Abstract
Semantic pathologies of self-reference include the Liar (‘this sentence is false’), the Truth-Teller (‘this sentence is true’) and the Open Pair (‘the neighbouring sentence is false’ ‘the neighbouring sentence is false’). Although they seem like perfectly meaningful declarative sentences, truth value assignment to their uses seems either inconsistent (the Liar) or arbitrary (the Truth-Teller and the Open-Pair). These pathologies thus call for a resolution. I propose such a resolution in terms of relative-truth: the truth value of a pathological sentence use varies with the context of its assessment. It always has a determinate truth value, but this truth value is relative to the context of its assessment. I start by considering a fairly esoteric pathology: the Truth-Teller, that is, sentences which assert nothing but their own truth. I make the case that truth value of a given truth-teller use must in general depend on the context of its assessment, and that one can indeed change its truth value at will. I then show how the notion of assessment-sensitive truth can help us provide solutions to other semantic paradoxes such as the Liar and the Open Pair and that those solutions are immune to revenge problems. I conclude by situating my proposal among the main approaches to the semantic paradoxes, and by drawing a very broad moral about pathological self-reference and intentionality.
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Notes
- 1.
- 2.
Occasions of use must solve all indexical ambiguities so they must determine a world, a location, a time, a subject, etc. Instead of ‘occasions of use’ I could have used Kaplan’s term ‘context of utterance’ or Lewis’ ‘context’.
- 3.
Because temporal and perspectival statements are sometimes said to be ‘relative’ (to the time of their use, to the subject who uses them) nonindexical relativism is sometimes called relativism (Recanati [19] speaks of moderate relativism, Kölbel [9] of relativism). We will, however, reserve the word ‘relativism’ for dependence of the truth value on the context of assessment.
- 4.
I consider contextualist objections to this line of reasoning in Section 2.4.1.
- 5.
Familiar counter-examples include cases of hyperintensionality (‘x is triangle’ is equivalent to ‘x is a trilatere’), failure of logical omniscience (‘1+1=2’ is equivalent to Fermat’s last theorem). More relevant to our point, if the Tr-principle is accepted, then any sentence
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(s): ‘p’
is equivalent to
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(t): Tr((s))
If (t) and (s) said the same thing, then (s) would say of itself that it is true. As a consequence, any sentence would be a truth-teller. Some philosophers have used considerations of this kind to solve the Liar paradox. For example, Mills [14] claims that every sentence attributes truth to the proposition it expresses. Prior, following Buridan and Albert of Saxony, has claimed that any sentence asserts its own truth. Accordingly, the Liar would entail a contradiction and be false. If the claim of this paper is correct, however, such a ‘solution’ would be too costly to deserve its name, for, as we shall see, it would imply that any sentence is a truth-teller so that its truth value on a given occasion of use can be changed virtually at will. But one should not accept the claim that (s) and (t) say the same thing anyway: a competent thinker could in general believe p without mastering the concept of truth or the concept of a sentence referring to itself, thus without believing that (s) is true.
Interestingly, Read [18] presents a solution to the Liar which is akin to the ones just mentioned but which is immune to the objections I have just raised against them. I discuss this solution in fn. 14.
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- 6.
Notice that the condition of equivalence is not redundant with the condition on beliefs. I cannot rationally believe that (I (de se) believe that it is raining) without believing that (it is raining and I (de se) believe that it is raining), and arguably no one can. The two embedded sentences nonetheless say different things.
- 7.
I owe this example to Williamson [22].
- 8.
There is actually a fourth part of this alternative. It might be the case that what (⋆) V says is both absolute and constant; that is, that (⋆) always express the same thing, and that what it expresses has an absolute truth value. The arguments above would then show that (⋆) V simultaneously makes a plurality of statements, some false, some true (actually, (⋆) V would say virtually everything that can be said). The problem for such an expressive pluralism consists in accounting for the fact that the truth value of (⋆) V can always vary with the context of assessment and turn out to be false in some contexts of assessment and true in others (notice that a pluralism like that of Read [18], which refuses 2nd RP would avoid such a problem (see fn. 14)). One could try to account for such variations by distinguishing between the statement made by a sentence use, which is absolute and plural, and the semantic content of that sentence use relative to a context of assessment. Each context of assessment would select a salient semantic content from among the statements made by the sentence use, and this semantic content could turn out to be true. Cappelen [3] defends the idea that such a Pluralistic Content Relativism can account for most of the usual data cited by relativists. In the case at hand, a defender of this view must motivate the intuition that (⋆) V says many things at a time (of assessment), and I am not sure how to do that.
- 9.
This is not to be confused with the question of whether if I believed/asserted that (⋆) V is true at V, I should also believe it at V’ and vice-versa. In general, and quite independently of relativism, there are often reasons reasons for not having the same attitude toward a single statement in different contexts of assessments. The relativity of the statement just adds one potential reason for such a change in attitude.
- 10.
This use of ‘radically relative’ should not be confused with Recanati’s [19] use of the term. Recanati uses the moderate vs. radical relativism distinction to contrast what we called nonindexical relativism (his ‘moderate relativism’) with relativism (his ‘radical relativism’).
- 11.
We could treat the Liar as we treated the truth-teller, showing that for any sentence p, one can make fully successful stipulations to the effect that a liar sentence says that p, even though for the usual problems, such a stipulation could not rationally be sustained very long.
Let us outline the argument roughly. In virtue of the Tr-schema, not Tr((L)) ⇔ Tr(‘not Tr((L))’). But of course, if I am to believe that not Tr((L), I must master the concept of truth and that of a sentence referring to itself. Accordingly, I, and this holds for any competent thinker, cannot believe that not Tr((L)) without believing that Tr(‘not Tr((L))’), and cannot believe that Tr(‘not Tr((L))’) without believing that not Tr((L)).
So by ISP (L) says exactly that it is true. We can then proceed exactly like in the case of the truth-teller.
- 12.
Some seem to believe that relativism threatens the Tr-schema and that, because our argument for relativism relied on the Tr-schema, it is self-defeating. This is not the case. We can easily reformulate the version of the Tr-schema we relied on so as to accommodate relativism. The following would work:
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If (x) names a sentence, and (x) U names the use of (x) is occasion of use U. If (x) U sates that P in the context of assessment A,
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(x) U is true in A iff P
We can consider the reference to the context of assessment as implicit in the first pages of this paper.
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- 13.
This list does not claim to be exhaustive. Thomas Bradwardine famously listed 9 different views on the insolubilia. I suspect that some of them would not belong on my list.
- 14.
I criticized the ‘solutions’ put forward by Mill and Prior in fn. 5. Read proposes a solution to the paradoxes which, as he pointed out to me, escapes those criticisms and seems to be in a position to dissolve the problems posed by (1) and (2). His solution relies on what he calls a meaning or signification pluralism:
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MP: a sentence signifies more than one thing; it signifies not only what its terms explicitly say, but also all the consequences of what it signifies.
Read uses this meaning pluralism to defend a principle connecting truth and signification aimed at replacing, or at specifying the Tr-schema:
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TS: a sentence use is true iff everything it signifies (as opposed to what its terms explicitly say) is true.
The main point is that this principle does not in general yield Tr-capture. It only yields Tr-release. So according to Read, our argument for the 1st RP would be sound, but not that for the 2nd RP. We could only show that some truth-tellers are false (not that some are true) and that it is always possible to make a truth-teller turn false by a mere stipulation. But the best explanation for this last fact would be that all truth-tellers are false. In the same way, the truth of the liars would entail their falsity, but without Tr-capture, their falsity would not entail their truth. As a consequence, liars would just be false.
I have two concerns with this elegant proposal. First, I am not totally convinced that it is not ad hoc. Second, I am not sure that it can account for the intuitive difference in meaning between liars and truth-tellers and for that between liars and ordinary contradictions of the form ‘p and not p’.
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- 15.
An interesting suggestion would be that some sentences are exclusively expressive (as opposed to, say, assertive or descriptive) and that those are the linguistic analogue of mere feelings. A claim along this line is endorsed by classical expressivists in ethics [1]. As speech-acts expressing mere feelings seem continuous with speech-acts expressing intentional states it is not clear that such a suggestion is compatible with the plausible claim to the effect that the semantic properties of speech-acts reflect those of the mental state they express.
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Acknowledgments
Many thanks to Shahid Rahman, Stephen Read, Tero Tulenheimo, Mathieu Fontaine, Laurent Keiff, the audience at the 2009 SOPHA conference for useful discussions and to Marie Guillot for a priceless collaboration on related topics.
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Billon, A. (2012). My Own Truth. In: Rahman, S., Primiero, G., Marion, M. (eds) The Realism-Antirealism Debate in the Age of Alternative Logics. Logic, Epistemology, and the Unity of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1923-1_2
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