I. Introduction
Paul Horwich has presented and defended, in a number of places,Footnote 1 the Minimalist theory of truth. Its main thesis is that the instances of the T-schema,
(T-schema) < p > is true if, and only if, p Footnote 2
are conceptually, explanatorily and epistemologically fundamental with respect to the notion of truth. That means, in the first place, that they implicitly define the truth predicate.Footnote 3 This is so because the basic and fundamental regularity of use that determines the meaning of ‘true’ is our disposition to accept all instances of the T-schema. This, together with the fact that, according to Horwich, meanings are concepts, implies the conceptual fundamentality of the instances of the T-schema. In the second place, the instances of the T-schema are all we need to explain all our uses of ‘true’. This explains why they are explanatorily fundamental.Footnote 4 Finally, the instances of the T-schema are “immediately known”Footnote 5; they cannot be deduced from anything more basic. This is why, claims Horwich, they are epistemologically fundamental.
Given these considerations, it is not surprising that Horwich’s theory of truth, Minimalism, contains as axioms all instances of the T-schema applied to propositions, and nothing else.Footnote 6
In this paper, I consider one of the main problems for Minimalism: the generalization problem. HorwichFootnote 7 presents a way to cope with this problem, which has been criticized by Bradley Armour-Garb.Footnote 8 The aim of this paper is to defend Horwich’s answer to the generalization problem from Armour-Garb’s criticism and raise some consequences that stem from it. I will present the problem in Section 2. In Section 3 I will introduce Horwich’s response and Armour-Garb’s objection to his response. In Section 4, I will present my rejoinder to this objection and, in Section 5, I will draw some consequences from it. Specifically, not only is Horwich’s solution to the generalization problem free from Armour-Garb’s objection but, the discussion will show that, given some provisos, Horwich’s response to the generalization problem can be simplified.
II. The Generalization Problem
As several authors have noted,Footnote 9 Minimalism is too weak and has serious problems explaining many generalizations about truth.Footnote 10 This is a major difficulty for Minimalists, for it means that the instances of the T-schema are no longer explanatorily fundamental. Consider, for example, the following claim:
(ID) Every proposition of the form ⎡α → α⎤ is true.
Can (ID) be derived from all the instances of the T-schema, that is, from the Minimalist theory of truth? Certainly, we can derive each instance of (ID), for every proposition p, but that does not mean that we can derive the general fact expressed by (ID). In Scott Soames’ words:
Because the Minimal theory is just a collection of instances, it is conceivable that one could know every proposition in the theory and still be unable to infer [(ID)] because one is ignorant about whether the propositions covered by one’s instances are all the (relevant) propositions there are. For example, given only the Minimal theory, one might think: perhaps there are more propositions and the [truth predicate] applies differently to them. A person in such a position has no guarantee of [(ID)] and might lack sufficient justification for accepting it.Footnote 11
The generalization problem has the undesired consequence that the Minimalist theory of truth is not enough to explain all our uses of the truth predicate, because it cannot explain our acceptance of (ID) only in terms of the instances of the T-schema (and basic logical principles not involving the truth predicate).
III. Horwich’s Solution
HorwichFootnote 12 offers a solution to this problem in which he proposes a further explanatory premise that, on the one hand, allows us to explain our acceptance of certain general facts concerning truth and, on the other hand, does not involve the truth predicate, for that would jeopardize the minimal character of Horwich’s theory of truth.Footnote 13 It should be stressed that this is not an unfamiliar point, for we need principles concerning other phenomena to explain all facts about truth;Footnote 14 what is important, though, is that such principles do not use the truth predicate, for, if they did, they would show that we need to go beyond the instances of the T-schema to explain all facts concerning truth. Horwich proposes the following extra premise:
(P1) Whenever we are disposed to accept, for any proposition of structural type F (henceforth, F-proposition) that it is G (and to do so for uniform reasons), then we will be disposed to accept that every F-proposition is G.
Furthermore, this premise is restricted to structural kinds of propositions F and properties G that satisfy the following condition:Footnote 15
(C) We cannot conceive of there being additional Fs—beyond those Fs we are disposed to believe are G—that we would not have the same sort of reason to believe are G.
To see how Horwich’s proposal works, interpret F as having the form ⎡α → α⎤ and G as truth.Footnote 16 First, let us suppose that they satisfy condition (C) (more on this below). Then, given that we are disposed to accept that every proposition of the form ⎡α → α⎤ is true, (P1) allows us to infer that we are disposed to accept that all such propositions are true and, hence, to explain why we accept that all such propositions are true. Finally, since (P1) does not involve the truth predicate, the explicative fundamentality of the Minimal theory is preserved.
Armour-GarbFootnote 17 criticizes and rejects this solution to the generalization problem. According to him, (P1), when well understood, makes Horwich’s argument to conclude (ID) circular. Let us see why. Armour-Garb claims that the extra explanatory premise should mention the awareness of the fact that we are disposed to accept, for every F-proposition, that it is G:
(P2) Whenever we are disposed to accept, for any F-proposition, that it is G—and to do so for uniform reasons—and we are aware of this fact—that is, we are aware that we are disposed to accept, for any F-proposition, that it is G—, then we will be disposed to accept that every F-proposition is G.
The reason for that is that being disposed to accept a given collection of facts is consistent with not knowing the existence of such a disposition and, hence, someone who is disposed to accept, for any F-proposition, that it is G, will accept that all F-propositions are G only if she knows that she has the disposition to accept, for any F-proposition, that it is G. Let us focus now on the partial instance of (P2) where G is interpreted as ‘true’:
(P3) Whenever we are disposed to accept, for any F-proposition, that it is true—and to do so for uniform reasons—and we are aware of this fact—that is, we are aware that we are disposed to accept, for any F-proposition, that it is true—, then we will be disposed to accept that every F-proposition is true.
At this point, Armour-Garb claims that we need to clarify the notion of being aware of the fact that we are disposed to accept, for any F-proposition, that it is true. And he proposes the following:
For one to be aware of the fact that, for every F-proposition, she is disposed to accept that it is true is for that person to be aware of the fact that she is disposed to accept that every F-proposition is true.Footnote 18
Hence, (P3) becomes (P4):
(P4) Whenever we are disposed to accept, for any F-proposition, that it is true—and to do so for uniform reasons—and we are aware of the fact that we are disposed to accept that every F-proposition is true, then we will be disposed to accept that every F-proposition is true.
The problem with (P4) is that, according to Armour-Garb, it makes Horwich’s argument for (ID) “viciously circular”Footnote 19; it infers that we have a certain disposition (that of accepting (ID)) from the fact that we are aware that we have such a disposition.Footnote 20
For the sake of the argument, I will grant to Armour-Garb that we need to be aware of the fact that we have the relevant disposition in order to be able to derive the desired generalization. But, as far as I can see, condition (C) is sufficient to guarantee this awareness. Let us see why.
IV. Conceivability and Imagination
Recall that condition (C) poses a restriction to the entities to be used in the extra premise Horwich proposed for the argument that allows us to conclude generalizations involving truth like (ID). The instance of (C) we are interested in is the following one:
(C1) We cannot conceive of there being additional F-propositions—beyond those F-propositions we are disposed to believe are true—that we would not have the same sort of reason to believe are true.
As I said, what I want to defend is that the reasons we have for accepting (C1) already imply our awareness of the fact that we are disposed to accept, for any F-proposition, that it is true. So, how are we convinced of the truth of (C1)? To answer this question, first, we need to address another question: what does it mean to conceive something?
Conceivability is an evasive notion. Nevertheless, as many authors have claimed,Footnote 21 there is a close connection between conceivability and imagination; in Stephen Yablo’s words:
Conceiving that p is a way of imagining that p; it is imagining that p by imagining a world of which p is held to be a true description.Footnote 22
I am not saying that conceivability conflates with imagination; it will be sufficient for my purposes to weaken Yablo’s idea and grant that conceiving that p implies imagining that p (in Yablo’s sense).Footnote 23 Thus, going back to (C1), according to the above characterization of conceivability, we cannot conceive of [there being F-propositions—beyond those F-propositions we are disposed to believe are true—that we would not have the same sort of reason to believe are true] if we cannot imagine a world of which [there being F-propositions—beyond those F-propositions we are disposed to believe are true—which we would not have the same sort of reason to believe are true] is a true description.
Now, what reasons might we have for accepting that we cannot imagine something? To my mind, the most natural response is because we tried and we failed. To wit, we tried to imagine a world with an F-proposition that we would not have the relevant reasons to believe is true and we realized that we were unable to. Since we tried, we became aware of our inability to imagine such a world. In other words, we just became aware of the fact that if we were presented with an F-proposition, we would consider it as true (if it were not the case, then we would certainly be able to imagine a world in which this proposition is not true; the actual world). Hence, we just became aware of the fact that we are disposed to accept, for every F-proposition, that it is true, which is what we needed to conclude.
For example, when F is the property of being a proposition of the form ⎡α → α⎤, (C1) holds because we try to imagine a world with a proposition of the form ⎡α → α⎤ that we would not have reasons to believe it true and we realize that we are unable to do it. We realize, hence, that we cannot imagine such a world and, since conceiving implies imagining, we conclude that we cannot conceive of such a world. (C1) holds. Moreover, it is in the process of trying and failing to imagine a world with a proposition of the form ⎡α → α⎤ that we would not have reasons to believe it true that we become aware of the fact that we are disposed to accept any proposition of the form ⎡α → α⎤; this is so because we realize that if we were presented with a proposition of the form ⎡α → α⎤ such that we would not accept as true, then we would be in a world with a non-true proposition of the form ⎡α → α⎤ and, hence, we would be able to imagine such a world.Footnote 24
To sum up, the reasons we have for accepting (C1) already provide us with the guarantee that we are aware of the fact that we are disposed to accept, for every F-proposition, that it is true.
At this point, the following objection could be raised. It may well be that there are some F-propositions that we are not disposed to judge true or non-true. This may be so, for example, because we are dealing with an F-proposition that can only be expressed in English with a sentence, say, a billion lines long. Let us call such a proposition ‘q’. Confronted with q, we might not be able to accept it as true but, nevertheless, we could not conclude that q is not true and, hence, we could not conclude that we can imagine a world in which q is not true.Footnote 25 As far as I can see, there are some idealizations that must be made explicit in order to cope with this objection. Such idealizations, though, are already present in Horwich’s view and, hence, they can be presupposed without being dialectically at fault. First, we might suppose that propositions are structured entities and that that structure is reflected in the syntactic structure of the sentences that express them. This, of course, seems to be presupposed by Horwich when he claims that we have a disposition to accept any instance of the T-schema (to wit, we need to recognize that the instances of the T-schema are biconditionals and that they have a proposition and its truth ascription as components). Second, we may presuppose that any subject will be able, in principle, to determine the logical form of any sentence, by inspecting its syntactic structure (again, for the previous reasons, Horwich seems to presuppose it too).
V. Concluding Remarks
The analysis presented in the previous sections has as a consequence that Horwich’s response to the generalization problem can be simplified, as premise (P1) is not needed at all; this means that Horwich can explain our disposition to accept truth generalizations like (ID) with the only aid of the fulfilment of condition (C1).Footnote 26 This means that Horwich can explain the fact that we are disposed to accept truth generalizations like (ID) with no extra explicit premise, but only with the aid of a restriction to F’s satisfying (C1).Footnote 27
As I said, for the sake of argument, I grant that, as Armour-Garb proposes, we need to be aware of the fact that we are disposed to accept, for every F-proposition, that it is true. I also grant the analysis he offers of this awareness. Taking this into account, it can be shown that only (C1) is needed to obtain the desired truth generalizations. For Armour-Garb is claiming that:
1. being aware of the fact that we are disposed to accept, for every F-proposition, that it is true,
is the same as
2. being aware of the fact that we are disposed to accept that every F-proposition is true.
This is the reason why, according to Armour-Garb, Horwich’s argument is eventually viciously circular. But, if this analysis is right (that is, 1 is equivalent to 2), we do not need (P1) at all, we just need condition (C1) which, as I said, implies 1 and, hence, according to Armour-Garb, implies 2, which is what Horwich needs to be able to explain our acceptance of truth generalizations like (ID).
Hence, Minimalism, with the only use of condition (C1), can give a satisfactory response to the generalization problem as stated in the second sectionFootnote 28; it is enough to guarantee that propositions with certain forms and the notion of truth are the kind of entities that satisfy condition (C1). And as we have already noted, we have good reasons to accept (C1), which are, precisely, what guarantees our awareness of the fact that I am disposed to accept that every proposition of the relevant kind is true.
Consequently, Horwich’s response to the generalization problem becomes much simpler; instead of an extra premise like (P1) to explain our acceptance of certain general facts concerning truth, it is enough that condition (C1) obtains for the relevant propositions.
Acknowledgements:
I would like to thank José Martínez Fernández, Elia Zardini and three anonymous referees for all their helpful comments and suggestions. I am also grateful to Susan Dimock and Jill Flohil. During the writing of this paper, I have benefitted from the project FFI2015-70707P of the Spanish Ministry of Economy, Industry and Competitiveness on Localism and Globalism in Logic and Semantics.
