Saturday, July 7, 2012

Deflationist account of the predicate 'true'

To: Mark S.
From: Geoffrey Klempner
Subject: Deflationist account of the predicate 'true'
Date: 18 December 2007 12:21

Dear Mark,

Thank you for your email of 8 December, with your University of London Logic essay in response to the question, 'Deflationists claim that the predicate ‘true’ does not stand for any property. What do they claim is the role of this predicate, and can this claim be justified?'

This is a very good answer to the question with which I have few real disagreements.

On the similarity between 'exists' and 'is true', the point could perhaps be expressed in the following way:

i. To assert that b exists, is equivalent to asserting Q(b) for some propositional variable Q(-).

ii. To assert that P is true is to assert that P.

Proposition i. defines a first-order existence predicate E, whose use corresponds 1-1 with that of the second-order existence quantifier. Possession of the first-order property E is not possession of a 'substantial property' for the reasons that Kant gave: the thought of fifty existing Pounds adds nothing to the thought of fifty Pounds.

Obviously, i. needs to be supplemented by a description theory to account for non-denoting terms.

I'm a bit worried, though about your statement that according to the deflationist there are different explanations for the truth of 'Canberra is the capital of Australia' and 'Gravity causes two particles to pull towards each other.'

Think what a correspondence theorist would say. Obviously, the two statements are true in virtue of different kinds of facts; nevertheless we can assert the following:

P is true if and only if either:

(a) there exists an explanation E (conjunction of propositions P1, P2,...Pn) which non-trivially entails P.

or:

(b) P is a brute fact (for which no explanation can be given).

I am unimpressed by quibbles about objectual and substitutional quantification with regard to the variable (p). You are right in what you say; however the upshot is that we are dealing with a species of shorthand: (p)(If the Pope says that p, then p) is shorthand for an infinite conjunction of conditional statements.

The alleged infallibility of the Pope adds nothing to the problem of comprehending infinity, which arises just as much with the case you do not consider, 'Mark said something true'. Here, we have an infinite disjunction of statements, 'Either Mark said that P, and P, or Mark said that Q, and Q....'.

This concedes a vital point to the anti-deflationist: namely, that the representational power of the language would be irreparably depleted by the removal of the truth predicate. The truth predicate is indispensable, and not redundant. This assertion is, however, fully consistent with a minimalist view.

The indispensability of the truth predicate can also be seen when we enter the arena of traditional theories of truth. As Dummett has extensively argued, there is a fundamental issue about how we understand truth, whether in a 'realist' or in an 'anti-realist' way. Although I do not accept Dummett's claim that realism about truth is equivalent to acceptance of a theory of meaning in terms of truth conditions (because I would argue that a Tarskian truth-theory can itself be understood either in a realist or anti-realist way), I do think that this is an outstanding metaphysical problem concerning truth, concerning which minimalism remains silent. (This corresponds to the point you make four paragraphs from the end of your essay.)

The existence of this problem (I am not claiming that it is the only problem) is sufficient evidence -- should evidence be needed -- that we need the generalising power of the truth predicate.

Dummett's claim that it is an essential part of the concept of truth that 'we aim at truth' has to be understood in the context of his account of the clash between realist and anti-realist theories of meaning. In Dummett's view, it is the realist who holds that we aim at truth. In an anti-realist theory of meaning, truth has a secondary role, explained along the lines of the redundancy theory. In asserting propositions, what we aim at, as good anti-realists, is to meet the standards of correctness set by the rules for the use of our language. There is no notion of truth as a goal existing beyond the standards of acceptance/ rejection manifested in linguistic usage.

My own view -- for what it is worth -- is that the clash between realism and anti-realism cannot be expressed in terms of theories of meaning. Rather, the issue of realism involves a 'dialectic' not unlike Wittgenstein's examination of the idea of a 'private language', where realist intuitions are explored, and the emptiness of the claims we want to make about 'realist truth' demonstrated. (Whether this counts as an argument for anti-realism is however a moot question -- as I discovered in numerous discussions with my supervisor McDowell.)

All the best,

Geoffrey