right to continue.

Sense of sentences: the thought
Now it is time to come to the sense of the sentence. Here Frege scorred a penalty! He was lucky in suggesting that the meaning of the whole sentence is the thought (Gedanke) expressed by it. He came to this result by applying his principle of compositionality, whereby the meaning of a complex expression is formed by the senses of its component expressions combined in a certain way. If, for example, in the sentence ‘The morning star is a planet’ we substitute the expression ‘the morning star’ for ‘the evening star’, which is co-referencial, though having a different sense, the reference of the sentence cannot change; but the sense of the sentence must change. And indeed, the sense of the sentence ‘The evening star is a planet’ is a different one. Now, considering that with the the change in the meaning we have a changed what we have thought, Frege concluded very consistently that the thought expressed by the sentence must be its sense.
   The word ‘thought’ is ambiguous. It can be used to describe a process of psychological thinking, as in the utterance ‘I was just thinking of you!’ But it also seems to designate something that is independent of specific mental occurrences, a content of thought, as expressed by the utterance: ‘The sentence “12 x 12 = 144” expresses a true thought’. Frege had the last meaning of the word ‘thought’ in mind. In this sense the word means simply what the sentence says and, according to Frege, is unchangeable and eternal (in the sense of not being in space and time). And it is relevant, because the word ‘thought’ is the only correspondent in the the natural language to more technical terms like ‘proposition’, ‘propositional content’ and ‘informative content’.[38]
   For Frege, everything that contributes to determining the truth-value of the sentence should belong to its thought. Thus, in Frege’s example, the sentences ‘Alfred hasn’t arrived’ and ‘Alfred hasn’t arrived yet’, express the same thought, for the word ‘yet’ expresses only an expectation regarding the arrival of Alfredo, not contributing to its truth-value.[39]  On the other hand, the sentences ‘The morning star is Venus’ and ‘The evening star is Venus’ can be counted as expressing different thoughts: the singular terms that make up these two identity sentences refer all to the same planet, but through different modes of presentation, that is, following different paths through the determination of their truth-value, or, we could finally say, by different combinations of identification rules producing verificacional procedures that are correspondingly different.

The thought as the truth-bearer
Another quite plausible Fregean thesis is that the bearer of the truth is not the sentence, but the thought expressed by it. Although we can say that sentences, beliefs and even things and persons are true, they are true in a derivated sense. Acording to this reasoning, when we say that a diamond is true, what we mean is only that it is authentic, when we say that Socrates was true, what we mean is only that he usually told the true, and when we say that a sentence is true this is only a queer way to say that the thought it expresses is true. The reason for preferring to say that the thought and not the sentence is the truth-bearer is that the trut-bearer must be something able to retain the same truth-value while it is what it is. What is true (or false) must be always true (or false), and only the thought, being unchangeable and eternal, has the required stability. Indeed, identical sentences can express different thoughts and in this case they can bear different truth values… This is the case of indexical sentences like ‘I am in pain’, which express different thoughts according with the speaker. These sentences can vary their truth-value. But the thought expressed by them remains with the same truth-value, and the explanation for this is that the truth-bearer is the thought and not the sentence. On the other hand, different sentences can express the same thought, as ‘Il pleut’ and ‘Es regnet’, when uttered in the same context. Their truth-value will remain the same, and the only explanation is that the thought, the truth-bearer, remains the same. In other words, the thought and the truth-values have a relationship of co-variance that is missing in the relationship between sentences and truth-values, which leads us to the conclusion that the proper bearer of truth must be the thought and not the sentence, which is said to be true or false only in a secondary and dependent sense.
   Frege also suggested that what we call fact is the true thought, because when the scientist discovers a true thought he says to have discovered a fact.[40] But this conclusion is not compulsory, for the scientist can also say the same thing – and with more property – understanding by fact what corresponds to the true thought, namely, some combination of elements in the world. After all, it is natural to think that if someone discovers the true thought, it is because a fortiori he discovered the fact corresponding to it.
   The reason why Frege thought that the fact is the true thought is, indeed, that he advocated a conception of truth as redundancy. However, the most natural and plausible conception of truth remains the correspondencial one, suggesting that facts are complexes of elements in the world, able to be at least somehow isomorphically represented by their thoughts, which, when it happens, are called true. The view of truth as correspondence is in conformity with my commonsensical methodological point of departure and I will struggle to hold it.[41]

The thought as a verifying rule
In line with my reconstruction, thoughts, being senses, shuld also be parafrased in terms of semantic rules. If the sense of the constituents of a sentence are rules, then the sense of the sentence should be a combination of these rules, as suggested by their syntactic dependence. But if the thought is a combination of rules, then what results from such combination must also have the character of a rule, even if it is not a conventionalized rule. This means that the thought is also a rule, a cognitive rule, since its function is to make us aware of a fact. And if the thought is the bearer of the truth-value, this also means that the cognitive rule that constitutes the thought is the bearer of the truth-value, which is a property of this cognitive rule or rule-combination.
   But what makes this sense-thought-rule true? The correspondentialist answer is that it is the fact that satisfies conditions given by the rule. Moreover, it is the fact an existing thing, not only as an imagined or conceived thing. But what is the existence of the fact? We can get an answer reflecting about what we said about the existence of the references of general and singular terms. Since the existence of the object or of the properties of objects designated by the conceptual rules must be, as we saw, the effective applicatility of these conceptual rules, the existence of the fact designated by the thought must be the effective applicability of the thought, rightly understood as the verifiability rule of the sentence. Consequently, the existence of the fact referred by the thought must be nothing more than the effective applicability of the verifiability rule constitutive of the thought.
   Moreover, the sense-thought-rule expressed by the declarative sentence will be true if this rule is effectively applicable to the fact and false if this rule isn’t effectively applicable to the fact. If the sentence does not have a sense-thought-rule that can be at least in principle effectively applicable to any fact, that is, whose application is neither imaginable nor conceivable, then this sentence will by definition be devoid of meaning.
   We find here a path to the famous principle of verifiability. This principle was suggested for the first time by Wittgenstein to the members of the Vienna Circle, who have attempted to precise it in order to make it useful to their own anti-metaphysical, scientist and apressados precisionist purposes. Their failure to achieve this made them to believe that the principle was wrong. However, why not to conclude that this failure was caused by a misleading treatment given to the principle? Philosophical ideas can be extrem complex and difficult to be developed, and it is too easy to conclude, after some attempts, that they are in some way unsolvable or simply wrong. In regard of this, I prefer to attain myself to the rough but intuitivelly irreprochable formulation of Wittgenstein, according to which the (cognitive, informative) sense of a sentence is its method (rule, combination of rules) of verification, and consider speculatively the conclusions lead us by this acceptance. If we assume that the sense of a sentence (as its cognitive or informative content) is its rule of verification, and we agree that this sense is the thought expressed by it, we conclude that the thought is nothing less than the rule of verification of the sentence. As the thought must be a combination of cognitive-semantic rules, this must be the case regarding the rule of verification, which in the case of a singular predicative sentence must be a combination of the the identification rule of the singular term (its sense) with the rule of characterization of the predicative expression (the sense of the predicate).
   The proposed identity between the Fregean concept of thought and the concept of a verifying rule is supported by the fregean suggestion that the criterion to the identication of what belongs to thought is to have any role in the establishment of its truth. That is, the thought that the sentence expresses is the same as the cognitive significance, to be identified by the verificacionist with the rule (procedure, method) that allows the recognition of the truth-value true of the sense-thought-rule when it is shown to be effectively applicable to the corresponding fact and to the truth-value false of the sense-thought-rule when it is show not to be effectively applicable to the corresponding fact.[42]
   Let us return now to the relationship between thought and truth-value. If the thought is the bearer of truth, and it is the verifiability rule of a sentence, then this verifiability rule is the bearer of truth (not in specific cases of its application, obviously, but in itself). And since what makes the thought true (assuming the correspondencial theory) is its correspondence with the fact, what makes the verifiability rule true must be match between criterial configurations demanded by this rule with what satisfies or fulfills these configurations, as ways of manifestation of the corresponding fact in the world. But that’s like saying that the verifiability rule is true when it is effectively applicable (i.e. it is proved to be applicable and not only applicable in principle), that is, when criterial configurations whose satisfaction it demands are met. So, the thought is regarded as true when it shows itself to be an effectively applicable verifiability rule; and the thought is regarded as false when it shows itself to be an effectively unaplicable verifiability rule. It is therefore possible to say that the effective (demonstrated, guaranteed, continuous…) applicability of the verifiability rule implies the truth of thought, and, on the other hand, that the effective (demonstrated, guaranteed, continuous) inapplicability of the verifiability rule implies the falsehood of thought.
   It seems also reasonable to think that the combination of elements constitutive of the fact must satisfy the verificacional rule when at least some aspects of it correspond (are isomorphic) to the criterial configurations demanded to the effective application of the verificacional rule. What we call a judgment, in turn, is our acceptance of a thought as true, which contains our recognition of the effective applicability of verificacional rule.
   These conjectural suggestions reveal an unexpected closeness between the concepts of truth and of existence as they were here discussed. As well as the existence of a higher order property is the property of effective applicability of a rule of characterization that constitutes a conceptual content, the existence of a fact is the higher order property of effective applicability of the verifiability rule constitutive of its thought. The truth of the thought, on the other hand, at least for the correspondentialist, is implied by this higher order property of effective aplicability. Truth is the correspondence with the fact derived from the effective applicability of a thought to the fact to which it should be correlated.

Frege’s Platonism
Before we finish it is important to note that for Frege the thoughts (including the senses that compose it) are Platonic entities belonging to a third ontological realm, which is neither psychological nor physical. For him there is first a realm of physical entities, such as the concrete objects, which are objective and real. They are objective in the sense of being intersubjectively accessible and independent of our will; and they are real in the sense of being located in space and time. There is a second realm, of psychological entities, mental states that he calls representations (Vorstellungen). These entities are subjective and real. They are subjective by not being interpersonally accessible and often dependent of the will. However, they are still real, because they are in the heads of those who have them and consequently, we could add, in space and time. There is, finally, a third realm, of thoughts and of their constitutive senses. This realm is objective but not real. It is objective because the thoughts are inter-subjectively accessible; yet it is not real, for the thoughts cannot be find neither in space nor in time.
   Indeed, for Frege thoughts are timeless (eternal), immutable, forever true or false, and not created but discovered (gefassen) by us. The reason he has to introduce this third realm of thoughts is that thoughts are comunicable and, to be comunicable, they need to be objective, that is, interpersonally accessible. Representations are rather subjective psychological states, qualia, which can vary in the dependence of the objects. Thus, for Frege the only way to explain how it is possible that we are able to share a same thought is to distinguish it strictly from mere psychological representations. Without this will be always possible to object that if the thoughts are psychological representations, so that they can vary from person to person. They will be like what Frege has called colorations, such as the feelings that a poem can evoque in different people. In addition, if thoughts were not on the level of representations, they would have the required stability of the truth-bearers.

Avoiding Frege’s Platonism
Despite the arguments above, very few would today accept Frege’s Platonist solution. After all, diverserly from the theory of tropes, it not only commits us with a duplication of the worlds, but seems to lack inteligibility. The price that Frege was willing to pay in order not to fall into psychologist subjectivism seems to us today too high.
   In my view, Frege’s Platonist solution is unecessary simply because the whole problem was wrongly stated. For there is a way to conform the view that the thought has a psychological nature with the required stability of the truth-bearer and the possibility of comunication. In order to show this, I want to apply a strategy inspired by the ontological particularism of the English empiricists from Locke to Hume, for whom the universal does not exist beyond the similarities under mental ideas.[43] In order to do it, I wish to show that the Fregean f-thoughts (atemporal, truth-bearers…) can be defined in terms of psychological f-thoughts (occurrences of thought).  It seems that we can warrant the existence and stability of f-thoughts without hipostasiating them as platonic entities and even without resorting to classes of p-thoughts using the following definition:

A f-thought X (Df) = a given p-thought X instantiated in some mind or any other p-thought Y qualitativelly identical to X, instantiated in the same mind or in any other mind.

   This definition reduces the f-thought to p-thoughts, but without forcing it to lose its stability. The so defined f-thought has no particular espacio-temporal location and can be seen as the truth-bearer. For example: the f-thought expressed in the sentence ‘The Eiffel Tower is made of metal’ can be paraphrased as the p-thought that I have in mind when writing this sentence, but also by, say, the p-thought that you have in mind when you read it, or yet, by any p-thought that we or any other person can have in any other time. Characterized by the disjunction between the same thoughts instantiated in single minds, the f-thought comes to be regarded in abstraction of the particular human minds that instantiate it. With this we avoid not only the appeal to specific occurrences of thoughts, but also the most expected alternative, which would be to explain one f-thought in terms of a class of p-thoughts qualitatively identical to each other, what would leave us to a petition of principle, given that classes are strong candidates to abstract entities.
   Under the proposed definition in order to exist an f-thought must have always some psychological instantiation. The f-thought is no less psychological than any of the p-thoughts, since it cannot be considered in the independence of its instantiation in at least one mind. So, when we say that we both have had the same idea or have reached the same thought, what we mean is only that we have psychological thought-contents which we have instantiated in our minds and which are qualitatively the same. This seems to me the right way to bring the Fregean thoughts from the Platonic to the psychological realm, without a commitment to a transient psychology of particular individuals.
   Indeed, it seems clear that one under the most common philosophical errors consists in making the mistake of seeing numerical identity where there is only qualitative identity (equality). It is true that we can speak of the number 2 in the singular and that we can ask for the meaning of the word ‘shoe’ using the definite article, but this is just for simplicity of expression. What we actually have in mind are instances of qualitatively identical cognitive concepts of number 2 and of qualitatively identical meaning occurrences of the word 'shoe’ and nothing more. In the same way, we can talk about the thought ‘7 + 5 = 12’, but if we are not intending an occurrence of this thought, we are referring to some occurence, without taking into account or specifying which occurrence it is, being this the reason why we speak in the singular of the thought that ‘7 + 5 = 12’, and not of the many thoughts alike that make ‘7 + 5 = 12’.
   The adoption of the definition of f-thoughts (which is easily generalizable to all kinds of Fregean senses) proposed above is the trafegable abstraction that we can arrive without falling into any of the various forms of reification that infested ontology along its history.
   Here arises, however, the following question: how is it possible that the above suggested psychologically dependent definition of f-thought be able to ensure the objectivity of f-thoughts, their intersubjective acess, their comunicability? As we saw, for Frege if thoughts were regarded as psychological representations, as it is the case of p-thoughts, they would be unavoidably subjective, not being able of being compared with each other. Hence, the need that Frege feels to admit that f-thoughts belong to a third realm of platonic entities seems too hasty. There is no doubt that what Frege calls representations, psychological mental contents, can be largely expressed through language and able to be through language subjectively identified and reidentified as being the same. It is true that a mental state that only one person is able of having, for example, some epileptic aura, is not communicable, except indirectly, metaphorically. But it seems that most mental states such as feelings, images, sensations, are things that all of us are able of communicate and learn to identify in ourselves, through induction, by exclusion in some cases, and, in others, through induction by analogy based on interpersonally acessable physical states. It is true that there are important philosophical arguments against this traditional response about our learning of autopsichic and heteropsychic, but this is one of those points which only philosophers would put in question, as in the famous private language argument challenged in the last chapter. As paradoxical arguments, they have an heuristic value, what does not mean that they should discredit reasoning. To do this is like to use the sorites paradox to prove that heaps do not exist. If the whole domain of philosophy is fulled with paradoxes and they are taken too seriously, they break the possibility of systematic philosophy.
   It is also important to note that it is not necessary to have a single model as the object of interpersonal consideration. What we do is simply alternate a variety of models that are usually given to us from memory: first the one and then some other, which we recognize as being identical to the first, and then we can use the second one as the model and so on. Important is to remember that none of these models can exist without being psychologically instantiated. And the language is only the vehicle of communication that allows the reproduction of a qualitatively identical psychological content of thought in the minds of the hearers.
   It may at first sight seem paradoxical that the language is capable of playing in other minds and even in the same mind repeatedly the same subjective model, the same content of thought, the same recognizable instantiation of a combination of conventionally established semantic rules. However, compare this case with the case of genetic information able to reproduce the same in successive biological individuals indefinitely:[44] why the conventions and the ways they can be combined in the constitution of p-thoughts couldn’t do the same? In addition it is easy to suppose that errors could be interpersonally and even intrapersonally corrected. There is no reason, exept an anti-empirist bias, to think that things should not be like that.
   Finally, the distinction made by John Searle between what is ontologically and what is epistemically objective and subjective to the objectivity of f-thoughts.[45] This philosopher noted that we have a strong tendency to take what is epistemically subjective for what is only ontologically subjective. However, one thing can be ontologically objective – for example, the extension of Napoleon’s influence in the European society – without ceasing to be epistemically subjective,  because we are not able to reach a common agreement about it. In contrast, a phenomenon can be ontologically subjective without ceasing to be epistemically objective – for example, the pain in point of knife caused by an acute crisis of pancreatitis – because everyone (doctors and patients) will agree on its form and existence. Something similar can be said about the nature of f-thoughts. They are ontologically subjective, since we admit that they are psychological events instantiated in some mind. But even so, they do not fail to be epistemically objective. After all, we are capable of both intersubjectively admit their existence as much as interpersonally access their true values. Thus, a sentence like ‘Love is the Amen of the universe’ (Novalis), differently from an f-thought, has no truth value. It has only coloration, being liable only to an aesthetic appreciation with some degree of subjectivity. However, a sentence like ‘The Eiffel Tower is made of metal’ expresses an f-thought that we all recognize as being true. This thought, like any other f-thought, is ontologically subjective, since it can be only psychologically instantiated. However, it remains, like any f-thought, epistemologically objective, given that both the thought and its truth-value are fully measurable and reportable, since structured through our conventions and based on our knowledge of the facts.
   Frege was not here an exception: as many others he believed that the ontologically subjective character of the psychologically conceived contents of thought would be inevitably commited with the admission of their epistemic subjectivity. And this was a mistake.

Further ontological consequences
This ultimatelly psychological interpretation of f-thoughts has ontologically interesting consequences. If the thought of the Pytagorean theorem isn’t in any platonic realm, as something eternal (timeless), always true or false, where and when is it? It is not in the individual mind, disappearing with his death. However, being at least one occurrence of thought, or any other similar, the Pythagorean theorem gains one existence that is dependent on minds, but that remains independent of any individual mind of the many who think it. Since this thought was thought by me and certainly also by you and by many others in the past, its existence must be scattered in space and time. This existence is scatered in the space and time occupied by the heads of geometers starting with Pythagoras himself and ending at some person at some unknown future time. However, unlike the platonic entity assumed by Frege, this thought in fact did not exist before Pythagoras has thought it for the first time, and will cease to exist when it ceases to be thought by anyone. If this sounds strange it is because nobody can truly think so. One cannot think: ‘The theorem according to which the squares of the catets equals the square of the hypotenuse is something which existed in the past and now no longer exists’, because this judgment will update the occurrence of the thought of the Pythagorean theorem. Nevertheless, the f-thought of this theorem would not have come into existence if nobody ever thinks it. We can imagine that a world would exist without any thinking being in it and that the Pytagorean theorem would still be true; but it is true in the sense that if a thinking being were there to think it, he or she would think it as true.
   This way of thinking is confirmed by our linguistic intuitions. We speak of f-thoughts. We can say that the Pythagorean theorem certainly exists, has existed and will exist in the sense that it is thought, has been thought and will probably be thought, referring to occurrences of this thought, but without having to take into account who thinks it. But it is not the case that such thought has always existed and will always exist independently of its being thought, as Frege has believed.
   An objection that could be made against the idea that the bearers of truth are non-platonic f-thoughts is the following. Many truths are discovered. Pythagoras discovered the theorem that takes his name; Archimedes was one under the discoverers of the law of lever, according to which magnitudes are in equilibrium at distances reciprocally proportional to their weights. But if something is discovered it existed before being discovered. Consequently, the thoughts that the sum of the squares of the cathets equals the square of the hypotenuse and that the weight that a lever can hold is inversely proportional to the length of its arm already existed before being discovered.
   This objection results from a confusion between the thought as the bearer of truth, on the one hand, and the situation, the state of affairs, the event, the process, namely, the fact, on the other. It seems clear in the case of empirical truths: that the law of lever was always applicable is true... but the thought of that just came into the world as scientists like Archimedes have thought about it. Similarly, the fact expressed by the Pythagorean theorem has always existed, but our f-thought of it only came into existence after the theorem was thought by Pythagoras and since then by many others. Such facts, however, as long-lasting as they may be, are not the bearers of truth, but the makers of truth. They were what occurences of their thought represent, what makes that the truth of their thoughts cannot have existed before them. No truth or falsehood would exist if there were no minds to think about them.
   However, would this mean that before conscious beings appear on Earth wasn’t the thought that the Sun is red true? The answer is yes and not. The thought wasn’t true, since it hasn’t existed. But we can say that it was true that the Sun was red in the sense that if the thought of the Sun being red were thought it would correspond to a fact that would make it true. And this is what we really mean when we say that the Sun would be read if there would have no human being to think it. A thought that has never been thought of does not exist, hence cannot be true. The same with falsities: the thought ‘The Colossus of Rhodes is floating in the Sargasso Sea’ certainly has never been thought of before. But as soon as we think that it has never been thought of we already think it, and we see that it is surelly false. Even the thought ‘The world could exist, even though there were no minds to think about it’, is only true because there are minds to think it. And if the world didn’t have minds to think about it? It would be true that the world exists? Well, why not, since we have just admited it?

Digression on contingent futures
Before we finish, it is curious to examine the Aristotelian problem of contingent futures in the light of these conclusions. It is the thought expressed by the sentence p = ‘There will be a sea battle tomorrow’ true or false? The answer seems to be: this is not a thought because thoughts (f-thoughts) are cognitive contents that follow the principle of excluded middle, that is we must be able to assign a truth-value to it. This, however, does not happen here. The declarative sentence p is unable to express a thought, since it cannot be correlated to truth-makers.
   However, the sentence p is misleading, for it at least seems to express cognitive content. Why this happens? The reason is, in my judgment, that it is very easily confused with the sentence q, ‘It is likely that there will be a sea battle tomorrow’, when there are reasons to think so. For example: having broken the Japanese naval codes and having lured them to an ambush at Midway, the Americans already knew on the night of June 3, 1942, which in June 4 almost surely it would be an intense aeronaval battle. The sentence q is easily confused with p because q appears very frequently abbreviated as q. For example: suppose that the American admiral Nimitz on June 3 have said ‘Tomorrow there will be a naval battle’; everyone would understand that he was saying that all clues lead to the conclusion that the expected battle would probably begin on July 4. This probability, made explicit or not, is here measurable in terms of empirical evidence. And by expressing a measurable probability, q is a verifiable proposition and may be considered in the moment in which it is expressed as a probabilistic thought aquilatable as true or false in the light of empirical evidence. Taken literally, however (and not as an abbreviation of p), the sentence p of Aristotle is a bluff devoid of meaning and justification. All that this sentence does is to induce us to imagine a naval battle taking place tomorrow, giving us the illusion of having verificational criteria. However, since the sentence is spoken today about tomorrow, and tomorrow does not exist, such strong criteria cannot be really given. The sentence q, on its hand, says something probabilistic about tomorrow that can be confirmed by criteria given today, like all the information regarding the embush prepared by the Americans.
   Finally, we should also distinguish the level of thought and the real ontological level assigned to facts. It may be that, because of causal determinism, the state of the present world has today established the occurrence of a naval battle tomorrow. But it would be a mistake to think that this state of affairs undoes the assertive bluff made by the utterance of p, making it the expression of a real thought.

Conclusion 
In this chapter I have used Frege’s theory as a basic structure to be analysed and shown how most fragile points of it can be replaced by alternative views. Though the results are still speculative, they seem to me nonetheless more plausible than Frege’s own suggestions.






[1] On the thorny issue of how to translate ‘Bedeutung’, see Michael Beaney (ed.): The Frege Reader, p. 36 ss.
[2] Ernst Tugendhat: ‘Die Bedeutung des AusdrucksBedeutung“ bei Frege‘, Philosophische Aufsätze, p. 231.
[3] Searching in the literature the only place where I saw this point being noticed was in W. Kneale and M. Kneale’s book, The Development of Logic (Oxford: Oxford University Press, 1985), p. 495.
[4] See the introduction of the distinction in Gottlob Frege, ‘Funktion und Begriff’, p. 14 (original pagination).

[5] Max Textor: Frege on Sense and Reference (London: Routledge, 2010) p. 134.
[6] Michael Dummett, Frege: Philosophy of Language (Harvard: Harvard University Press, 1990), p. 92.

[7] This understanding is mainly due to Michael Dummett. But similar guidelines can be found in authors such as P.F. Strawson and Ernst Tugendhat.
[8] See Edmund Runggaldier‘s comments on the interpretation of Dummett in his book Zeichen und Bezeichnetes: sprachphilosophische Untersuchungen zum Problem der Referenz (Walter de Gruyter, 1985), p. 91 ss.

[9] G. Frege: "Über Sinn und Bedeutung", p. 28, note (original pagination).

[10] See G. Frege: ‘Ausführungen über Sinn und Bedeutung‘, in Hermes, H., Kambartel, F., and Kaulbach, F. (eds.), Nachgelassene Schriften, (Hamburg: Felix Meiner, 1969).

[11] There are, of course, more sophisticated readings of Aristotle. See, for example, Christopher Shields, Aristotle (London: Routledge, 2007).
[12] The theory of tropes was introduced by A.D. Williams in his article ‘The Elements of Being’, 1953, having since then sparked growing interest.
[13] I suggest this trope-model way of construction of the universal in order to circumvent the usual but problematic definition of universal as a set of tropes that are exactly similar one with the other. This definition using set is problematic because a set seems to be a universal and because sets are quantitative: they can be bigger or smaller, can grow or diminish, what isn’t the case of the universal. An additional point is that usually the trope-model needs to be intermediated by memory: we usually don’t bring a physical pattern to compare, but have the memory of one. The memory is not the trope, but is, as all psychological elements, also composed of mental tropes.
[14] Although lacking adequate development, a similar suggestion was made by Paul Simons in ‘Particulars in Particular Clothing: Three Trope Theories of Substance’, pp. 553-575.

[15] Aristotle: Categories, sec. 5.

[16] Ernst Tugendhat used the expression Verwendungsregel (rule of application) to name the rule of designation of the predicate. See E. Tugendhat: Logisch-Semantische Propädeutik, cap. 13.

[17] This dependency that a characterizing rule of a predicative expression has of a prior application of the identifying rule of a singular term was investigated by Ernst Tugendhat in his analysis of the real conditions of a predicative singular statement: ‘‘Fa’ is just the case, to the extent that the rule of identification for ‘a’ is followed and, based on the result ‘F’ is applicable in accordance with its rule of application’. E. Tugendhat: Logisch-Semantische Propedeutik, p. 235.
[18] For a similar view, see Anthony Kenny: Frege: An Introduction to the Founder of Modern Analytic Philosophy  (Oxford: Blackwell Publishers, 1991), pp.122-125
[19] Gottlob Frege: Die Grundlagen der Arithmetik, sec. 53. I will not try to interpret the details of Frege’s view on existence.
[20] Bertrand Russell: ‘The Philosophy of Logical Atomism’, pp. 232, 250-54.This position held by Russell and Frege is disputed by many contemporary philosophers, who prefer to consider the existence as a first order predicate. For what reasons? João Branquinho, for example, suggests that we can only make sense of a sentence like ‘There are things that don’t exist’ if we admit that predicates of existence are of first order, while quantifiers mean only an assignment of ‘being’ in the meinonguian sense. Thus, the above sentence would be symbolizing Ex (~Ex), where E means ‘there is at least one’ (see ‘Existence’, in Enciclopedia de Termos Lógicos e Filosóficos, eds. J. Branquinho, D. wilted, Garcia, (Martins Fontes: São Paulo 2006, p. 300). But the sentence above could also receive a Fregean interpretation. We can translate it as ‘There are things in the mind that do not exist in the external reality’. In this case, being M = ‘... in mind’ and R = ‘external reality’, it seems that we can symbolize ‘There are things that do not exist’ as ‘Ǝx(Mx) & ~Ǝy(Ry)’. This discussion, however, goes beyond the limits of the present text.
[21] I take this example from J.R. Searle: ‘The Unity of Proposition’, p. 176.

[22] A neodescriptivist theory of proper names presenting the structure of the identifying rules of proper names was developed in the chapter 2 of my book, Lines of Thought: Rethinking Philosophical Assumptions (Oxford: Oxford Scholars Publishing, 2014).
[23] See J.R. Searle: Intentionality (Cambridge: Cambridge University Press), cap. 9.
[24] See the balanced assessments of David Braun and Marga Reimer in their respective articles for the Stanford Encyclopedia of Philosophy.
[25] See ‘Outline of a Theory of Proper Names’, in my Lines of Thought: Rethinking Philosophical Assumptions (Cambridge: Cambridge Scholars Publishing, 2014), chap. 2.
[26] However, if the assertion that there are round squares is only an equivocal manner to say that we can combine syntactically adjectives square and round, that is, a way of saying that there is a syntactic rule allowing the mere combination of these adjectives, then it makes some sense to attribute existence here. But in this case what we are trying to say is more correctly expressed by the metalinguistic sentence: The rule to the building of the expression ‘round square’ is applicable, the expression ‘round square’ exists as a grammatical construction’. The Meinongian Sosein seems to reduce itself in the affirmation of this syntactic triviality.

[27] I say unnoficial view because according to his official view things that are not actually perceived by us exist because they are always being perceived by God. See J. G. Urmson: Berkeley (Oxford: Oxford University Press, 1983).
[28] Principles of Human Knowledge, part 1, section 3.
[29] John Stuart Mill: Examination of Sir William Hammilton’s Philosophy, in J. M. Robson (ed.), The Collected Works of John Stuart Mill  IX (Toronto: University of Toronto Press), pp. 178-179
[30] J. S. Mill, Examination of Sir William Hammilton’s Philosophy, Ibid. pp. 181-2.
[31]  I take it from Chris Daily, Philosophy of Language: An Introduction 1596.
[32] See Max Black, ‘Frege on Functions’, in his Problems of Analysis: Philosophical Essays (London: Routledge and Kegan Paul, 1954), pp. 235-6
[33] A. Kenny: Frege: An Introduction to the Founder of Analytic Philosophy, p. 133.
[34] Gottlob Frege: ‘Der Gedanke‘, p. 74 (original pagination).
[35] P. F. Strawson: P. F. Strawson: ‘Truth’, in Logico-Linguistic Papers (London: Methuen 1971). This position was later abandoned by Strawson. See ‘Reply to John Searle’, p. 402 in The Philosophy of P.F. Strawson (New York: Open Court, 1999).
[36] J. R. Searle: ‘Truth: the Reconsideration of Strawson's Views’, in The Philosophy of P.F. Strawson, ibid.
[37] See also J.L. Austin: ‘Unfair to Facts’, in his Philosophical Papers (Oxford: Oxford University Press, 1990).
[38] As Tyler Burge in ‘Sinning against Frege’ wrote, ‘the word “thought” is the best substitute of ‘proposition’ for the naturalness of its semantics within the scope appropriate to the linguistic philosophy’, in T. Burge: Truths, Thoughts, Reason: Essays on Frege, pp. 227-8.
[39] G. Frege: ‘Der Gedanke‘‚ p. 64 (original pagination).
[40] ‘“Facts! Facts! Facts!” exclaims the researcher of nature, when he wants to proclaim the need for a secure basis of science. What is a fact? A fact is a thought that is true.’ Gottlob Frege: ‘Der Gedanke‘, p. 74 (original pagination).
[41] Although the pictorial theory of thought, as presented by Wittgenstein in the Tractatus, is indefensible, his fundamental insight, according to which the representation is not conceivable without some kind of possible structural isomorphism between what representant (the thought) and what it represents (the fact) exemplifies a kind of transcendental argument impossible to circumvent: if we reject any form of isomorphism, then it seems that we are forever unable to explain representation.

[42] See Ludwig Wittgenstein: Wittgenstein's Lectures Cambridge 1932-1935, p. 29.
[43] The basic idea is clearly expressed in the following passage of Berkeley: ‘...an idea, that if considered in itself is private, becomes general by being made to represent or be in the place of all other particular ideas of the same type. (...) a private line becomes general by being made a sign, so that the name line, which considered absolutely is private, to be a sign is made general.’ George Berkeley: Principles of Human Knowledge, introduction, section 12. See the more sophisticated but also more obscure view of David Hume in A Treatise of Human Nature, book I, part 1, section VII.

[44] Their own mutations are accidents whose probability of incidence would be evolutionarily calibrated. Only species whose bodies would be able to mutate in adequate amounts would be able to preserve. A fixed species, no mutations, is something probably possible, but do not have the flexibility necessary for the survival of its members.
[45]  John r. Searle, Mind, Language, and Society, pp. 43-45.