sexta-feira, 21 de julho de 2017

### SKETCH OF AN UNIFIED THEORY OF TRUTH (1)

Advanced draft for the book PHILOSOPHICAL SEMANTICS, to be published by CSP in 2017/2




– 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 wahre.
[The veridical picture of the error is the indirect picture of truth; the veridical picture of truth is the only true one.]
Novalis
                                                  
We have drawn some conclusions from the 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. The verifier (truthmaker) of a proposition is the fact it refers to, a fact composed of tropical arrangements. Moreover, consistent with our idea that the effective applicability of a conceptual rule is the same as the existence of at least one trope or cluster of tropes that satisfies it, we can expect that by symmetry the effective applicability of a verifiability rule in its proper context should be the same as the existence of the fact that satisfies it. Finally, since the property of a verifiability rule of being definitely applicable in the right context also makes such a thought-sense-rule true, it seems that the existence of the fact referred to by it should be the same as its truth.
   However, this conclusion seems at odds with another view, namely, the correspondence theory of truth, according to which the truth of a thought-content is its correspondence or (as I prefer) adequation (adaequatio) with a fact and not the existence of the fact referred to by it. This is disturbing, for as already noted we have the best methodological reasons for defending truth as adequation. This theory 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 nowadays most theorists are inclined to accept it (Mosteller 2014, Ch. 2). Notwithstanding, existence and truth, in terms of effective applicability and correspondence/adequation, seem to have little in common.
  Nonetheless, I believe I have found a simple way to overcome the difficulty. The solution consists in remembering that, as dictionaries show, the word ‘truth’ has two very distinct main bearers in natural language (Ch. IV, sec. 31). Indeed, among a variety of irrelevant senses, dictionaries always distinguish clearly between:

(a) thought-truth, which is the ‘truth of a thought in conformity with things being as we believe they are,’ (I would say, the property of a thought-content-rule, of adequateness with a fact), and
(b) fact-truth, truth as the ‘actual, real or existing thing or fact.’

Even if thought-truth is primary and fact-truth derivative, my view is that fact-truth is more properly identified with existence – the existence of a fact, which is the same as the satisfaction of the condition of effective applicability of the verifiability rule that forms its thought-content. However, truth in the archetypical sense of thought-truth continues to be reserved to the property of the thought-content of correspondence with facts, which is the same as the property of the verifiability rule of being effectively applicable by us. It is so because we need to distinguish the match from the mismatch between the verifiability rule and the contingent arrangement of tropes. Thus, my proposal is that thought-truth expresses a first order property of the truth-bearer of being a verifiability rule (a thought-content-rule) effectively applicable to its fact. The fact-truth, on its side, is the higher-order property of the fact, since it is a first order property of the fact’s proper verifiability rule (the thought-content-rule) of being effectively applicable to it.
  There is an essential difference between these two cases: The thought-truth is the truth of a thought-content-rule, a verification rule, saying that it is effectively applicable to the fact. This attribution of truth demands the existence of the verification rule effectively applicable to its fact, which implies the existence of (i) the fact, (ii) the verification rule, and (iii) at least one cognitive being able to apply it. However, the fact-truth demands much less. It demands only the existence of (i) the fact in question with its being able to have a possible verifiability rule (thought-content) effectively applicable to it. It does not demand either the existence of a verifiability rule or the existence of an epistemic subject able to apply this rule to it. As we have already seen (Ch IV, sec. 35), a world without cognitive beings would have fact-truths but no thought-truths.
  Based on what we have learned thus far, the purpose of this last chapter is to outline a sufficiently detailed and plausible adequation analysis of truth; one that is able not only to better clarify the above distinction, but also to take account of the real complexity of the issue.

1. The deceptive simplicity of correspondence
I begin by addressing what I consider to be the shallowest objection against the correspondence theory of truth. It is the claim that the theory is nothing but a trivial, empty truism. According to this widespread objection, to say that truth is agreement with facts is a too obvious platitude to deserve philosophical attention (Blackburn 1984, Ch. 7.1; Davidson 1969).
  The uncertainty that this objection can produce comes from the fact that in philosophy careful scrutiny has too often shown that what at first seems to be a plain, uncomplicated meaning conceals unexpected complexities. One impressive example of this was the causal theory of action. Who could at first glance foresee that analysis would show that such an apparently simple thing as human action could involve such a variety of often very complex processes? Another example is the analysis of knowledge. One does not come to the definition of knowledge as justified true belief without analysis, one does not see its difficulties just from the start, and one does not come to the many alternative analyses without first reflecting upon it.[1] In what follows, I hope to convince you that the correspondence theory of truth is no exception to this rule. The supposed simplicity of the correspondence relation is only apparent, revealing our lack of awareness of what we really do when making truth-claims.
  Methodologically, my strategy consists in reconsidering the best insights that we have inherited on the correspondence theory and in asking how far they can be developed and combined in order to lead us to a full-blooded philosophical analysis of the adequacy relation. As you will see, this ultimately requires a pragmatic investigation of the dynamic constitution of adequation, which in the end exposes its intrinsic relationship with verifiability, criteria of truth, coherence, and its dependence on a solution to the problem of perception.

2. Compatibility between verification and adequation
Some think that verificationism and the correspondence theory of truth are incompatible. One apparently compelling argument for this is the following: a statement can be verified in many different ways, insofar as its verifiability rule may be satisfied by an indeterminate range of diversified sub-facts, which are tropical arrangements acting as verifiers. By contrast, correspondence is a one-one relation: the fact corresponding to a true thought-content seems to remain univocally related to the thought-content expressed by the statement. Consequently, it does not seem possible that what verifies the content stated is a corresponding fact, as claimed by the old adequation theory.
  My view is that the above argument is deeply misleading and that one only reaches such conclusion by searching for adequation in the wrong way and in the wrong place. In its most proper sense, adequation is not a relationship between a thought-content-rule and one or more of the multiple external criterial arrangements of tropes – the many possible aspectual sub-facts – that by means of sensory-perception can reached, this being sufficient to verify a thought-content (Ch. IV, sec. 25-27). Adequation is here, we can say, either between an immediate thought-content and its sub-fact or between the more encompassing mediated thought-content and its grounding fact. What interests us most here is the adequation between the mediated thought-content as a ramified verifiability rule and the grounding fact with its many different sub-factual manifestations. Concerning this, the central point is that the resulting cognition of the grounding fact can be inferred from the satisfaction of this or that partial external criterial tropical arrangement, a sub-fact, often the only one immediately experienced. For instance: I say that I see the grounding fact that there is a ship on the bay, even though I can see this grounding fact only from one side and at a certain distance, that is, by visualizing those specific tropical arrangements constitutive of a criterial sub-fact. Consequently, the comprehension of a grounding fact is very often more or less indirect and inferential. Summarizing, correspondence or adequation can occur on two different levels:

1)     Immediate, as the matching between the internal criterial configuration generated by some perceptual thought-content-rule and the external criterial configuration formed by the tropical arrangement constitutive of a sub-fact.
2)      Mediated, as the matching between a main thought-content constituted by the whole verifiability rule (containing the encompassing thought-content) with its possible ramifications (containing the encompassing thought-content) and the grounding fact to which the many tropical arrangements constitutive of its derived sub-facts belong. The satisfaction of any suitable criterial configuration by means of a sub-fact enables us to indirectly infer the correspondence between the main thought-content and the grounding fact. And this is all we need.

These two levels of correspondence or adequation work in the same ways that will soon be explained, although the last case is of greatest interest to us. We can explain this higher level of adequation as follows. By means of the experience of sub-facts as external criteria we may indirectly infer that overall the main verifiability rule or mediated thought-content corresponds to a whole grounding fact. Consider, for instance, the thought-content-rule expressed by the statement ‘The ship is approaching.’ We may conclude this, for instance, by means of the verified criterial dynamic sub-fact of the form of a ship-bow rising up before our eyes. Using this sub-fact as a criterion, we conclude that the independent identification rule for the object that constitutes the grounding fact – say, for the whole ship – is applicable. Also using this sub-fact as a criterion, we conclude that the dependent ascription rule for the property of the grounding fact – say that something is approaching – is also effectively applicable to the real grounding fact of a ship that is approaching. What we have are two isomorphic pairs of elements, each pair conjoined in a similar way – which, as we will see, belongs to correspondence as a structural isomorphism.
  This is why we can still say that a thought expressed by p, its cognitive meaning, corresponds to the factual content q, even if the verifications are very often variable, partial and perspectivist, relying on sub-facts. However, in order to bring more clarity to these views we need to delve more deeply into the waters of the correspondence theory of truth, beginning with an analysis of the proper nature of the relation of adequation.

3. Analysis of adequation: structural isomorphism
Assuming that truth in a privileged sense is the adequation (correspondence, agreement, match…) 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 as s-thought, properly built upon psychological p-thoughts, as the archetypical truth-bearers in our discussion of Frege’s semantics (Ch. IV, sec. 34). We did this along with a detailed defense of the idea that an atomic fact in its most interesting sense is a cognitively independent arrangement of elements which are tropes and clusters of compresent tropes. In this sense, as we also saw, ‘fact’ is an umbrella-term that includes actual static facts (situations, states of affairs…) and dynamic facts (events, processes…), serving in this way as universal truthmakers – the most proper verifiers of statements (Ch. IV, sec. 23). What is now in need of analysis is the concept of adequation in its relevant sense.
  Wittgenstein, as is well known, insightfully defended an adequation theory of truth in his Tractatus Logico-Philosophicus (1984g, sec. 2.21). I prefer to ignore the implausible atomistic metaphysics of this work, though not its deeper insights. And one deep insight of the Tractatus is the idea that a fundamental condition of representation is a pictorial relationship between an analyzed sentence or what he calls a thought (Gedanke) and the possible fact, called a state of affairs (Sachverhalt), or the given fact, called a fact (Tatsache), the only thing able to make the thought true.[2] The idea was resourcefully explored by E. G. Stenius in an important monograph on the Tractatus (1960) and several later articles (particularly that of 1981) by applying to it the mathematical concept of structural isomorphism.
  Applied to the correspondence view of truth, a true thought-content must have at least structural isomorphism with a fact. As I understand it, the structural isomorphism is completed by three conditions, which are at least partially explanatory of the idea of adequation:

(i)                A bi-univocal relation: the semantic elements constituting a thought-content (or the sentence expressing it) and the elements constituting the possible or actual fact must have a one-to-one relation.
(ii)              A concatenation: the elements of a thought-content (or analyzed sentence) must be combined in the same form (e.g. ‘Subj.-Pred.’) and order (e.g. ‘First S then P’) as that of the elements composing the possible or actual fact.
(iii)            A 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 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 condition for the falsity of a thought-content is that it must be structurally isomorphic, not necessarily with an actual fact, but at least with a possible fact, that is, with a conceivable or imaginable fact. These conditions are necessary because a supposed thought-content-rule or proposition must at least be possibly classified as true or false in order to have any cognitive usefulness and deserve its name. But these conditions are not sufficient.
  Notice that we do not need to believe that possible facts inhabit some Platonic realm in order to accept the requirement of conceivability. To conceive or imagine a possible fact is simply a psychological phenomenon, and it doesn’t seem that we need to imagine it in all the details we would be forced to consider if it were a real fact. In other words, a true thought-content must be correlated to a fact in the world, while a false thought-content, though not correlated with a fact in the world, must at least be correlated with a possible (conceivable, imaginable) fact by means of which we know that in principle it could be correlated with an actual fact in the world.
  The natural way to apply this view to real statements is to begin with singular predicative or relational statements in their linguistic practices, taking their logically analyzed sense-components 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 singular sentences of the form Fa (e.g., ‘John is easygoing’) or aRb (e.g., ‘John is the 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 propositions must at least satisfy the following conditions of structural isomorphism:

(i)                Each sense or semantic-cognitive rule of each nominative and  predicative expression must correspond bi-univocally to the respective elements constitutive of the respective fact in the world. This fact is an arrangement made up of simple or complex property-tropes (like being easygoing, being the father of, giving something to someone, giving something to someone to please someone else) and tropical objects, made up at least of tropes like those of form, solidity, mass… displaying compresence, (John, Mary, Jane, the flower…) (See Ch. IV, sec. 5)
(ii)              The concatenation, i.e., what we called order and form of connection between the elements of the thought-content-rule and the fact 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 abR (‘John is the father of Mary’ cannot be replaced by ‘Mary John is the father of’). Regarding the form of connection, I mean that the predicates along with their references are relatively dependent on nominal terms and their references (being easygoing depends on John’s existence, being a father depends of the existence of John and Mary). (See Ch. IV, sec. 7-9)
(iii)            the whole thought-content must be bi-univocally related with its possible or actual corresponding fact.[3]

This view should apply even to complex and vague predicates. Take, for instance, statements like ‘Céline had a strange personality’ and ‘The Irish potato famine was caused by late blight.’ Insofar as these expressed thought-content-rules are able to be objectively-interpersonally verified, they are in order – although it is surely not so easy to explain Céline’s strange personality or how the late blight caused the Irish potato famine, these concepts are surely open to investigation.

4. Analysis of adequation: categorical match
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 adequation. 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-content-rules 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 relational 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.
  However, if structural isomorphism were all that was required, then statement (1) could have as its truthmaker the facts represented by (2) that Kitty is in the kitchen or by (3) that John is the father of Mary, since these facts are also isomorphic with statement (1). Moreover, any of these sentences, having a similar intransitive logical structure aRb, can be structurally isomorphic with the unlimited number of facts with a similar structure.
  These remarks lead us to the conclusion that structural isomorphism, though necessary, is far from sufficient to explain adequation, since sharing the same logical structure isn’t enough. Erik Stenius was aware of this difficulty when he suggested that there must be what we call 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 here ‘indices’ is too uninformative, 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 of this topic is frustratingly 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 specifying power of semantic-cognitive rules. Restricting ourselves to the simplest case of the singular predicative statement, what we have is the following. First, the conceptual senses expressed by singular and general terms – identifying and ascription rules – along with their joint 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 of tropes (p-properties), clusters of compresent tropes (objects) and arrangements of these configurations of tropes and these clusters (facts). Once all these internal criterial configurations are satisfied by the suitable tropical arrangements or actual facts in the proper context, the verifiability rule is considered definitely applicable. Since this rule is nothing but the thought-content, once definitely 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 distinguish the isomorphic elements constitutive of particular facts, in this form explaining how concepts apply.
  What we first need to add to our understanding of adequation as structural isomorphism are the individualized senses of the component expressions, that is, the semantic-cognitive criterial rules that constitute the thought-content or verifiability rule. As already noted, we typically identify the corresponding grounding fact by means of its many variable aspects, its sub-facts. In order to achieve this what we do is, by means of the partial structural isomorphism reached with the sub-facts, to intentionally relate senses of different interpretations of a statement with different aspectual actual or possible sub-facts in order to get the sense of the main statement in its actual (true) or only possible (false) isomorphism with the grounding fact. Coming back to the old example: adequation can be expressed 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. However, this is only one aspect of the sense leading us to the statement ‘The morning star as Venus is the same as the evening star as Venus’. This statement can be understood as corresponding (referring) to the grounding fact that can be expressed by the sentences ‘Being Venus (as the morning star) is the same as being Venus (as the evening star)’ or, in the standard form, ‘Venus [in full] is Venus [in full].’ (Ch. IV, sec. 27).
  Furthermore, we must remember that we can make all these rules explicit by means of definitions that bring their criteria of application to the surface, as I have exhaustively shown using the concept of chair as an example (Ch. II, sec. 8). In the aforementioned examples, we can do something similar. Concerning names, in the examples (1), (2) and (3), this would be done by means of the (semantic-cognitive) criterial definitions given by the identification rules of the nominal terms ‘the book,’ ‘the table,’ ‘Kitty,’ ‘kitchen,’ ‘John,’ ‘Mary’ (see Appendix Ch. I). Concerning predicative expressions, in examples (1), (2) and (3) this would be done by means of definitions of the relational predicative expressions ‘…is on…’, ‘…in the…’, ‘…is the father of…’ Such definitions will show how the elements can or cannot be adequately concatenated one with another (the table cannot be on the book, the kitchen cannot be in Kitty, Mary cannot be the father of John) and how they can be applied to the elements constitutive of the corresponding grounding fact.
  These explanations entitle us to suggest that when two thought-contents p and q display structural isomorphism and the (semantic-cognitive) criterial rules that form the elements of p are the same as the (semantic-cognitive) criterial rules that form the elements of q, then both thought-content-rules are the same. That is, p and q express what we may call the same thought-content. This is a point about content that will be useful later, when we arrive at the pragmatics of the correspondence relation.

5. Excurse on logical form
At this point, I would like to make an excurse to consider a deep but obscure insight related to Wittgenstein’s view of adequation. It seems that we can relate the above-considered conditions of adequation with what he called 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 two of the three dimensions of space; a melody and its score (when it is read) must have in common the dimension of time. However, according to his doctrine there must be something common between a thought-content and the fact represented by it, something unsayable, common to any representation and what it represents, which is the logical form. He sees logical form as the possibility of structure, or rather obscurely as the possibilities of the occurrence of an object in a state of affairs.[4] Without logical form, a sentence could not be meaningful. The idea of logical form should settle the ultimate bridge between the thought and the world, since both must share the same logical space of possibilities. This is allowed because in its fundamentals logic is ubiquitous: no cognition and therefore no cognoscible reality can be 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 narrow our understanding of logical form when we speak of logical structure 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 element in the factual (actual or not) reference. Consider the following:

The same logical structure is shared when there is identity between the logical possibilities of combination among the elements of the thought-content and the logical possibilities of combination among those bi-univocally related elements represented, either in the possible or in the actual fact.

Suppose now that the elements of the linguistic realm are the semantic-cognitive rules and that the elements of the real world are tropical combinations that have the same logical structure as the semantic-cognitive rule. In this case, in order to have a truth-value, elements of atomic thought-contents with forms like Fa, aRb… molecular thought-contents of the forms ~Fa, Fa & Fb, Fa Fb, Fa → Fb… general thought-contents of the forms (x)(Fx) and Ǝx(Fx)… must not only be structurally isomorphic with respectively represented possible or actual facts. They must also be able to share the same logical possibilities of combination with other elements of their proper ontological level, as a condition for meaningfulness in the case of the thought-contents and as a condition of conceivability in the case of facts in the world. This suggests that speaking about the logical form of a mediate thought-content-rule amounts to something correlative to the multiplicity of ways of satisfying these rules. A multiplicity of criteria generated by this thought-content-rule is able to match the wide but simultaneously non-arbitrarily limited multiplicity of tropical elements constituting the possible or actual sub-facts able to satisfy them by remitting to the same grounding fact. If the semantic-cognitive rules are able to give us logical forms, it seems that we have a better clue for explaining how their categorical match with the elements of reality is possible.
   Finally, I disagree with Wittgenstein thesis that logical constants do not represent (1984g 4.0312). I think this result comes from a confusion between the fact that they are qualitatively identical to what they represent with a numeric identity. If I say ‘The mother and the child are playing together’ or ‘The triangle and the square are geometrical figures’, these two conjunctions in the language are representing the similar conjunctions in the world, even if the temporality of the first conjunction is abstracted and the temporality of the second has found no begin or end. This way of thinking is in conformity with my thesis that logical properties are spatio-temporal properties, being consequently tropes, even if the thinnest and the widest ones (see Appendix to chapter III, sec 4).[5]

6. Analysis of adequation: intentionality and causality
There are still two elements that I believe we need to consider in order to complete our analysis of adequation: (v) intentionality and (vi) causality. In judging something to be true, we must be aware that we are applying a verifiability rule to a fact, we need to have a ‘referential directionality’ that leads us from semantic-cognitive rules to the tropical criteria that should satisfy them, from judged thought-content to the fact it aims to represent.[6] One could say that intentionality (as thought-truth) gives to the adequation a ‘mind-to-world direction of fit’ in the sense of a ‘mind-to-world responsibility of fit,’ defining the direction of fit of a mental state as its responsibility to fit an independently existing reality,[7] presupposing the broader structure of our consciousness. The upshot is that adequation restricted to isomorphism is symmetrical, while adequation cum intentionality is asymmetric. Since correspondence (as agreement, accordance, congruence, conformity, matching) is clearly symmetrical, correspondence is the right word for distinguishing isomorphism, but not isomorphism cum intentionality. More appropriate words would be ‘picturing,’ ‘adjustment’ and ‘adequation,’ since these relations are not necessarily symmetrical (if A is adequate to B, B does not necessarily need to be adequate to A). Because of this, I prefer to use the old term ‘adequation’ (adaequatio) instead of correspondence.
  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. This causal relation does not need to be a direct one, in fact, more common is a very indirect form of causality, which can mislead us to the belief that it does not exist. Causality has a ‘world-to-mind direction of fit’ or a ‘world to mind responsibility of fit’ in the sense that it is what causes thought-content to match reality. We can speak here of the effective applicability of its verifiability procedure and, in the case of indexical thoughts, even of the initial construction of such a rule in the given context. To the symmetrical correspondence relation, adequation adds two opposed asymmetrical relations: intentionality and causality.
  For reasons of clarity, I will consider a final example of a composite thought-content that I adapt from Stenius. If someone says: ‘John (j) is the father (F) of Peter (p) and of Mary (m), who is a violinist (V)’, the logical structure of the thought-content expressed by the statement is:

1.     ‘jFp & jFm & Vm’.

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 violinist’, 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 clear meaning. If the statement is false, the discovered adequation stops here, as an adequation 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 logical) components of the composed thought-content expressed by (1) and the isomorphic fact.
(ii)              the same concatenation (order and form of connection) between the semantic cognitive rules constituting the verifiability rule of each singular thought-content, together with the relations of conjunction among them 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 and composed fact).
(iv)            a satisfaction of the criteria formed by each semantic-cognitive rule with its proper objective correlate, together with the rules of conjunction, assuring us the proper individuation of the correlated entities.
(v)              the intentionality (directionality) we link to the rules, leading us to distinguish what is representing – a composite thought-content – from what is being represented – the actual corresponding composite fact.[8]
(vi)            We assume that ‘jFp & jFm & Wm’ is true because we think of it to be suitably caused.

On the other hand, for a disjunction like ‘jFp jFm Wm’ to be true at least one of the disjuncts must represent by adequation, not only a possible fact, but also the actual fact. Finally, any false disjunct must correspond to only one possible (conceivable or imaginable) fact, if we want the statement as a whole to remains cognitively meaningful.

7. The logical form of the adequation relation
Assuming the suggested analysis of adequation, we can symbolically express what could be called a formal definition of truth: the logical structure by means of which we can identify the predicate ‘…is true’ with the predicate ‘…corresponds with a fact’. As with the predication of existence, the predication of truth is of a higher-order. It is a semantically metalinguistic predicate applicable to thought-contents. We call a predicate semantically metalinguistic when it refers primarily to the content of the object language, contrasting it with a syntactically metalinguistic predicate, which refers only to the symbolic dimension of the object language. The statement ‘“Themistocles won the battle of Salamis” is a historical statement’ serves as an illustration. The semantic metapredicate ‘…is a historical statement’ refers metalinguistically primarily to the semantic content of its object-sentence, that is, to its thought-content, and by means of this, secondarily, also to the real historical fact. According to this view, for any thought or content of belief p, to say that p is true is the same as to say that p adequates to a real factual content. We can express this symbolically, using p to express the thought-content, replacing the predicate expression ‘…is true’ with T and the predicative expression ‘... adequates to a real fact’ with A. The predicates T and A 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)   Tp Ap[9]

According to this identification, truth is the property of a thought-content expressed by a sentence p, namely, the property of adequating to a real fact.
   This formulation depends on the application of the monadic predicates ‘...is true’ and ‘...adequates to a fact’. However, monadic predicates can often be unfolded into non-monadic predicates such as, for instance, ‘…is a father’ into the more discernible ‘…is the father of…’ The same can be said of the predicates ‘…is true’ and ‘…adequates to a fact’, which can be unfolded as more complete relational predications of a semantic metalanguage relating the thought expressed by p to the fact or factual content that q as ‘…is true for…’ and ‘…corresponds to the fact that…’ (cf. Künne 2003: 74). We can also illustrate this point using an example. One could say ‘“Themistocles was the victor at the Battle of Salamis” expresses the same historical occurrence as “The Battle of Salamis was won by Themistocles”’, where ‘…expresses the same historical occurrence as…’ is a relational semantic metapredicate primarily applied to the thought-content of the two object-sentences.
  This means that the definition above can be more thoroughly explained as stating that for a given thought-content p, to say that p is true for the actual factual content q is the same as to say that the thought-content p adequates to the actual factual content q. For this explanation one can understand adequation as a relation of identity of contents expressed by p and q, so that we can say that p = q. (I underscore q in order to show that its content, though also interpretable as an 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 ‘...adequates to the fact that…’ for A*, we have the following formalized version of a more complete formal definition of truth. In this definition, the thought-content expressed by p and the actual factual content expressed by q are metalinguistically related by the metapredicates T* and A* as follows:

(2)   ‘pT*‘qpA*‘q

  More than an unpacking of (1), the formal definition (2) is a more complete formulation that individualizes the corresponding fact as q. According to (2), the assignment of truth is the same thing as the assignment of the relational property of adequation, that is, the assignment of a qualitative identity of content between a thought-content and an actual corresponding factual content. (As we saw, this identity of content is to be analyzed in terms of structural isomorphism, added to the satisfaction of criteria for applying the component terms of p).
  Finally, assuming 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 a fact. Symbolizing the semantic metapredicate ‘…is a verification procedure that applies to a fact’ with V, we have:

(3) T‘p’ A‘p’ V‘p’

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

(4) ‘p’T*‘q’ ‘p’A*‘q ‘p’V*‘q

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

8. Negative truths
Now, consider a false singular predicative or relational statement p. Since it is false, such a statement does not correspond to any real fact in the world. However, to say that p is false is the same as to deny that p is true, namely, to say that the statement ~p is true.[10] And here the problem arises. 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) ‘Theaetetus is flying.’ In this case ~p is (ii) ‘Theaetetus is not flying.’ Then, at first glance it seems that we have in (ii) a true statement that does not correspond to any fact in the world! This would lead some to suspect that (ii) is true because it refers to a ghostly negative fact: the unworldly fact that Theaetetus isn’t flying.
  With the help of 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 Theaetetus is in fact sitting, since according to ~p he could also be standing or lying down. However, ~p means the same as ‘p is false’, and by saying that p is false one denies correspondence with a real fact in the world. Despite this, as I have insisted, by imagining the false idea that Theaetetus is flying, we already accept that p corresponds with a possible fact, namely, with our imaginary dynamic fact of Theaetetus flying... But a possible fact is no fact in any metaphysical sense; it is something that is located somewhere in our brains when we imagine it. In summary, ~p and ‘p is false’ only mean that p expresses a verifiability rule that although applicable to an only conceivable or imaginary state of affairs – a possible fact – does not effectively apply to any 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.’ What this statement says is 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.[11]

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

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 the simplest 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 adequation, the general answer is that self-referential statements like these are mistakenly constructed because in all these cases the predicate ‘…is true’ does not work as a semantically metalinguistic predicate referring to a complete thought-content. Rather it functions as a normal predicate built into the thought-content, also belonging forcefully to the object language. Being mistakenly 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 ‘p is true’ or ‘p 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 definitely applicable verifiability rule. 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 if it should be true. The statement ‘This sentence is true’, to the contrary, affirming its own applicability, though also devoid of any 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. Why? The reason is that the metapredication of truth is applied to the thought-content (verifiability rule) that the sentence in question has nine words without belonging to this thought-content. One could unpack what is implicit 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 built into the relevant thought-content.
  Furthermore, we can predicate the truth of a metalinguistic thought-content insofar as this semantic predication is meta-metalinguistic and so on, since the s-thought, as an arrangement of only apparently disembodied mental tropes is also a fact.

10. Pragmatics of the adequation relation
What we have seen to this point was the frozen logical structure of truth as adequation. Now we will see how it works in the practice of truth-attributions that provides us with what some have called truth criteria. The view I wish to defend here was inspired by Moritz Schlick’s brief defense of the adequation theory of truth (1910), though in my judgment this should be regarded as an empiricist reconstruction of a fundamental insight attributable to Edmund Husserl (see sec. 27 of the present chapter). The idea is that adequation has a pragmatic or dynamic dimension that deserves to be explored and cannot be captured in static formal definitions – an idea that should not sound strange to those who wish to combine correspondentialism with verificationism. We can begin by considering that very often we can establish an idealized sequence of 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.[12]
  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 developed a hypothesis. This hypothesis was later confirmed by observation, which made the hypothesis true because the contents of both were the same. I next offer a more trivial example. Suppose that it is the rainy season in Northeastern Brazil and that I ask myself p: ‘Will it rain in Natal tomorrow?’ This is the suppositional step. Now, when tomorrow comes, I open the door of my house and see that in fact it is raining heavily outside. This is the second, the evidential step. 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 step. Finally, considering that these contents are qualitatively identical (in fact, satisfying conditions (i) to (iii) of structural isomorphism and (i) to (iv) of adequation), I conclude that the thought-content of my earlier hypothesis p is true by adequation with the fact that today it is raining in Natal. This is the judgmental or conclusive moment. Now, if instead of seeing rain outside I see a very blue sky, my observation contradicts my supposition. Seeing that the content of my observation in this proper context diverges from the content of the supposition p, I conclude that p must be false: it is not raining in Natal today.
  Examples like these are common, and an analogous procedure, as we will see, applies to non-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 step: this is a consideration, hypothesis, conjecture, guess, question... In this first step we ask ourselves whether some thought-content is true, that is, if the verifiability rule that constitutes it is not only imaginatively, but also definitely applicable in its proper context. We can express this as ‘I suppose that p’, ‘It is possible that p’, ‘I guess that p’, ‘Is it the case that p?,’ where p expresses a content that can be perceived. This step can be formalized as ‘?p’ (call ‘?’ the operator for supposition). This supposition is always made in the context of some linguistic practice.
2)     What follows is the evidential or perceptual step: the realization of a perceptual experience under already more or less 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 a suitable 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 must be stipulated as indisputable within the context of the language-game or practice in which it occurs; otherwise we would be daunted by the question of the truth of o!, which would also need to be grounded, leading us to an infinite regress.
3)     Confrontational step: it is the comparison between the sup­posi­tion­al content and the factual content of the perceptual experience which makes possible the verification or falsification of the 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 (isomorphic, categorical, intentional…). In the case of a perceptual experience the positive answer can be summarized as p = o (where the ‘=’ expresses qualitative identity). As will be better 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 p o. (In its concrete details it is more complicated: as we already noted, usually the fact o is only partially and aspectually experienced, which does not prevent me from saying, for example, that I see that it is raining all over Natal. Moreover, in practice it is often the case that we must have more than only one perceptual experience and in more than one way...)
4)     Judgmental or conclusive step: Finally, in the case in which p = o, the thought expressed in the supposition will be accepted as true, otherwise it will be rejected as false. When p = o, there is adequation and the conclusion is an affirmative judgment that can be symbolized as ├p. In the case in which p ≠ o, that is, in the absence of the expected adequation, the thought p is false. This can be expressed by the negative judgment symbolized as ├ ~p.

Now we can summarize the four steps of this whole verifiability process regarding the discovery of 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 adequation between some suppositional thought-content (which is only a considered or imagined verifiability rule in its possible application) and some perceptual content (given by the definitely applied verifiability rule) that within the linguistic practice in which it is stipulated as indoubtable. In other cases, the adequation is only between the supposition and an imagined, non-actualized fact, being distinct from what is found in the observation. In these cases, the statement must be false.
  It is also worth noting that the standard statement of ├p (a judgment) has the form of the report of an assertion that is settled. However, this assertion can always be questioned again. In this case, new verifying procedures can reconfirm the judgment or detect some inadequacy refuting it in an at least virtually interpersonal way (cf. Sokolowsky 1974, Ch. 9).[13]
  Now, how can we understand the adequation relation as qualitative identity of content (structural isomorphism, identity of cognitive rules, 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 indexical identifying rule of a spatio-temporal region to which it adds the predicate ‘…is raining’: ‘Now in Natal it is raining.’ This predicate expresses an ascription rule definitely applicable to the region by the satisfaction of configurations of tropes constituted by the countless drops of water falling from the air above. This combination of satisfactions gives me the arrangement that constitutes the sub-fact that is the truthmaker which allows me to infer the content building the grounding fact q that it is raining in (the region of) Natal today. These facts, I suppose, should have a structure similar to that of the verifiability rule inversely projected on the outside world (Ch. IV, sec. 19) (Maybe we could say that each side should share the same logical possibilities.)

11. 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 perceptual experience, progressing from evidence to the affirmation of a supposition – a way to discover truth that we may call retrograde.[14]
  Here is a simple example of a retrograde verification procedure. 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 raw initial sensory-perceptual state was different from the state of conscious awareness that immediately followed, namely, that it is raining. (Suppose I open the door to get some fresh air and do not even pay 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 raw observational experience ‘o!’ This momentary experience makes me immediately 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. I think that this process is normally very short, which accounts for our lack of awareness of its various different steps. Anyway, this is a retrograde discovery of truth to be summarized in the following sequential formulation:

!o, ?p, o = p /├ p

Clearer cases of retrograde awareness of truth occur when someone has an unexpected sensation or perception that only slowly comes to be conceptualized in its true nature. Suppose that in the middle of the night I have a strange sensation in my right arm. I may call it ‘!s’ and at first not identify it as pain. In the process of awaking, I unconsciously recall the idea of pain, subjecting it to consideration: ‘?p.’ 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. (Paul Feyerabend once related a similar experience: as he was sleeping he first mistakenly identified a feeling with a cramp and only upon awaking did he see what it was: a severe pain in his leg). Here is another experience I myself once had. Someone gave me a tea cup at his home containing a sweet beverage (‘!t’) without saying what it was. Since the context gave no clue as to what the fluid in the cup was, I needed at least a minute to remember the taste of juice from pressed sugar-cane (‘?p’). Then, by comparing this memory with the taste of the liquid in the cup, I came to the obvious conclusion: the liquid was pressed sugar-cane juice (t = ?p).

12. A more complex case
The cases I have considered until now are the simplest sensory-perceptual ones. However, the pragmatics of adequation can be extended to the truth of non-observational 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 lasts approximately five hours. She calls her daughter, who lives on a farm in Senegal and asks her how the weather is in the city of Dakar, 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 providing adequate 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 observational! It is the result of testimonial inferences that are unknown to Lucy. Suppose that her daughter got this information from her husband, who had read a weather report in the internet, and that this information had its origin in meteorological observations of weather conditions around Dakar. In this case, putting ‘>>>’ in the place of some chain of reasoning unknown to Lucy that leads to !q, and putting ‘!o’ in the place of the observational meteorological thought-contents that in some way led to !q (which will probably be similar to those that she will have when she arrives in Dakar five hours later), we can formally structure the verification process in which p is presently made true for Lucy as follows:

?p, (!o >>> !q), !q, p = q /├ p

Important to note is that the evidential character of the observation !o is taken as preserved in the supposed inferential chain that leads to !q (I put the process in parentheses in order to show that it is unknown to Lucy and even to her daughter). The informational content is transmitted from thought-content to thought-content up to the conclusion !q, which inherits the evidential character of !o , then !q is compared with the guess expressed by ?p. So, against our most natural expectation of how adequation should work, the truth of ?p isn’t directly confirmed 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 adequation is between unfulfilled and fulfilled thought-content rules, the last ones also interpreted as being fulfilled by a factual content composed of trope-based arrangements which we suppose have an inversely similar structure, as I intend to explain later.
  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 by matching a derived piece of evidence with a supposition. So, imagine that at the beginning of the flight to Dakar the pilot informs the passengers that the weather in Dakar will be 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 also unknown evidential chain. However, in this case it is the evidence that recalls the concern regarding weather conditions. This concern is satisfied by means of a comparison of contents from which the final judgment results that the weather in Dakar will 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 mediated levels. We may guess whether the intuitions of some researcher who still does not know how to prove some hypothesis, though having a glimpse of its truth, depends on unconsciously noticing that the knowledge of some factual content expressed by !q might be derived from evidential observations or postulates.

13. General statements
General thought-contents – universal and existential – can also be explained by means of a pragmatic process of adequation, as an identity between the contents of the hypotheses and 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 assertion: ‘All the books on this shelf are in English.’ Further suppose that I reach this generalization casually in a retrograde form from the casual observations ‘o1, o2… on,’ that is, of each book on the shelf, as follows:

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

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

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

Now, suppose that for another person doing the same thing,├p means: ‘There is at least one book in Italian on this shelf,’ First, she asks herself ‘?p,’ namely, if there is a book in Italian on that shelf, and after searching, she finds just one in Italian: Princìpi di scienza nuova by Giambattista Vico. We call it ‘!o1.’ This enables her to affirm that there is at least one book in Italian on the shelf, which enables her to conclude by means of an anterograde procedure:

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

As in the previous cases, this example deals with a general deductive conclusion, but it is easy to see that inductive generalizations should also have similar structures, given that they are also restricted to some more or less vague domain (see Appendix to Chapter V, sec. 3).
  The next point is the old question of knowing if there must be general facts (the all facts) over and above singular facts (Russell 1918; Armstrong 1997, Ch. 13; 2004, Ch. VI). Bertrand Russell, who seems to have discovered the problem, defended their existence as follows:

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

In my view, this is a much worldlier question than Russell supposed, since it can be shown that what he calls a general fact is not a fact hanging over any other. In the examples above, all that is needed to get the totality of facts is an additional limiting fact restricting the extension of the generality, first to books belonging to the first shelf and then to books belonging to the second shelf. I agree that descriptions of such limiting facts need to be added to the given sequences of particular conjunctions or disjunctions in order to close their domain. But these limiting facts are singular. And the harmless affirmation ‘those are all’, meaning ‘there is nothing beyond these’ can be inferred as a consequence of adding the conjunction or disjunction of the singular facts to the corresponding singular limiting facts, in the given case the facts of the spaces that the shelters have for their books. Using a still simpler example, if I say that all the coins I have in my pocket are three euro coins, the ‘all fact’ is given by the domain established by the fact that there is a pocket in my pants that I use to carry coins. Moreover, the only difference between the examples given above and 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 Russell’s mysterious all fact disappears.

14. Some funny facts
There are many puzzling cases of strange (funny) facts, and I will only select a few to give some indicative solutions. One of these is that of self-psychic (self-reported) truths. It is easy to know the truth-value of the thought p: ‘I am in pain.’ I believe that here as well there is adequation and that it is as follows. First, I learn interpersonally to identify the location of pain. Then, helped by analogies and by a network of other concomitant and previously observable occurrences, along with the fact that I am told by others that pain is none of these, I discover particularly using induction by exclusion, that pain must be an invisible feeling of hurt or intense discomfort and nothing more. Even if others cannot have interpersonal access to the subjective feeling of my pain in order to confirm it, I am able to make this kind of identification highly plausible. Moreover, even the logical possibility of interpersonal access to my pain itself cannot be excluded.[15] Now, 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, being led to the conclusion ├p:

!s, ?p, s = p /├ p

Here I discovered the truth that I have a headache in a retrograde way. An anterograde way to reach the same truth would be the case of a person who guesses that she will have a headache because she has drunk red wine, and she knows she always has a headache after drinking red wine.
  Wittgenstein offered, as is well known, an expressivist explanation for such cases. For him the utterance ‘I am in pain’ is nothing more than an extension of natural expressions of pain like ‘Ouch!’ (Wittgenstein 1984c, I, sec. 244). In this case, our schema would be something like ‘!s ├ p’ without adequation. I do not reject this possibility. But I find it easier to believe that this could be the expression of a more direct reaction that turns out to be seen as true only after the exercise of the previous, more elaborate cognitive process of induction by exclusion and analogy concerning the hetero-psychic state.[16]
  Another 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 Evelyn isn’t the queen of England. However, statement (i) seems to be a true! Nevertheless, the solution is easy. Although there is no actual fact that can make statement (i) true, this is not what the conditional requires. What statement (i) requires as its verifier is not an actual fact, but only a possible fact. The possible or conceivable fact that makes the statement true is that under the assumption that the antecedent were true, namely, that Evelyn is in fact the queen of England, the truth of the consequent will be nearly unavoidable, that is, she will be a well-known person. The truthmaker of (i) is a modal fact that could also be expressed using the vocabulary of possible worlds. We can suppose that there is a near possible world We where 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 also be 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 a conceived counterfactual circumstance given in We. A second similar example: (ii) ‘Gandhi never killed anyone, but he could’ (Wrenn 2015: 78). This is true because it means the same thing as ‘Although Gandhi never killed anyone in the actual world, there is a near possible world Wg (a possible set of circumstances) where he killed someone.’ This is a true statement, since it corresponds to the conjunction of an actual and a possible (conceivable) 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 despite being a very good swimmer, Dennis didn’t even try to help the drowning child, because he is a sadist. We would not be inclined to say that (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 would be morally right because it is in conformity with a utilitarian norm, let us say, the rule according to which:

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

What is in question in this case is not truth, but normative correctness – adequation with a norm, though the mechanism of validation is similar. (iii) is validated by the moral fact UR. Finally, there is still the case of the validity of utilitarian norms. In an attempt to achieve this, consider the following utilitarian principle:

UP: A morally correct rule is one which under normal circumstances when applied brings the greatest possible amount of happiness to almost everyone, without relevant unhappiness to anyone.[17]

Suppose it is a fact that when people act in accordance with this principle, the well-being of their whole community increases. In such a case, this principle can be considered correct or true, and we can say that UP validates UR (or makes it true), which validates (iii) (or makes it true). (Of course, all these moral facts should be made up of mental tropes.)
  Obviously, all this is nothing but an illustration. The greatest problem faced by ethical statements, like aesthetic and other statements of the kind, 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 the statements of natural science, philosophical statements belong to what we are still far from being able to know for sure.

15. Expansion to formal sciences
Analogous logical structures and dynamic procedures can be found in the formal sciences, allowing us to generalize adequation theory to a domain traditionally claimed by coherence theories of truth. The main difference is that while for empirical truths inferences are mainly inductive, for formal truths they are deductive. Suppose we want to demonstrate that the sum of the angles of any Euclidean triangle is 180°. We can do this by first proposing that this could be the case: ‘?p’ and then searching for proof. One proof would proceed by drawing a straight line through one of the vertices of the triangle, so that this line is parallel to the side opposite to this vertex. Since the three juxtaposed angles formed by the parallel and the vertex of the triangle are the same as the internal angles of the two opposed vertices of the triangle plus the angle of the first vertex, and their sum is obviously 180°, we conclude that the sum of the internal angles of this and indeed of any Euclidean triangle must be 180°. This deductive conclusion is the evidence ‘!q’ – the truthmaker as a geometrical fact constituted, I suppose, by geometrical tropes (cf. Appendix of chapter III). 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 to see that !q, stating the fact that makes the thought-content p true, as in the case of Lucy’s question, should not be placed at the beginning, but at the end of a chain of reasoning. Unlike Lucy, a geometrician can easily follow the whole procedure.
  Now, an example from arithmetic: we can prove the statement (i) ‘2 + 2 = 4’ in a Leibnizian manner.[18] We begin with definitions (which here correspond to basic perceptual experiences in empirical sciences). First, we define 2 as 1 + 1, 3 as 2 + 1 and 4 as 3 + 1. We call this set of definitions ‘d.’ Replacing in statement (i) the numbers 2 and 4 with their definiens, we get (ii) ‘(1 + 1) + (1 + 1) = (3 + 1)’. Since 3 is defined as 2 + 1, and 2 as 1 + 1, 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 has the same content as ‘2 + 2 = 4.’ In this way, we have derived the confirmatory evidence for the hypothesis ‘?p’ posed by statement (i), which is the (supposedly tropic) factual content of ‘!q’ described in (iii). This confirmatory evidence serves to check the hypothesis ‘?p’ that 2 + 2 = 4. Again, abbreviating the definitions as ‘d’ we have the following anterograde 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 might be initially assumed. It is the result of a deductive reasoning process based on these definitions, a reasoning process deductively derived from its definitional premises. This result, 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 it by making use as assumptions of the axioms AS1, ◊P ↔ ~□~P, and AS3, □~P → ~P. Taking these axioms and a few rules of propositional logic as the evidence ‘as’, we construct the following anterograde proof of the theorem:

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

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

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

?p, !as >>> !q, p = q, /├ p

Since the logical fact represented by !q, which carries with it evidence derived from the assumed axioms, expresses the same thought-content as the hypothesis ?p, we conclude that we have adequation. We conclude that p is true, or ├ p. (Also relevant is to note that in the case of logical facts we do not need to underline statement letters like a or q: there is no need to distinguish between the conceived and the real facts, since here both can be regarded as the same.[19])
  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 to be compared with an unexpected observation.
  The upshot is that the procedures with which we demonstrate the adequation of formal truths are structurally analogous to the procedures with which we demonstrate the adequation of empirical truths. Even so, there are some differences. The most obvious is that formal truths are deductively inferred, while empirical truths are allowed to include inductive inferences.

16. Why can analytic truths be called true?
Finally, we can apply a similar procedure to analytic-conceptual statements, showing that they are also called true because of adequation, even if this is a limiting-case. It is possible to say, for instance, that the analytic statements ‘It is raining or it is not raining’ and ‘Bachelors are not married’ are true because they correspond to the respective facts that it must be either raining or not, and that by definition it isn’t possible for a bachelor to 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 the proper combination of the component senses of their expressions. In this case, our question is: are there facts that make analytic statements 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 logic-conceptual fact that the brother-sister relation is reflexive. Statement (3) is made true by the conceptual fact that a bachelor is conventionally defined as an unmarried adult male. Statement (4) is made true in Euclidean geometry by the conceptual fact that a triangle is defined as a closed plane figure with three straight-line sides. And statement (5) is made true by the conceptual fact that part of the definition of a material body is that it must have some spatial extension. These are facts belonging to our defined conceptual structures; they are conceptual facts supposedly instantiated by arrangements of mental tropes and their combinations.
  Moreover, we can summarize the process of self-verification of the above statements 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 true by the application of a truth-table to the sentence. 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 move in which which we find the adequation in the same anterograde way as in the first of our examples:

?p1, !p2, p1 = p2 /├ p

Put differently: in this case, the thought-content is identical with an instantiation of a logical truth of propositional logic that is incorporated in itself, being because of this 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 take the definition of a bachelor as our 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 self-verificational procedure, we get:

 ?p1, (!d → !p2), p1 = p2 /├ p1

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

?p, (!q → ~p), p ≠ ~p, ├ ~p

The conclusion is that p is false, since the principle of non-contradiction shows that p cannot be the case and that strictly speaking there can be no fact in the world able to verify p. The verifying procedure that falsifies p is the self-falsifying move that gives the contradiction its contradictory meaning.

17. The insufficiency of coherence
That truth has something to do with coherence is beyond doubt. If Mary 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 sleeping 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 visited 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 under ordinary life circumstances and our system of scientifically confirmed beliefs. Coherence is obviously related to truth, and according to most coherence theorists, a belief is truer the more it is integrated into our system of beliefs, which also means that truth is a question of degree (Blanshard, 1939, Ch. XXVII).
  Bernard Bosanquet (2015: 24) once gave an interesting example intended to show that a greater amount of supporting information makes a statement more true, which seems to vindicate the idea that 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 his 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. also Blanchard 1939, Ch. XXVII, sec. 4-5). The aim of this example is to show that increasing the coherence of a statement increases its degree of truth. Nevertheless, we can interpret this example differently. It shows that the historian’s claim to know the truth (his truth-holding) is more probable, as truth has no degrees. The example confuses the degrees of probability that a person knows the truth (his or her degree of truth-holding) with an illusory degree of truth.
  Since countless possible belief systems can be constructed, the first objection against the coherence theory of truth 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 the objection that some thought-content p can be true in one system and false in another in a way that leads to a contradiction as follows. 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 at our disposal’), which we may also call the real-world system. In this case, the novel Madame Bovary, for instance, would be a fictional subsystem belonging to the all-encompassing real-world system. Carlos’ statement, ‘It is the fault of fatality’ at the end of the story is true in the context of the novel, but false for the real-world system. Carlos was only a fictional character, and thus his comment does not lead to a contradiction. Consider, for instance, the statement that the sum of the angles of a triangle is 180°. This is true in the system of Euclidean geometry, but false in Lobachevsky’s and Riemann’s systems. And it is in the end false regarding the physical real-world system (though not the psychological system). Consider, finally, the statement that the value of a good is determined by the importance that people give to it in order to achieve desired ends. It is considered true in Ludwig von Mises’ economic theory and false in Marx’s theory, since for the latter the value of a good is determined by the amount of labor required to produce the good. Nonetheless, regarding the real-world system, von Mises’ measure of value seems to be much more probably true. In his own very convincing example, someone can work for thirty years inventing a machine that in the end has no monetary value, simply because no one finds it useful for reaching desired ends.[20] A strategy like that of admitting a real-world system seems to block the objection of contradiction. Nonetheless, even so 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 a contradiction. Consistency may be a necessary condition for coherence, but it is surely not sufficient. For instance, consider the elements of the consistent set {Shakespeare was a playwright, lead is a heavy metal, 7 + 5 = 12}. Since they do not have anything in common, taken together the elements of this set increase neither the coherence nor the truth of its elements; and we could create a set of this kind as large as we wish with ‘zero’ coherence. Coherence may be a necessary, but not a sufficient condition of truth. Moreover, any definition of truth based on consistency alone would be circular, since consistency, being defined as the absence of contradictions generated by the elements of a set of propositions, assumes that their conjunctions cannot be false, in this way 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 p should be determined by its inductive and/or deductive relationships with the system to which it belongs (cf. Bonjour 1985: 98-100). Indeed, we know it is true that Mary was breathing the whole night long, because this claim is inductively supported by everything we practically and scientifically know about what keeps the human organism alive.
  However, if we consider coherence as the only and proper mechanism able to generate truth, this definition also leads to circularity, since 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 blatantly circular. Any form of pure coherence theory is the victim of a petitio principii, as it simply assumes what it aims to explain.

18. Coherence as mediator
The view of coherence that I propose here enables us to circumvent the difficulty. The reason is that in my understanding, coherence is a complementary dimension of adequation theory, namely, the condition that enables the transmission of truth in a network of thought-contents, usually beginning with those that are based on empirical (sensory-perceptual) experiences and/or some assumed formal evidence (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 such a statement is true by adequation 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 probability of truth higher than 0.5 – from one proposition to the other. However, this veritative force cannot arise from propositions without truth-value, but instead is derived from propositions ultimately based on a myriad of judgments corresponding to perceptual experiences that are the sources of our knowledge of biological laws, as well as our commonsense awareness that Mary is a living human being like us and subject to the same biological constraints.
  We begin to see that even if coherence cannot be regarded as defining truth, it plays an important role as a mediating procedure whereby adequation is an indispensable ground. The modal proof of P → ◊P in our formal example does not come directly from AS1 and AS3 plus some rules of propositional logic. We first take a series of deductive inferential steps, and these steps are already constitutive of a linear coherential dimension of the verification procedure, which some coherence theorists erroneously saw as the proper criterion of truth for the formal sciences. In the present case, coherence is constituted by material implications transmitting the veritative force – here understood as material implications of logic-conceptual, self-verifying truths postulated as axioms – but, as already noted, it inevitably contains inductive inferences in the case of the verification of empirical thought-contents.

19. Roles of empirical coherence
The case of the coherence of empirical truth can be better illustrated by two examples that make clearer the relationship between coherence and adequation. First, suppose that someone anonymously sent me a gift per post. 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 realize that this book could have been sent by someone else. But then, I remember that Sylvia was born and lived most of her life in Rio de Janeiro and could well be back home in Brazil. 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) The book could have been sent by Sylvia (s)
5.     But the book was mailed from Rio de Janeiro (t)
6.     (from 4, 5) The book wasn’t sent by Sylvia, whom I knew in Rome (u).
7.     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 adequation is verified via coherence. To see this better we need only revise the above reasoning, excluding s because of v and insofar rejecting the partial conclusion u in order to build the following coherent set of beliefs: {r1, r2, r3, t, v}. Such beliefs inductively reinforce the conclusion w, which as a whole makes q very probable. This anterograde set of reinforcing premises makes me, starting with the guess ‘?p’ = ‘Was it Sylvia who sent me the book?,’ see the identity of contents p = q and conclude with practical certainty ├ p, affirming that it was Sylvia who sent me Calvino’s book.
  As Stephen Walker has convincingly argued, a pure coherence theory is impossible (1989). Coherence could exist independently of adequation 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 axioms or postulates of a formal system. But this is not the case. Consider again the example offered above. The thought-contents expressed by the statements that by means of coherence make the adequation between p and q probable are all in some way correspondentially anchored, either describing a perceptual thought (‘I knew her in Rome,’ ‘I gave her a book…,’) or reporting testimonial information (‘She told me she lived all her earlier life in Rio’) or a personal experience (‘I read the book…’) or an inference (‘She may be back home in Rio…’) from testimony (‘She told me…’) based again on the sensory experience of others (‘She lived all her earlier life in Rio…’).
  What was given to me as a fact in the above example was an indirect product of adequations of other thought-contents with their own factual contents. And the addition of the veritative forces of these experiences is what warrants w and consequently q to me as the derived proposition representing the fact that Sylvia sent me the book. This warrant 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, t, v}~> !w ~> !q, p = q, / ├ p

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

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

Putting my argument in other terms: I obviously agree that although sensory-perception is the origin of the veritative force of an 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 its own veritative force only by means of other sensory-perceptual observations whose truth is based on adequation. Reflection on this leads us to the inevitable conclusion that the actual origin of the veritative force of empirical judgments is always sense-perception, giving coherence the second­ary, even if indispensable role of transmitting the veritative force gained by means of sensory-perceptual experiences of adequacy. My conclusion is that under better scrutiny the supposed counter-example shows that adequation comes first, simply because adequation 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 probably classify as an ‘impure’ adequation theory and what I prefer to call an adequation theory that incorporates coherence.
 Trying to show this point in a more detailed way, I offer a last empirical example of the incorporation of coherence in adequation. It concerns 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 (proof by means of circumstantial evidence). This was the case with an American minister named Reverend David, who shortly after marrying a certain Mrs Rose was admitted to a hospital suffering from severe abdominal pain. Since examination showed a high level of arsenic in Reverend David’s blood, a thought-content that we abbreviate as ‘!r, the following suspicion arose as the result of abductive reasoning: ‘Did Mrs Rose try to poison Reverend David?’, in short, ‘?p.’ The following additional factual evidence later confirmed this suspicion:

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

We can now construct the following retroanterograde verification process:

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

Certainly, the conjunction of the statements r, s, t, 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 r, s, t, and u are all considered true either by direct adequation with public factual observation or by derivation from publicly observable perceptual factual contents. Again, what is shown is that the element of coherence cannot stand alone. The plausibility of q is grounded on the conjunction of the observational statements r, s, t and u by means of coherence. But these statements are all true because of their adequation with observational contents, even if they may also rest on empirically grounded theoretical assumptions, the latter in some way also derived from other perceptual experiences. As we see, coherence alone cannot prove truth, because inductive and deductive coherence relations are defined as ways of preserving and not of finding truth.
  The conclusion is the same: coherence relations work like the high voltage lines of an electrical power grid: though they are not able to generate electricity, they are able to transmit it. A plausible coherent system is not an independent mechanism, but only an inferential network by means of which the truth arrived at by means of adequation is conducted. In other words: coherence only transfers the veritative force generated by the adequation of the contents of more basic beliefs in empirical or formal facts to derived beliefs or thought-contents. This transference of veritative force within a belief-system can act to produce a thought-content that we believe corresponds to a non-observed fact, which in my example is q: the attempted murder using poison. The thought-content p is accepted by us as representing the factual content q because both have the same content (structural isomorphism, etc.), which makes p true. Because in various ways q is reinforced in its application, we accept it as factual evidence of p’s truth. And statement p is true because it corresponds to the fact that Mrs Rose poisoned her husband, Reverend David, even if we know this fact not by observation, but only indirectly, from its coherence with other thought-contents that are observational and match facts in a direct way.
  The thought-content q, the truthmaker of p, as we will explain, has a kind of Janus face: on the one hand, it expresses a grounding thought-content (an s-thought, 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. In sum: coherence is just an interdoxal mechanism by means of which adequation can transfer its veritative force. It is by being connected with adequation that coherence is involved in truth.
  Now, concerning the truth of the observational statements r, s, t, u, we return to the point already noticed when we analyzed our 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 adequation with a fact (r or the 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 (like s, t, and u), or even be rejected by other beliefs of this same system. But here again, the force of the belief-contents that lead us to this reinforcement or weakening is gained from direct adequation with facts, though often in a very derivative way. The consideration of this network of giving and taking among sensory-perceptual and derivative beliefs leave no room for a veritative force arising from coherence.
  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 factual content, namely, the real, the actual fact. Are these two possibilities reconcilable?[21] This crucial question will be tackled in the following sections.

20. What about the truth of the truthmaker?
One of the most serious problems for the adequation theory of truth concerns the infinite regress that arises from factual evidence that verifies hypotheses, that is, verifiers or truthmakers. We can pose the problem in the form of a dilemma: Either the truthmaker – the evidential fact or real factual content – is unquestionable, or it can be doubted. Suppose (a) that the evidential fact is unquestionably true. In this case, we seem to be guilty of dogmatism, because we treat our normal perceptual and even purely self-sensory truths[22] as if they were beyond any possibility of being false. But this would be to deny 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. Since we cannot stop this regress, we have no way to ground our suppositions, because any ground we find will lack the necessary solidity.
   Restricting myself here to empirical truth, I think we can resolve 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.’[23] Imagine that the truth of this sentence depends on the observation of a dolphin surfacing from time to time – an observation that can be interpersonally shared. For the first person who sees the dolphin, the procedure has a retrograde form:

!o, ?p, o = p /├ p.

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

p ~> ?p, !o, p = o /├ p.

But this does not mean that !o, the given evidence, is absolutely warranted! It can be defeated. Suppose that due to a scarcity of real dolphins and in order to entertain tourists, a diver is hired who swims just below the surface with a rubber dolphin 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, it should not be hard to find a solution to the problem. What we believe to be factual content need not be regarded as absolute. It is only postulated or assumed to be unquestionable factual content (or the real truthmaker) within the context of a practice that typically presupposes we have the right background information and leaves aside the unlikely 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 that are large enough and near enough to be identified as dolphins, and they are employed in the context of a tourist beach where people expect to see dolphins swimming in the water offshore… In this practice we are allowed to assume that the observational content ‘I am seeing a dolphin that has just emerged from the sea’ is unquestionable evidence expressible by !o. It is thereby a real fact, a truthmaker or verifier that we accept as giving practical certainty that there is a dolphin in the sea. Assuming the information content and the context at our disposal in this practice, and assuming that all other things remain the same, seeing a dolphin must undoubtedly be accepted as the truthmaker of the hypothesis ?p. Assuming that o also has internal phenomenal content (psychologically given sensory impressions), we could say that in this case we are allowed to assume that the thought-content of o, that is, o without the underline (expressible as: ‘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 (expressible as: ‘There is a real dolphin that has just emerged from the sea’). But in practice our willingness to accept evidence is contingent on ceteris paribus conditions, namely: the assumption that the observation isn’t being defeated by some condition extraneous to the expected informative contextual background.
   Now, in the given case the defeating extraneous condition can be found in a shortage of real dolphins in the area, and it is constituted by a diver swimming just below the surface with a rubber dolphin on his back and sometimes rising to the surface in a way that gives people on the shore impressions of seeing a real dolphin… Assuming that some observer S is aware of this information, what is given to him isn’t the practice (A) but a very different observational practice that we can call (B), which includes information about the very unusual background circum­stances. In this (B) practice, we cannot postulate the observation of a real dolphin merely because we see what appears to be a dolphin emerging from the sea. Under the circumstances presented by (B), in which a rubber dolphin can be carried on the back of a diver swimming just below the surface, to know that one is observing a real dolphin would certainly require closer and far more careful examination. Closer underwater inspection, for instance, might reveal factual evidence of a fake rubber dolphin, which can be symbolized by o.’ In this new practice, the thought-content expressed by p could not be verified by !o, because !o isn’t really given to S, since we already know that in its context o cannot be trusted to be a real dolphin. But ?p could be falsified by more careful observation of o’, 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 absolute, but must be postulated as certain or irrefutable. It must be treated as beyond the level of a merely probable truth, under the assumption that the factual context involves the background information that characterizes some well-known linguistic practice. In other words, we must assume that there is no defeating evidence hidden beyond the believed background information. If we get information indicating different background circum­stances able to discredit a given context in the assumed practice, as in the case above, the postulated irrefutability vanishes.
  I will offer a second, similar example, merely to reinforce the point. Yvonne is driving a car along a road through a desert and imagines she sees a lake, which is really only a mirage. At first, she believes the lake she sees on the horizon is real. We can symbolize this through the following retrograde verification procedure:

!o, ?p, o = p / ├ p

However, it soon becomes clear to her that she has made a naïve mistake; what she really sees is a so-called inferior mirage. This is caused by the refraction of sunlight by a layer of hot air near the ground. In this way she adds to the background conditions 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, which asserts sentences like ‘I am seeing a mirage’ or ‘I am seeing the refracted blue of the sky,’ which represent a different factual content that I call o’. Consequently, what was at first accepted as external evidence is now viewed as an erroneous interpretation of data, since practice (A) was replaced by the new practice (B). Its contexts allow the defeat of what was at first postulated as an unassailable truthmaker. We can symbolize this change through a sequence of the two following anterograde verification procedures belonging to practice (B):
        
?p, !o’, p ≠ !o’├ ~p,
?q, !o’, q = !o’ ├  q

It is worth noting that the phenomenal content of perception is in any case the same: an impression of seeing the color blue near the horizon. But the interpretation of this content is very different, as o’ is read as a different factual content, existing in the world. And she understands what she sees differently, because a more complete awareness of the background information given by the surrounding circumstances is able to defeat the earlier seemingly reasonable interpretation of the visually-given content as o.

21. Objection of the linguistic-cognitive circle
Probably the most influencial epistemic objection to the adequation theory of truth 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 irrefutable, we remain trapped in our language and thought. Even if we find the strongest factual evidence, this evidence could only be considered in the form of linguistic expressions of propositions (as s-thoughts, thought-contents, 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 ending up in an infinite regress with epistemic skepticism as a corollary.
   A prima facie general reply to this objection is that saying we are trapped in an intra-linguistic or intra-cognitive world already assumes we know there exists an extra-linguistic and extra-cognitive external world – 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 argument contains a strong appeal to common sense. Nevertheless, this appeal seems to contradict another enduring idea, which is also not alien to common sense, namely, the idea that the whole content of our usual perceptual experience should be some kind of conceptually structured belief-content and therefore should be mental in 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 (cf. Blanchard 1939, vol. 2: 228).
   One reaction to this dilemma would be to accept the sort of last resort solution called idealism (e.g. Foster 2000). But today idealism seems to be a forbidden solution. It is the view according to which all reality is in some sense mental. It conflicts with one of our main modest commonsense principles, namely, that we live surrounded by an independent material world. 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 (including biochemical and biological) world, dependent on it to exist, just as the phenotype is dependent 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 stay on the side of our principle of established knowledge (Ch. II, sec. 4), idealism will remain 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 external 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 micro-physical atomic world. Finally, from an anthropological perspective, idealism seems to appeal to wishful thinking, as in the philosophy of culture and the humanities, as is argued by authors ranging from Nietzsche to Freud and from Weber and Durkheim. Humanity pays a high price for having acquired consciousness. It is like the price paid by Prometheus for his theft of fire for the benefit of mankind. Even if this makes us better able to provide for ourselves, it also makes us aware that we live in an unpredictable and dangerous world with an uncertain future, along with a clear sense of our own finitude. Idealism, by making the external world in some way mind-dependent, is helpful in the creation of those illusions of power over the external world that could give us more hope of beating the odds. However, due to all the knowledge we have at our disposal today, more than ever before we have strong external reasons to reject idealism in favor of epistemic realism.

22. Answering the objection of the linguistic-cognitive circle
It seems we can preserve a categorical opposition between the mental and the material worlds in the sense that the mental is cognitively-dependent and only experienced in the first-person, while the material is (usually) cognitively-independent and able to be experienced in the third-person. For such reasons, I will now defend direct realism as able to give us the kind of epistemological framework that will help us break the linguistic-cognitive circle. Direct realism is the view that our senses provide direct awareness of the external world, showing it pretty much as it is. Direct realism differs from indirect or representational realism, which is the view that we have direct experience only of our sensations (percepts, sense-data), which inform us about the external world, so that the latter is never directly experienced. It also differs from a third traditional epistemological position, called phenomenalism. According to this view, since we can have experiential access only to our sensations or sense-data, there is no rational ground to postulate an external world independent of actual or possible sensations. This view leads almost inevitably to idealism and to rejection of a really existing non-mental external world.[24]
   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 external world can always be interpreted as two different types of entities: one psychological and the other physical, as follows:

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

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

Psychological experience (A) gives us what we may call sensory impressions or sensory contents (also called percepts, sensations, sensa, qualia, phenomena, representations, ideas and even sense-data). It seems beyond doubt that sensory contents are always present in perceptual experience (even if we are usually unaware of them) as I intend to show later. But experience (B) also seems beyond doubt: it is the view that in addition to sensory experience, when we perceive something, this something is given to us as an external, material entity. Indeed, it is also commonsense knowledge to say that we usually perceive the external world as it really is. And this external world, as we have shown, would be formed by physical or external tropes (properties), by clusters of compresent external tropes with form and mass (mainly called material objects), and by arrangements (or combinations of arrangements) of both, also called facts (respectively simple and complex).
   The clearest evidence favoring this double view is given by tactile experience). Suppose I touch a hot stove with my hand. I can say I have a sensation of heat: this sensory-impression is the psychological sensory-based content of experience (A). Alternatively, I can also say that I have perceived that the stove is hot; this is the correct perceptual experience of the externally given physical entity (B). The essential point often noted by Searle is that in the normal case we cannot phenomenally distinguish experience (A) from experience (B) (cf. Searle 2015: 24). We can always conceptually distinguish the two cases, as the following examples show:

(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-based contents occurring in my head, while in the (B) cases I speak of independent physical contents – perceived 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).
   Accepting the above difficulty of understanding what is given as only one phenomenal content is not hard and does not compromise direct realism. I can illustrate how harmless the duplicity is by comparing it with the kind of complexity involved of our interpretation of objects that I see in a mirror. What I see in a mirror can be understood as: (A’) a simple image of things, for instance, the image of a vase of flowers on a table. But it can also be understood as: (B’) the vase in itself that I am seeing in a mirror. For instance, I can point to the object I see in a mirror, and you can ask me if I am pointing to the reflected image of the vase of flowers or to the real vase of flowers. That they belong to different domains of experience is made clear by contextual differences: the image isn’t considered real, because I cannot touch or smell it. The real vase of flowers, on the other hand, can be touched, smelled, directly seen from all sides, manipulated, broken; its weight and its size can be definitely measured and shown to remain constant, independently of the changeable apparent size of its image… Alternatively, I can change the apparent size of the image by bringing the vase closer to the mirror. And this apparent size always doubles the real distance of the vase from the mirror and the vase… Nevertheless, to some extent the properties and relations of both, image and reality, will be alike. Finally and unavoidably, looking at the mirror I would not be able to see the vase on the table without the help of the image.
   In fact, access to the real vase is dependent on access to its image. As in cases (B) 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 I pay attention to an object in a mirror I interpret it as perceptually dependent on its image, but when I pay attention to the image, I see it as causally dependent on the real object. I can easily say I see the reality through the image. But I will never say that I cannot see the actual object because what I really see is only its image. Moreover, I can also say (if I wish) that I am seeing the real vase directly through its image, for instance, if I compare it with the same vase seen in a photo. Finally, I can see either the real vase or its image – but not both together.
   Although the mirror-analogy, like all analogies, has its limits, it reinforces the idea that we can answer the objection of the linguistic-cognitive circle by saying that the phenomenal content of any real experience can be interpreted in two ways: (A) internally and psychologically, as a first-person sensory-based thought-content, and (B) externally, as a third-person component of a physical fact or factual content. Insofar as we are also able to apprehend the same given phenomenal content as an external factual content, we are able to escape the linguistic-cognitive circle.
   A complementary but also indispensable point that I have dealt with several times already is that we almost never have a complete sensory-perceptual experience of external factual content. Our perceptual experience is typically perspectival. We experience only facets, aspects, sub-facts. If from a position on shore I see a fishing boat entering the mouth of Pirangi River, I may experience (see) only one side of the fishing boat. However, based on this dynamic sub-fact (an aspect of a process), I am able to say not only that I am seeing one side of the boat – the sub-fact – but also that I see the whole boat and that I am following the whole process of the real fishing boat entering the mouth of Pirangi River – a dynamic grounding fact (see Ch. IV, sec. 25-27).
   These almost commonsensical remarks show us how can we in principle escape from the linguistic-cognitive circle. We can observe an external factual content or alternatively consider its phenomenal experience as inevitably involving purely sensory content – constituted by the so-called sense-data – which is internal. That this purely sensory content exists can be illustrated by the examples of after-images: after looking at the sun one can close one’s eyes but still see the image of the sun for some time in the form of an after-image, which is sensory content without any perceptual object.[25] Furthermore, for those still sceptical of the existence of sense-data the present experiments with vision reconstruction, in which computationally reconstructed brain experience of moving images is scanned by means of fMRI (e.g. Nishimoto et all 2011) is more than a proof that sense-data or sensory contents in the brain really exist: now we can see them!
  The dichotomy considered above is also important, because it is a necessary condition for the already noted defeasibility of observational evidence: under anomalous conditions we can withdraw from real perceptual content to mere sensory content, reinterpreting the experience.

23. Answering traditional arguments against direct realism
Against the form of direct realism explicated above and favoring indirect realism, there are two well-known traditional arguments: the argument of illusion and the argument of science. As almost too much has been written against these arguments,[26] I will emphasize only the essentials. I think that answering these arguments strengthens my own modulated kind of direct realist view.
  I begin with the argument of illusion. It usually concerns cases of perceptual illusions in which we seem to perceive something that should not be perceived, particularly in the extreme case of hallucinations. There are many examples that support this argument. They all aim to prove that in the best case perception is indirect, since it always occurs through the ‘veil of sensations.’ In what follows, I summarily present several examples, some of which were already known in antiquity:

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

If the argument of illusion applies to cases (1) to (9), why not to all cases? Why not, as Bertrand Russell once said, be democratic and admit that in all cases we first need to perceive sense-data in order to get information about the external world?
  This conclusion, suggested by the argument of illusion, seems to refute direct realism, which should then be replaced by the indirect realism already accepted by Descartes and mainly attributed to Locke. The suggestion is that the objectively real world is always perceived indirectly through the veil of sensations, which is formed by sensory impressions or sense-data. One could object, using the Kantian argument, that we experience 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 what they can be in themselves, what they are for us must also be 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 formed by sensory impressions or sense-data, since by accepting (A) I accept these assumptions. 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 normally perceive the world directly through our sensations or sensory impressions. This means 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, since it is a category mistake to defend this view. Put simply: the main problem with the argument of illusion is that it is based on a misunderstanding of the semantics of our concept of directness.[27] Consider the following four sentence pairs:

1. I saw the Sun directly, through my glasses.
2. I saw the Sun indirectly, projected on a screen using a telescope.

1. The package was sent directly to the recipient (by air).
2. The package was sent indirectly to the recipient (by ship).

1. The trip is direct (the bus travels directly through Germany from Constance to Munich, with a lunch stop of thirty minutes).
2. The trip is indirect (it starts with a bus trip from Constance to Lindau, followed by a direct train to Munich).

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

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

1.      I soak my cold, stiff hands in water that feels as if it were warm. I am fully aware, however, that the water is actually at room temperature, and although I perceive the temperature directly, my perception is deceptive. If my hands were not cold, I would feel the true temperature of the water directly and in a non-deceptive way.
2.      I hear the car’s sound directly, though in distorted ways. If I could drive alongside the car at the same speed, I would hear it in an undistorted way; I would hear it directly as it really sounds, that is, free from the Doppler effect.
3.      A person may say, ‘I see things directly as if they were yellow, though I know that isn’t their true color,’ because she knows she has jaundice. What we call the true colors of things are by convention the colors we see under normal conditions. This presupposes enough proximity, having normal vision, seeing things in adequate illumination with a neutral white balance, etc.
4.      Even if I show by pressing my eye that I see things as if they were moving through my visual field, this does not mean that I am not seeing them directly. In fact, I can even say, ‘I see external things directly and precisely as they are, though having the false impression that they are moving.’
5.      In this example, as Searle has noted, one can instead say, ‘I do not see two fingers… In fact I am directly seeing my own index finger as if it were doubled.’
6.      Concerning the form of the coin, it appears elliptical, but I can say that I directly see a round coin that only ‘looks elliptical’ because it is being held at an angle. – As A. J. Ayer pointed out, what we consider to be the true form or the real color is partially a matter of conventions (cf. 1973, Ch. 4). We have the convention that the real form of a coin or 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 on the level of the base at a certain distance, but not an aerial view from above (e.g., the Matterhorn, the Sugarloaf). Based on conventions defining normal perception, we say that the real color of a tropical mountain is green, even if it may seem blue when viewed from a great distance, etc.
7.      In the case of the different sensory images of the table, you already assume that the table is always one and the same table. This shows that the different perspectives and distances are only what the same table ‘looks like.’ And these different ways of seeing are different ways in which you directly see the same table.[28]
8.      In the case of mirages, I see what looks like a lake, but I can say that I am aware that what I really see is the image of the sky refracted by layers of hot air on and above the desert sand, and I say that I see this mirage directly.
9.      Finally, in the case of a hallucination, it is simply incorrect to say that I see the content of my hallucination. 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 factual, external content, and not to a merely sensory content. Even if we agree that it is by means of sensory content that we have perceptions of things, this does not make our realism indirect. In a similar way, when we say that a bullet struck a victim after piercing a windowpane, we do not mean that the bullet struck the victim indirectly.

This kind of explanation is not as new as it might seem. It was already present in the following comment by the direct realist philosopher Thomas Reid aimed at his contemporary David Hume, almost three centuries ago:

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

To most present-day philosophers including myself, this is the correct answer, and we can see the persistence of competing doctrines as a testimony to how slow and uneven progress can be in philosophy.
   Summarizing: we perceive things directly, even under misleading conditions like those of delusions, which justifies the direct realist view of whatever is given in perception; and this does not mean that there cannot be a necessary 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 causal physical stimulation of distal neuronal cells that through synaptic activations ultimately leads to the stimulation of cortical regions in the brain, which produces in us an awareness of the objects of experience. Thus, our experience is in fact the experience of something occurring in our brain, which is nothing but the experience of sensory impressions or sense-data. Consequently, our direct experience can only be of sensory impressions occurring in our brain. From this it follows that we cannot have direct experience of the world around us and that we cannot even be sure that our contents of experience reflect how the external world really is or even warrant its existence. 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 projected image of the object causing the activation of photo-receptor cells in the retina and in a corresponding activation of the striate cortex in the occipital region, which is then analyzed by the visual-association cortex. In my view, the relevant point is that the sentence ‘we directly see the objects’ belongs to our natural language, while expressions like ‘by means of…’ or ‘through…’ in the argument of science belong to a physical-neurobiological language concerning the underlying intermediating processes responsible for what in our ordinary language we call ‘direct experience of the world around us.’ Each language works well in its proper field and each language has its own segmentation of the process of perception. Mixing both languages is what leads to fallacies. In the present case the fallacy arises when we use the semantics of the physical-neurobiological language – which has discovered complex causal processes at the physical and neuronal levels – to deny the semantics of our ordinary language – which establish a direct relation of seeing or being aware of things in the outside world. This confusion is a clear case of equivocity (Ch. III, sec. 11).
   Finally, as far as I know, what we call sensory impressions or sense-data in the visual case has much to do with the activation of the striate cortex, since the stimulation of this region without the activation of photoreceptors in the retina is apt to produce hallucinatory phenomena (Teeple, Caplan, Stern 2009: 26-32). However, this fact alone does not make visual perception indirect, since it isn’t captured by the semantic conventions governing what we are used to calling the directly perceived objects around us.




[1] One example is my own perspectival version of the tripartite definition of knowledge (2014, Ch. 5).
[2] Thus, I do not refer to as a ‘thought’ that which the completely analyzed sentence expresses, as in the very implausible atomism of the Tractatus. Instead, I suggest that we simply refer to as a thought that which is expressed by a sentence as it is sufficiently analyzed in accordance with the context (in the widest material-psychological sense of the word ‘context’) of the practice in which it is applied.
[3] We certainly could 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)
[4] 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’].
[5]  Bertrand Russell suggested that there is no object in the world corresponding to a logical property (1918). But suppose you see alternately a red lightning followed by a green lightning. You know that both are not seen together. Although this sequence is not seen as an object, it is anyway disjunctively seen as something occurring in the external world.
[6] We can intentionally produce factual contents that are true, for instance, by acting in the world in order to change it according to our views, as a constructivist philosopher like Giambattista Vico perceived, inverting the direction of fit of the correspondence. However, even in this case the truthmaker of the proposition, as the product of human effort, is the final fact in the world and not what generates human effort. That is: we can make the fact that makes truth, but not the fact as truth.
[7] I take these expressions and explanations (though not my application of them) from Searle 2004: 167-9.
[8] It is the sense determining (bestimmend) the reference in Frege’s way of speaking, or the meaning-fulfilling intention (Bedeutungserfüllende Intention) in Husserl’s way of speaking.
[9] We remember here Alfred Tarski’s disquotational formula, according to which ‘“p” is true in L ≡ p’. Tarski’s approach has the great merit of properly emphasizing the meta­linguistic character of the truth-assignments in a formal language (cf. Tarski 1944: 341-375). However, his formula does not overcome the philosophical problems of correspondence. If you replace the sentence p with Fa, Tarski’s theory does not provide criteria that tell us why we should apply F to a 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. Undoubtedly, the formal definitions presented in this section are more adequate, particularly regarding our natural language, preparing the way for a more complete approach.
[10] Frege writes that the negation belongs to the thought, while the attribution of truth/falsity belongs to the assertive force (behauptende Kraft), requiring an epistemic subject. But consider the statements: (i) ├John is not at home, (ii) ├It is not the case that John is at home, (iii) ├It is false that John is at home. The three statements deny that John is at home and they have the same assertive force external to them. Hence, there is no special reason to equate the denial to the attribution of falsity. (cf. Frege 1918-1919a)
[11] This points to an easy way to analyze composite statements of the forms p & q, p q, p q and p q. As is well known, we can respectively use negation together with conjunction in the following descriptions of facts: p & q, ~(~p & ~q), ~(p & ~q) and ~(p & ~q) & ~(~p & q). Negation always means that some thought-content is false, and in the simplest case also means that the verifiability rule that constitutes this thought-content has proved not to be effectively applicable under suitable circumstances. That is, there is no corresponding real fact, only a possible one.
[12] Normally only three moments are distinguished, since the third and the fourth moments are usually seen as a unity. I distinguish them only for reasons of clarity, because we can separate the verification of the qualitative identity of content from its verbal attribution of truth.
[13] 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).
[14] I think the anterograde and retrograde procedures are a more detailed version of a distinction already present in Husserlian phenomenology: the distinction between ‘truth as correctness’ (Wahrheit als Richtigkeit) and ‘truth as discoveredness’ (Wahrheit als Entdecktheit) respectively.
[15] See my objections to the private language argument in Chapter III, sec. 13 of the present book.
[16] A sufficiently detailed argument concerning this point was developed in Costa 2011, Ch. 4.
[17] My preferred moral theory is two-tiered utilitarianism. According to this view, we should apply rule-utilitarianism in ordinary situations, but in extreme situations, utilitarian rules are derogated and we must turn to act-utilitarianism. (cf. Hare 1981, Ch. 2)
[18] Leibniz’ somewhat different proof can be found in his 1921, liv. IV, Ch. 7, Sec. 10.
[19] Here I am leaving out of consideration the application of formal sciences to physical facts.
[20] Surely, this suggestion would relativize truth, limiting it to a time and a community of ideas, making 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 agree that ‘the truth,’ that is, the absolute truth, is simply a kind of normative ideal that helps us evaluate our taking something to be true, but has no necessary relationship to what we normally accept as true or false, since, as Karl Popper insisted, even if by chance we discover an absolute truth, we will not be able to know that we have found one (see his 1972, Ch. 2). That is, when we say that p is true, we only assume that p is the final truth until we find some 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 instead of a theory of absolute truth. The same can be said regarding the concept of knowledge.
[21] If q were only the direct expression of a factual content, we would fall into a kind of strong externalism that admits that part of our content-thought-meaning is a directly given fact in the world (a ‘structured proposition’ or something of the kind). However, without more qualification this view demands 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.
[22] I think here of cases such as false feelings or emotions or sensations, as, for instance, imagined pain induced by hypnosis.
[23] I rely here on a story about a rubber dolphin that I read many years ago, although I have forgotten the source or the arguments it employed.
[24] See Ch. IV, sec. 18.
[25] Here we come close to the old boring controversy over sense-data, its status, its existence, its location. An after-image is a kind of sensory datum produced by the over-stimulation of photo-receptors in the retina with effects in the occipital cortex. It is necessary to say that although others cannot have my after-image, no non-philosopher would deny that someone could see an after-image under the right circumstances (see Ch. III, sec. 13; cf. also the experiments with visual reconstruction referred above).
[26] For an admirably smart and vivid defense of direct realism, rejecting the argument of illusion, see John Searle 2015.
  
[27] For similar lines of defense, see Cornman 1975, Ch. 2 and 6; Dancy 1985, Ch. 10; Lowe 1992; Huemer 2001, Ch. VII. As Huemer proposes, 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.
[28] Searle’s conclusion: ‘The whole discussion presupposes that I am actually seeing the table throughout, for there is no way that the table could continue to present to me different appearances from different points of view, if I were not actually seeing the table.’ (2004: 273) See also Huemer 2001: 119-124.

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