yablo - truth, definite truth and paradox.pdf - sikula

Journal of Philosophy, Inc.

Truth, Definite Truth, and Paradox

Author(s): Stephen Yablo

Source: The Journal of Philosophy, Vol. 86, No. 10, Eighty-Sixth Annual Meeting American

Philosophical Association, Eastern Division (Oct., 1989), pp. 539-541

Published by: Journal of Philosophy, Inc.

Stable URL: http://www.jstor.org/stable/2026663

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KRIPKE'S THEORY OF TRUTH

539

complexity of IF, is staggering. We have merely described IF,, from

an external vantage point. The essentially richer metalanguage is still

with us.

We can do better. One can give an effective version of this con-

struction in which the theory r is actually written down, concretely

and explicitly.9 The mathematical details are somewhat intricate,'0

but their unmistakable basis is the Kripke construction.

As Tarski saw clearly, if we insist that our semantic theory entail

schema (T), we shall only be able to give a semantic theory for a

language if we can look at the language from the perspective of an

essentially richer metalanguage. This implies that we cannot give a

semantics for the very language we speak, for we have no external

vantage point. On the other hand, if, as I recommend, we weaken

our requirements from (T) to (DT), we find that we can give a con-

sistent theory of truth for our own language. Thus, there will be no

logical grounds for supposing that human language must lie beyond

the reach of human understanding.

VANN MCGEE

University of Arizona

TRUTH, DEFINITE TRUTH, AND PARADOX*

T HE STORY we are given has three parts:since (1) the para-

doxes show that our "naive understanding of truth" is in-

consistent, (2) a new understanding is required, which (3) is

obtainable by redeployment of Saul Kripke's methods in the form of

a theory which (i) does minimal violence to semantic intuition, (ii) can

be formulated in the language of which it treats, (iii) discovers an

error in the naive reasoning that leads to paradox, and (iv) generates

no new paradoxes of its own. Just to be contrary, I quarrel with most

all of this.

Suppose that our naive understanding of truth is inconsistent.

Since the truth about anything, truth included, is consistent, does it

not follow that naive truth theory, like any theory which misdescribes

the facts, needs revision? Only, I think, if it purports to describe the

9 The effective version uses A-logical consequence in place of the mathematically

obstreperous supervaluational consequence.

'1 See ch. 8 of my Truth, Vagueness, and Paradox: An Essay on the Logic of

Truth (Indianapolis: Hackett, 1989).

* Abstract of a paper to be presented in an APA symposium on Kripke's Theory

of Truth, December 29, commenting on a paper by Vann McGee, this JOURNAL, this

issue, 530-539.

0022-362X/89/8610/539-541

C) 1989 The Journal of Philosophy, Inc.

540

THE JOURNAL OF PHILOSOPHY

facts, an assumption which sits as ill with Vann McGee's "meaning

postulates" and "linguistic conventions" as with Kripke's guiding

metaphor of "explaining the word 'true' to someone who does not

yet understand it." Meaning something by a word involves the obli-

gation to employ it in a certain manner, or else incorrectly; and the

paradox's legendary intransigence suggests that the contradiction, if

such there be, is forced on us by the meaning we attach to 'true'.

But then its lesson is not, as the analogy with genetics suggests,

that we are caught up in factual errors, but that the meaning of

'true' imposes irreconcilable obligations. If a "scientifically re-

constructed" understanding of truth is indicated, that is because

semantics would go better, if we meant something different by

'true'. Maybe it would. But it can hardly relieve any genuinely

philosophical discomfort about the liar paradox, generated as it is by

the meaning that we have, to be told that another is now available.

What would relieve the discomfort is an explanation of what para-

dox is, and how something like that can issue from procedures whose

general workability has never been questioned. The "definitely"

theory pins the blame on our use of a definite-truth preserving

inference rule (e.g., TrS'p/lo) in a context (conditional proof) where

a (definitely) truth-preserving rule was needed; in essence, we err in

supposing that, if r<i is true, then p. Unless it is denied, implausibly,

that this is, in our usage, analytic, this diagnosis discovers an error

only relative to an alien construal of 'true'. What, if anything, is the

error, given the actual meaning of 'true'?

To judge by the claim that our naive understanding of truth, if

paradoxical, is classically inconsistent, paradox is equated with clas-

sical inconsistency among naively acceptable classical formulae.

Thus, the naively acceptable (T)Tr&p'S?, in combination with the

empirical L = - TrLW,classically entails L &- L. By these standards,

it should also be a paradox if 'Spiderman enjoys soup' lacks truth-

value (in symbols, - T'S' & - T'-S'); for - TrS' & - T-S', in

the presence of (T), classically entails S &-S. Insistence on classical

methods, in this case as in others, turns the light of reason so blind-

ingly bright that intuitive distinctions are lost from view. The assimi-

lation of paradox to contradiction is a case in point. That our naive

understanding generates paradox may mean that it prescribes

contradictory assertions (e.g., in the obvious notation, O(F S?)and

0(F -S?)); but it may equally mean that it prescribes incompatible

actions (O(F Sp)and O(Y so)); or that its instructions are incoher-

ent (O(F S?) and -O(F (p)), or even ill-defined (O(F So,

if Y S?) and O(Y ep, if F so)). On these latter hypotheses, note there is

no real question of descriptive inaccuracy, because the conflicts are

all at the level of obligation.

KRIPKE'S THEORY OF TRUTH

541

McGee's positive proposals take off from his complaint that the

gap theory, though effective against the ordinary liar ('I am false'), is

powerless against the strengthened liar ('I am not true'). In fact, the

same problem arises in connection with both; if 'I am false' ('I am not

true') is neither true nor false, then it is afortiori not false (not true),

whence, given what it says, it is false (true) after all. Another problem

with the gap theory is that, if true, it is inexpressible in the language

of which it treats (if the liar is neither true nor false, then so is 'the

liar is neither true nor false'). Likewise, though, the "definitely"

theory cannot, on pain of contradiction, allow as definitely true its

own (apparent) prediction that X = 'X is not definitely true' is not

definitely true.

Perhaps this is to forget that it is not (yet) definite that X is not

definitely true (we may yet adopt conventions, given which it be-

comes definitely true). Such a response seems disingenuous, since

any convention that would make X definitely true would lead to

contradiction. Indeed, realizing this, will we not want to enact a

convention which precludes the determination of X as definitely

true? Only if we are willing to contradict ourselves; resolved though

we may be that X must never become definitely true, we cannot

consistently express this resolution except by ascent to the metalan-

guage (this is the kind of thing that troubles the sleep of the ghost of

Tarski's hierarchy). To make the point vivid, an appropriate formali-

zation of 'I am not definitely true, unless everything is' seems likely to

generate contradiction.

Grant that 'Xis not definitely true' is not definite; by what right do

I then assert that X is not definitely true? Perhaps the answer is that

assertibility goes not with definite truth, but with truth simpliciter; it

is true that X is not definitely true, because X is not entailed by facts

plus current conventions. On the other hand, in calling Xindefinite,

I describe it as (in McGee's words) 'either true or false, but it is not

clear which', which appears to commit me to the belief that it is not

clear whether Xis true. But Xis what I assert; and what business have

I in asserting something such that it is not clear whether it is true? If

'X is not definitely true' is not true, then it appears that 'one may

sincerely assert . . . statements that one does not believe to be true';

if so, then 'I no longer understand why the notion of truth . . . has

any real importance'. Could it be that we do not assert that X is not

definitely true? Why not, since such is evidently the case? (The ghost

stirs.)

STEPHEN YABLO

University of Michigan

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