- 1 Many thanks to two anonymous referees and to Diego Marconi for their insightful comments which mad (...)
1The adjective ‘true’ is used to characterize both the things we say or believe (“What Nicola said is true”, “It is true that Palermo is in Sicily”, “The Pythagorean Theorem is true”) and things of any kind (“He is a true friend”, “Is this a true Picasso?”). I will call the first property “Words’ truth” and the second “Things’ truth”.
2Thomas Aquinas considered the two truths within a unitary framework: according to him both were in fact species of a single characteristic, adaequatio intellectus et rei, that is to say, the correspondence/fitting of the mind and the thing. Truth-of-words is in fact a matter of conforming to the objects that human intellect represents: for instance, when I utter a sentence such as “Orlando is clever”, what I say will be true if the object referred to by the name “Orlando” actually possesses the property referred to by the predicate “being clever”. The truth-of-things, on the other hand, consists in the conformity of them to their models in the mind of God, in the same way as the perfection of an artefact consists in its greater or lesser conformity to its model in the mind of its designer (Summa Contra Gentiles, LXII).
- 2 Conte (2006; 2007), Tuzet (2010) and Caputo (2016) are an exception to the almost general lack of (...)
3The contemporary philosophical discussion on truth has abandoned this attempt to consider words’ truth and things’ truth as species of a single genus. It is sufficient to have a look at one of the many books on the problem of truth to realize that the topic of things’ truth and of its connection with words’ truth is either entirely absent or at most briefly mentioned in the preliminary chapter, with reference to Aquinas’ conception, in order to briefly stress that we are dealing with two different uses of the term “true” and that there can therefore be no theory of a single property, however generic, to which both of them refers.2
- 3 According to Marconi (2022, pp. 71-80), Thomas Aquinas already regarded words’ truth as the core o (...)
4This divorce between the two kinds of truth and the widespread lack of interest concerning things’ truth has certainly its roots both in the increasing disaffection toward the correspondence theory of truth in the 20th century philosophy and the sheer lack of interest in things’ truth on the part of the founding fathers of analytic philosophy (such as Frege, Russell, Wittgenstein, Tarski, Carnap) to whom we owe many of the later developments in the philosophical and logical reflection on truth.3
- 4 Tuzet (2010) identifies the attempt to reduce things’ truth (which he calls, following Conte (2006 (...)
5But, apart from the misadventures of the correspondence theory, there is a strong reason in support of the claim that words’ truth and things’ truth are different properties: that is that a thing can possess the latter property without possessing the former. For instance, the sentence “Paris is in Italy” is a true (things’ truth) sentence of English (unlike “Italy in is Paris”) but is not a true (words’ truth) sentence, since Paris is not in Italy. Therefore, the word ‘true’ must refer in the two cases to two different properties.4
6However, two different properties can still be species of a single genus (like the properties of being a cat and being a dog with the genus <animal>) or determinates of a single determinable (like the determinates being crimson and being scarlet with the determinable <red>).
7This seems to be the view of Thomas Aquinas: in fact, he did not claim that things’ truth and words’ truth were the same thing, but that they could be regarded as two different forms assumed by the correspondence of the intellect and the thing, i.e. somehow two species of the same genus.
8In what follows I will defend Aquinas’ idea, that is to say that words’ truth and things’ truth are indeed two species of a single genus or, if you prefer, of a single general concept; but I will do this without committing myself to a correspondence conception of truth. I will in fact make appeal to what, according to many philosophers, is an essential feature of the concept of truth and should therefore be accepted by any theory of truth as a basic fact concerning truth itself. This is what W. V. O. Quine called “Transparency”.
9Pointing to the disquotational character of the truth-predicate, Quine (1990, p. 82) said that truth is “transparent”. This means that whoever understands the predicate “is true” and a sentence of English “p” should be disposed to accept biconditionals of the form
(T) “p” is true if and only if p
(T1) It is true that p if and only if p.
10Sentences of this form are called “T-biconditionals” or “Tarskian biconditionals”, since notoriously Tarski (1935) claimed that they express the core of the concept of truth and that, consequently, a definition of the notion of truth is adequate insofar as these biconditionals are deducible from it.
11That the acceptance of the sentences of the form (T)/(T1) is at the core of our concept of truth shows up in the fact that the following two sentences (which entail the negation of the correspondent instance of (T1)) seem to assert a contradiction:
1) It is true that Turin is in Italy and Turin is not in Italy
2) It is not true that Turin is in Italy and Turin is in Italy.
12Although these are not explicit logical contradictions such as
(3) Turin is in Italy and Turin is not in Italy,
asserting (1) and (2) seems indeed equivalent to asserting (3).
13The reason for this is that when we say that it is true that Turin is in Italy we are also disposed to assert that Turin is in Italy and when we say that Turin is in Italy we are also disposed to assert that it is true that Turin is in Italy: attributing truth to something we say or think is equivalent to asserting that things are a certain way. Truth is therefore transparent in the sense that by attributing truth to the things we say or think we are indirectly talking about the world: through the lens of truth, we see the world.
14Is things’ truth also transparent? In order to answer this question, one has to find the analogous of T-sentences for things’ truth. This is easily done. Attributions of things’ truth have usually the form “a is a true F”, where “a” is a singular term and “F” is an adjective modified by “true”. Two instances of this form are
4) This is a true Picasso
5) Andrea is a true friend.
15Since in the case of words’ truth we obtain the right-hand-side of a T-biconditional by erasing the truth predicate from its left-hand-side and disquoting the sentence to which it is applied we can proceed in a similar way in order to obtain the right-hand-side of a T-biconditional in the case of things’ truth. So, the T-biconditionals corresponding to (4) and (5) are respectively
6) This is a true Picasso if and only if this is a Picasso.
7) Andrea is a true friend if and only if Andrea is a friend.
16Are (6) and (7) true?
17In order to answer this question let’s consider the sentences which should be true if (6) and (7) were false, that is to say:
8) This is a true Picasso and it is not a Picasso
9) This is not a true Picasso and it is a Picasso.
10) Andrea is a true friend and he is not a friend
11) Andrea is not a true friend and he is a friend.
18(8) and (10) sound as contradictory as (1): in fact, if something is a true F, a fortiori it is an F.
19What about (9) and (11)? There is a reading of them in which they sound as contradictory as (2). This is the reading according to which a painting which is not a true Picasso and a person who is not a true friend are respectively a fake Picasso and a fake friend, things which look like being a certain way without actually being such: true friends/Picassos are in this reading opposed to false friends/Picassos and the latter are precisely things which appear to be friends/Picassos without actually being such. If we find out that the person that we considered our best friend is having an affair with our wife we would strip him of the title “friend” along with the title “true friend”: to discover that someone is not a true friend is often to discover that he is not a friend for real, i.e. not a friend at all. Since in this reading to be a true Picasso/friend is to be an authentic, real Picasso/friend, there are no Picassos/friends which are not also true Picassos/friends; therefore (6)/(7) are true and things’ truth turns out to be as transparent as words’ truth.
- 5 On this contrastive use of “True F” see §4.
20In these cases, when we say that something is a true F, we seem to be doing nothing more than attributing to it, with particular emphasis, the property of being an F, i.e. the same thing we do when we assert with conviction that it is an F, and we seem also to do it in a contrastive way, that is to say having in mind the contrast class of the things that are only seemingly Fs.5
21Things are yet more complicated.
22Consider in fact a painting made by Picasso at an early and still immature stage of his career or one he made just by joke; these paintings, although made by Picasso, are not paradigmatical Picassos, since they are not endowed with those specific stylistic traits typical of Picasso’s mature work. Or consider, as far as friendship is concerned, a case in which Andrea, who has always behaved as friends are expected to do, at one point refrains from doing something that one would expect from friends in the fullest sense of the word, a case in which he is not willing to go the extra mile for you. In such cases we would probably say that the paintings in question are not true Picassos and that Andrea is not a true friend; but would we still be willing to say that the paintings are Picassos and that Andrea is a friend?
23Here much depends on the different policies for predicates application that can be adopted: one can adopt either more relaxed policies and to be willing to apply a predicate also to individuals that are not perfect/prototypical instances of a given property, so that “Andrea is a friend”/”This is a Picasso” come out true, or more demanding policies and to consider them as borderline cases of the application of the concept, so that those sentences come out neither true nor false, or even more demanding policies, pushing non-paradigmatic cases outside the extension of the concept and making the corresponding sentences false: this happens when one is disposed to apply a word such as “friend” only to the set of persons who fully possess a whole set of properties.
24Although each of these three semantic policies is an open option for speakers, it seems to me that many ordinary speakers, upon reflection, would adopt the intermediate policy, considering neither fully true nor fully false the sentences in question. In the case of the immature or made by joke Picasso, for instance, we would say upon reflection things like “Well, it is in some way a Picasso and in some other not” or “It is a Picasso in a manner of speaking”. This oscillation depends on the fact that speakers may use different and also contrasting application conditions for a predicate like “being a Picasso”: one condition appeals only to the origins of a work of art, the other demands also the possession of some stylistic traits; the immature or made by joke Picassos satisfy the first condition but not the second and the latter, differently from the former, can be satisfied at different degrees by different objects.
25Similarly in the Andrea case we would say things like “he is neither exactly a friend nor a non-friend: he is partially but not entirely a friend; he is almost a friend”; likewise in front of a shade of color that is between green and blue, we would say that it is neither fully green nor not green but quasi-green, between green and blue.
- 6 So, in order to show that transparency fails with things’ truth, it is not necessary to claim, as (...)
26It must be stressed that both the first (more relaxed) and the second (intermediate) semantic policy make things’ truth non-transparent: both policies make in fact diverge the truth-values of “Andrea is a true friend”/”This is a true Picasso” on the one side and “Andrea is a friend”/”This is a Picasso” on the other side when Andrea and the painting are not paradigmatical/perfect cases of their categories. In such cases in fact while the former sentences come out false the latter come out either true (by the most relaxed policy) or neither true nor false (by the intermediate one), so the “Tarskian” biconditionals (6)/(7) turn out to be false, since their right and left-hand-sides have not the same truth-value; but this amounts to the failure of transparency for things’ truth.6
27Transparency of things’ truth is on the contrary preserved by the third, more demanding policy: by adopting this policy things will in fact be sharply divided between those who are friends/Picassos and those who are not. Since in this case not only “a is a true friend” entails “a is a friend” but also “a is not a true friend” entails “a is not a friend”, the biconditional “a is a true friend if and only a is a friend” is true and transparency is saved.
28The reason of the failure of transparency for things’ truth lies therefore in the fact that many our concepts have, as we know after E. Rosch’s (1975) work on concepts, a radial structure which allows for the existence of central/paradigmatic cases and more peripheral cases. This depends on the fact that many concepts, and the corresponding properties, can be conceived as clusters of several other concepts/properties, many of which can have different degrees of exemplification by different individuals. So, for instance, as Tuzet (2010) stresses, we can think the concept/property <friend> as a cluster of several concepts/properties (like being trustworthy, loyal, ready to help in hard times, unwilling to hurt and so on) which can be possessed in different degrees by different persons (one person can be more or less trustworthy or loyal than another): a true friend is someone who exemplifies all these properties at a sufficiently high degree; someone (like the fake friend who has an affairs with my girlfriend) who doesn’t exemplify many or all of these properties or exemplifies them at a low degree is not a friend at all; in between these two extremes there are people who, depending on the policy for concepts application adopted, are classified either as neither definitely friends nor definitely non friends or as friends (although not in the fullest sense of the word).
29Finally, it should be noticed that there are cases of concepts/properties like <being a dollar> for which there seems not to be any difference between something which is an F (a dollar) and something which is a true F (a true dollar): something which is not a true dollar is not a dollar at all. In cases like this transparency of things’ truth holds. The reason for this fact is that the application conditions of this concept appeal only to the origins of the things in its extension and their satisfaction is therefore a question of yes or no.
30Does the failure of transparency for things’ truth mean that things’ truth and words’ truth part ways? It doesn’t, at least if the intermediate semantic policy is adopted.
31In fact, as Dummett (1959) stressed, if bivalence fails for the right-hand side of a Tarskian biconditional the latter is false. Sticking to our example, if “Andrea is a friend” is neither true nor false, “‘Andrea is a friend’ is true” must be false and therefore
12) “Andrea is a friend” is true if and only if Andrea is a friend
is also false.
32Therefore, it seems that transparency fails also for words’ truth in such cases: words’ truth and things’ truth are in the same boat when bivalence fails.
33As is well-known H. Field (1994) claims that the truth of the Tarskian biconditional (12) can be restored, when Andrea is a quasi-friend, a borderline case of friendship, by embracing a purely disquotational understanding of the truth-predicate and interpreting the conditional “if p then q” in a non-classical way (Field, 2008). A purely disquotational notion of truth is one according to which asserting “‘p’ is true” is cognitively equivalent, for a speaker who understands “p”, to asserting “p”; the non-classical interpretation of the conditional is one in which “If p then q” is true whenever the antecedent and the consequent have the same evaluation (even if this is for both not determinately true), i.e. a conditional in which “if p then q” means “q is not less true than p”.
34Notice that, first, if one embraces the purely disquotational notion of truth, then “‘p’ is true” inherits the degree of indeterminacy of “p”; in other words, if Andrea is a quasi-friend, someone who is not determinately a friend, then also the sentence “‘Andrea is a friend’ is true” is, at the same degree, neither determinately true nor determinately false. Therefore, given the non-classical interpretation of the biconditional, (12) turns out to be true even when Andrea is a borderline case of friendship.
35It is worth noticing that this strategy for regaining transparency is the opposite of that adopted for things’ truth. While in fact in that case transparency was regained by strengthening the policy for the application of a concept, in this case it is restored by adopting a more relaxed, purely disquotational truth predicate which applies also to sentences involving non-paradigmatic cases.
36According to Field (1994) a stronger notion of straightforward truth (TRUTH) which applies only to non-borderline cases can be defined starting from the disquotational notion in the following way:
“p” is TRUE =DEF “determinately p” is true,
- 7 According to Field (1994), the stronger, non-disquotational notion of truth can also be used to ma (...)
where “determinately” is a primitive operator whose content can be clarified, according to Field, describing some basic regularities of its use.7
37Notice that since, given a purely disquotational notion of truth,
13) “a is an F” is true if and only if a is an F
is a conceptual truth, while
14) a is a true F if and only if a is an F
is sometimes false,
15) “a is an F” is true if and only if a is a true F
- 8 This is also stressed by Tuzet (2010).
is not always true.8 This happens when a is a non-paradigmatic case of being F: in this case in fact the left-hand-side of (15) is neither determinately true nor determinately false while the right-hand-side is determinately false.
38The equivalence between the sentences ascribing things’ truth and those ascribing words’ truth holds on the contrary when what is ascribed is the strong truth predicate (TRUTH): in fact, given the definition above, to ascribe TRUTH to a sentence amounts to saying that it is determinately true, so
16) “a is an F” is TRUE if and only if a is a true F
can never be false, given that a is a true F when a is determinately an F and when this is the case “a is an F” is determinately true, so TRUE.
39This equivalence between ascriptions of TRUTH and ascriptions of things’ truth depends on the fact that they have the same expressive role: the expressive role of the notion of things’ truth is in fact that of marking the central/paradigmatic cases of the exemplification of a property and distinguishing them from more peripheral or borderline cases. But this means that the notion of things’ truth is a tool we have in our languages to say that something definitely has a given property, a tool therefore which has the same role of the notion of straightforward truth which can be construed starting from a purely disquotational notion of truth.
- 9 This paragraph is an attempt to take into account a strong point that has been put forward to me b (...)
40Consider the sentence
17) Sara is not a true ice cream.
41As Sara is a woman which, as such, doesn’t resemble at all to an ice cream, (17) seems mistaken: women in fact are not the kind of things to which it can be sensibly either attributed or denied the property of being a true ice cream. So, it seems correct to say that (17) is neither true nor false. But
18) Sara is not an ice cream
is clearly true. So, by adopting a non-classical interpretation of the conditional, according to which “P → Q” is true just in case “Q” is not less true than “P”, we have that
19) Sara is not an ice cream → Sara is not a true ice cream
is false since its antecedent is true and its consequent is neither true nor false.
42But (19) is equivalent, by contraposition, to
20) Sara is a true ice cream → Sara is an ice cream.
43So, we have a counterexample to the left to right direction of the biconditional “a is a true F if and only if a is an F”, whereas until now the direction of the biconditional that seemed problematic was the right to left one (from “a is an F”, to “a is a true F”). Moreover, in this case
21) Sara is a true ice cream if and only if it is true that Sara is an ice cream
comes out false, since, given that Sara is not an ice cream the right-hand side of the biconditional is false whereas the left-hand side is neither true nor false.
44What does this failure of the left to right direction of T-biconditionals for things’ truth and of the extensional equivalence between things’ truth and words’ truth reveal on the nature of the former? As we have seen the failure of the right to left direction is a consequence of the expressive role of things’ truth, that of marking the difference between central and peripheral cases of a property’s instances. It could be pointed out that the failure of the left to right direction of the biconditional is inconsistent with this expressive role: in fact, if, going from paradigmatic to non-paradigmatic instances of a property, things’ truth get lost, a fortiori it should be lost when we jump outside of the extension of the property; in other words, if the only role of things’ truth were that of marking the distance between paradigmatic and peripheral cases, and if it is correct to say of a peripheral case of being F that it is not a true F, it should a fortiori be correct to say the same of something that is not at all an F: if Sara has not the property of being an ice cream, a fortiori she has not the property of being a true ice cream.
45Concerning this point notice, first of all, that there is a reading of (17) in which it comes out true; this is the reading according to which the sentence is true just when Sara has not the property of being a true ice cream; since true ice creams have surely the property of being ice creams and Sara lacks this property, Sara lacks trivially also the property of being a true ice cream, and so she is not a true ice cream, end of the story, however strange or inappropriate the latter sentence may sound. So, in this reading of (17) both the left to right direction of the T-biconditional and extensional equivalence of things’ truth and words’ truth hold.
46The reading of the sentence making troubles for the T-biconditional is therefore that in which “x is not G” is not understood simply as saying “x has not the property of being G” but as “x is H” where being H is some intended polar property of being G. In this case the polar property at stake is of course being a false F: notice in fact that while there is at least an understanding of (17) in which the sentence is true,
22) Sara is a false ice cream
seems to be clearly unacceptable.
47But does this failure of the left to right direction make really troubles for my claim concerning the role of things’ truth and its similarities in logical behavior with words’ truth? Not so much. Let’s see why.
48Notice, first of all, that the failure of the left to right direction of the T-biconditional depends in this case by a quite general semantic phenomenon like polarity in properties ascription, a phenomenon which concerns not only things’ truth but also words’ truth and many other properties.
49Consider in fact the following sentences:
23) number 3 is not true
24) number 3 is not hot.
50As in the case of things’ truth there is a reading of (23) and (24) in which they come out true: that according to which they say that number 3 has not the property of being true and the property of being hot. There is also a reading in which (23) and (24) sound mistaken: that in which “is not true” and “is not hot” are read as “is false” and “is cold (or lukewarm)”, that is to say the reading according to which the negation of the exemplification of a property is considered equivalent to the attribution of some polar property and exemplification of both properties is constrained to objects of a given kind (in the case of words’ truth, to so-called truth-bearers).
51Does the specific kind of ontological restriction on the range of objects that can exemplify things’ truth makes troubles for what I have been saying concerning its expressive role and its similarities to words’ truth? I think just in part and not dramatically.
52The reason why it is totally mistaken to say of women that they are false ice creams is in fact that they have nothing of ice creams, they are not, no-doubt, ice creams, no one could mistake them for ice creams. But all this is consistent with the expressive role I attributed to things’ truth: in fact, we need to mark the difference between central and peripheral cases of a property’s instantiation because it is important for us not to confuse them, and this is important for us since peripheral cases may behave at some point differently from central cases. Therefore, it is pointless to mark the difference between central cases of being F and things that nobody could sensibly mistake for things that are F. This is not however the end of the story. Imagine in fact that Sara is dressing a perfect ice cream costume: in this case it seems to me that it would be perfectly correct to say that Sara is a false ice cream, despite the fact that she is not an ice cream at all and therefore not even a peripheral case of being an ice cream. The reason why Sara can correctly be said to be a false ice crem is in this case that, although she is in no way an ice cream, she looks like an ice cream and therefore she could be mistaken for an ice cream (a walking one): in a sense things’ truth has to do with the possibility of being deceived by something’s appearances, it has his place where a gap between appearance and reality lurks: a true F is, in a sense, something which doesn’t lie about itself, something whose appearances are not deceiving.
53This function of things’ truth seems to me to ground its expressive role of marking the difference between central and peripheral cases of a property instantiation: in fact, we need to distinguish central from peripheral cases since we don’t want to be deceived by the similarities, up to a certain point, of the latter to the former.
- 10 An interesting point, that cannot be gone through here, is whether this role of the truth predicat (...)
54Finally, it should be noticed that also in this respect things’ truth and words’ truth seem to be interestingly on a par: propositions, if one grants that they are the primary truth-bearers, are in fact the content of beliefs and assertions and these are representations of reality; but an essential feature of representations is that they can misrepresent reality: both words’ truth and things’ truth thus seem to be deeply intertwined with our capacity to get wrong and our willingness not to do so10.
55Although things’ truth and words’ truth are two different properties, they exhibit interesting similarities and differences when transparency, that is to say their compliance with Tarskian biconditionals, is at stake. In fact, while they both are transparent when predicates whose application conditions are not a matter of degrees and whose extensions have sharp boundaries are involved, their transparency is threatened when concepts with radial structure and borderline cases are at stake.
56Transparency can be regained for words’ truth by considering the truth predicate as purely disquotational, a feature that, according to Deflationism, is essential to explain the expressive role of the truth predicate (see Field, 1986; Horwich, 1990).
57As far as thing’s truth is concerned transparency can also be regained by adopting demanding practices for concepts application which do not admit borderline cases. Yet, this move deprives things’ truth of what seems to be its essential expressive role: that of marking the difference between paradigmatic and non-paradigmatic cases of the application of a concept.
58Moreover, we have seen that both words’ truth and things’ truth seem to be deeply intertwined with our capacity to get wrong: our representations can misrepresent reality and things can engender, by looking like what they are not, such misrepresentations. I think that all these similarities as far as transparency is concerned allow to consider words’ truth and thing’s truth as species of a single genus or determinate properties of a single determinable: they are one but not the same. So, after all Aquinas was right in taking them as two different kinds of correspondence, “adaequatio rei et intellectus”.
59The good news is that we can spell this out without committing ourselves to the correspondence theory of truth but just sticking to Tarskian biconditionals.
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