terça-feira, 16 de dezembro de 2014

CLAUDIO COSTA: PHILOSOPHICAL TEXTS



DEAR READER!
THE AIM OF THIS "BLOG" IS TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE TO A WIDE PUBLIC. THERE ARE APPROXIMATELY 80 TEXTS. MANY TEXTS ARE INTRODUCTORY. SOME OF THEM, MARKED WITH "#", CAN BE OF INTEREST FOR THE PHILOSOPHICAL RESEARCH . ANYWAY, MOST TEXTS ARE ONLY MORE OR LESS DEVELOPED DRAFTS.

PREZADO LEITOR!
 O OBJETIVO DESSE "BLOG" É TORNAR MEU TRABALHO EM FILOSOFIA ACESSÍVEL A UM PÚBLICO MAIS AMPLO. MUITOS TEXTOS SÃO INTRODUTÓRIOS. OS TEXTOS MARCADOS COM "#" SÃO DE INTERESSE PARA A PESQUISA. A MAIORIA DOS TEXTOS SÃO ESBOÇOS MAIS OU MENOS DESENVOLVIDOS. O "MEMORIAL" CONTEM UMA ESPÉCIE DE MAPA DAS QUESTÕES TRATADAS.

I am a CNPq researcher since 1992. I am philosophy professor at the UFRN (Brazil). After a medical doctor study, I made my M.S. in philosophy at the IFCS (Rio de Janeiro, 1982), followed by a Ph.D. at the university of Konstanz (1990). I also made Sabbatical stages of one year as a visiting scholar in the Hochschule für Philosophie, München (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 is here presented under the title "Outline of a Theory of Proper Names". The best selection of papers in Portuguese is Paisagens Conceituais: Ensaios Filosóficos (Rio de Janeiro: Tempo Brasileiro, 2011).

 More developed versions of the papers listed above, among others, were recently published in the book called Lines of Thought: Rethinking Philosophical Assumptions (Cambridge Scholars Publishing, 2014). Personally, I find this book exceptional in its methodology and relevance. But I have found my attempts to convince others of the obvious truth of some ideas opposed to the mainstream philosophy disappointing.

My present 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 in a sufficiently sophisticated form, able to answer the important challenges presented mainly by Kripke, Putnam and Kaplan. Moreover, I believe that the contemporary philosophy of language has challenged our commonsensical intuitions too much. This is why I would like to reestablish some old plausibilities and show how they can be linked together in a more sistematic way.


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quarta-feira, 10 de dezembro de 2014

#FREGE, RUSSELL, AND THE PUZZLES OF REFERENCE


 Rough DRAFT for the book Philosophical Semantics. The English wasn't corrected.





FREGE, RUSSELL, AND THE PUZZLES OF REFERENCE



Russell’s theory of description was conceived as a way to solve the puzzles of reference. Frege’s theory of sense suggests a different way to solve the same puzzles. These two kinds of solution are usually considerered irreconciliable alternatives. Nonetheless, each of them has it own appeal. In this appendix I will propose to build a bridge between Russel’s and Frege’s solution by transforming each of these views and making them fully reconciliable. I will proceed, first by subtracting from each of these views its metaphysical load, and then by showing that if the appropriate changes are made they can be viewed as different ways of saying the same.

Russell’s solutions to the puzzles of reference
I will first present the puzzles and then Russell’s solutions to them by means of his theory of descriptions.
(i) Reference to non-existent. Consider first a sentence whose grammatical subject does not refer to anything, for example, ‘The present King of France is wise’. How can we attribute wisdom to someone who does not exist? Russell’s response is that this problem only arises if we understand the description ‘the present King of France’ as a referential expression functioning as a proper noun. But this is not the case. Calling the predicates ‘…present king of France’ ‘F’ and ‘…is wise’ ‘W’, the theory of descriptions allows us to symbolize ‘the present King of France is wise’ as: ‘(Ex) (Fx & (y) (Fy → y = x) & Wx)’. Or, to use a more intuitive formulation in which we summarize ‘at least one and at most one’ as ‘exactly one’, we have the following false sentence:

1.     There is exactly one such that x is the present king of France, and x is wise.

In any of these formulations, one thing is clear: there is no wisdom predicated from a present king of France. The definite description ‘the present king of France’ was replaced by quantified predicates. Hence, we don’t need to assume the existence of any present king of France.

(ii) Negative Existential.The second puzzle, a variant of the first, concerns the apparent impossibility of denying the existence of an object when the expression that denies the existence is on the same object. To clear it up, consider the following sentences:

     1. The present king of France does not exist,
     2. Sentence (1) is on the present king of France.

Both seem to be true. But they are inconsistent with each other. If the sentence (2) is true and (1) is on the present king of France, so the sentence (1) needs to be false and vice versa.
   Russell solves the riddle suggesting that (2) is a false sentence. In order to show this he interprets the negation in the sentence (1) as possessing a narrow scope in relation to the definite description. The form of the sentence (1) is: ~(Ex) (Fx & (y) (Fy → y = x)), or, in a more intuitive formulation:

2.     It is not the case that there is exactly one such that x is the present king of France.

This is a true sentence, since it is the negation of a false conjunction. But it does not commit us with the existence of the present king of France in order to deny that it exists. We commit ourselves only with the denial of the existence of anything that has the property of being the present king of France.

(iii) Identity Sentences. The third puzzle is the Fregean paradox of identity. Consider the statement: (1) ‘The author of Waverley was Scott’. It contains two referential expressions, both denoting the same person. But if this is so, then the sentence (1) should be tautological, saying the same thing as (2) ‘Scott is Scott’. However, Husserl thinks that we know for sure that (1) is a contingent and informative sentence. Why?
   Russell’s solution is again to make disappear the definite description. Calling Scott ‘s’, we can paraphrase the identity sentence as “(Ex) (Wx & (y) (Wy → y = x) & (x = s))”. Or, more intuitively:

3.     There is only one x that is the author of Waverley, and this x is Scott.

Through these formulations it is clear that (1) is an informative sentence, because what seemed to be a tautological identity appears now as an informative statement.

(iv) Opacity. A final riddle that the theory of descriptions is called up to solve is that of intersubstitutivity in sentences that express propositional attitudes, which are relational states connecting a mental attitude to what we call a proposition or thought. Consider, for example, the sentence (i) ‘George IV believes that Scott is Scott’. This is true, since George IV knew was certainly able to apply the principle of identity. But since the name ‘Scott’ and the description ‘the author of Waverley’ refer to the same person, it seems that we can replace the first occurrence of the word ‘Scott’ in the sentence (i) for this description, obtaining the sentence (ii) ‘George IV believes that the author of Waverley is Scott’ so that (ii) preserves its truth. But this is not what happens: it may well be that sentence (ii) is false, despite the truth of sentence (i). Why is this so?
   To respond to this objection, we can use the theory of descriptions to replace the description that comes after ‘George IV believes…’ as:

George IV believes that there is only one x that is the author of Waverley, and that this x is Scott.

Certainly, this is an informative belief that is clearly distinct from the tautological belief that Scott is the same as Scott. This is why it can be false.

Fregean solutions to the puzzles of the reference
Frege has an explicit solution for the last two puzzles of the reference. As for the first two, the solution can be only reconstrutively suggested.

(i) Reference to non-existent. Frege suggested that in one ideal language a singular term without reference could be seen as referring to the empty set. We can apply this suggestion to ordinary language, suggesting that a sentence like

(1)   The present King of France is wise.

is false, since the empty set isn’t wise. However, in addition to being artful, this suggestion leads to absurd conclusions, such as that the sentence ‘Pegasus is the current King of France’ is true, since both ‘Pegasus’ and ‘the present King of France’' refer to the same thing, namely, the empty set.
   The alternative suggestion that I would like to propose is that we can say things about non-existents simply because singular terms without references still have senses. Consequenly, we are still able to articulate the dependent sense of the predicate with the independent sense of the singular term, producing a complete thought, notwithstanding the fact that this thought is false, since the truth of a thought demands not only that its predicate has its reference, but also its singular term, and in this case the prior reference of the singular term is lacking. This falsity is not clear when we consider the statement ‘The present king of France is wise’. But the falsity turns clear when we consider other statements with a similar structure but more semantic content. Consider, for example, the statements:

1.     The present king of France isn’t wise since there is no present king of France.
2.     Yesterday the present king of France washed the swinbad of my mother.
3.     I saw the present king of Fance making exercises on the beech last week.
4.     The present king of France has forbidden the turists to visit the palace of Versailles.

   The first statement is true, since it denies the statement that the present king of France is wise is true and gives the reason for its falsity.[1] The other three statements are all clearly false. The reason why the statement (i) can be seen as lacking truth-value is only a pragmatic one, namely, we normaly see a statement as false when the predicate does not apply, while we assume that the singular term apply; so the statement ‘Bertrand Russell used a beard’ is obviously false. But we are not used to consider the truth-value of statements when the singular term has no reference, since these statements are very rare in our language. Indeed, it makes no sense make attributions to something we know that does not exist! Notwithstanding, these statements are also false, and they are false by the same reason, namely, by the lack of reference of a constitutive part of it, as the above examples clearly show.[2]
   Or, consider the statement ‘Santa Claus has a white beard’. In a fictional context it is undoubtly true. But if understood as a statement about the real world, its truth-value does not seems to be clear. The statement does not seem to be false because it is about a property of Santa Claus and we have difficulty to see it outside its fictional realm. But this kind of sentence shows itself to be definitely false when we make a statement like ‘I have locked Santa Claus in my room after he has fallen from the chimney’.

(ii) Negative Existential. The enigma of negative existentials receives a nice Fregean explanation. Consider, for example, the statement:

   (1) The present king of France does not exist.

The existence is for Frege the property of the reference of a predicative expression – which he calls a concept – that under which at least one object falls. Thus, the sentence (1) is not on the present king of France, but on his concept, saying that it is satisfied. Consequently, the sentence (1) isn’t on the present king of France, but on its existence, which it denies.
   The same applies to the denial of the existence regarding proper names. If proper names, as Frege would have suggested, are abbreviations of bundles of defined descriptions, then a similar strategy would be applicable to negative existential with empty names, like ‘Pegasus does not exist’. What this sentence means is that the concepts expressed by some descriptions abbreviated by the name ‘Pegasus’ are not satisfied by any object.

(iii) Identity Sentences.The riddle of identity between descriptions can be exemplified by the most discussed sentence of the analytic philosophy: ‘The morning star is the evening star’. For Frege, this identity sentence is informative because the descriptions ‘the morning star’ and ‘the evening star’ express different senses or modes of presentation of the same object, the first as the most briliant celestian body that appears to us on the east in the morning and the second as the most briliant celestian body that appears to us on the weast in the afternoon… It is informative to say that these two very different modes of apresentation are of the same object.

(iv) Opacity. As for the enigma of opaque contexts, Frege suggests that in statements of propositional attitudes the subordinate sentence does not have the usual reference, but an indirect reference, which is its own sense. Thus, in saying ‘George IV believes that the author of Waverley is Scott’, the reference of the subordinate sentence ‘The author of Waverley is Scott’ is neither its truth-value (as Frege thought the reference of a sentence should be) nor the correspondent fact, but simply the thought expressed by this sentence. As ‘The author of Waverley is Scott’ expresses a thought other than ‘Scott is Scott’, the replacement Save-veritate between the stataments ‘George IV believes that the author of Waverley is Scott’ and ‘George IV believes that Scott is Scott’ are not replaceable salva veritate.

   I don’t want to discuss here the objections of detail that could have been made to each one of these solutions. I want to respond only to the general objection made at Fregean solutions of riddles of the reference, according to which they induce us to accept some kind of Platonism of senses and thoughts, unlike ontologically cheaper solution of Russell.
   I do not believe that the commitment to abstract entities is necessary to the Fregean solutions. As we have seen in the chapter on Frege, the best way to make sense of the Fregean senses is to identify them with rules or combinations of cognitive-semantic rules, which determine the referential uses of expressions. Under this understanding, the meaning of a definite description is a rule of identification for the object it should refer to.
   Here too the objection can be made that we are only replacing the word ‘sense’ with the word ‘rule’, and that this is a merely verbal solution, because if the senses are abstract entities, the rules also appear to be. However, here too it is possible to respond, as we have already done, that the rules in question do not exist outside of their instantiations as cognitive-psychological events able to demonstrate publicly by means of behavioral manifestations, and that there is nothing else out of it. Such cognitions can be identified as equal to each other, not because they are instantiations of any abstract object, the Rule of Identification in itself, but by qualitative identity between the cognitive act of the application of the rule of identification that we are considering and the cognitive act of application (real or only in thought) of the rule of identification that we are using as a model. This assumption prevents our paraphrasis of sense in terms of semantic rules to be unjustly severed by Occam's razor.

Reviewing Fregean assumptions
Who’s right? Russell or Frege? Much ink has been spilled in the dispute on the correct theory. As I noted at the outset, my hypothesis is that it is not a matter of choice between theories. If it were a matter of choice, then one or the other theory should be seen as faulty. The fact that we have achieved no consensus regarding the faulty theory brings us to the suspiction that both theories have something true. But then, why we do not see them as two ways of saying the same? The answer would be that each of them has implausible metaphysical assumptions mixed with insightful content, and that these implausible metaphysical assumptions makes then appear irreconciliable. Thinking in this way, my proposal is to reconstruct these theories pulling out off them their fatness of metaphysical assumptions and filling the gaps that are left with new assumptions. If our hypothesis is right, this will allow us to show that they are only two different ways of saying the same.
   Let’s start with Frege. We have already seen that we must eliminate the anachronistic ontological realism of the senses, which should be seen as simple psychological instantiations of contents or semantic rules. Repeating what has already been proposed in our reading of Ernst Tugendhat in the introductory chapters, it is perfectly plausible to identify what Frege called the senses in terms of semantic rules, so that[3]:

(i)           The sense of the singular term (mode of presentation of the object) is the same as the identification rule of the singular term, whose criteria for application are identifying properties of the object.
(ii)      The sense of the general term (conceptual content) is the same as the rule of application of it as a predicative expression, whose criteria of application would be singularized properties (tropes) associated with the object;
(iii)    The sense of the assertive sentence (the thought expressed by it) is the same as its verification rule, whose criteria of application would be its truth-maker, which as we have seen can be better identified (against Frege) with the fact referred by the sentence (see chapter 3 of this book).

   A further thing we have done was paraphrasing the Fregean concept of existence.[4] We saw in Chapter 3 that for Frege and Russell the existence is the poperty of a concept of being satisfied by at least one object, or, as we understand it, the property of a concept of applying effectively (and not merely supposedly) to at least one object during a certain period of time (in which the object is said to be existent). To know that an object exists is to know that its concept is effectively and continuously applicable during the time in which the object can be said to exist. Now, we have found Frege’s concept of a concept as the reference of predicative expressions unecessary (except for realists), and we have suggested to replace it with a different view, according to which the concept must be simply the sense of the predicative expression. If we accept this, we get a further analysis of the concept of existence. The existence is the property of the sense of a predicative expression of being satisfied by object. More precisely, since the sense of a predicative expression is its rule of characterization, the existence must be the property of the rule of characterization of being satisfied, that is, effectively applicable. Moreover, as we saw, this does not deprive the existence of objectivity, because if the effective applicability of a conceptual rule is a property of it, it is also the property of a conceived object of having this rule effectively applicable to it. This result can be admitted to each of the rules (senses) already supposed by Tugendhat: (i) the existence of an object is the effective applicability of rule of identification of the singular term that names it, (ii) the existence of a s-property is the effective applicability of the rule of characterization of its predicative expression, and (iii) the existence of a fact is the effective applicability of the verificational rule of the statement to a fact in the world – its truth-maker. Finally, since the effective applicability of the verification rule of the statement is the existence of the fact, and the verificational rule is the f-thought, then the existence of the fact is the effective applicability of the thought expressed by the statement.[5]
   Now, what about the relation between existence and truth? We have here the truth of the thought and the existence of the fact depicted by the thought. If the existence is the effective applicability of a conceptual rule, then, since the thought is a complex conceptual rule, a verificational rule, the existence of what is thought, namely, the fact, is the effective applicability of the thought. And the existing fact is a fact to which the verifiability rule of its thought is applicable. This means that assigning existence to a fact is the same as assigning truth to its thought. To say that the f-thought expressed by the sentence ‘Socrates is bald’ is true is to say that the thought, namely, the verificacional rule expressed by this sentence, is effectivelly applicable to the fact, namely, that the criterial configurations that are required to warrant its application correspond to criterial settings that have been in some way found, that it is a fact that Socrates is bald, that is, that this fact exists. The existence of the fact is the truth of its thought.
   Finally, I want to treat the sentences without referrence as being ultimately false and not as being devoid of truth-value, as Frege suggested in some examples. After all, the reason why Frege thought that sentences with unreferenced components are devoid of true-value lies in its insistence on undefensible idea that the reference of the sentence should be its truth-value. But as, unlike Frege, we are willing to admit that the reference of the sentence is a fact, the absence of such a fact – due to the lack of reference to the singular term – just drive us to the falsity of the sentence, as we have shown in our discussion of the Fregean solution to the question of the reference of non-existents. Well, that is pretty close to our Frege reviewed the position of Russell, who saw sentences with empty set descriptions as being false.

Reviewing Russellian assumptions
Now it is time to review the assumptions Russell’s theory of descriptions. A first step is to rule out the thesis according to which defite descriptions and even our usual names (which for him are sets of descriptions) are not referential expressions in the proper nense.
   This thesis from Russell flies in the face of our commonsesical intuitions. For what could exemplify better a referential expression than a proper name or even a definite description? One could even say that names and definite descriptions are definitory of singular terms, since they are nominators, terms whose function is to appoint to. They are what provides the templates for our understanding of what is the nomination: the singularization of an object indicating which it is among all objects of a certain domain. Russell’s intention in his logical atomism is to use the theory of descriptions, paraphrasing definite description and proper names in terms of quantified predictive expressions and put in its place the logical proper names. However, as we have seen in the second chapter of this book, the doctrine of logical proper names espoused by Russell is hopeless and his form of semantic referentialism is implausible.[6] Once we reject the existence of logical names, there is no reason to reject that definite descriptions are referential expressions. Even when definite descriptions can be analysed in the form of a conjunction of quantified predicative expressions, they do not let to be referential expressions, for they are able to pick up an only object and to distinguish it from all other objects of a given domain, and this is all that is required for a definite description to be referential. The is the conclusion of the abandonment of Russell’s metaphysicas of logical proper names.[7]
   Secondly, we must also reject another from Russell, namely, his obscure suggestion that defined descriptions do not have any meaning in themselves.[8] This idea sounds as an amalgam of the Fregean principle of context and his concept of incompleteness of predicates: If the meaning is the object, as the referential view proposes, and definite descriptions fail to appoint to it, they cannot have meaning outside the context of something else that is offered by the sentence. However, once we reject the doctrine that the senses of the so-called logically proper names are their referents, and we admit that the reference is always given by semantic rules, it is clear that the requirement of applying the predicate to a single object with such and such properties made by the russellian analysis already constitutes a rule of identification allowing us to refer to something and as such constituting a complete sense. A definite description should work as a fully meaningul term, and its meaning should be given by the identification rule expressed by it.[9]

Building the Frege-Russell theoretical bridge
Once in possession of a different view of Frege’s and Russell’s analysis, one that deprives them from their implausible speculative wrappers, the essentials of my strategy is to use the rules of identification constitutive of the senses and the concept of existence as the effective applications of these rules in order to build a conceptual bridge allowing us to travel from the Fregean solutions to the riddles of reference to the Russellian solutions and vice versa. In this way I want to demonstrate that Frege’s and Russell’s answers to the puzzles of reference are intertranslatable. Here is how this can be done:

(i) Reference to non-existents. As we have seen, the most reasonable answer to the Fregean problem of how to give meanings to sentences refering to non-existent objects is that we can at least understand how the incomplete sense of the predicative expression can be supplemented by the complete sense of the singular term, thus constituting the complete content of a thought. That’s what allows us to think that the present king of France is wise without having to admit that it exists.
   A better understanding emerges when we translate the Fregean senses in terms of cognitive-semantic rules. In this case we will say (returning to Tugendhat’s suggestion) that the true predicative rule applies to its usual reference always by means of the application of the singular term identification rule. Coming back to an example considered in the beginning of this book, at the sight of the Earth for the first the first cosmonaut Yuri Gagarin said: ‘The Earth is blue’. But in order to express this thought he needed first to identify something in space, an object, the planet Earth. And by means of this identification he could he apply the predicate ‘…is blue’ to the a property of the object that he had located. We see that the rule of applying the predicate ‘…is blue’ needs to be first, say, driven by the application of the identification rule (which selects among others the one called ‘Earth’) in order to find the object, only then being able to be applied in the identification of the singularized property (trope) of the object of being blue. The application of the craracterizing rule of the predicate needs therefore apply in combination with the rule of identificaion of the object, so that she can find if th object satisfies it or not. It should be noted that if the sentence was ‘The Earth is red’, it would be false, because the object located by the identification rule would not satisfy the rule of characterization od the predicate ‘…is blue’.
   Let’s see now the case of enpties singular terms, the alleged reference to non-existent, as found in the sentence ‘Vulcan is red’. Vulcan, as it is known, should be a small planet that astronomers believed that should exist between the Sun and Mercury in order to explain the variations in the perihelion of the latter, having been according to the calcul of Le Verrier be approximately at 21 million kilometers of the Sun… This is the Fregean sense of meaning of this name: the mode of presentation of its reference. However, since Vulcan does not exist, the reference of the name is empty and its identification rule inapplicable. As a result, the application of the rule of characterization of the predicate ‘…is red’ is also unable. As the identification rule of the singular term doesn’t quite apply to any object, the application of rule predicate cannot reach it too, remaining non-satisfied by any property actually given, so that the predicate does not apply, making the sentence false (pace Frege).
   However, here we have a more appropriate explanation for what happens. This is explanation takes resource to our capacity of imagination. We are capable of at least conceive of in some measure how it would be to apply both rules in combination, although we are unable to apply then to the real world. It is only to the extent that we are able to conceive the possibility of application of both combined rules in the constitution of what Tugendhat called a verification rule, that we understand the epistemic sense of the sentence, its f-thought, even knowing that the proper name is empty and the this f-thought has no effective application to any fact in the world.
   This is why the sentence ‘The present King of France is wise’ is already able to express a complete sense, a thought. We are capable of conceiving the two rules used in combination in order to form the verification rule, the sense of the phrase, the thought, which for lack of object and, therefore, a correlative fact, remains without application, what makes the thought false.
   The question of how it is possible to assign wisdom to something that does not exist, the response is now clear: we are capable, at least in some measure, of conceiving the application of the semantic-cognitive rules in their combination, and by doing this we give meaning to the terms and the sentence as a whole. We are able to make a fictive predication, without assertoric or judicative force.
   Now, in the light of this reconstruction it is easier to make the theory of sense agrees with the theory of descriptions. We can paraphrase the description ‘the present king of France’ in a russelian way as

   At least one and at most one is such that x is presently king of France.

And we can say that what is in it for us is a different formulation of the Fregean sense, of the same rule of identification for the present king of France, which is seen as having two components:

(i)                 the condition of oniqueness,
(ii)             the rule of application of the predicative expresion ‘…is presently king of France ‘.

Both (i) and (ii) forms a rule of identification because they allows us to distinguish one and no more than an object through the criterial properties derived from it, such as the presence of a hereditary authority governing France today.
  The absence of the present king of France corresponds to the inapplicability of the identification rule consisting of (i) and (ii) and, therefore, to the lack of reference. As for the predicate 'x is wise ', its characterizing rule also does not apply, since there is no such thing with the property of being the present king of France that it can apply. But this predicate also expresses a rule of application and therefore a Fregean sense. Joining the wires, by the sentence ‘there is only one x such that x is presently the king of France, and x is bald’, we do nothing more than try to apply the same verification rule expressed by the phrase ‘the present King of France is bald’. Since we realize that the identification rule cannt find its bearer, we realize that the rule of characterization is also inaplicable, the same occuring with their combination, namely, the verification rule. Analyzing the case of the reference to non-existent, we see already how the “Fregean” explanation can be exchanged to a “Russellian” explanation and vice versa.

(ii) Negative Existentials. In Chapter 3 we have in despite of Frege’s view identified the concept with the sense of a predicative expression. To say that the present king of France does not exist becomes the same as saying that the meaning of ‘the present King of France’ does not determine a reference.
   How would we express this by measns of semantic-cognitive rules in the place of the senses? Well, we would say that the meaning or concept expressed by a singular term as ‘the present King of France’ is given by the identification rule of this definite description. We know this because we can at least to some extent conceive the applicability of this definite description. But we cannot get the awareness of the effective applicability of the conceptual rule, that is, we cannot say that the object refered by this definite description does exist.
   Now we come to the corresponding "Russellian" analysis. A description like ‘the present King of France’ is here transformed into

at least one x and at most one x is such that x is presently king of France.

    Here again, this is the same as the identification rule for a particular object, being composed of two subrules:

(i)                the condition of unicity
(ii)              the rule of application of the predicate ‘...is presently king of France’.

   Now, to say that the current King of France does not exist is at least saying ‘This is not the case that there is at least one x and at most one such that x is presently king of France’, and this is to say that the identification rule composed by the conditions (i) and (ii) is not effectively applicable. What is the difference between this rule and the Fregean sense of the description? The answer is that it comes from diverse exhibitions of the same thing. The "Russellian" analysis only decomposes the rule into two: the rule of unity and the rule of characterization of the predicate. Saying that the present king of France exists is to say that the characterizing rule of the predicate ‘is presently the king of France’ effectively applies, and that it applies to a single object. Once more, the "Russelliana" and "Fregean" analyses of negative existentials converge towards becoming two different ways to try to say the same.

(iii) Identity. Consider now identity sentences like ‘the morning star is the evening star’. How can this sentence be informative if the two descriptions refer to the same object? Frege’s reply is that despite the fact that these descriptions refer to the same object, they express different modes of presentation of this object, and in this way they are informative. Paraphrasing the concept of meaning in terms of a semantic-cognitive rule, what Frege suggests is that the sentence above is informative because it tells us that we identify the same object through two different identification rules, which call for different criterial settings.
   In terms of the theory of descriptions, calling the predicate ‘…morning star’ M and the predicate ‘…evening star’ T, the identity sentence can be symbolized as:

(1) Ex ((Mx & Tx) & (y) (My → y = x)) & (z) (Tz → z = x)).

   In other words:

(2) There is only one x that is morning star, and the same x is the evening star.

   In this case, what we are doing is (i) a conjunction of two different characterizing rules of  predicates, adding to it (ii) that they both apply to the same object. Thus, the “Russellian” analysis only ensures us that the identification rule constituted by "Ex (Mx & (y) (My → y = x))" applies to the same object that the identification rule constituted by "Ex (Tx & (z) (Mz → z = x))", since by transitivity y = z. But this is like saying that we have two different identification rules, two modes of presentation, two different Fregean modes of presentation of the same object. Again, the two analyses demonstrate to be intertranslatable.

(iv) Opaque Contexts. Finally, consider the utterances of propositional attitudes as:

(1) George IV believes that Scott is Scott.

and

(2) George IV believes that the author of Waverley is Scott.

   Why the truth of (1) does not guarantee the truth of (2), if both subordinate sentences are identity sentences on the same person?
   For Frege the answer is that in such cases the subordinate sentence doesn’t have its usual reference, which for him is the truth-value. These sentences refer, he thinks, to the thought expressed by them, and this thought is different. As a consequence, the truth-value of the sentence that expresses propositional attitude ceases to be a partial function of the truth-value of the subordinate sentence, making the intersubstitution salva veritate impossible.[10]
   Since we reject Frege’s implausible idea that the usual reference of the sentence should be its truth-value, we must first rebuild his solution. We can preserve his idea that in utterances of propositional attitudes the reference of the subordinate sentence is its sense as ‘aAp’, in which ‘a’ is in the place of the perso who has the attitude, ‘p’ is in the place of the thought referred by the subordinate clause, and ‘A’ is in the place of the attitudinal verb, which can be of belief, of knowledge, of desire etc. But in ‘aAp expresses a proposition such that it does not refer anymore to any fact in the world that could eventually match, making it true. In the statement of propositional attitude, what matters is a certain relationship between the contents of the main clause (usually expressing a mood or mental act that attach to certain person) and the thought expressed by the subordinate clause, so that the truth of a sentence of propositional attitude depends only on the fact of this relationship being really in the mind of the person a in the independence of the truth or falsity of the thought expressed by p. Indeed, according to this reasoning, Frege is right: the subordinate clause has as its reference the content of thought expressed by it, to which we state that the person has the propositional attitude. Thus, a statement of the form ‘aAp’ is true iff the reference of aAp is a fact constituted by the existence of the person having his or her attitude regarding his or her thought of p. This is why after all the thought expressed by the subordinate clause cannot be overridden saves veritate: it is part of the the fact that is being referred, and the entire fact is composed by A and p, that is Ap.
   Now, to paraphrase thoughts as verification rules of sentences, we can say that the rules of verification of the sentences (1) and (2) are different, without for that commiting ourselves with the effective applicability of these rules, with the actual existence of what satisfies them, which is the fact that a has Ap. So, considering the singular sense of the term as an identification rule, we can paraphrase (1) as:

   (1') George IV believes that the identifying rule (sense) what he has for Scott applies the same object as the identifying rule (sense) what he has for Scott,[11]

and we paraphrase (2) as

(2’) George IV believes that the identifying rule (sense) what he has for Scott applies to the same object as the identifying rule that he has for the author of Waverley.

As in (1) and (2’) the contents of thought with respect to which George IV has the relationship of belief are different, and, as we have noted, the truth-value of the propositional attitude statements depends only of the fact that a has the property Ap, and these properties are different in each case, we conclude that this truth-value doesn’t need to be the same in each of them. The subordinated clauses cannot replace one another salva-veritate because the thoughts-references expressed by them are different.
   Now to a russellian paraphrase: The subordinate sentence of (1) can be stated as:

(1’’) George IV believes that there is only one x which is Scott and that x is Scott.

And the subordinate sentence of (2) is analyzed in order to obtain:

(2’’) George IV believes that there is only one x which is the author of Waverley and that x is Scott.

Now, as the sentences ‘only one x that is Scott’ and ‘only one x that is the author of Waverley’ express different predicates, ‘Scott is Scott’ cannot mean the same as ‘Scott is the author of Waverley’.
   The point to be noted is that the Russellian analysis is only better clarify one aspect of our version of Fregean analysis. After all, the Fregean analysis in (2’), for example, can also be presented as

(2’’’) George IV believes that there is only one x such that the rule of identification for Scott, as well as the rule of identification for the author of Waverley, apply to x.

But (‘2’) and (‘2’’’) do not differ essentially. After all, to say as Russell that George IV believes that the rule of identification that he knows for the name ‘Scott’ and that the rule of characterization that he knows for the predicate ‘…is author of Waverley’ apply to one and the same object, comes to the same (or nearly the same) as the Fregean suggestion that George IV believes that the identification rule – the sense – he knows for the singular term ' Scott ' has the same referent the rule of identification – the sense – of the definite description ‘the author of Waverley’. Conclusion: also in the case of propositional attitudes the two analyses are intertranslatable.

Conclusion
Summarizing, we can analyze the referential function of definite descriptions in at least three ways: (i) in terms of abstract entities, such as Frege did, when speaking of senses or modes of presentation, (ii) in terms of semantic criterial rules, inspired by Tugendhat’s approach that has its origins in Wittgenstein, and (iii) using resources from the predicative logic, as Russell did with his theory of descriptions. These are, however, only different and complementary ways of saying (approximately) the same.
   The impression of strangeness of the proposed approach comes from the acceptance of the metaphysical assumptions that permeate what each one of these philosopher write on the issue. Against Russell’s belief, his paraphrases produced by the theory of descriptions are nothing more than expressions of semantic rules by which it becomes possible to express formally the referential function of the definite descriptions in their attributive use, doing it through predicative expressions used in a domain that grants them univocal application, which makes them appear as expressions of Fregean senses or modes of presentation, which are nothing more than semantic-cognitive rules. As these rules only apply in real cognitive instantiations, the commitment of the theory of descriptions so understand with our semantic cognitivism is clear.




[1] See Stephen Neale’s defense of Russell’s analysis in Descriptions (Cambridge MA: MIT Press 1990), pp. 26-28.
[2] I reject in this way doctrines of presupposition suggested by Frege and defended by P.F. Strawson, according to which statements like these are neither true nor false because in order to have a truth-value they presuppose the truth of the statement ‘The present king of France exists’.
[3] Ernst Tugendhat: Vorlesungen zur Einführung in die sprachanalytische Philosophie, p. 262. Ver também Ernst Tugendhat e Ursula Wolf: Propedêutica Lógico-Semântica, p. 185.
[4] Gottlob Frege: Die Grundlagen der Arithmetik, par. 53.
[5] Each of these three cases can be expressed by a predictive logic, to the extent that transform the referential expressions in predicative expressions, of them: consider existence predicando the phrase "flying mammals exist"; symbolizing ' mammals ' by M and high-fliers for V, we have "(Ex) (Mx & Vx)". Consider a description set to "the morning star exists"; symbolizing the predicate ' morning star ' as M we have "Ex (Mx & (y) (My → y = x))". For the forename in the phrase ' Socrates ' exists, abbreviating the descriptive content that the name can contain through the predicate ' socratiza ' and symbolizing the last by S, we have (Ex) (Sx & (y) (Sy → y = x)). Consider the phrase "unique predictive Socrates is bald", which can be translated as "there is only a something is Socrates and he is bald". Understanding ' Socrates ' as the abbreviation of analysable descriptions by means of predicates, abbreviating these predicates using the predicate ' socratiza ', that sort of symbolize as S, and we symbolize the predicate ‘…is bald’ as C, we have “Ex (Sx & (y) (Sy → y = x) & Cx)”.
[6] See also E. Tugendhat: Einführende Vorlesungen in die sprachanalytische Philosophie, p. 437.
[7] Gareth Evans (Varieties of Reference, p. 56) Note that the descriptions defined can refer to different individuals in different possible worlds, variously the names. But as saw in the apêndix 1, only set descriptions are rigid while they are semantically linked to proper names, otherwise they become flaccid. This demonstrates that there is nothing special about differentiating the semantics of the usual names, unlike modern referencialistas as Kripke believed.
[8] ‘I Advocate that an expression denotativa is essentially part of a sentence, and not, like most single words, any meaning by itself ‘. B. Russell: “On Denoting”, p. 489.
[9] We can speculate if would not be parsed description predicates expressions that would allow us to designate sets of sense data that uniquely established as existential and universal quantifiers by existing, if would translate in terms of properties and constitutive singularizadas relations of the object referenced. Russell did not have the notion of individualized property in space and time (trope), or via the predicates as designating less than universal themselves. But we are at least in principle allowed to parse the description predicates as designators properties through sense-data.
[10] One need to remember that lack of intersubstitutivity in subordinate sentences in statements of propositional atitude are only one under the diverse cases considered by Frege in “Über Sinn und Bedeutung”.
[11] I am assuming that George IV knows who is Scott. In the case he does not knows the expression ‘that he knows’ must be excluded.

quarta-feira, 19 de novembro de 2014

(c) # SKETCHES ON TRUTH

Draft A, 2014/1




- 5 -
TOWARDS AN UNIFIED THEORY OF TRUTH


Concerning statements we have got some conclusions from the last chapters: the epistemic meaning of a statement is its rule of verification, which is the same as a thought (that is, an f-thought: I will usually call f-thoughts simply as ‘thoughts’); the truth-maker of the thought is the fact stated by the statement; the effective applicability of the rule of verification or (f-)thought is the existence of the fact. We also saw that the thought, the rule of verification, when effectively applicable, is true. Maybe we should conclude from this that the truth of this rule or thought is the same as its effective applicability, so that the truth would be the same as the property of existence of a fact. Indeed, is beyond doubt that the assertion of the truth of a thought is equivalent to the assertion of the existence of a fact. But equivalence is not the same as the identity: truth and existence seem to be distinct concepts. The fact that truth and existence are properties of thoughts does not mean that they are the same property.
   There is another reason to question a supposed identity between the truth of a thought and the existence of a fact, namely, the vague truism that we can find even in the dictionaries, according to which truth (in association with statements) is the property of being in accord with the way things actually are (facts). If our first methodological principle, according to which we should at least prima facie accept our commonsensical and ordinary language views, then the correspondence theory of truth must be the most correct one. Thus, in order to see how the concept of truth fits with our general picture we must begin by reconsidering in some detail the correspondence theory of truth.

Truth as correspondence
Some would think that the adoption of the verificationism means the abandonment of the view that truth is the correspondence between a statement and a fact. As we saw, a statement can be verified in many different ways, as far as it satisfies a multiplicity of different criterial configurations, while the fact corresponding to the true statement must remain univocally related to it as being one and the same. Consequently, according to the kind of verificationism we have proposed, it does not seem possible that what verifies the statement is a fact.
   My view is that this is a treacherous reasoning, and that we come to this conclusion only because we are searching for the correspondence in the wrong place. As we will see, usually the correspondence is not between the thought and the many diverse criterial configurations given in sense-perception and able to verify it, but between the content of a thought (an f-thought) and a fact, that is, the content of a fact, also aprehended by us and usually inferred from a diversity of criterial configurations which can be given in sense-perception.
   In order to make this suggestion clearer, I need to develop what I believe to be the most adequate and comprehensive form of correspondential theory of truth, which requires a pragmatic investigation of the dynamic constitution of truth as correspondence. First, however, we need to make clear the structure of the relation of truth as correspondence.

The structure of correspondence
Assuming that truth is the correspondence or agreement between the thought and the fact referred by the thought, we need first to have clear each term of this formula. The thought must be the f-thought (even if always conceived by means of p-thoughts) expressed by a statement, which is also, was we already saw, the truth-bearer. The fact or factual content is what we have analysed as the reference or correlate of the thought, its truth-maker in the most proper sense. And the correspondence should be seen at least as a structural isomorphism between both, the thought-content and the factual content, in the sense of a biunivocal relation between the concatenated components of both.
   Assuming this nearly standard understanding of the correspondence, we can produce an identification between truth and correspondence in which the predicate ‘…is true’ is identified with the predicate ‘…it corresponds with the fact’, an identification in which both predicates work as semantically meta-linguistic predicates applicable to thought-contents. According to this definition, for any content of belief p, to say that p is true is to say that p corresponds to a fact. We can express this symbolically using p as the expression of an f-thought, V for the predicate ‘is true’, and C for the predicate ‘... corresponds to a fact’. The predicates V and C apply to p in a semantic metalanguage concerning the thought-content expressed by p, what is shown by putting p under quotation marks. Here is the formulation:

(1)  Vp’ = Cp[1]

According to this identification, truth is the property of a thought-content expressed by a sentence p, namely, the property of corresponding with a fact.
   This formulation depends on the application of monadic predicates ‘...is truth’ and ‘...corresponds to a fact’. However, monadic predicates like ‘…is true’ as much as ‘…corresponds to a fact’ can be unfolded as diadic predicates of a semantic metalanguage, relating the thought expressed by p  with the fact that q.
   This means that the definition above can be explained more thoroughly as stating that for a thought-content p, to tell that p is true for the factual content q is to tell that the thought of p corresponds to or is adequate to the fact of q, understanding correspondence as a relation of identity of contents expressed by p and q so that we can say that p = q. Giving a simple observational example: suppose that the thought expressed by ‘The Moon is white’ is true. We do it because of the factual content that the Moon is white. And this is the same as saying that the thought-content expressed by ‘The Moon is white’ corresponds to the content of the observation that the Moon is white, which is factual.
   Now, using the symbol V in the place of the semantically metalinguistic predicate ‘…is true for the fact that...’ and using the symbol C for the also semantically metalinguistic predicate ‘...corresponds to the fact that…’, we have the following formalized version of a more complete definition, in which the thought-content expressed by p and the factual content expressed by q are being metalinguistically accessed:

(2)  ‘pVq = ‘pCq

   According to the identification (2) the assignment of truth is the same thing as the assignment of the relational property of correspondence, that is, the exact similarity of the thought-content with the factual content – a similarity of content that, we suppose, could be analysed in terms of structural isomorphism.
   Although limited, these identifications already enable us to deal with paradoxes of self-referentiality. They preserve the analogy between existence and truth: in the same way as the existence is a property of concepts, truth or correspondence is a property of thought-contents or f-thoughts or propositions expressed by entire statements. Because of this, the thoughts expressed by sentences like:

    It is true that ‘2 + 3 = 5’,
    ‘2 + 3 = 5’ is a true statement,
    It isn’t true that ‘2 + 3 = 6’,
    ‘2 + 3 = 6 isn’t a true statement,

Contain grammatically correct attributions of truth, while self-referencial sentences like:

   This statement is true,
   This statement isn’t true,

aren’t grammatically correct. One cannot say that they are wrong because they are self-referential, since there are self-referential sentences that have truth-value as ‘This statement has five words’. The problem is that the attribution of truth cannot belong to a content of thought in the same level of its other constituents, since it is not a constituint of a thought. The same applies to indirectly self-referent statements like:

   The next statement is false… The previous statement is false.

   In this case we try to apply the predication of falsity indirectly to the same statement we have begonnen, so that if it is true it is false and if it is false it is true. But this circularity results from the fact that truth cannot play a role as a constituint of a thought in the same level as the others: truth is a meta-property of a complete thought.
   Finally, we need to remember that according to the results of chapter 4, the f-thoughts are rules of verification. If it is so, to say that an f-thought corresponds to the fact is the same as to say that a rule of verification corresponds to a certain fact. But how could a rule of verification correspond to a fact, except by being effectively applicable to a fact? It seems also that for a rule of verification being true it must be effectively applicable to its required fact. Hence, it seems that we can replace ‘correspondence’ with ‘effective applicability’ symbolized as A, and say that a rule of verification is true when it is effectively applicable to the fact that it requires or:

(3) pVq = ‘pAq

   Identifications (1) and (2) and (3) lay down structural relations explaining how truth can be equated with correspondence in the first two cases and with verification in the last one. However, we can add to them a dynamic dimension that seems ultimately indispensable, though often unoticed. This is what we will see next.

The pragmatics of the correspondence relation
According to the view I wish to defend here, which is influenced by Moritz Schlick’s short defence of the correspondence theory of truth,[2] the correspondence has a pragmatic side that needs to be explored. Very often we can establish an idealized sequence with three successive temporal steps: a supositional, an evidencial and a conclusive. Together they form what we could call a verificational procedure.
   The best way to explain this is beginning with a very simple example. Suppose that I asked yesterday to myself: will rain in Natal tomorrow? This was the suppositional step. Now, imagine that today I go out of my home and I see that it is reining. This is the second, procedural step. Once I do this, I compare my earlier question with the observational evidence that it is raining, and I conclude that the content of the question is the same as the content of my observation and that therefore they agree, they correspond, that is, it is true that it is raining today. Certainly, I could make this question as a hypothesis after hearing some drops of water on my cellar, or I could have seen the weather forecast yesterday, telling that (probably) would rain in Natal today. A similar procedure, as we will see, applies also to non-observational truths. But first things first: we can formulate the three steps as follows:

1)    In the supositional step a hypothesis or a question is posed. In this moment, we ask ourselves whether an f-thought is true, if its constitutive rule of verification is effectively aplicable. We can formalize this step as: ‘?p’.
2)    What follows is the evidential (or procedural) step, the way by means of wich we try to verify the truth of the supposition. In the case of observational truths this step is very simple. We look for an expected adequate thought-content that, in an adequate context, we simply accept as a truth-maker, call it ‘!o. As we will see, there is no question about the truth of o: It is considered as an evidence that cannot be false within the framework of the assumed context or practice or language game in which it occurs.
3)    What follows is the conclusive (comparative) step. Here we ask ourselves whether the supposition matches the evidential result of the procedural step. In the simple case of the perceptual experience, we ask ourselves whether the thought-content of the hypothesis is like the thought-content given to me. In the case of a perceptual experience this step can be summarized as p = o. When the contents are the same, this means that there is a agreement between both, what means that the thought expressed in the supposition is accepted as true. This conclusion can be symbolized as ├p. It can also be that the thought-content expressed by the hypothesis is diferent from the factual content given in the contextually expected sense experience. In this case p o, that is, there is no correspondence, the thought is false, what can be expressed as ├~p.

We can summarize this whole verificational process regarding observational truths as follows:

?p, !o, p = o,├p

This is what we may call an anterograde way to get the truth, since we go here temporaly from the hypothesis to the observational evidence that confirms the hypothesis by being identical to it.
   However, the opposite direction is also possible. We can also have a truth resulting from the observation, progressing from the evidence to the hypothesis, what we may call a retrograde way to get a truth-value.[3] For example, I can go out of my home and unexpectedly see that it is raining, what brings me obviously to the conclusion that it is raining. In this case the perceptual evidence comes first. But it seems that the recognition of truth does belong to the perceptual experience as a direct product of it, since one can see the rain without taking account of it. I think that here we can explain the process of getting the truth in the following way. First we have the observational experience o! Then (still during or after it) we make the supposition ?p, which direct our minds to an aspect of th experience. And finally we answer the supposition appealing to the evidence that has been given: we see that o = p. This is what brings me to the conclusion that it is true that it is raining. We could give to this process the following formulation:

!o, ?p, o = p, /├p

   However, this is only the simplest case. The dynamic view of correspondence can be extended to the truth of non-observational mediated thoughts. Suppose that I am in the airport of Munich, from which I will take a flight to Stuttgart. The time of the flight is of 50 minutes. I ask myself if the weather in Stuttgart is good; this is ?p. So I look in the internet to know how looks like the weather in Stuttgart, and I read that it is good. There is no significant reason for doubt, and I take this information as giving me the appropriate evidence. The thought belonging to !q that I have when I read in the internet that the weather is good is the same as the thought belonging to the question ?p. Consequently, since p = q, I conclude that p is true, that the weather there is good. But the thought in !q is not an observational thought. It is the result of from me unknown reasonings that are based on some kind of observation of the weather conditions in Stuttgart. In this case, using ‘<<<’ in the place of the chain of reasoning (unknown to me) that leads to !q, and ‘!o’ to the observational thought(s) that in some way have originated !q (similar to those that I will have when I arrive in Stuttgart), we can formalize the verificational process in which p is presently made true for me as:

?p, q! (!q <<< !o), p = q/p

Important to note is that the evidencial character of the observation !o is preserved in the supposed inferential chain, being transmited from thought to thought until the conclusion !q, which inherites its evidecial character.
   The foregoing example is of anterograde verification, beginning with one hypothesis and ending with the comparison between hypothesis and a derived evidencial thought. However, we also may have a retrograde procedure with a chain of reasons that ends with the match of a derived evidence with a supposition. Suppose that another person take the same fly and that the commander informs us that the weather in Stuttgart is very good. The other passage is brought to the conclusion that the weather in Stuttgart is in fact good by means of another indirect and for him unknown evidential chain. In this case it is the evidence that produces the question that is answered by means of a comparison of contents, from which the final judgment that the weather in Stuttgart is good results. This process can be summarized as follows:

!q (!q <<< !o), ?p, q = p/p

It is possible that intuitions of scientists that still do not know how to proof their hypotheses, but have a glimpse in their truth, depend on the unconscious feeling that their !q is or may be derived from an observation or postulates.
   Also the general belief – universal and existential – can be explained in this way, as the identity between the contents of the hypotheses and the contents of sets formed by the respective conjunctions and disjunctions of factual contents, often resulting from inductive inferences based on observational facts. So, suppose that ├p is the assertion: ‘All the books in the shelf of my room are in English’. This generalization can be derived in a retrograde form from my observations o1, o2on, of each book in the shelf as follows:

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

   Obviously, I can also first ask myself if all the books of my shelf are in English, and after looking each one of them to conclude that this hypothesis is true in an anterograde procedure:

?p, {!o1 & !o2& !on } → !q, q = p, /p

   As the former, this is a deductive generalization, but it is easy to see that inductive generalizations should also have not very different structures.
   Another point is that we have understood the f-thought as a rule of verification. How would all these f-thoughts as rules of verification fit with our schemas? This is a question that I will let to consider later.

Generalization to formal sciences
Similar structural and dynamic forms can be found in the formal sciences, allowing us to generalize the correspondence theory to a domain traditionally occupied by the coherencial theories of truth. Suppose that we want to demonstrate that the sum of the angles of a triangle is 180°. We can do it first by suspecting that this could be the case: ?p. Then we search for a proof. We can trace a straight line that passes through one of the vertex of the triangle, so that this line is parallel to the side opposed to this vertex. Since the three justaposed angles formed by the parallel and the triangle are the same as the internal angles of the other two vertexes of the triangle plus the angle of the first vertex, and their sum is 180°, we conclude that the sum of the internal angles of one euclidean triangle must be 180°. This conclusion is the evidence !q. Since we see that the content of !q is the same as the content of the hypothesis ?p, we conclude ├p. Using ‘a’ for axioms, the form of this procedure could be rendered as:

?p, !a>>>!q, p = q, /p

   This is an anterograde procedure.
   Now one example from the arithmetic: we can prove that ‘2 + 2 = 4’ in the Leibnizian manner. We begin with definitions (which correspond to basic perceptual experiences in empirical sciences). First, we define 2 as 1 + 1, 3 as 2 + 1, and 4 as 3 + 1. We call these definitions d. Replacing the numbers by the definiens, we get ‘(1 + 1) + (1 + 1) = (3 + 1)’. Since 3 was defined as 2 + 1, and 2 as 1 + 1, 3 can be replaced by (1 + 1) + 1. Replacing the 3 by this result we get: (1 + 1) + (1 + 1) = ((1 + 1) + 1) + 1), which proofs that 2 + 2 = 4. In this way we derive the confirmatory evidence of the hypothesis !q, which is ‘2 + 2 = 4’; this confirmatory evidence serves to check the hypothesis !p that 2 + 2 = 4. Again, abbreviating the definitions as ‘d’, we have the following anterograde verification:

?p, (!d>>>q),  p = q, /p

   We see again that the evidencial content of !q, which serves to check the hypothesis that ‘2 + 2 = 4’, is not the same as the definitions of 2, 3 or 4. It is the same as the result of a reasoning that we make from them, a reasoning that derives from the definitional character of its premisses.
   Finaly, we can give examples concerning logic. Consider the following theorem of modal logivc: ‘P → ◊P’. This can be seen as our hypothesis ?p. How to prove it? Using the S5 modal system we can do it making use of the axioms AS1, ‘◊ P ↔ ~□~P’ and AS3, ‘□~P → ~P’ as assumptions. With this and with the help of the rules of propositional logic, we construct the following proof of the theorem:

     The hypothesis is: ?p, where p = (P → ◊P)

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

Nun, the result  P → ◊P = !q.
Since p = q, we conclude that p is true, we conclude ├p.

   Since the !q, which carries with itself the evidences derived from the axioms, expresses the same thought-content as the hypothesis ?p, we conclude that there is a correspondence, that p is true, that ├p. Also in this example the verificational reasoning has an anterograde form.
    Of course, the retrograde form could be also found regarding any of the three above exemplified cases. Considering the first case, suppose that someone draws a straight line that passes throught a vertex of a triangle, being this line parallel to the opposite side. This person could easily be lead to the conclusion that this triangle and in fact any triangle would have 180°. In this case we would have the following retrograde verificational procedure:

!a >>> !q, ?p, p = q, /p
I suppose that this could be the case when a mathematician or a logician has an insight of a certain theorem as true. The upshot is that the procedures whereby we show the correspondence of formal truths are structurally analog to the procedures whereby we show the correspondence of empirical truths.

Why analytic truths are called true?
Finally, we can apply a similar procedure for the so-called analytical sentences, showing that they are also called true because of correspondence, even if this is, as we will see, a limit-case. It is possible to say, for example, that the analytical statements ‘It is raining or it is not raining’ and ‘Singles are non-married’ are true because they correspond to the respective facts that necessarily either it is raining or not, and that no adult single man can be married. What entitles us to say this? Now, understanding the analytic propositions such as those that are true by means of a combination of the senses of their component expressions (pace Quine), consider how sentences such as hypotheses ?p1: ‘Is it raining or not?’, ?p2: ‘Are singles non-married?’. Here the verificacional relationship is not with the world outside the content of thought, but with a conventional derivation showing that the logical structure of those sentences is tautological. Thus, in the case of ?p1, which is already in this form, we realize right away that its structure is the same as !q1, which is the statement of the principle of excluded middle or ‘p ˅ ~ p’, which can be seen as a logical truth. This is enough to make !p1 true because, independently of the senses of the constituents of !p, one can see its logical structure as warranting its truth. Calling l something we accept as a logical truth, we can formulate this correspondence as follows:

?p1, !l !q, p1 = q1, /p

    As ?p2 (which means ‘Is every single non-married?’) is not already in the form examined, we need to bring it to this form before we see the match. To do this, we begin with the definition !d of single as ‘a non-married adult male’. Calling ‘male’ H, ‘adult’ A, and ‘non-married’ ~M, we can see that from !d we can derive !q: ‘All single are non-married’ as a tautology. Now, we have the following correspondence:

?p2, !d !q2, p2 = q2, /p
  
As we see that ?p2 has the same content as q2, which is derived from a truth by definition, we see that p2 must also be true.[4]

Coherence as an intermediator
Another interesting point regardig the proposed understanding of the correspondence is that it allows the absorption of the coherence theory of truth into the correspondence theory. Coherence can be understood simply as a procedure whereby the correspondence is obtained. The modal proof above does not come directly from AS1 and AS3, plus some rules of propositional logic, to ‘P → ◊P’. We use inferencial steps, and these steps are what constitute the coherence, which is often erroneously considered the proper criterion of truth in formal sciences. In the present case coherence is constituted by material implications, but it includes inductive inferences in the case of the verification of empirical thoughts.
   To illustrate the latter case I will consider two examples. First, suppose that a gift is anonimously sent to me. I open it and see that it is the book The Cloven Viscount, from Italo Calvino. I wonder if Silvia has sent it. I know that I presented Silvia with a copy of the book The Invisible Cities by the same autor and that she told me than that the The Cloven Viscount was a funny book. But Silvia lives in Rom and the present was sent from Rio de Janeiro. So I realize that this book could have been sent from somewhere else. But then I remember that Silvia could be back in Rio de Janeiro, a city where she lived most of her life. An advocate of coherence theory of truth would say that the proposition p ‘My friend Sylvia sent me a copy of the Cloven Viscount’ is made true by its consistency with other propositions like r = ‘I gave an exemplar of The Invisible Cities for Silvia’, s = ‘Silvia told me that The Cloven Viscount is a funny book’, t = ‘Silvia’s gift could have been sent from Rio de Janeiro’. The belief in p is true because it is consistent with the beliefs r, s and t.
   However, what we really have here is an indirect procedure of verification of the correspondence via coherence. I can assume that I have started with the hypothesis ?p. The beliefs r, s and t together make inductively probable the conclusion !q, namely, ‘Sylvia has sent me an exemplar of The Cloven Viscount’. But since I see that p = q in content, I am allowed to conclude that the thought expressed by p corresponds to the thought expressed by q, namely, that p expresses a true f-thought, that p. But it is important to note that this conclusion is due to the consistency of p with the propositions r, s and t, that is, r & s & t make q probable, what makes me to conclude the thought expressed by ?p corresponds to the reality expressed by !q. It is curious but important to note that the second term of the correspondence is in these cases, as in the most ones, not an observation, but the result of a chain of reasoning grounded in the observation.
   Now we could ask what comes first: correspondence or coherence? Is the coherence dependent on the correspondence or, on the contrary, the correspondence is dependent on the coherence, as coherentists would prefer. The answer is that coherence would be independent of correspondence at least if thought-contents could get their probability independently from any observation. But this is not the case. The thought-contents expressed by r, s and t either describe observational propositions or are based on them, for example, r is something that Silvia gave to me personly. They should have more directly to do with the correspondence with the empirically observed factual contents. And they are the ones who guarantee to me q as derived evidence and not the other way around. This guarantee of q, in turn, is what makes the thought of p true for me. Coherence would have no force if it weren’t at some point grounded on observational propositions, in the case of empirical truths, and on axioms or postulates, in the case of formal truths. Indeed, any fairy tail can be coherent and it will not gain any truth with the increase of coherence, since it is not grounded in any evidencial fact.
   A second example concerns the veredict of a judge. It is often coherencial, since crime can be only rarelly receive direct testimony. The following example teaches us something important about the limits of coherencial theory and its relationship with the correspondencial theory. Shortly after his marriage with Ms. Rose, the American pastor David was interned into a hospital with severe abdominal pain. Since the exams have shown a high amount of arsenium in the blod of reverend David, which we abbreviate as r, the following question was posed: ?p = ‘Tried Ms. Rose to poison Reverend David?’. This supposition was later confirmed by the following further evidences:

s: Mrs. Rose had the habit of preparing soups for her husband, taking them even to the hospital.
    t: Traces of arsenic were found in the pantry of Rose’s hause.
u: The bodies of the first three husbands of Ms. Rose, with have been all died from unknown causes, were exhumed, with the surprising discovery of a large amount of arsenic in their hairs.

We can now bild the following verificational process:

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

   Certainly, the statement p is made true by its consistency with the statements r, s, t, and u. But a crucial point to be noticed is that the statements r, s, t, and u are all made true by corresponding to evidencial factual contents publicly observed. Now, what this suggests is that the coerencial view of truth cannot stand alone. The plausibility of q is grounded in the conjunction of the observational statements r, s, t and u; and they are true because of their correspondence with observational contents, even if they also have theoretical assumptions. Coherence cannot originate truth, even because implication and induction, the two central forms of coherencial relation, are defined as ways of preserving truth, begging in this way the question. Hence, coherence works only like the wires of an electric power grid: though they do not generate the energy, they are able to transfer it. We see that coherence is not an independent mechanism, but only a interdoxal mechanism by means of which the correspondence is made. Coherence transfers the truth-force generated by the correspondence of contents of more basic beliefs to the derived evidences acting in the interior of the belief system in order to produce the content of thought expressed by q, which is accepted by us as evidential, corresponding with the proposition p when having the same content, what means the same as making p true. This is why we also can say that the statement p is true because it corresponds to the fact that Ms. Rose has poisoned the Reverend, but that we know about this fact indirectly, from the consistency of the hypothesis with other contents that correspond with the facts that have been observed by us. This thought q, we could say, also expresses what we are sure to be a fact, namely, the fact that Ms. Rose tried to poison reverend David. It is by being involved in the correspondence that coherence is involved with truth; consistency is just an interdoxal mechanism by which correspondence takes place.



[1] We remember here Alfred Tarski’s discotational formula, according to which ‘"p" is true in L ≡ p’. Although Tarski’s formula hasn’t overcoming the philosophical problems concerning correspondence, it has properly emphasized the metalinguistic character of the truth-assignments. (See Alfred Tarsky: ‘The Semantic Conception of Truth’, Philosophy and Phenomenological Research, 4, 1944, 341-375).
[2]  Moritz Schlick, ‘Wahrheit als Korrespondenz nach der modernen Logik’ (1910), in Philosophische Logik (Frankfurt: Suhrkamp 1996).
[3] A similar distinction can be found in the fenomenological distinction between ‘truth of correctness’ and ‘truth of disclosure’. See Robert Sokolowski, Introduction to Phenomenology (Cambridge: Cambridge University Press, 2000), chap XI.

[4] To demonstrate the truth of logical principles, Schlick suggested the reverse procedure: to obtain the required intuitive assessment of its application, the principle needs to be compared with a concrete example. M. Schlick: ‘Das Wesen der Wahrheit nach der modernen Logik‘, p. 82.