quinta-feira, 2 de fevereiro de 2017

### SKETCH OF AN UNIFIED THEORY OF TRUTH

 This is an advanced draft to be published by CSP in 2017/1 in the book 
PHILOSOPHICAL SEMANTICS



– VI –
SKETCH OF A UNIFIED THEORY OF TRUTH


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

We have drawn some conclusions from the previous chapters: the cognitive meaning of an assertive sentence is its verifiability rule, which is the same as an s-thought or thought-content or proposition – the primary truth-bearer. On the other hand, the truthmaker or verifier of a proposition is the fact it refers to, a fact composed by arrangements of tropes. Moreover, consistent with our conclusion that the effective applicability of a conceptual rule is the same as the existence of the trope or cluster of tropes denoted by it, we can expect that the effective applicability of a verifiability rule in its proper context should be the same as the existence of the fact in the world that satisfies it. Finally, since the property of a verifiability rule of being effectively applicable in the right context also makes such a rule-thought-sense true, it at least seems that the existence of the fact referred to by it should also be the same as its truth.
   However, this suggestion is at odds with another view, namely, the correspondence theory of truth, according to which the truth of a thought-content is its correspondence with a fact and not the existence of the fact referred to by it. As already noted, we have the best methodological reasons for defending correspondence theory, since it expresses a modest (even lexicalized) commonsensical view with a long tradition. Historically, it has been the standard truth-theory, from Plato to the nineteenth century, and even today most thinkers still largely accept it (Mosteller 2014, Ch. 2). Moreover, existence and truth, like applicability and correspondence, seem to have clearly different meanings.
   Nevertheless, it seem that there is a simple way to overcome the difficulty. The solution consists in remembering that the word ‘truth’ has two very distinct main bearers in natural language. Dictionaries distinguish clearly between (a) thought-truth, which is truth in the correspondence sense, consisting in things being as we believe they are, conformity with reality (the property of a thought-content of corresponding to a fact), and (b) fact-truth, truth as the actualreal or existing thing or fact. Thus, my suggestion is that in the last sense of fact-truth, truth can be more easily identified with existence – the existence of a fact or the applicability of the thought-content. However, truth in the philosophically privileged sense of thought-truth continues to be reserved to the property of correspondence with facts. This will become better understandable later in this chapter.
   Based on what we have learned thus far, the purpose of this last chapter is to outline what a sufficiently detailed and plausible correspondence analysis of truth should be. This is one able not only to better clarify the above distinction, but also to unify some conflicting views.

1. Compatibility between verification and correspondence
Some think that adopting verificationism forces us to reject the correspondence theory of truth. One apparently compelling argument is the following: a statement can be verified in many different ways, insofar as it may be satisfied by an indeterminate range of diversified criterial compositions of tropes serving as verifiers or truthmakers, while the fact corresponding to a true statement seems to remain univocally related to it as being one and the same. Consequently, according to verificationism, it does not seem possible that what verifies a statement is a corresponding fact.
   My view is that this reasoning, as with other examples of its kind, is deeply misleading and that one only reaches such conclusions by searching for correspondence in the wrong way and the wrong place. As we will see, in the usual sense, correspondence is not a relationship between a thought-content and multiple external criterial arrangements of tropes (the many possible aspectual sub-facts) that sense perception can directly perceive, this being sufficient to verify a thought (Ch. IV, sec. 24-26). Correspondence must be between a thought-content and some grounding fact that because of sufficient satisfaction of such criterial arrangements (sub-facts) we usually only apprehend in mediated form. For instance: I say that I see the grounding fact that a book is on the table, even though I can only see this grounding fact partially and from different perspectives, by means of specific arrangements of tropes that I’ve called sub-facts. Thus, the apprehension of a grounding fact is nearly always more or less indirect and inferential. Moreover, the correspondence must be not only (indirectly) between the thought-content of the grounding fact and the real grounding fact, but also between the intermediating thought-content of the sub-fact and the real sub-fact, both normally belonging to the external world. Nonetheless, in order to make these ideas clearer, we need to delve more deeply into the waters of the correspondence view of truth.
   Such concerns lead us to consider a first and more superficial objection against the correspondence theory of truth. It is the claim that the theory is nothing but a trivial, empty truism. According to this view, to say that truth is agreement with facts is a too obvious platitude to deserve philosophical attention (Davidson 1969; Blackburn 1984, Ch. 7). The problem with this objection is that in philosophy careful analysis can often show that what at first seems to be a mere truism may conceal unexpected complexities. One impressive example of this is the causal theory of action. Who could at first glance foresee that after analysis such a simple thing as human action would reveal such a great variety of often very complex processes? In what follows, I hope to convince you that the correspondence theory of truth is a similar case. The supposed simplicity of the correspondence relation is only apparent, revealing our lack of awareness of what we really do when making truth-claims.
   Methodologically, my strategy consists in reconsidering the best insights on the correspondence theory and in asking how far they can be developed and combined in order to lead us to a full-blooded analysis of the correspondence relation. This, as will be seen, ultimately requires a pragmatic investigation of the dynamic constitution of correspondence, which in the end exposes its intimate relationship with verifiability and the criteria of truth. To begin with, however, I need to make clear the definition of truth handed down by tradition, which is nothing but an abstract description of the general form of the correspondence relation.

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

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

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

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

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

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

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

The concept of dog means a rule according to which my imagination in general delineates the figure [pattern] of a four footed animal, without being limited to any particular figure offered by experience or by any possible image that I can represent in concreto. (Kant 1988, A 141)

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

1.     ‘jFp & jFm & Wm’.

Assuming that we know the identification rules for John, Peter and Mary, along with the ascription rules of the predicates ‘…is the father of…’ and ‘…is a writer’, along with the semantic rule of application of the logical operator ‘&’ (which is provided by its truth-table), we know that this statement might be true. In other words, we know that we can combine these semantic-cognitive rules, applying them imaginatively in order to conceive a possible state of affairs corresponding to the thought-content, giving to the statement, if not truth, at least a full meaning. If the statement is false, the discovered correspondence stops here, as a correspondence with a possible but non-actual fact. Now, suppose that statement (1) is true. In this case, we have:

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

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

3. Formalizing the correspondence relation
Assuming the suggested analysis of correspondence, we can symbolically express what could be called a formal definition of truth: the logical structure by means of which the predicate ‘…is true’ is identified with the predicate ‘…it corresponds with a fact’. As with the predication of existence, the predication of truth is of a higher-order. It is a semantically metalinguistic predicate applicable to thought-contents. We call a predicate semantically metalinguistic when it refers primarily to the content of the object language, contrasting it with a syntactically metalinguistic predicate, which refers only to the symbolic dimension of the object language.  The statement ‘“Themistocles won the battle of Salamis” is a historical statement’ serves as an illustration. The semantic metapredicate ‘…is a historical statement’ refers metalinguistically primarily to the semantic content of its object-sentence, that is, to its thought-content, and by means of this secondarily also to the real historical fact. According to this view, for any thought or content of belief p, to say that p is true is the same as to say that corresponds to a real factual content. We can express this symbolically, using p to express the thought-content, and replacing the predicate expression ‘…is true’ with T and the predicative expression ‘... corresponds to a real fact’ with C. The predicates T and C are semantic metapredicates belonging to a semantic metalanguage by means of which they refer to the thought-content expressed by p, which can be shown by placing p in quotation marks. Here is my first formal definition of truth:

(1)   T ‘p’ = C ‘p[6]

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

(2)   ‘pT*‘q’ = ‘pC*‘q

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

(3) T‘p’ = C‘p’ = V‘p’

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

(4) ‘p’T*‘q’ = ‘p’C*‘q’ = ‘p’V*‘q

These are, I believe, the best ways to present in an abstract formal way the general identifications between attributions of truth, correspondence and the verifiability procedure.

4. Negative truths
Now, consider a false singular predicative or relational statement p. Since it is false, such a statement does not correspond to any real fact in the world. But to say that p is false is the same as to deny that p is true, to say that the statement ~p is true. And here we have a problem. If ~p is true and we accept correspondence theory, it seems that ~p must correspond to a fact. However, suppose that we replace p with the false statement (i) ‘Thetetus is flying.’ In this case ~p is (ii) ‘Thetetus is not flying.’ Then, at first glance it seems that we have a true statement that does not correspond to any fact in the world! This would lead some to suspect that sentence (ii) is true because it refers to a ghostly negative fact: the unworldly fact that Thetetus isn’t flying.
   With the help of our preceding formulations, it is easy to reach a more plausible answer. The statement that ~p is true does not correspond to any actual fact in the world, even if we know that Thetetus is in fact sitting, since according to ~p he could also be standing. However, as ~p means the same as ‘p is false’, and by saying that p is false one denies correspondence with the real fact in the world. Despite this, as I have insisted, by considering the false idea that Thetetus is flying we still accept that p corresponds with a possible fact, namely, with our imaginary state of affairs of Thetetus flying... But this imaginable, conceivable fact, is no fact in any metaphysical sense; it is something that is located somewhere in our brains when we imagine it. Finally, ‘p is false’ means that p expresses a verifiability rule that although applicable to an only conceivable or imaginary state of affairs, a possible fact, does not effectively apply to any real, actual fact in the world.
   Summarizing, if you consider the following general statement: ‘There is no cat with three heads’, it means the same thing as ‘It is false that there is a cat with three heads’. This simply affirms that although there is a corresponding conceivable fact-object that is a cat with three heads, there is no actual fact-object in the world that is a cat with three heads. One could still argue that the statement that there is no cat with three heads is true, because it agrees with the fact that there is indeed no cat in the world with three heads (Searle 1998: 393). However, here I must disagree. It is more reasonable to think that this is a mere façon de parler allowed by the flexibility of our natural language.[7]

5. Self-referentiality
As expected, the identifications we have made until now also enable us to develop a kind of Tarskian answer to the so-called liar paradoxes of self-referentiality. Consider the following standard self-referential statement:

This statement is false.

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

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

If statement (1) is true, then (2) is true; But if (2) is true, then (1) must be false... On the other hand, if statement (1) is false, then (2) must be false; but if (2) is false, then (1) is true.
   Having in mind our formal definitions of truth as correspondence, the general answer is that self-referential statements like these are incorrectly constructed because in all these cases the predicate ‘…is true’ does not work as a semantically metalinguistic predicate referring to a complete thought-content. Rather it functions as a normal predicate built into the thought-content, also belonging forcefully to the object language. Being incorrectly constructed, these state­ments have no real cognitive meaning beyond their grammatical form. They might seem meaningful on the surface, suggesting that we should treat them as we would treat a statement with the form ‘is true’ or ‘is false.’ Once we have fallen into this trap, paradoxical consequences follow.
   Normally a statement does not need the addition that it is true in order to be understood as expressing a truth, that is, a verifying rule that is effectively applicable. As in the statement ‘The sky is blue’, typically the truth-claim is already implicit. Because of this, the statement ‘This sentence is false’, though affirming its lack of applicability, naturally generates its truth-claim, since what it affirms is seen as true. The statement ‘This sentence is true’, to the contrary, affirming its own applicability, though also devoid of content, resists a paradox-generating interpretation, because the affirmation of its own applicability does not generate a statement that implicitly affirms its lack of applicability or falsity.
   Now, consider the sentence ‘It is true that this sentence has nine words.’  This is a perfectly normal true sentence referring to itself. But why? The reason is that the metapredication of truth is applied to the thought-content that the sentence in question has nine words without belonging to this thought-content. One could unpack what is compressed in this sentence as: ‘The thought expressed by the sentence “It is true that this sentence has nine words” is true’, which makes it clear that the attribution of truth is not inbuilt in the relevant thought-content.
   Furthermore, we can predicate truth of a metalinguistic thought-content insofar as this semantic predication is meta-metalinguistic and so on, since the s-thought, as an arrangement of only apparently disembodied mental tropes, is also a fact.

6. Pragmatics of the correspondence relation
What we have seen until now was the frozen logical structure of truth as correspondence. Now we will see how it works in the practice of truth-attributions that provides us with what some have called the criteria of truth. The view I wish to defend here was inspired by Moritz Schlick’s short defense of the correspondence theory of truth (1910), though in my judgment this might be seen as the reconstruction of a fundamental insight attributable to Edmund Husserl (see sec. 20 of the present chapter). The idea is that correspondence has a pragmatic or dynamic dimension that deserves to be explored and cannot be captured in the earlier formal definitions – an idea that should not sound strange to those who wish to integrate correspondentialism with verificationism. We can begin by considering that very often we can establish an idealized sequence of four successive temporal moments, which we may call: (1) suppositional, (2) evidential (3) confrontational and (4) judgmental or conclusive. Together they constitute a very common form of verification procedure.[8]
   The best way to introduce the idea is by means of examples. Schlick used the example of Le Verrier’s prediction of the planet Neptune’s existence based on orbital perturbations of Saturn: he first made a hypothesis that was later confirmed by observation, which made the hypothesis true, since the content of both is identical. I can offer a more trivial example. Suppose that it is the rainy season in Northeast of Brazil and that I ask myself p: ‘Will it rain in Natal tomorrow?’ This is the suppositional moment. Now, when tomorrow comes, I open the door of my house and see that it is in fact raining outside. This is the second, the evidential moment. Once I do this, I compare my earlier question with the observational evidence that it is in fact raining and see that the content of the question is like the content of my observation. This is the confrontational moment. Finally, considering that these contents are qualitatively identical (satisfying the conditions (i) to (vi) of correspondence) I conclude that the thought-content of my earlier hypothesis p is true by correspondence with the fact that it is raining today in Natal. This is the judgmental or conclusive moment.
   Examples like the former can be multiplied, and a similar procedure, as we will see, applies to non-observational truths. But for now, restricting myself to perceptual judgments, I can say that at least regarding cases like those considered above, we can formulate the following action-schema with four steps:

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

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

?p!o, p = o /├ p

This analysis shows that in many cases one finds correspondence between some suppositional thought-content (which is only a considered or imagined verifying rule in its possible application) and some perceptual content (given by the effectively applied verifying rule) that within the linguistic practice in which it is given is stipulated as beyond doubt.
   It is also worth noting that the standard statement of ├p (a judgment) has the form of the report of an assertion that is settled and finished. However, this assertion can always be questioned again later. In this case, new verifying procedures can reconfirm the judgment or detect some inadequacy in an at least virtually interpersonal way (cf. Sokolowsky 1974, Ch. 9).[9] 
   Now, how can we understand the correspondence relation as qualitative identity of content (structural isomorphism, identity of rules in their connection, intentionality…) for the example ‘It is raining now in Natal’ in terms of application of verifiability rules? The indexical phrase ‘now in Natal’ expresses the building of an identifying rule of a spatio-temporal region to which it adds the predicate ‘is raining’ (‘Now in Natal it is raining’). This expresses an ascription rule that effectively applies to the region by the satisfaction of configurations of tropes constituted by countless drops of water falling from the sky. This combination of satisfactions gives me the arrangement that constitutes the sub-fact that is the truthmaker which allows me to infer the content building the grounding fact that it is raining in Natal today. This supposedly has the same structure as its verifiability rule inversely projected on the outside world (Ch. IV, sec. 19).

7. Anterograde versus retrograde procedures
Now, what was presented above is what we may call an anterograde way to reach truth, since we went temporally from the hypothesis to the perceptual evidence that confirms the hypothesis by having a qualitatively identical content. However, a move in the opposite direction is equally feasible. We can have a truth-value attribution that has its origin in own perceptual experience, progressing from the evidence to the hypothesis – a way to discover truth that we may call retrograde.[10]
   Here is a simple example of a retrograde verifiability process. I open the door of my home with the intention of going out and unexpectedly see that it is raining. Then I go back inside to look for an umbrella after reaching the obvious conclusion that it is raining... In this case, the perceptual evidence comes first. However, it seems clear that the recognition of truth does not occur as a direct product of sensory experience, since I could see rain without taking note of it. This means that the sensory-perceptual state that comes first is different from the state of conscious awareness that follows, namely, that it is raining. (Suppose I open the door to get some fresh air and do not even pay any attention to the fact that it is raining outside. If someone then asks me if it is raining, I will recall the conceptual rule for rain, compare the rule with just memorized perceptual data and answer in the affirmative). Thus, it seems that here we can explain the process of arriving at the truth included in the judgment of the given example in the following way: First, I have the observational experience o! Then (during or after it) I recall the ascription rule for raining, which is like a consideration of the supposition ?p. Finally, I compare the content of my observation with the content of the recalled idea of raining; once I see that o = p, I am led to the conclusion that it is true that it is raining or ├p. We could summarize this process of retrograde discovery of truth in the following sequential formulation:

!o, ?p, o = p /├ p

Clearer cases of retrograde awareness of truth occur when someone has an unexpected sensation. If I wake up in the middle of the night with a strange feeling in my right leg, I may at first not identify this as pain, and we may call it !s. Then I unconsciously recall the idea of pain, subjecting it to consideration: ?p (it can be that I require some time to identify the pain as pain, first mistaking it for a cramp). Since now I clearly identify s with p, I decide that I feel pain in my right leg, i.e., I reach the conclusion ├p. A similar example is the case when someone gives me a sweet beverage to drink without saying what it is. Since I do not know what happened before in the context, I may need some minutes to bring to memory the obvious answer: it is juice of pressed sugar cane.

   The cases I have considered until now are the simplest sensory-perceptual cases. However, the pragmatics of correspondence can be extended to the truth of non-observational thoughts, which I will here call mediated thought-contents. Suppose that Lucy is at Charles de Gaulle Airport in Paris, waiting to board a flight to Dakar. The flight time is approximately five hours. She calls her daughter, who lives on a farm in Senegal and asks her how the weather is in the city of Dakar, that is, if it is good; this is ?p. Suppose that after a while her daughter answers that the weather in Dakar is and will remain good and warm enough. There is no significant reason for doubting this information, which she takes as giving appropriate evidence. The thought-content !q that she had after she heard about the weather in Dakar is the same as the thought-content belonging to her hopeful question ?p. Consequently, since p = q, she concludes that p is true, that the weather in Dakar is and will remain good. But the thought-content expressed by !q is not an observational thought! It is the result of testimonial inferences that are unknown to Lucy. Suppose that her daughter got this information from her husband, who had read a weather report in the internet, and that this information has its origin in meteorological observations of the weather conditions around Dakar. In this case, putting ‘>>>’ in the place of some chain of reasoning unknown to Lucy that leads to !q, and putting ‘!o’ in the place of the observational meteorological thought-contents that in some way led to !q (which is similar to those that she will have when she arrives in Dakar five hours later), we can formally structure the verification process in which p is presently made true for Lucy as follows:

?p, (!o >>> !q), !q, p = q /├ p

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

 (!o >>> !q), !q, ?p, q = p /├ p

We see that the difference between anterograde and retrograde verification repeats on its mediated levels. We may guess whether the intuitions of some researcher who still does not know how to prove some hypothesis, though having a glimpse of its truth, depends on unconsciously noticing that the knowledge of some factual content expressed by !q might be derived from evidential observations or postulates.

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

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

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

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

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

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

As in the previous cases, this example is about a deductive general conclusion, but it is easy to see that inductive generalizations should also have similar structures, given that they are also restricted to some more or less vague domain (see Appendix to Chapter V, sec. 3).
   The next point is the old question of knowing if there must be general facts over and above singular facts (Russell 1918; Armstrong 2004, Ch. VI). Bertrand Russell, who seems to have discovered the problem, defended their existence as follows:

I think that when you have enumerated all the atomic facts in the world, it is a further fact about the world that those are all the atomic facts there are about the world, and that is just as much an objective fact about the world as any of them are. It is clear, I think, that you must admit general facts as distinct from and over and above particular facts (Russell 1956: 236, my italics).

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

9. Some questioned facts
There are many puzzling cases, and I will only select a few to give an indicative solution. One of these is that of self-psychic (self-reported) truths. It is easy to know the truth-value of the thought p: ‘I am in pain.’ I believe that here as well there is a correspondence and that it is as follows. First, we learn interpersonally to identify the location of pain. Then, simply by inductive exclusion (helped by many other concomitant observable occurrences…) we learn an ascription rule to identify the kind of feeling we have when we feel pain, applying this rule to verify our headache. Even if we cannot have interpersonal access to pain, we can make our identification highly plausible, and even the logical possibility of this interpersonal access isn’t excluded.[11] Second, suppose that I have a headache. The first thing I have is the feeling of pain: !s. Then comes ?p: the actualization of the memory of what the feeling of having a headache means, which is what I associate with the word. Then I make the identification s = p and reach the conclusion ├p:

!s, ?p, s = p /├ p

I discover the truth that I have a headache in a retrograde way. An anterograde way to reach the same truth would be the case of a person who guess that she will have a headache because she has drunk red wine, and she always has a headache after drinking red wine.
   Wittgenstein offered, as is well known, an expressivist explanation for such cases. For him the utterance ‘I am in pain’ is nothing more than an extension of natural expressions of pain like ‘Ouch!’ (Wittgenstein 1984c, I, sec. 244). In this case, our schema would be something like ‘!s ├ p’ without a correspondence. This is possible. But I find it easier to believe that this could be the expression of a more direct reaction that turns out to be seen as true only after the exercise of the previous, more elaborate cognitive process of induction by exclusion and analogy concerning the hetero-psychic state (cf. Costa 2011, Ch. 4).
   An odd case is that of true counterfactual conditionals. Consider the statement (i) ‘If Evelyn were the queen of England she would be a well-known person’. The objection is that there appears to be no fact that can make this sentence true, since the truth-value of the antecedent is false: she isn’t the queen of England. However, statement (i) seems to be a true! The solution is easy. Although there is no actual fact that can make the statement true, this is not what the conditional requires. What statement (i) requires as its verifier is not an actual fact, but only a possible fact. The possible or conceivable fact that makes the statement true is that under the assumption that the antecedent were true, namely, that Evelyn were the queen of England, the truth of the consequent would be nearly unavoidable, that is, she would be a well-known person. The truthmaker of (i) is a modal fact that we could also express using the vocabulary of possible worlds. We can say that there is a near possible world We in which Evelyn is in fact the queen of England. Since in our world all queens of England are well-known, we can infer that if someone is the queen of England in We, this person will be also well-known. Assuming that Evelyn is the queen of England in We, she is also well-known in We. We conclude that it is true that if Evelyn were the queen of England she would be well-known because the expressed thought-content corresponds with a fact belonging to conceived counterfactual circumstance given in We. A second example: (ii) ‘Martin Luther King never killed anyone, but he could’. It is true because it means the same thing as ‘Although Martin Luther King never killed anyone in the actual world, there is a possible world Wm where Martin killed someone’. This is a true statement, since it corresponds to the conjunction of an actual and a possible (imaginary) fact, both existing, the first as an actuality and the second as a mere possibility.
   We could also ask about ethical truths. Consider the statement (iii) ‘Dennis should help the drowning child’. Suppose that Dennis didn’t even try to help the drowning child, because he is a psychopath. We would not say that (iii) is true, but that (iii) is right. It is right in a similar way as an illocutionary act like ‘I promise to go to your anniversary celebration’ can be felicitous. The statement about Dennis is morally right because it is in conformity with a rule, let us say the rule according to which (iv) ‘One should help another person in mortal danger, as far as one does not put oneself in great danger’. What is in question in this case is not truth, but normative correctness – correspondence with a norm, if you will. Finally, there is still the case of ethical norms and principles. Consider the following utilitarian principle: (v) ‘A morally correct rule is one which when applied (ceteris paribus) brings the greatest possible amount of happiness to all’. If it is a fact that when people act in accordance with this principle the well-being of their whole community increases, then this principle is true. The truthmaker of statement (v) would be a fact in the world.
   The greatest problem with ethical statements, however, is the same as with any other philosophical statement. They belong to speculative domains wherein we are only able to make the truth of our statements more or less plausible. Unlike natural science, philosophy is inseparable from all that we are still unable to know for sure.

10. Extension to formal sciences
Analogous logical structures and dynamic procedures can be found in the formal sciences, allowing us to generalize the correspondence theory to a domain traditionally occupied by coherence theories of truth. The important difference is that while for empirical truths inferences are typically inductive, for formal truths they are deductive. Suppose we want to demonstrate that the sum of the angles of any Euclidean triangle is 180°. We can do this by first proposing that this could be the case: ?p. Then we search for proof. We can do this by tracing a straight line that touches one of the vertices of the triangle, so that this line is parallel to the side opposite to this vertex. Since the three juxtaposed angles formed by the parallel and the triangle are the same as the internal angles of the two opposed vertices of the triangle plus the angle of the first vertex, and their sum is obviously 180°, we conclude that the sum of the internal angles of this and indeed of any Euclidean triangle must be 180°. This deductive conclusion is the evidence !q – the truthmaker as a geometrical fact.  Since we see that the content of !q is the same as the content of the hypothesis ?p, we conclude ├p. Using ‘as’ for the axioms or assumptions, the form of this anterograde procedure can be summarized as:

?p, !as >>> !q, p = q, /├ p

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

?p, !d  >>> !q,  p = q /├ p

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

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

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

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

?p, !as >>> !q, p = q, /├ p

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

!q, !as >>> !q, ?p, q = p, /├ p

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

11. Why can analytic truths be called true?
Finally, we can apply a similar procedure to analytic-conceptual statements, showing that they are also called true because of correspondence, even if this is a limiting-case. It is possible to say, for instance, that the analytic statements ‘It is raining or it is not raining’ and ‘Bachelors are not married’ are true because they correspond to the respective facts that it is necessarily either raining or not, and that it isn’t possible that a bachelor can be married. But to what extent are we entitled to say this?
   Assume first, as we did in our objections to Quine’s argument against analyticity, that analytic statements are true due to a proper combination of the component senses of their expressions. In this case, our question is:  are there facts that make analytic thoughts true? In the case in which these facts exist, how are they true? Consider the following analytic statements:

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

   Surely, these statements are all true by definition: if there is a fact making them true, it is not a fact in the world. However, we are still allowed to say that they are made true by conceptual or logical-conceptual facts. Statement (1) is made true by the logical fact that ‘j ˅ ~j’ (the law of the excluded middle) that it instantiates. Statement (2) is made true by the logical-conceptual fact that the brother-sister relation is reflexive. Statement (3) is made true by the conceptual fact that a bachelor is conventionally defined as an unmarried adult male. Statement (4) is made true by the conceptual fact that a triangle can be defined in Euclidian geometry as a closed plane figure with three straight-line sides. And statement (5) is made true by the conceptual fact that it is part of the definition of a material body that it has some spatial extension. These are facts belonging to our defined conceptual structures; they are conceptual facts instantiated and constituted by mental tropes.
   Moreover, we can summarize the process of self-verification of the above statements in the same way we did with the statements considered in the last section. Thus, in case (1) we can begin with the question ?p1 = ‘is it the case that it is raining or not?’ Faced with this, we immediately realize that the sentence instantiates the principle of the excluded middle or ‘j ˅ ~j’, and that this instantiation, like any other, can be symbolized as the instantiation of the logical truth or fact !p2, which can be proved to be true by means of a truth-table. This is enough to make ?p1 true, because we can see that independently of the senses given to its constituents, its logical structure warrants its truth. We can summarize the self-verifying process in which we find the correspondence in the same anterograde way as in the first of our examples:

?p1, !p2, p1 = p2 /├ p

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

 ?p1, !d → !p2, p1 = p2 /├ p1

It is correct to say that analytical thought-contents are true by cortesy, since they cannot be false. But it is not meaningless to speak of their truth as correspondence with facts. The reason is clearer in cases like the last one. For even if these cases are all of self-verification, the procedure is not always direct and transparent, often demanding some degree of reasoning.

12. The insufficiency of coherence
That truth has something to do with coherence is beyond doubt. If Mary tells us she was breathing while she was asleep last night, we accept her statement as obviously true. We believe Mary even if we did not watch her sleep last night, because her statement is coherent with our accepted belief-system. We are certain that people will die within minutes if they cannot continuously breathe oxygen. If Mary says that she was on the planet Mars while asleep last night, nearly everyone would consider this statement to be false, because it clashes with the generally accepted commonsense understanding of what is possible or impossible in ordinary life circumstances and with our system of scientifically confirmed beliefs. Coherence is obviously related to truth, and according to most coherence theorists, a belief is more true the more it is integrated into our system of beliefs, which also means that truth is a question of degree (Blanshard, Ch. XXVII).
   Bernard Bosanquet (2015: 24) once gave an interesting example intended to show that a greater amount of supporting information makes a statement more true, which seems to vindicate the idea that the integration of a statement within a system of beliefs is what makes the statement true. He notes that the sentence ‘Charles I died on the scaffold’ seems quite true when said by a leading historian and far less true when said by a mere schoolboy. The child has at most a name and a picture in mind, while the historian knows from documents and historical studies by other historians the context, reasons, sequence of causal events, and a wealth of meanings associated with the sentence (cf. Blanchard, Ch. XXVII, sec. 4-5). If this example does not show that increasing the coherence of a statement increases its degree of truth, it at least shows, I think, that it makes the historian’s claim to know its truth (his truth-holding) more probable.
   Since countless possible belief systems can be constructed, one basic objection against coherence theory is that any proposition p could be true in one system and false in another, violating the principle of non-contradiction. This objection, however, does not seem to be regarded as a major difficulty by coherence theorists (e.g. Bradley 1914; Blanshard 1939, vol. 2: 276 f.; Walker 1989: 25-40). One could, for instance, answer that what ultimately counts as the truth of a belief is its coherence with the system of all systems, namely, the most encompassing system of beliefs agreed upon by a community of ideas at time t (preferably ‘the best informed community of our present time’), which we may call the real-world system. This would answer the objection that some thought-content can be true in one system and false in another in a way that leads to a contradiction. For instance, the novel Madame Bovary would be a fictional subsystem belonging to the all-encompassing real-world system, as much as do the subsystem of Marxism-Leninism and the subsystem of Euclidean geometry. And some could be seen as true in its coherence with one of these subsystems, but still ultimately false in its coherence with the all-encompassing real-world system, since these subsystems are held to be false in their coherence with the latter.[12] Nonetheless, even after this or any other strategy, coherence theory remains problematic, since the insurmountable problem of this view is located elsewhere. One can call it the problem of circularity.
   The problem of circularity arises when we try to define coherence. Traditionally coherence has been conflated with consistency. A set of propositions (thought-contents) is said to be consistent when the conjunctions of propositions belonging to it do not generate contradictions. Consistency may be a necessary condition for coherence, but it is surely not sufficient. For instance, consider the elements of the consistent set {Shakespeare was a playwright; lead is a heavy metal, 7 + 5 = 12}. Since they do not have anything in common, this set increases neither the coherence nor the truth of its elements; and we could build a large set of this kind with ‘zero’ coherence. Moreover, any definition of truth based on consistency would be circular, since consistency, being defined as the absence of contradictions between the elements of a set of propositions, affirms that their conjunctions cannot be false, in this way including the concept of truth-value in its own definiens.
   More than just being consistent, coherence must be defined as inferential. The coherence of a system of propositions is in fact determined by the dependence of this system on the inductive and/or deductive relationships between its propositions. The degree of coherence of a proposition should be determined by its inductive and/or deductive relationships with the system to which it belongs (cf. Bonjour 1985: 98-100). Indeed, we know it is true that Mary was breathing the whole night long, because this claim is inductively supported by everything we practically and scientifically know about what sustains a human organism alive.
   However, if we consider coherence as the only and proper mechanism able to generate truth, this definition also leads to contradictions. For the concepts of inductive and deductive inference are also defined by means of truth! A strong inductive inference is defined as an inference that makes a conclusion probably true, given the truth of its assumptions, while a valid deductive inference is defined as an inference that makes its conclusion necessarily true, given the truth of its assumptions. Consequently, the coherence account of truth can only generate the truth of any proposition of the system by assuming the truth of at least some of its other propositions, which makes the coherence view circular. Any form of pure coherence theory is a victim of a petitio principii, as it simply assumes what it aims to explain.

13. Coherence as mediator
The view of coherence proposed here enables us to circumvent this difficulty. The reason is that in my understanding coherence is a complementary dimension of correspondence theory, namely, the condition that enables the transmission of truth in a network of thought-contents, usually beginning with those that are based on empirical (sensory-perceptual) experiences and/or some assumed formal evidence (theorems or postulates). This condition allows us to finally accept some factual content that should make some proposition true without the need for reducing this factual content either to some corresponding formal axiom or to an evident perceptual or self-psychic thought-content. For instance, we know that the statement ‘Mary was breathing when she was asleep last night’ is true, and it is true because it corresponds to the factual content that Mary was breathing during her sleep. But usually we reach our belief that a statement like that is true by correspondence to a fact by means of coherence, that is, by means of inferences derived from our system of beliefs. These inferences transmit what we may call the veritative force – which we may define as any positive probability of truth – from one proposition to the other. However, this veritative force cannot arise from the inferential transmission of propositions without truth-value, but instead derives from propositions ultimately based on a myriad of perceptual experiences that have provided our knowledge of biological laws, as well as our commonsense awareness that Mary is a living human being like us.
   We begin to see that even if coherence cannot be regarded as defining truth, it plays an important role as a mediating procedure whereby correspondence is found. The modal proof of P → ◊P in our example does not come directly from AS1 and AS3 plus some rules of propositional logic. We have some deductive inferential steps, and these steps are already constitutive of the coherential dimension of the verification procedure, which some coherence theorists erroneously saw as the proper criterion of truth for the formal sciences. In the present case, coherence is constituted by material implications transmitting the veritative force (here understood as a material implication from postulated truths), but, as already noted, it inevitably contains inductive inferences in the case of the verification of empirical thoughts.
   This latter case can be better illustrated by two examples that make clearer the relationship between coherence and correspondence. First, suppose that someone anonymously sent me a present. I open it and see that it is a book called The Cloven Viscount by Italo Calvino. I wonder if a friend named Sylvia sent it to me. I once knew Sylvia as a literature student in Rome, and at that time I gave her a copy of Calvino’s book The Invisible Cities. However, the package was mailed from Rio de Janeiro. Thus, I realized that this book could have been sent by someone else, for example, a person living in Brazil… But then, I reflect that Sylvia could well be back home in Rio de Janeiro, a city where she was born and lived most of her life. An advocate of the coherence theory of truth would say that the thought-content of the statement p = ‘My friend Sylvia sent me a copy of The Cloven Viscount’ is made true by its coherence with other thought-contents, which can be ordered in the following way:

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

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

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

We understand now how coherence is a part of truth-discovery processes. And we see why the coherence of our empirical claims would have no force if it weren’t anchored in perceptual experience taken as evidence in the case of empirical truths, and in axioms or postulates in the case of formal truths. This is why a fictional text can be perfectly coherent without in this way giving us any factual truth. Its anchors are imaginary ones.
   This kind of reasoning invites us to think that correspondence comes first, since correspondence is what reveals truth. Moreover, there can in this way be correspondence without coherence, but no coherence without correspondence. However, this conclusion seems too hasty at first, when we consider that all observation is conceptually charged or theory-impregnated, as Pierre Duhem (1906, Ch. VI, sec. II), Karl Popper (1972, Ch. 2, sec. 18) and many others have insisted. For to be conceptualized, experience requires coherence with at least parts of our belief-system. One could reply that one should not confuse meaning with truth: it is the meaning of experience that requires inferential relations with our belief system, but veritative force arises from correspondence and not coherence. This answer seems to work when we consider the retrograde correspondence process, since it begins with a kind of raw experience (!o) and in itself does not seem to demand even the inferential relations inherent in conceptualization. But the problem threatens to return with the conceptual recognition of ?p and its subsequent perceptual confirmation.
   Nonetheless, I think that I can give a stronger justification for the necessity of correspondence as the origin of veritative force by analyzing the kind of input that our system of beliefs gives to a particular observation. Suppose that you go for a walk in a nearby field and are surprised to see what seems to be a living unicorn. You probably distrust your own senses, since you know that unicorns do not exist. Later you learn that it was actually a fantasy unicorn: a film production team had fastened a fake horn on a horse to create this illusion. Between scenes, the pretend unicorn was allowed to graze in the field. The defender of coherence theory would say this proves that even sense-perceptual observation can be falsified by our system of beliefs. But wait a moment! This argument is completely refuted when we consider that what was responsible for our mistrust was not the system of beliefs as a whole, but the correspondence of other perceptual experiences. Indeed, we know that unicorns are mytho­logical creatures, and there have been no scientifically confirmed observations of unicorns or their remains. Moreover, we know that evolutionary classifications of animals like horses and goats rule out the possible existence of unicorns. But these firm beliefs against the existence of unicorns were all gained with the aid of induction by means of a myriad of other sensory-perceptual testimonial observations that were historically and scientifically made and passed on to us. This means that our sensory-perceptual observation that we truly saw a unicorn was in the end discredited, not by the system of beliefs as a whole, but by counter-evidence given by other direct correspondences also originating from perceptual observation. In other words: we agree that although sensory-perception is the origin of the veritative force of empirical judgment, this judgment can gain or lose veritative force due to greater or lesser coherence with a system of beliefs. However, this confirming or rejecting coherence can acquire veritative force only indirectly from other sensory-perceptual observations. Reflection on this leads us to the inevitable conclusion that the true origin of the veritative force of empirical judgments is always sense-perception, giving coherence the second­ary but indispensable role of transmitting veritative force. My conclusion is that under scrutiny the supposed counter-example only shows that correspondence comes first, because it is the only real source of truth. Thus, instead of defending an impure coherence theory, as Walker tried to do, I defend what he would call ‘impure’ correspondence theory.
At the risk of boring readers, I offer a second and clearer example, this time concerning a judge’s verdict. It is well known that court judgments in criminal trials frequently cannot rely on direct perceptual evidence supplied by witnesses; because of this, they are often heavily dependent on coherence. This was the case with an American minister named Reverend David, who shortly after marrying a certain Mrs Rose was admitted to a hospital suffering from severe abdominal pain. Since examination showed a high level of arsenic in Reverend David’s blood, a thought-content that we abbreviate as !rthe following suspicion arose as the result of abductive reasoning: ?p, which abbreviates the question: ‘Did Mrs Rose try to poison Reverend David?’ The following additional factual evidence later confirmed this suspicion:

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

We can now construct the following retroanterograde verification process:

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

   Certainly, the conjunction of the statements rst, and u combines all the statements to form a strong inductive inference assuring us practical certainty that !q, which states an unobserved factual content (namely, that Mrs Rose did indeed try to poison her husband). This stated factual content confirms our initial suspicion ?p derived from !r. However, a crucial point to be noticed is that factual statements rst, and u are all considered true due to correspondence with public factual observation or by derivation from publicly observed perceptual factual contents. Again, what is shown is that the element of coherence cannot stand alone. The plausibility of q is grounded by means of coherence on the conjunction of the observational statements rst and u. But they are all true because of their correspondence with observational contents, even if they may also rest on empirically grounded theoretical assumptions, the latter in some way also derived from perceptual experience. As we see, coherence alone cannot prove truth, because inductive and deductive coherence relations are defined as ways of preserving and not of finding truth.
   The conclusion is the same: coherence relations work like the cables of an electrical power grid: though they are not able to generate electricity, they are able to transmit it. A coherent system is not an independent mechanism, but only an inferential network by means of which the true derived from correspondence makes its ways. In other words: coherence only transfers the veritative force generated by the correspondence of the contents of more basic beliefs in empirical or formal facts with derived ones. These act within a belief system in order to produce the thought content expressed by the non-observed fact, which in the example is q. Here this content is accepted by us as representing the factual content corresponding with the thought-content of p because it has the same content, which means the same as making ?p true. Because q is in various ways reinforced in its application, we accept it as factual evidence that statement p is true. Statement p is true because it corresponds to the fact that Mrs Rose poisoned her husband, Reverend David, even if we know this fact not by observation, but only indirectly, from its coherence with other thought-contents that are observational and match facts in a direct way.
   The thought-content q, as we will explain, has a kind of Janus face: on the one hand, it expresses a thought-content (an s-thought, a proposition), and on the other hand, it represents what we are sure is objective factual content, namely, the fact that Mrs Rose tried to poison Reverend David. It is by being involved in correspondence that coherence is involved in truth. In sum: coherence is just an interdoxal mechanism by means of which correspondence can transfer its veritative force.
   Now, concerning the truth of the observational statements rstu, we return to the point already noticed when we analyzed the first example. All obser­vation is embedded in some (sub)system of beliefs. Although a chosen observa­tion r makes its own contribution to truth by means of direct correspondence with a fact (high level of arsenic in the blood), it can be reinforced by its coherence with the accepted system of beliefs in which it is embedded, or be rejected by this same system. But the force of the beliefs that lead us to this reinforcement or weakening is gained from direct correspondence with facts, though usually in a very derivative way. This finding leaves no room for a veritative force arising from coherence alone.
   The important question that remains open is about the precise status of q. It is the expression of a thought-content, but it must also be seen as able to represent the factual content, the real or actual fact. Are these two possibilities reconcilable?[13] This crucial question will be tackled in the following sections.

14. What about the truth of the truthmaker?
One of the most serious problems for the correspondence theory of truth concerns the infinite regress that arises from the factual evidence that verifies hypotheses – the truthmakers. We can pose the problem in the form of a dilemma: Either the evidential fact or factual content is unquestionable, or it can be doubted. Suppose (a) that it is unquestionably true. In this case, we seem to be guilty of dogmatism, because we treat our normal perceptual and even purely sensory truths[14] as beyond any possibility of being false. But this would not be in conformity with the fallibility of empirically based knowledge. We cannot be absolutely certain about the evidence for any (or almost any) empirically given factual content. Even formal axioms always have a degree of arbitrariness in their choice and can lose their applicability after changes in our broader system of beliefs. Now, suppose (b) that the evidential content believed to be a fact can be doubted. In this case, it seems that we need to search for new evidential content that would warrant its truth. Since this new factual content is likewise not beyond doubt, we would have to look for further evidential content and so on endlessly. If we cannot stop this regress, as it seems, we have no way to ground our suppositions, because any grounds we find will lack the necessary solidity.
   Restricting myself here to empirical truth, I think we can overcome this dilemma if we consider examples in sufficient detail. Consider the following example of an observational sentence !o: ‘There’s a dolphin swimming in the sea.’[15] Imagine that the truth of this sentence depends on the observation of a dolphin surfacing from time to time – an observation that can be interpersonally shared. For the first person who sees the dolphin, the procedure has a retrograde form:

!o, ?p, o = p /├ p.

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

p ~> ?p, !o, p = o /├ p.

But this does not mean that !othe given evidence, is absolutely warranted. It can be defeated. Suppose that due to a scarcity of real dolphins and in order to entertain tourists, a diver swims under the surface with a rubber dolphin attached to his back, surfacing from time to time in a way that gives dolphin watchers the illusion that they are seeing a real dolphin. In face of this, the factual content !o that should ground the verification of ?p is defeated. Those aware of the deception could exclaim: ‘It is false that there is a dolphin swimming in the sea’.
However, the answer to the problem does not seem very difficult. What we believe to be factual content need not be regarded as absolute. It may be only postulated or assumed to be an undoubtable factual content (or the real truthmaker) within the context of a practice that typically presupposes some background information and leaves aside the possibility of atypical circumstances that if present would defeat the assumption. Thus, consider the language-game or practice (A), in which we recognize things in normal daylight, great enough and near enough, put to work in the context of a tourist beach where dolphins are supposed to be sighted … In this practice we are allowed to assume that the observational content ‘I am seeing a dolphin that has just emerged from the sea’ is unquestionable evidence expressible by !o, that is, a matter of fact, a truthmaker or verifier that we accept as giving practical certainty that there is a dolphin in the sea. Assuming the informational content and the context at our disposal in this practice, and assuming that all other things remain the same, seeing a dolphin must undoubtedly be accepted as the truthmaker of the hypothesis ?p. Assuming that o also has internal phenomenal content (psychologically given sensory impressions), we could say that in this case we are allowed to assume that the thought-content of o, that is, without the underline (‘I am having the experience of seeing a dolphin emerging from the sea’) can be considered the vehicle of our experience of the real fact o given in the world (‘A real dolphin has just emerged from the sea’). But this assumption of evidence in practice can only be sustained under a ceteris paribus, namely: the assumption that the observation isn’t being defeated by some condition extraneous to the assumed informative contextual background.
   Now, in the given case the defeating extraneous condition is due to a shortage of real dolphins in the area, and is constituted by a diver swimming under the surface with a rubber dolphin on his back and sometimes rising to the surface in a way that gives tourists the impression they are seeing a real dolphin… Assuming that some observer S is aware of this information, what is given to him isn’t the practice (A) but a very different observational practice that we can call (B), which includes information about these unusual specific background circum­stances. In this (B) practice, we cannot postulate the observation of a real dolphin merely by experiencing the sight of a dolphin emerging from the sea. Under the circumstances presented by (B), in which rubber dolphins are carried along by a diver swimming under the surface, to observe a real dolphin would certainly require a closer and far more careful examination. For example, close underwater inspection might reveal a possibly fake rubber dolphin, which can be symbolized by o.’ In this new practice, the thought-content expressed by p could not be verified by !o, because !o isn’t really given to S, since he knows that o cannot be trusted to be a real dolphin. But ?p could be falsified by o,’ the more careful observation, as the following retroanterograde schema shows:

p ~> ?p, !o,’ p ≠ o’ /├ ~p

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

!o, ?p, p = o ├ p

However, it soon becomes clear to her that she has made a naïve mistake; what she really sees is a so-called inferior mirage caused by the refraction of sunlight by a layer of hot air near the ground. To the background conditions she adds unusual circumstances able to defeat normal perceptual evidence. As she has learned that unusual circumstances defeat the rules of normal observational practice (A), instead of thinking !p: ‘I am seeing a lake’, she thinks ├ ~p ‘I am not seeing a lake,’ eventually concluding:├q, ‘I am seeing a mirage’ or ‘I am seeing the blue of the sky’, which has the same content as what is regarded as the fact o’. What was first accepted as external evidence is now viewed as an erroneous interpretation of data, being replaced by the new practice (B), which allows the falsification of what was at first postulated as an unassailable truthmaker. We can state this change through the two following anterograde verification procedures belonging to practice (B):
         
?p, !o’, p ≠ !o’├ ~p
?q, !o’, q = !o’ ├  q

It is worth noting that the phenomenal content of perception is in any case the same: an impression of the color blue near the horizon. But the interpretation of this content is very different once it is read as factual content existing in the world. And it is different because a more complete awareness of the informational background given by the surrounding circumstances is able to defeat the natural interpretation of the visually-given content.

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

We break the circle by using our senses, by actually making the observations as a result of which we accept one statement and reject another. Of course, we use language to describe these observations. Facts do not figure in discourse except as true statements. But how could it be expected that they should? (Ayer 1963: 186)

Ayer’s words contain a strong appeal to common sense. Nevertheless, this appeal seems to contradict another enduring idea, which is also not alien to common sense, namely, the idea that the content of perceptual experience should be a kind of conceptually structured belief-content and therefore should be mental by nature. Consequently, we could never have direct and unquestionable access to anything referred to by a perceptual thought, namely, external facts as they are in themselves (e.g. Blanchard 1939, vol. 2: 228).
   One reaction to this dilemma would be to accept the sort of last resort called idealism, but today idealism sounds as a forbidden solution. This is the position that all of reality is in some sense mental. It conflicts with one of our most modest commonsense principles, namely, that an independent physical world exists around us. Furthermore, it seems to be the other way round: our empirical knowledge (particularly scientific knowledge) tells us that the mental is in some sense a minuscule emergent portion of the physical (even biochemical and biological) world, dependent on it to exist, something like the phenotype, which depends on the genotype to exist. In other words, it seems that the mental supervenes the physical insofar as experience – scientific or not – has shown. Moreover, if we remain on the side of our principle of established knowledge (Ch. II, sec.  4), idealism remains an anathema, since it denies not only the modest commonsense truth that the external world is non-mental, but also the scientific truth that the physical world as a whole has almost nothing to do with the mental. In some sense of the word, ‘emergent’ mind is an emergent property of life, which is an emergent property of organic chemistry, a carbon-based chemistry that is an emergent property of the atomic level of the physical world. Finally, from an anthropological perspective, idealism seems to appeal to wishful thinking, as in the philosophy of culture and the humanities, as thinkers from Nietzsche to Freud, Weber and Durkheim, have shown. Humanity pays a high price for having acquired consciousness. Although this makes people better able to act in self-defense, its also makes them aware that they are living in an unpredictable and dangerous world, and also gives them a clear sense of their own finitude. Idealism, by making the external world mental, can help them create the illusion that they could have some power over the external world. This is made to seem continuous with their minds and, last but not least, gives some hope of being able to gamble with their tragic fate. The upshot is that today more than ever before we have strong reasons to reject idealism in favor of epistemic realism.

16. Answering the objection of the linguistic-cognitive circle
It seems we can preserve a categorical opposition between the mental and the physical in the sense that the mental is cognitively-dependent and only experienced in the first-person, while the physical is (usually) cognitively-independent and experienced in the third-person. I would now like to defend direct realism as able to give a better answer to the objection of the linguistic-cognitive circle. Direct realism is the view that our senses provide direct awareness of the external world that shows it pretty much as it is. Direct realism differs from indirect realism or representationalism, which is the view that we have direct experience only of our sensations (or percepts or sense data), which inform us about the external world, so that the latter is never directly experienced.[16]
   My defense of direct realism begins with a demonstration that everything experienced in normal perception has a kind of Janus face. I mean that what is given in sensory-perceptual experience of the outside world can always be conceived as two different entities: one psychological and the other physical, as follows:

(A) The psychological experience of cognitively-dependent internally given sensory or psychological contents, also called sense data.

(B) The proper perceptual experience of cognitively-independent, externally given perceptual or material contents (understood as physically singularized properties or tropes, objects as clusters of tropes, real facts as arrangements of them).

Psychological experience (A) gives us what we may call sensory impressions or contents (also called ideas, phenomena, representations, sense data, sensations, sensa, qualia…). It seems beyond doubt that sensory contents are always present in perceptual experience, as I intend to show later. But thesis (B) also seems beyond doubt: it is the idea that in addition to sensory experience, when we perceive something, it is given to us as an external entity. Indeed, it is also commonsense truth to say that we usually perceive the external world as it really is, namely, as minimally constructed of cognitively-independent entities that are material or external tropes, by clusters of compresent external tropes with form and mass (mainly called material objects), and as arrangements of the first and second (rightly called facts).
   The clearest evidence favoring this double view is given by tactile experience (cf. Searle 2015: 24). Suppose I touch a hot stove with my hand. I can say I have a sensation of heat: this sensory-impression is the psychological content of experience (A). Alternatively, and correctly, I can also say that I have perceived that the stove is hot; this is the correct perceptual experience of the externally given physical entity (B). The essential point to notice in this example is that in the normal case we cannot phenomenally distinguish experience (A) from experience (B). Thus, for example, based on the same tactile experience I can say:

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

In a similar way I can say:

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

Now, from auditory experience, I can say:

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

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

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

As you can see, the phenomenal descriptions outside the brackets are the same, but in the (A) cases, I speak of sensory contents occurring in my head (sense data), while in the (B) cases I speak of independent physical contents – factual contents pre-existing in the external world. The real thing (B) is epistemically dependent on sense impressions (A), because without sense impressions (A), I couldn’t know (B). On the other hand, sense impressions (A) are ontologically dependent on (B), which causes (A).
   I think that the acceptance of the above duplicity of interpretation of one only phenomenal content is harmless and does not compromises direct realism. I can illustrate how harmless this duplicity is by comparing it with the kind of duplicity of our interpretation of objects that we see in a mirror. What we see in a mirror can be interpreted as: (A’) a simple image of things, for instance, the image of a vase of flowers on a table. But it can also be seen as: (B’) the vase in itself that I am seeing in a mirror. For instance, I can point to an object I see in a mirror, and you can ask me if I am pointing to the reflected image of the vase of flowers or to the real vase of flowers. That they belong to different domains is made clear by contextual differences: the image isn’t considered real, because we cannot touch or smell it. The real vase of flowers, on the other hand, can be touched, smelled, directly seen from all sides, manipulated, broken; its weight and its size can be definitely measured and shown to remain constant, independently of the changeable apparent size of its image, etc. We can change the apparent size of the image by bringing the vase closer to the mirror, this apparent distance doubles the real distance of the vase from the mirror, remaining only within its frame. However, by looking at the mirror, we would not be able to see the vase on the table without the help of the image; and the elements and relations between both will coincide, at least partially. Moreover, in this case access to the real vase is dependent on access to its image. As in the cases above, (B’) is epistemically dependent on (A’), because without the image (A’) you couldn’t see (B’). Alternatively, (A’) is ontologically (causally) dependent on (B’). This is why when you pay attention to an object in a mirror you see it as perceptually dependent on its image, but when you pay attention to the image, you see it as causally dependent on the real object. You can easily say that you see the reality through the image. But you will never say that you cannot see the object because what you really see is only its image. Moreover, you can also say (if you wish) that you are seeing the real vase directly through its image, if you compare it with the same vase seen in a photo. Finally, you can see either the real vase or its image – but not both together.
   As with any other metaphor, this one has limits, but I think it reinforces the idea that we can answer the objection of the linguistic-cognitive circle by saying that the content of any real experience can be interpreted in two ways: (a) internally and psychologically, as a first-person sensory-perceptual thought-content, and (b) externally, as a third-person physical fact or factual content. Insofar as we are able to interpret the given content also as an external factual content, we escape the linguistic-cognitive circle.
   A complementary but also fundamental point is that we almost never have a complete perceptual experience of factual content. Our experience is typically perspectival. We experience only facets, aspects and sub-facts. If from a position on the bank I see a fishing boat entering the mouth of Pirangi River, I experience (see) only one side of the fishing boat. However, by means of this dynamic sub-fact (an aspect of a process) I am not only able to say that I am seeing one side of the boat – the sub-fact – but more often that I also see the whole boat and the whole process of the real fishing boat entering the mouth of Pirangi River – the dynamic grounding fact (on facts, see Ch. IV, sec. 20-25).
   These are the almost commonsense ideas that in my view enable us to break the linguistic-cognitive circle. We can observe an external factual content and at the same time consider its phenomenal experience as involving a purelly sensory content, which is internal. The phenomenon of post-images illustrates the point: after looking at the sun one can close one’s eyes, and the image of the sun, its sense data, does not disappear immediately. The dichotomy considered above is important, because it is a condition for the already noticed defeasibility of observational evidence: under some conditions we can withdraw from perceptual content to sensory content.
   There is, however, a traditional argument designed to show that the kind of direct realism suggested above must be wrong.

17. Answering traditional arguments against direct realism
Against the form of direct realism that I have explicated above and favoring indirect realism or representationalism, there are two famous traditional arguments: the argument of illusion and the argument of science. I think that answering these arguments strengthens my own view. I will consider each of them separately.
   I begin with the famous argument of illusion. It usually concerns cases of perceptual illusions in which what we think we perceive is not what we should perceive, particularly in the extreme case of hallucinations in which we only imagine we are perceiving something. Although some hallucinations can be phenomenally indistinguishable from products of real perception, they are not real. There are many examples supporting the argument. They all aim to prove that in the best case perception is indirect, since it always occurs through the ‘veil of sensations.’ In what follows I summarily present several examples, some of which were already known in antiquity:

1.     I go outside in mid-winter without wearing gloves, although the temperature is minus 26 degrees. When I come back inside, my hands are stiff from the cold and I cannot feel them. I soak my hands in water at room temperature, but I feel that the water is warm! Thus, what I really feel is my sensations, and only through them can I gain information about external temperatures.
2.     I am near a speedway. A car passes me driving at high speed and because of the Doppler effect, its sound changes pitch from high to low. Thus, I do not hear the true sound, but only my auditory perception, which can inform me about sounds.
3.     A person with jaundice may in some rare cases see the world as yellow due to an accumulation of bilirubin in his eyes. Thus, what allows us to claim that we see the world in its true colors? 
4.     If I press the side of my right eye with my right finger, I have the impression that things in front of me move in the opposite direction. Consequently, what I see directly are only images of things, that is, sensory impressions, and not things as they are in themselves.
5.     If I hold my index finger fifty centimeters from my face and look at the other end of the room, I see two images of index fingers when focusing on the far wall. If I then focus my eyes on the finger, the two images merge into a single image. Since they are not phenomenally different in the two cases, I conclude that what I really see are sensory impressions of my index finger, even if I can locate my finger through these sense data.
6.     I look at a coin that I am holding at an angle. I know it is round, but it appears elliptical. Indeed, only occasionally do I see a coin with a round form, which is called its real form. So, what I primarily see are my sensory impressions.
7.     I see a lake in the desert, but soon I perceive that it is an inferior mirage caused by layers of hot air near to the sand, which refract the blue fron the sky. Since my sensory impressions are phenomenally the same, what I primarily see are my sensory impressions of a lake.
8.     Suppose I have a perfect hallucination of a white horse. What I see is not a real white horse, but only a hallucinatory image. Since this image made of sense data isn’t different from what I see when I see a real white horse, the primary object of perception must be my sensory impressions or sense-data.

The main conclusion of the argument of illusion is the rejection of direct realism, which should then be replaced by indirect realism, already accepted by Descartes and mainly attributed to Locke. The suggestion is that the objectively real world is perceived indirectly through the veil of sensations, which is formed by sensory perceptions or sense data.
   There is nowadays an extense philosophical literature aiming to show that the argument of illusion is fallacious and we directly perceive things around us as they really are.[17] One could object using the Kantian argument that we see how external things are for us and never how they really are in themselves. But since what they are for us is the only way to tell meaningfully that they can be something in themselves, what they are for us is also what they really are in themselves.
   In my understanding of direct realism I do not wish to deny that there are sensory impressions or sense data. I do not even wish to deny that we perceive the world through a veil of sensations or sense data, since by accepting (A) I accepted these conclu­sions. What I reject is the claim that these things make our perception indirect. For we never say we perceive our sensations; what we might say is that we perceive the world directly through our sensations or sensory impressions. This suggests that just because we can show that we perceive the external world through one or even several veils of sensations doesn’t make our perception of the external world indirect, and it is a category mistake to defend this view. Put simply: the central problem with the argument for illusions is that it is based on a misunderstanding of the semantics of our concept of directicity.[18] Consider the following three sentence pairs:

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

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

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

These examples show that what makes some relations direct is not necessarily the fact that we cannot find intermediaries between the relata – they very often exist and there can be more than just one. Directness/indirect­ness is an essentially conventional distinction that depends on the relevance of the intermediaries for what we aim to consider.
   In the case of perception, language conventions allow us to say that we perceive things around us directly, even if by means of a causal process involving a number of intermediaries. And there is nothing wrong in accepting the view that we perceive things directly by means of sense data or through a veil of sensations, just as much as there is nothing wrong in saying that the victim was struck directly by a bullet, though it first had to cross window glass.
   Having this in mind, if we again consider the examples of the argument of illusion one by one, we clearly see that perceiving things through sensory impressions does not mean that we perceive them indirectly:[19]

1.      I soak my cold, stiff hands in water that feels warm. I am fully aware, however, that the water is actually at room temperature, and I am perceiving the temperature directly, though in a deceptive way. Normally, if my hands were not cold, I would feel the true temperature of the water directly and in a non-deceptive way.
2.      A person may say, ‘I see things as if they were yellow, though I know that isn’t their true color.’ What we call the true colors of things are by convention the colors we see under normal conditions. These presupposes enough proximity, having normal vision, seeing things in adequate illumination, etc.
3.      I hear sound directly, though in distorted ways. If I could follow a car driving at the same speed, I would hear its sound in an undistorted way; the real sound, which means free from the Doppler effect.
4.      Even if I show by pressing my eye that I see things moving through my visual field, this does not mean that I am not seeing the things directly. In fact, I can even say, ‘I see external things directly and precisely as they are, although as if they were moving.’
5.      In the second example, as Searle has noted, I can instead say, ‘I do not see two fingers… I am directly seeing my index finger as if it were doubled.’
6.      About the form of the coin, it appears elliptical, but I can say that I directly see a round coin that only ‘looks elliptical’ because it is being held at an angle. – As A. J. Ayer noted, what we consider to be the true form or real color is often a question of convention (cf. Ayer 1973, Ch. 4). We have the convention that the real form of a coin or of a table is the form we see when we see them from above. In the same way, we have a convention that the real form of a mountain is the form we see when looking at it from the ground below it at a certain distance, but not an aerial view from above (e.g., Matterhorn, Sugarloaf). The real color of a tropical mountain is normally green, even if it may seem blue when viewed from a great distance, etc. 
7.      In the case of mirages, I see what looks like a lake, but I can say that I now know that what I really see is the image of the sky refracted by layers of hot air on the surface of desert sand, and I can say that I see this mirage directly.
8.      Finally, in the case of a hallucination, it is simply wrong to say that I see the content of my hallucination. I only believe I see it, when in fact there is nothing there to be seen! Verbs like ‘seeing,’ ‘perceiving,’ ‘being aware of’ are primarily related to the factual, objective content, and not to a merely sensory content. Even if it is through sensory content that we have perceptions of things, this does not make our realism indirect. In a similar way, when we say that a bus made a stop of thirty minutes for lunch, this does not mean that the bus trip was indirect.

This kind of explanation is not as new as sometimes supposed. It was already present in the following comment by the direct realist philosopher Thomas Reid against his contemporary David Hume, nearly three centuries ago:

…visible appearances of objects are intended by the nature only as signs or indications and the mind passes constantly to the things signified without making the least reflection upon the signs or even perceiving that there is such a thing. It is in a way something similar that the sounds of a language after becoming familiar are overlooked and we attend only to the things signified by them. (Reid 1967: 135)

To me and most present-day philosophers, this is the correct answer, but the persistence of competing doctrines is a demonstration of how slow and irregular progress can be in philosophy.
   Summarizing: we perceive things directly, even under misleading conditions like those of delusions, which justifies the direct realist view of whatever is given in perception; and this does not mean that there cannot be a veil of sensory impressions or sense data in between. This justifies our psychological interpretation (A) of a given content as based merely on sensory data, without forcing us to reject interpretation (B).
   Finally, a word about the argument of science. According to this argument, perceptual experience depends on the stimulation of distal neuronal cells that in the end lead to the stimulation of occipital cortical regions in the brain. Thus, our experience is in fact the experience of something occurring in our brain, which is nothing but the experience of sensory impressions or sense data. Consequently, our direct experience can only be one of these sensory impressions occurring in our brain. From this it follows that we cannot have a direct experience of the world around us. From this it also follows that we cannot be sure that the contents of experience reflect the way the external world really is. Worse yet, we may be led to the incredible conclusion that since our brain also belongs to the external world, we cannot even be sure that our brain exists... All we can be sure of is that there are these sensory impressions!
   The answer to the argument of science is that there is nothing semantically wrong in saying that we directly experience things given in the external world, even if this experience demands the underlying work of complex neuronal structures as intermediary means. In the case of visual perception, we have simulacra of things seen, first in the activation of photoreceptor cells of the retina by light-waves and in the end in a corresponding activation of the striate cortex (region V1) in the occipital region, which are then analyzed by the visual-association cortex. The relevant point is that the sentence ‘we directly see the object’ belongs to our ordinary language, while expressions like ‘by means of…’ or ‘through…’ indicate that they are about the underlying intermediating neurobiological processes responsible for this direct experience, belonging to a neurobiological language with a different semantic import. As far as I know, it seems that what we call sensory impressions or sense data in the visual case have to do with the activation of the striate cortex, since the stimulation of this region without the activation of photoreceptors in the retina is apt to produce hallucinatory phenomena (Teeple, Caplan, Stern 2009: 26-32). However, this fact alone does not make visual perception indirect, since it isn’t captured by the semantic conventions ruling what we should call directly perceived objects.

18. Axioms of externality
As we learned from our discussion of Berkeley’s and Mill’s phenomenalism (Ch. IV, sec. 19), sensations, even if warranted possibilities of sensations, being dispositional, seem to be inevitably psychological, which seems to lead us into the pitfalls of idealism. For reasons given above, this is far from being my intention here. The only way to prevent this result is to admit that in the normal case a verifiability rule is effectively applicable in a context belonging to the external world. Thus, what satisfies its criteria can be seen as belonging to the external world, either (inferentially) as a grounding fact constituted by the full arrangements of tropes, or (more directly) as its aspectual sub-facts, which are only partial arrangements of tropes. Nevertheless, both sub-facts and grounding facts belong to the external world (Ch. IV, sec. 24). The problem is that so exposed our answer is incomplete, because it does not explain how the magic trick is performed of replacing internal psychological content with external material content, both having the same phenomenal appearance.
   A justified answer begins to appear when we press the question further. Suppose we ask: when are semantic-cognitive rules like the verifiability rule not only conceivable, but also effectively applicable to the real external world? What are the conditions responsible for our awareness that the rule is effectively applicable to really existing entities in the external world? In still other words: when do those entities that we otherwise could be able to recognize as mere sensory contents become likely to be seen as external physical contents – as simple and complex material property-tropes, as material objects (clusters of tropes displaying compresence…), and as real factual contents resulting from their variety of arrangements?
   The answer I wish to propose is that what makes semantic-cognitive rules effectively applicable to entities in the external world when contents of experience are given to satisfy these rules are suitable conditions of external reality. I hold that adequate satisfaction of these conditions is ultimately responsible for the magic of transforming our reading of our indexical thought-contents, supported by sensory-impressions (internal criteria) in our reading of them as real factual contents belonging to the external world and constituted by material external tropes (external criteria). I maintain that by definition, once the suitable conditions of reality are adequately satisfied, they constitute the criterion for the reality of the contents of experience that fall under their scope.
   However, are there such conditions? In my view, these conditions obviously exist, and their adequate satisfaction always constitutes what we implicitly assume in our attributions of external reality. The issue was already touched on when I explicated some of Mill’s complementary conditions for external reality in chapter IV. In fact, conditions for external reality were (in a variety of philosophical frameworks) already largely explored by modern philosophers, beginning with Descartes and ending with analytical philosophers from G. E. Moore to John Searle!
   Restricting myself to the main ones, I begin with Locke. According to Locke, our opinions about physical objects are justified by the properties associated with our ideas of sensations, such as the involuntariness of their character, their order, their coherent agreement reflecting law-governance, and their interpersonal access (Locke 1690, Book IV, Ch. 11). According to the immaterialist Berkeley, the ideas that form external reality are stronger, distinct and independent of the will (Berkeley 1710, III). For Hume the impressions of a real thing are those that enter into the soul with the ‘most force and violence.’ (Hume 1738, Book I, sec. 1) For Kant conformity with laws (Gesetzmäβigkeit) is what defines the formal aspect of nature (Kant 1783, § 16). For J. S. Mill, as we have already considered in some detail, the external world consists not only of continuous or guaranteed or certified possibilities of sensation, but in their conformity with the regularities of nature, like the causal laws of physics and their independence of our will (Mill 1889, Ch. XI). According to Frege – already an analytic philosopher – the externally objective realm (his erste Reich) has as a criterion for objectivity its interpersonal accessibility and independence of will, while its reality has as its criterion spatio-temporal location (Frege 1918). A direct realist analytic philosopher of the early twentieth century, G. E. Moore, attempted to summarize the main conditions of external reality in the following passage:

The real is something independent of the mind that is verifiable by others, continuously connected with other things, and in this way has certain causes, effects and accompaniments (I would say that it ‘displays regularities’) with the highest degree of reality. (Moore 1953)

The list continues up to the present. In a recent book, John Searle noted certain characteristics of the object or state of affairs really perceived, like presentation (instead of representation), causation, non-detachability, indexicality (they are presented here and now), continuousness and determinacy (Searle 2015: 60-70; see also Huemer 2001, Ch. 4).
   Finally, there were also psychologists like Sigmund Freud (1911), who took account of conditions of reality. Freud suggested that we begin our lives under the governance of the pleasure principle (Lustprinzip), which seeks immediate gratification of our desires and avoidance of pain. Since the external world does not grant us this painless immediate satisfaction, we gradually learn the reality principle (Realitätsprinzip), according to which we need to act rationally toward the external world, postponing the immediate gratification of our desires in order to assure lower levels of gratification accompanied by a foreseeably lower level of pain. For Freud it is by means of this transition to the principle of reality that we learn the existence of an external material world with its own rules and independent of our will.
   It is true that when considered in isolation none of these conditions warrants that the contents of perceptual experience are externally real contents built up of material tropes. Indeed, criticizing Locke, Laurence BonJour correctly noted that none of the conditions of reality given by this philosopher is sufficient for warranting the external reality of anything (Bonjour 2002: 130-135). For example: a mere content of sensation can have the highest degree of intensity and determinacy and yet be hallucinatory, as may occur in some rare cases. A perfectly realistic dream could be in tedious conformity with the expected regularities of our physical and social world. Though many mental acts are dependent on our will, a dream is usually independent of our will, though not always (as in the case of lucid dreams). Even interpersonal agreement about states of affairs can occur without these states of affairs being real, as in the rare case of a collective hallucination (suppose that several people with similar beliefs take a hallucinogenic drug and, moved by suggestion, have similar pseudo-perceptions…). Finally, external occurrences can possibly be directly dependent on our will (as in the case in which someone has a brain-reader connected with his motor cortex, enabling him to move objects in the outside world using his thoughts alone).
   However, in my view Bonjour’s criticism can be easily surmounted. For there is a way in which these mere conditions of externality can be transformed into a definitional criterion for the existence or reality of entities outside us like external facts, that is, into a sufficient condition for the ascription of external reality in the most usual sense of the word. It consists simply in the demand that these conditions should be given more or less altogether, in accordance with conventional peculiarities of the expected kind of entity (property, object, fact). Hereby we find a decisively subsumed criterion that, once given, allows the perceptual contents that satisfy a semantic-cognitive rule to be interpreted as belonging to the world outside us, as externally existing tropes or constructions made up of them.
   We can better establish this point by proposing that the entities that can be seen as externally real are those that suitably satisfy all the main conditions of reality. I call these conditions axioms of externality, because when put together they form what we could in the proper sense of the word call a definitional criterion of external reality. Here is how this view can be explicated:

DEFINITIONAL CRITERION OF REALITY:

When a perceptual content of belief, satisfying its verifying rule, also fulfils the following axioms of externality:

(i)                it is given to our senses in its most intense degree and detail,
(ii)              it is (more or less, depending on the case) co-sensorially given,
(iii)            it is (in the normal case) independent of our will.
(iv)            It can be assured as always being an object of perceptual experience and agreement under adequate conditions (namely, it must be subject of ‘continuous, guaranteed or certified possibilities of sensations,’ to use Mill’s terms),
(v)              it is able to reach agreement on its truth through interpersonal experience.
(vi)            it follows the laws of nature, possibly displaying expected agreement with other contents with similar characteristics,
(vii)          can be seen as causally related to the cognitive subject who applies the rule.

…then it can be considered to be an externally real factual content (as constituted by arrangements of external or mainly external material tropes).

I am not sure whether this list is complete, and I am unable to order the axioms hierarchically, though I believe they are the most relevant and all that we need. However, the thesis that I wish to defend is that, once all these axioms are suitably satisfied, there is nothing in the world that can defeat the external material reality that we attribute by means of them. They are sufficient for the attribution of external reality in the most proper sense of the word, which I will call the inherent one. – However, though together they are sufficient for reality attributions, they are not necessary. For instance, a subject can be under the influence of some drug or suffer from some perceptual deficiency… so that several of these conditions are lacking, although the person is indeed experiencing a state of affairs that is externally real.
   This idea can be made clearer by means of an example: Suppose that under normal circumstances I see my notebook computer in front of me. I know that this device is presented to me as a complex of mental images and sensations (i.e., as variable contents of sensation or sense data). But I am much more aware that this device is given to me as a material object existing externally (a perceived and independently existing combination of material or external tropes of solidity, volume, form, etc., displaying compresence). Now, how do I know that I effectively apply my notebook’s identification rule in its proper context? What warrants my understanding of the perceptual content as an object in the outside world to which I might effectively apply its identification rule? The answer is obvious: the suitable satisfaction of the above listed axioms of externality. That is:

(i) The device is given to my senses in its most intense degree and detail.
(ii) The device is co-sensorially given (I can see, touch and hear it).
(iii) The device exists and is constituted independently of my will.
(iv) The device is continuously able to be given to sensory-perception under adequate conditions (I have seen this notebook computer intermittently in my home for many months).
(v) I am (because of similar past experiences) sure that other persons would agree that this notebook computer is here in front of me now if they were here to see it; so my experience is, if not presently, at least virtually interpersonal.
(vi) The device follows expected physical regularities (it responds normally to my commands, sometimes I have to recharge its battery, etc.)
(vii) The device satisfies its identifying rule in a causal way (I am continuously interacting causally with my notebook computer, and I am aware of this).

Even if the whole world were nothing but a dream, my notebook computer inclusive, I would remain entitled to affirm that my notebook computer is very real indeed, that it exists externally, since it suitably satisfies the criterion of reality by satisfying the axioms of externality from (i) to (vii).
   On the other hand, internal sensory contents, even those of a hallucination, typically do not satisfy, or do satisfy too limitedly, the externality axioms – except in skeptical scenarios and in the cases of artificial reality, which will soon be discussed. Indeed, if they satisfy all the externality axioms, they satisfy the criterion of reality and must be considered externally real. It must be so because the totality of the partial conditions constituting the axioms simply constitute a definitional criterion that grammatically warrants that the object – in the case the notebook computer in front of me – is a real material object that must be considered as belonging to the real world around me, and not as something merely mental. In other words, the satisfaction of the externality axioms from (i) to (vii) warrants to me, for conceptual reasons, that my notebook computer’s identification rule is effectively applicable to a real object in the external world, because it is definitional of this effective application to the external world, which is definitional of existence in the external world. This satisfaction warrants to me that the object of its application really exists in a very concrete sense of the word, as a nuclear cluster of stable tropes of solidity, volume, form… effectively satisfying its identifying rule and being constituted in conformity with it. And it is so because of the senses we give to our words. Skeptics will protest against this conclusion. They will complain that they can imagine a brain in a vat, a Cartesian soul, a dreamer… who is continuously and systematically misleading about a whole world that perfectly satisfies all our usual axioms of externality without being truly real. But there is an answer waiting to them.
   It is also important to remember that the sensory-experience of mere sensory content is also a cognitive experience. If I have the feeling that the stove is hot or that I am holding a tennis ball, if I seem to hear a thunder clap or have the mere visual experience of a fishing boat or of my notebook computer, these are all indexical thought-contents with, one many suppose, their own verifiability rules satisfied in these by sensory experiences – by sense data. And these sensory experiences will be understood as internal because they do not satisfy the criterion of external reality (I may be hallucinating my notebook) and as external when they satisfy this criterion (I am presently working with my notebook computer, others can confirm this). Furthermore, in the last case it is supposed to be something external unifying the diverse aggregates of sensory experience which is the real, actual fact in the world. And it seems plausible to think that this fact should have a unifying structure similar to the unifying structure of the verifiability rule, because only such a structural similarity would justify the effective applicability of the rule in all its different ramifications.
   Before we consider the objections suggested by skeptical scenarios, it is important to notice that the application of the criterion of reality can be inductively extended to contents that can be experienced only indirectly. This is the case of (1): all things that we cannot experience directly with the unaided senses but that can be experienced indirectly, as the cases of viruses, atoms, magnetic forces, gravitational forces (one can indirectly verify the existence of atoms using scanning tunneling microscopy, and one can indirectly verify the existence of electromagnetic forces by manipulating magnetized material). These things can be considered externally real because they indirectly satisfy axioms (i) to (vii), in their complex of causes and effects. This is also the case with (2): everything I can remember having experienced as satisfying the criterion of external reality, but that is not present now, like the village where I lived as a child or a childhood friend… This is the case with (3): the many things I know to satisfy the criterion of external reality by means of testimony or any reliable informative source, from Napoleon’s coronation to the extinction of the dinosaurs. (4) This is finally also the case of my inductive belief that because I have always had new experiences of real external things in the past, the world is full of other real external things that I never experienced but that directly or indirectly are able to satisfy the criterion of external reality. We can extend the axioms of externality to all these cases simply because they are part of a network of causes and effects that satisfy these axioms. Finally, this also allows us to inductively prove the reality of the external world, which cannot be more than the mereological sum of all that can be obtained from cases (1) to (4).[20]
   These extensions help us to explain how we can make ordinary attributions of truth to statements based on correspondence with inferentially derived facts that aren’t presently given to our senses. Consider as an example the judgement ‘It is true that Mary tried to poison Reverend David with arsenic,’ symbolized as ├p, which is true by corresponding to the inductively reached fact symbolized by q. We know that q expresses a thought-content that can also be read as a factual content. But what entitles us to give the status of a fact to something that no person (with the exception of the suspect) has ever observed? The answer is that we are aware that this dynamic fact occurred, inductively satisfying all the axioms of externality (i) to (vii) by the direct satisfaction of the criteria of reality of observational thought-contents rst, and u corresponding to their respective external facts. This entitles us to conclude that the verifiability rule of q is effectively applicable in its proper context, that is, that the fact-event of Mary’s attempt to murder her husband really existed.

19. Skeptical scenarios
Now, what about skeptical scenarios or experiments with artificial reality? The challenge to our view is that in these cases the satisfaction of the definitional criterion of external existence considered above can be in part or even totally emulated. Thus, the brain in a vat (pace Putnam) has experiences that seem as real to him as experiences we have in our actual world, though he (a male brain) is on a very different planet, Ômega, interacting only with the program of a supercomputer... However, curiously enough, if this were the case and, for instance, the brain were removed from the vat and implanted in a living organism, so that he can now experience the world of the planet Ômega as it really is, or if someone knows he has been the object of a flawlessly executed virtual reality experiment, the past normal attributions of reality would not be denied. That is, happenings belonging to the life of a brain in a vat were very real indeed, since the axioms (i) to (vii) were all satisfied, even if everyone would agree that this hard reality was in a sense not real, since it was a sub-product of what from a comparative point of view is the ultimately real world. Now, it seems that the world presented to the brain in a vat was simultaneously real and unreal, which would be contradictory.
   We can solve this riddle simply by considering that there are two different senses of external reality which should not be confused:

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

The inherent sense of external reality (a) is the foregoing, demanding the suitable satisfaction of the externality axioms from (i) to (vii). The inherent external reality can be warranted by the satisfaction of the definitional criterion of reality, and we all are very much acquainted with it, since it is the sense of reality that we apply on a daily basis. The brain in a vat can have the criterion of inherent reality satisfied, and it is in this sense that the brain can think that the experiences given to him of the world are perfectly real: they are real in the inherent sense.
   Nonetheless, the external world of the brain in a vat remains unreal in the adherent sense, the sense (b) of external reality. The adherent sense is reserved only for skeptical scenarios and circumstances of virtual reality. The criterial conditions for the satisfaction of the adherent sense of reality are very different, producing a different sense and application of the word ‘reality.’ They are much more coherential. We would be able to reject the adherent reality of something based on the fact that we now know (or always knew) that we have been subjected to an experiment of virtual reality, since the coherence of that experience with the actual surrounding circumstances is lacking. One example is the use of special digital gloves that give us a sensation of touching holographic images of objects... Moreover, it is important to note that the concept of adherent reality is relative and that independently of any comparison we cannot speak of adherent reality. The idea of an ultimate or absolute adherent reality of things is an empty one.[21]
   To exemplify the relative character of the application of the concept of adherent reality, suppose that I were a brain in a vat, after my brain was removed from the vat and implanted in the head of an extra-terrestrial creature. My new fellows could give me coherential reasons to think that the present world is adherently real if compared with the first one, even if both are equally inherently real (they can show me the vat, the supercomputer, give reasons for the experiment and make me acquainted with their wonderful new world, populated by fascinating creatures…). But the application of the concept is only relative, since I have no warrant that the present world is after all the ultimately real world. It may be that I was deceived. I can be in another vat where the program ‘From the planet earth to the planet Ômega’ is running, merely being deceived a second time…
   On the other hand, the conditions of inherent reality are and have been equally well satisfied in both worlds and in this sense they are both real worlds. Thus, the first world was adherently unreal, while the present world is adherently real though both are inherently real. However, since the inherent sense of reality is our usual one, and I do not aim to deal here with the problem posed by radical skeptical questions, what follows from this is of no further interest to our present concerns.[22] 
   My main point is that in perceptual experience, when sub-facts sufficiently satisfy the verifiability rule, and this rule has proven to be effectively applicable by satisfying the externality conditions, we have the conditions for accepting the aspectual match between thought-content and an external sub-factual content. This satisfaction of the inherent sense of external reality also applies in a mediated form to the grounding fact, whatever it is. This means that for its effective application to facts belonging to the outside world, the verifiability rule must satisfy the axioms of externality (which are conditions that can conventionally vary depending on the case). Only in this way can the contents of perception and thought be read not as something merely mental, but as something (inherently) existing in the real external world, as constituents of the sub-facts belonging to a grounding fact, and in this form to the grounding fact itself.
   The suitable satisfaction of the axioms of externality is what performs the magic of allowing us to convert sensory content into an externally real material content, which otherwise could only be seen as merely psychological. The satisfaction of the criterion of reality by our phenomenal content is all that is needed to promote the displacement necessary to set this content within the so-called material external world.

20. Verification and intentionality: Husserl
Maybe it can be helpful to recall some of Edmund Husserl’s views on truth in his sixth Logical Investigation. I believe that it was his deepest insight, even if his many attempts to develop it entangled him in a speculative maze. As we saw, Frege spoke of senses as meanings and thoughts, understanding them as abstract entities. Wittgenstein suggested, instead, something that leads us to the admission that factual meaning is given by semantic-cognitive rules or combinations of rules considered in a particularist (nominalist) way, coming to being only in their application. These rules are something that can be applied either effectively (to the real world) or at least to some extent imaginatively (as a possibility), if they not remain as dispositions to which we are conscious. He spoke of intentional acts as ephemeral instantiations of meanings, maintaining the Platonist view that meanings in themselves should be abstract entities, as Frege and others have done.
   Nevertheless, it is important to see that Frege, Wittgenstein and Husserl, were all struggling with the very same issue, although from different perspectives, strategies and assumptions. Thus, Fregean senses, as we saw, if they are something analyzable, must be semantic-cognitive rules or combinations of such rules. But a similar reasoning should be applicable to Husserl’s intentional acts: they should essentially include – in accordance with our view of semantics as always psychologically embodied – cognitive instantiations of semantic rules or combinations of rules, which can be expressed respectively in a cognitivist (psychological) or in a semanticist (logical-linguistic) fashion.
   In what follows, I will first present a summary of Husserl’s theory of intentionality and its relation to his correspondence theory of truth. Then I will translate his main insights into my own conceptual framework.
   As already noted, according to Husserl’s view, the meaning (sense) of a linguistic expression is an ideal, an abstract (Platonic) object, as it was for Frege and others. However, the meaning of an expression can be instantiated by two fundamental kinds of ephemeral intentional acts:

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

In case (b) the object of the act is not only intended. It is also given to us ‘in person,’ even if always in perspectival ways, by means of distinct intuitions that can successively reinforce one another. Finally, there is a third act, an act (c) of synthesis, through which we make ourselves aware that the object intended in the meaning-giving intentional act is the same as the object intended and actually given in the meaning-fulfilling intentional act. For Husserl, by means of this last act we achieve an awareness of truth and knowledge. Truth, according to him, is correspondence because it is the identity of the object intended by the meaning-conferring act and the object intended by the meaning-fulfilling act. As he writes, truth is ‘the complete agreement of what is intended with what is given as such.’ (1980 vol. II/2, VI sec. 38) Knowing that there can be an unlimited diversity of perspectival acts of fulfillment, which can be added to one another in order to warrant our knowledge of the object by giving the experience increasing evidential value, he also writes:

When a presentative intention finds its ultimate fulfillment, the genuine adequatio rei et intellectus is realized. The object is really presented as intended. So is the idea of all signitive fulfillment. The intellect is the intention of thought, the intention of meaning. The adequation is realized when the intended object in the strict sense is given to us as it is thought. (Husserl 1980 II/2 VI, sec. 37)

This ‘correspondence’ as the identity between the ‘objects’ of the two intentions is what seems to me to be Husserl’s chief insight on the nature of truth, since the process he describes is clearly in the origin of what I called the pragmatics of correspondence, as developed in the present chapter.[23]
   Now, we can read the meaning-conferring and the meaning-fulfilling intentional acts as essentially constituted by instantiations of two semantic-cognitive rules. What Husserl identifies as the meaning-conferring intentional act is the same as a semantic-cognitive rule that isn’t effectively applied, but only take into consideration; in other words, we see that it is possible for this rule to be effectively satisfied or applied because we know that we can to a greater or lesser extent imaginatively apply it (as in the case of ?p). On the other hand, what he identifies as the meaning-fulfilling intentional act at least involves a semantic-cognitive rule in its effective satisfaction or application within some actually given domain or context. In the case in which it is expressed by an assertive sentence, this semantic-cognitive rule is a verifiability rule that can be said to be true or false in the existential sense that it can be shown to be effectively applicable or not (as in the cases of ├ p or├ ~p). In the case in which we can express the effectively applied semantic-cognitive rule in the form of an assertive sentence, we are considering it as a verifiability rule that is effectively applied in its proper context, which also confers existence on the fact that satisfies it.

21. Solving two Husserlian Problems
Now, comparing the kind of empiricist approach that I am defending with Husserl’s theory of truth, we see that we are able to overcome two main drawbacks pointed out by his critics.
   The first and more serious one is that working only with intentional-phenomenal material, Husserl was unable to explain the linkage of the object ‘in person’ with the object in itself, since this would require him to go beyond the phenomena. As Günter Patzig once wrote: ‘the daring bridge called evidence intended to connect the judgment with the fact had the drawback, rather unfortunate in a bridge, that it ended on the same side of the river from which it began.’ (Patzig 1977: 194)
   Our understanding of correspondence allows us to escape from these limitations. As already noted, the thought-content expressed by ?p, which for us is only a regarded thought, a verifiability rule whose application is only imagined towards a possible state of affairs, can be approximated with what Husserl calls a meaning-conferring intention; a thought-content that can be read as a perceptual content !o, which is for us another verifiability rule that may be expected to be similar in content with p and which is the effectively applied and therefore also an effectively applicable verifiability rule. This is approximately what Husserl has called the meaning-fulfilling intentional act. And the awareness of the qualitative identity of content represented by ‘o,’ which brings us to the conclusion ├p (that is true), can be approximated to Husserl’s conclusion that we reach truth by seeing that the objects of the two acts are the same.
   However, by doing this we do not need to follow Husserl, assuming any form of meaning Platonism. As you will recall, according to our analysis existence is the effective applicability of a conceptual rule, while the object of its application should only be conceived as what satisfies the sum of conditions able to satisfy the rule, and its ‘having existence’ is only its effective potentiality of having the conceptual rule applied to it. The same holds for the verifiability rule; this rule demands for its effective application the satisfaction of criterial configurations by means of which the factual content, the fact in the world, presents itself to us. These external criterial configurations – tropes and constructions from them – on the other hand, are manifestations of the empirical fact and can be interpreted in a double way, according to our intentions: (A) as configurations of sensory impressions characterized by not satisfying our normal inherent conditions of external reality; (B) as real aspects of external facts (that is, as tropes and constructions from tropes), as far as they conjunctively satisfy the inherent definitional criterion of external reality (as we saw: the possibility of being interpersonally accessed, maximal intensity of sensation, independence of will, displaying natural regularities, etc.). These are at least external aspects of what Husserl called the ‘object in person,’ but in our case even being called sub-factual contents, they are always cognitively-independent and externally real, since they satisfy the inherent criterion of reality that defines what is externally real in the usual sense. As I insisted by writing about existence, they exist in themselves because the existence of the fact is not only the second-order property of its verifiability rule of being applicable to it, but also the second-order property of the fact of having its verifiability rule with the property of being effectively applicable to it.
   The second objection against Husserl’s view is that the object is never given to us in its entirety. Since what we experience are always parts of the object, it can never be really given to us ‘in person.’ Husserl saw this problem and suggested that the object could still be seen as a pure or empty X of ideal nature.[24]
   Here I partially agree with him. Also, in the view I have proposed it is assumed that neither the object nor the fact are perceptually given to us in their entirety, with the consequence that we can never be absolutely sure that what is given to our experience is the real object or fact. However, we can infer that the object (fact) is given with enough probability, with practical certainty, assuming or postulating as warranted the evidence posed by the factually interpreted !o and, consequently, the corresponding truth of p under the circumstances of an adequate linguistic practice and the assumption that all other things remain the same. As we saw, we can infer that we have seen a dolphin and not only a rubber dolphin gliding over the water, and we can postulate what is given as indisputable evidence, insofar as we assume that the circumstances in which the observational practice is applied remain undefeated.
  Anyway, the nuclear clusters of tropes that constitute the objects, insofar as the linked complex tropes and the resulting facts are in themselves for us inexhaustible, and we can never be absolutely sure that our semantic-cognitive rules are sufficient to completely match them in order to warrant their existence in an absolute sense.

22. Truth and existence
Now I return to our initial problem. We have distinguished, based on dictionaries, two uncontroversial usages of the word ‘truth’:

(a)  Thought-truth: ‘Truth as consisting of things being as we believe they are, as the conformity or accordance or correspondence of the thought with its fact.’
(b)  Fact-truth: ‘Truth as the actual, real, existing thing or fact in the world.’

Now I hope to find a more precise explanation for the distinction. Sense (a) is the sense of truth as correspondence based on the qualitative identity of content between a supposition and some factual evidence, as we have shown by means of numerous examples. This is the correspondential sense that was identified as the most proper one, since the s-thought is the archetypical truth-bearer. Sense (b) of the word ‘truth’ has been unmasked as derivative, since it can be better replaced by words like ‘existence,’ ‘reality,’ ‘actuality,’ as second-order properties of facts. And it is easy to justify the derivation, since a true thought-content refers to a real, existing, actual fact.
   Now, paralleling the idea that the existence of a property-trope is the effective applicability of an ascription rule for a predicative expression, and paralleling the idea that the existence of a material object is the effective applicability of the identification rule of a nominal term, we are led here, by symmetry, to the conclusion that the existence of a fact should be the effective applicability of a statement’s verifiability rule. This makes us ask whether the existence of a fact isn’t the same thing as its truth, since truth is also a property of a verifiability rule of being effectively applicable in a proper context, as has been suggested by the formal definitions (3) T‘p’ = C‘p’ = V‘p’ and (4) ‘p’T*‘q’ = ‘p’C*‘q’ = ‘p’V*‘q. I believe, however, that this is a mistake. ‘Truth’ can be identified with the existence of a fact only in its derivative sense, as fact-truth. But ‘truth’ in its proper correspondential sense, as thought-truth, can be identified only with the result of the effective application of the concrete verifiability rule or procedure that we have schematized in our many examples of the dynamic processes that lead us to regard a thought-content as true or false. Consequently, the variables and V* should be understood as abbreviations of such results.

23. Verifiability rule and truth-making procedure
I think the above considered distinction helps us see more clearly the difference between the truth of a thought-content (thought-truth) and the existence of a fact (fact-truth). Consider the identity of contents verified in p = q. The existence of the fact is represented by q (a fact-truth), and the truth of the thought-content is expressed by ├ p (a thought-truth). Even if and q have qualitatively identical semantic contents in the case of a true statement, the fact that they are differently identified on the symbolic level points to a more substantial difference.
   To see this, consider again the truth-making procedure described in the case of Mrs Rose’s unfortunate husband:

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

This action-schema gives truth to p, and it contains two senses of ‘verification’. In the first sense (a) of ‘verification’ we are considering verifiability rules independently of their possible or actual application. One by one the sentential letters of the above summarized process exemplify what I prefer to call verifiability rules. In this sense, the above example gives us five different verifiability rules: most of the above symbolized sentences express a different verifiability rule, effectively applicable or not. But in the second sense (b) of ‘verification’ we are considering what we could call an installed truth-making procedure. This is usually only a branch of the whole verifiability rule that is effectively applied in order to reach a truth-value. This case of the truth-making procedure can be summarized in the conclusion ├p, insofar as it is seen as a way to summarize the whole action-schema.[25] Senses (a) and (b) of verification can be better explained as follows:

(a)       Verifiability rule: In this first sense, a verifiability rule can be regarded in abstraction from its application in an effective correspondence procedure and even from truth as thought-truth. In this sense, the verifiability rule is the thought-content, the sense, the proposition, the cognitive meaning of a declarative sentence. It is the verifiability rule that can be considered as a whole, with all its many possible ramifications, namely, all the criterial configurations that it is able to generate. This can be (i) the rule effectively applied when we see or conclude that !q in regard to a real or existing fact (truth can be employed here in the derived sense of fact-truth). This can be (ii) the rule whose application was only imaginatively conceived in ?p. And this can also be (iii), the case of effectively applied verifiability rules like !r, !s, !t and !u in regard to Mary’s example, which by their effective applicability allow the attribution of existence or reality to the respective facts (also called ‘true facts’). All of them are rules of verification identifiable with propositions, thought-contents s-thoughts or sense/mean­ings expressed by the respective sentences. The effective applicability (and not the application) of any of these verifiability rules in their proper context is what makes the respective facts appear to be existent or real. They provide a better explanation of what could be meant by what we have called fact-truth.
(b)     Installed truth-making procedure: with this second sense of ‘verification’ we need to consider only the effectively concretized procedure of verification summarized in the above-presented action-schema and in all the others. It is important because this is the sense in which verification can be explicitly equated with correspondence and in which we can gain cognitive awareness of truth in the best sense of the word: as thought-truth.
In other words: when we speak of the cognitive sense of a sentence – its thought-content – we are speaking of a verifiability rule, for instance, of p, whose multiple forms of application we are able to conceive in the same measure as its meaning and as composing its meaning. But when we consider a concrete verification procedure, we are not considering individual meanings, but rather the already settled process of reaching awareness of correspondence or lack of correspondence with a fact. This is the match or mismatch between this or that ramification of a verifiability rule or thought-content or s-thought. In the foregoing example, for instance, what we had was a match of contents between what is only regarded, that is, the merely imaginatively applied verifiability rule ?p and the effectively applied verifiability rule !q (which requires structural isomorphism, intentionality, etc.). And this last rule is assumed as effectively applied in the case where it is the inductive result of the effective application of the conjunction of the different verifiability rules {!r & !s & !t & !u}, each of them having already been subjected to a similar verifiability procedure. Truth as correspondence will then be the meta-property of the verifiability rule expressed by a supposition ?p of being confirmed as the effective result of the whole verifiability procedure. This resulting confirmation can then be summarized as ‘p is true’ or simply as ‘├p’, which is a thought-truth. Thus, we should not be misled by the obvious fact that where there is a thought-truth, there must also be a fact-truth, as if they were the same. For where there is a fact-truth, the thought-truth does not necessarily appear, which is confirmed by the fact that there are many unknown facts.

If I am right, the conclusion is that although truth and existence are twin concepts, they can be distinguished. If truth is a property of an s-thought, this points to the results of some effectively realized verifiability procedure that includes correspondence. Existence concerns a property of a possible verifiability rule, namely that it could be effectively applied to a fact, even if this rule does not exist and the fact is unknown (see Ch. IV, sec. 33). That is, truth is an epistemic term, while existence is an ontological term. The ontological (fact-truth) exists independently of the epistemic, while the epistemic (thought-truth) requires the ontological to be effectively applicable. This is why we prefer to attribute truth to thought-contents and existence to the facts represented by them.

24. The rule’s structural mirroring of the world
Let us recall that for J. S. Mill material substance was the ‘permanent or warranted possibility of sensations.’(Chap., IV, sec. 19) We have corrected this idea. Not the matter or substance, but the existence of the material object should be approximated to its permanent possibility of sensations, since permanence is always one and the same property, while objects can be indefinitely multiple and diverse. Or, in my own paraphrase, external existence is the effective applicability of the semantic-cognitive rule to entities of a chosen (normally its proper) domain or context, this effective applicability being measured by the satisfaction of the criterion of inherent reality. This suggests a metaphysical question: should not matter or substance be for Mill the multiple and variable configurations of sensations, insofar as they are permanently accessible to our experience? Or, in our direct realist paraphrase: isn’t the material object something formed by the unlimited multiple and variable objective configurations of tropes able to suitably satisfy the axioms of externality necessarily required for the effective applicability of the identifying rule?
   The answer to this question seems to be ‘yes, but not only.’ Indeed, the internal criterial configurations demand external criterial configurations for the application of semantic-cognitive rules, that is, mainly material/external tropes and constructions from them (objects, facts) that are able to satisfy the rule insofar as they suitably satisfy the axioms of externality. This allows us to classify these tropes as belonging to the external material world.
   This we already know. However, if it were just this, how could these multiple and diversified configurations of tropes that satisfy the criteria for the application of semantic-cognitive rules be conceived as belonging to only one entity (a complex property, a material object, a fact)? What is the glue that holds them together? How could they be unified and not remain inevitably dispersed? The only answer seems to be that what unifies all these aspects, building things like material objects, cannot be other than structures that in an inverted way mirror the structures of the identifying semantic-cognitive rules. In this way the external structures furnish in a unified way the corresponding multiplicity and diversity of external criteria. That means the external criterial configurations, the configurations of tropes able to satisfy or match the internal criterial configurations, though displaced in the domain of the external material world by satisfying the criterion of inherent reality.
   Generalizing: the objective real entity, the physical entity, be it (i) only a trope (complex or not, monadic or n-adic), be it (ii) a nuclear cluster of tropes displaying compresence and having the specific properties constitutive of a material object (like volume, solidity, mass…), or be it (iii) any fact primarily conceived as an arrangement of tropes (which inevitably includes (i) and (ii)), should mirror the same structure of the semantic-cognitive rules by means of which we ascribe predicates to (i), identify (ii) and represent (iii). We apply the semantic-cognitive rules to facets or aspects of the external entities identifying them as unities. This is only possible because these facets or aspects are associated with unperceived facets or aspects in ways that are structurally similar to those of the corresponding semantic-cognitive rules. In chapter IV we used the metaphor of two identical trees that touch one another at the ends of their branches: on the one side the internal criterial configurations, on the other the external ones – the configurations of material/external tropes (possibly mixed with mental/internal tropes). And the last structures are seen as external only insofar as they suitably satisfy the axioms of externality, which allow us to attribute inherent external reality to them. Otherwise they would be indistinguishable from the internally conceived rules and their possibly generated configurations of sensory contents or sense data as internal criteria requiring satisfaction.
   An example can help make clear the idea that the rule must mirror the structure of the world, which on its side must be mirrored in the structure of the rule. Suppose I start driving to the university, where I expect to hold a class. As I drive onto the freeway, I see that the number of cars on the road is unusually small. I begin to ask myself if it is a holiday. (I do not consider the many ways I know to verify this hypothesis; but I know well the implications of its falsification. One of them is that I will not hold any class today; another is that I am wasting my time.) These inferences are more or less derived from my awareness of the meaning of the supposition that it is a holidaythough they do not properly belong to its meaning. I do not have a mobile phone to check whether it is a holiday, but some minutes later I arrive at the university only to verify that it is closed. I ask a security guard, who tells me that today is indeed a public holiday. I have used aspects of the verifiability rule to confirm the truth of (I) ‘Today is a holiday.’ This is confirmed by three facts: the symptom (a) that there are few cars on the freeway, the secondary criterion (b) the university is closed; and the primary criterion (c) when asked, the security guard informs me, as expected, that it is indeed a holiday. Now from the thought-content of (I) I derived parts of the verifiability rule which were the thought-contents of (a), (b) and (c). But on the other hand, from the institutional fact (I*) that today is a holiday, many sub-facts follow. Three of them are the following: (a) there are few cars on the roads, (b) the university is closed, (c) if I ask the security guard, he will say that today is a holiday. That is: the same things that follow from statement (I) as its verifying criteria or symptoms follow from the institutional fact (I*) that today is a holiday. And this means that the structure of the applicable verifying rule mirrors the structure of the sub-facts derived from the fact that today is a holiday. I think that in this way we can also give an ontological answer to the problem of the unity of propositions: the proposition, the verifiability rule, is unified by the fact in the world, insofar as the structure of the fact should reflect and confirm its structure.
   It is also important to see that this mirroring of structures is putative. We always assume that our semantic-cognitive rules are fallible, since they concern an open world of experience. Hence, we only assume as probable that the structure of the internal semantic-cognitive rules mirrors the structures of their external references. These can in principle always be corrected by new experiences, leading us to changes or expansions in the structure of the semantic-cognitive rules. We can see this better when we consider rules expressing laws of nature.
   Summarizing: material objects, property-tropes and facts, must have some structure, which is a unifying structure that explains why the entity in question remains the same even when experienced from many different perspectives. And since what allows us to nearly always experience these physical entities by aspectual or partial perception, is a synthetizing rule, the conclusion follows: These external configurations of property-tropes, objects as clusters of tropes, and facts as arrangements of trope-properties and objects, should have an internal structure that mirrors the structure of the semantic-cognitive rules that allow us to refer to them. By the experiential process of their learning, these rules end in putatively mirroring the structures of the entities to which they apply.
   I believe that these remarks help make it understandable why very different perceptual experiences can be of the same entity. For example, human eyes, an eagle’s eyes, a crab’s eyes, a fly’s eyes … can see the very same p-property or object or fact, though in very different phenomenal ways. But the external structure of what is seen should be the same, insofar as the referring rule of all these experiences is the same, even though the criterially given tropes certainly constitute qualitatively different criterial configurations.
   Now, suppose there is some kind of inverted spectrum, so that when I see red you see blue and vice versa. In this case other invariances must exist in order to preserve the inversion: what I call ‘red’ is felt as a warm color by me, while your ‘blue’ must be felt as a warm color by you, and your ‘red’ will be felt by you as a cold color… so that we continue to apply the same names to the same external tropes of color. Thus, though subjective, the true phenomenal trope of color could in the end remain interpersonally unknown, since the structural relations between color and the warmth or coldness of a color is preserved, helping to fix our shared convention. This leads us to ask whether the question of the proper nature of the trope – how the trope is in itself – isn’t an idle question. This even leads us to ask if mirroring structures aren’t all that is needed for our knowledge of the external world.
   Nonetheless, this last hypothesis cannot be true. It cannot be the case that only structure is sufficient, because very different things might have identical structures. One suggestion to solve this difficulty would be to admit the existence of something like external tropes in a sense like that of Locke’s primary qualities (e.g., solidity or resistance to pressure, extension, figure, motion…), which would be tropes similar to their mental sensory data and able to individuate structures diversely composed by them (1975: 136 f.).
   This means that against Berkeley’s famous immaterialist objection that we could be merely comparing weak dependent ideas (said to be internal) with strong independent ideas (said to be external) (1975, III: 225), remaining imprisoned in a mental, immaterial world, we could reply that we are indeed comparing ideas with material things. We are really comparing configurations of sensations or sense data (resistances to pressure, figures, motion…) within the mind with configurations of tropes or p-properties (resistances to pressure, figures, motion…) belonging to the external material world, that is, we are comparing sensory-psychological contents with really external perceptual-material contents or trope-structures. But what warrants that the configurations of material tropes and what comes out of them really belong to the external world? Well, here we need to repeat ourselves. What warrants the external reality of these configurations is just the fact that our experience of them satisfies the suitable axioms of externality, since this satisfaction defines what belongs to the external, material world. It may be that both experiences are phenomenally identical (e.g., the sensation of heat and the real heat), which fosters confusion, but they are categorically distinct. For there is a world of difference between the internal mentally-phenomenal (the ‘phenomenological’ of philosophy) and the external materially-phenomenal (the ‘natural phenomena’ of empirical science), and the satisfaction of the criterion of inherent reality is what warrants this.

25. Synopsis of this book
We can now briefly summarize the main findings of this book. What I have done was to analyze cognitive meanings as ways of reference. Cognitive meanings are constituted by semantic-cognitive rules and their combinations. Though they are cognitive, they are usually non-reflexive, which means that we are not conscious of their real structure. Suitable combinations of semantic-cognitive rules build thought-contents or verifiability rules. Existence is the effective applicability of such rules within an established context. In the pregnant sense, truth is correspondence between only conceived verifiability rules and what can be seen as the result of effectively applied ones – facts in the world. Correspondence is supported by coherence. The external and internal worlds are constituted of tropes, and facts are arrangements of tropes and their combinations. Contents of experience can be sensory-psychological or perceptual-material. Insofar as contents of experience that satisfy semantic-cognitive rules also suitably fulfill axioms of externality, they may be seen as material or external tropes and all the variety of their combinations belonging to the external world. These facts in the world are supposed to mirror the structure of the verifiability rules and possibly some privileged mental tropes. In my judgment the arguments in favor of these views cut deep into the inherited wisdom of much of the present mainstream philosophy of language.




                                                                     








[1] Instead of calling the thought what the completely analyzed sentence expresses, as in the very implausible atomism of the Tractatus, I suggest that we simply call the thought what is expressed by a sentence as it is normally and completely analyzed in accordance with the context (in its widest material-psychological sense) of the practice in which it is inserted.
[2] We could certainly not go further, requiring that there must be some R1 relating F with a in Fa, etc. as explained in the Appendix to Chapter III, sec. 3)
[3] Wittgenstein: ‘Die Möglichkeit seines Vorkommens in Sachverhalten, ist die Form des Gegenstandes.’ (1984g 2.0141) (‘The possibility of its occurrence in states of affairs is the form of the object’).
[4] We can intentionally produce factual contents that are true, for instance, by acting in the world in order to change it, as constructivist philosophers since Giambattista Vico have noted, but even in this case it is the final fact in the world, as the product of human effort that is the truthmaker of the proposition, and not the opposite. That is: we can make the fact that makes truth, but not the fact as truth.
[5] It is the sense determining (bestimmend) the reference in Frege’s way of speaking, or the meaning-fulfilling intention (Bedeutungserfühlende Intention) in Husserl’s way of speaking.
[6] We remember here Alfred Tarski’s disquotational formula, according to which ‘“p” is true in L ≡ p’. Tarski’s approach has the great merit of properly emphasizing the meta­linguistic character of the truth-assignments in a formal language. However, his formula does not overcome the philosophical problems of correspondence. If you replace the sentence p with Fa, Tarski’s theory does not provide criteria that tell us to apply F to instead of to any other object. Moreover, it does not consider the necessity of criteria for the reference of the name a, as if it were self-evident. For reasons like these, I think that the formal definitions presented here are more adequate, particularly regarding our natural language. (cf. Tarski 1944: 341-375).
[7] This points to an easy way to analyze composite statements of the forms p & qp ∨ q→ q and  q. As is well known, we can respectively use negation together with the conjunction in the following descriptions of facts:  p & q, ~(~& ~q), ~(& ~q) and ~(& ~q) & ~(~p & q). Negation always means that thought-content is false, and this also means that the ver­ifiability rule that constitutes this thought-content has proved not to be effectively applicable in its proper context, that there is no corresponding real fact, only a possible one.
[8] Usually only three moments are considered, since the third and the fourth moments are usually seen as a unity. I distinguish them only because verifying identity of content seems to me distinguishable from the attribution of truth.
[9] Consensual theories of truth demand that truth must ultimately satisfy an interpersonal consensus made authentic by its achievement through adequate agreement within a critical society of ideas (attempting to reach an ideale Sprachsituation). This is a point particularly relevant in regard to the collective acceptance of law-like generalizations (cf. Habermas 1983).
[10] The anterograde and retrograde procedures can be compared to what in Husserl’s phenomenology would be called ‘truth as correctness’ (Wahrheit als Richtigkeit) and ‘truth as discoveredness’ (Wahrheit als Entdecktheit) respectively.
[11] See my objections to the private language argument in Chapter III, sec. 13 of the present book.
[12] Surely, this suggestion would relativize truth to a time and a community of ideas that would make this truth-theory a theory of our taking things to be true (das Fürwahrhalten). But in the end this would not be a problem if we agreed that absolute truth is simply a kind of normative ideal that helps us evaluate our take something to be true, but has necessarily nothing to do with what we normally accept as true or false, since even if we reach absolute truth, we cannot know that we have reached it. That is, when we say that p is true, we only assume that p is the final truth until we find a reason to falsify p (if p is empirical) or abandon p (if p is a formal statement). A theory of truth is a theory of what leads us to take something to be true, rather than a theory of absolute truth. The same can be said regarding the concept of knowledge.
[13] If q is only the direct expression of a factual content, we fall into a kind of strong externalism that admits that part of our content-thought-meaning is a directly given fact in the world (a ‘structured proposition’ or something of the kind). However, without more qualification this view seems to demand too much from our epistemic powers, leaving unexplained not only the possibility of falsity, but also the inevitable fallibility of our supposed knowledge of truth.
[14] I mean cases like the false feeling of pain induced by hypnosis and many others.
[15] I recall reading the story of a rubber dolphin many years ago, but I cannot remember where.
[16][16] The third traditional epistemological position is phenomenalism. According to it, since we can have experiential access only to our sensations or sense data, there is no reason to postulate an external world independent of these sensations. This view leads almost inevitably to epistemic idealism and rejecting the existence of a non-mental external world (see Ch. IV, sec. 18).
[17] For an admirably vivid contemporary defense of direct realism, see John Searle 2015.
[18] For similar lines of defense, see Cornman 1975, Ch. 2, 6; Dancy 1985, Ch. 10; Lowe 1992; Huemer 2001, Ch. VII. As Huemer notes, we should sharply distinguish the object of perception from its vehicle, and as Lowe points out, the veil of sensations must be seen as a bridge or a window to the real world.
[19] In what follows, I am indebted to John Searle (cf. Searle 2002, Ch. X).
[20] See Costa 2014d: 145-157. In that paper I claim that when the plain man affirms the obviousness of the reality of the external world by unconsciously extending the criterion of reality to the cases (1) to (4) and inferring the existence of a whole external world from it.
[21] This is the main difference between the inherent and adherent senses of reality and Rudolph Carnap’s similar distinction between internal and external questions of existence: for him external existence results from fiat (a decision to accept a system). However, we cannot produce adherent reality (that is, answer an external question) simply by fiat, as he has proposed, for we are unwittingly led to this acceptance. The point was sufficiently criticized by Barry Stroud (1984) and P. F Strawson (1987).
[22] For a detailed answer to the modus tollens skeptical argument as a result of failure in distinguishing between inherent and adherent attributions of reality, see Costa 2014d.
[23] Within this general view, Husserl distinguished four different concepts of truth. However, the question of their justification is controversial. (Husserl 1980, II, VI, sec. 39; cf. Tugendhat 1970: 91 f.)
[24] Peter Simons summarizes Husserl view of intentional objects as follows: ‘In particular, each noema has a kernel or nucleus which consists of three elements: a substratum, a set of qualitative moments, and modes of fulfilment of these qualities. What he calls a pure or empty is the subject of predicates that are intended in the nucleus and which are more or less intuitively fulfilled. … this X is not a further concrete constituent in the noema; it is an abstract form occurring in it (Ideas 131).’ (Simons 1995: 127).
[25] Against the objection that in this case the verifiability rule cannot be equated with cognitive meaning, we answer that meaning must be equated with verifiability (Ch. III) independently of the concrete verification. While the verifiability procedures of our action-schemas are in fact cases of concrete verification, they are installed truth-making procedures.

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