Monday, April 26, 2010

The Truth Operator

A modified version of my comment on Maverick Philosopher, about the distinction between truth as a predicate, which as Bill argues seems to commit us to realism about truthmakers, and truth as an operator, which does not appear to lead to such a commitment.

I subscribe to an 'operator' theory of truth. Each sentence has a syncategoric semantic component which corresponds to assertion. This component is always locked inside the main verb of the sentence. The operator 'that', which forms a that-clause from the sentence, strips out this assertoric component to convert the sentence into a categorematic expression signifying a possible object of thought, belief, assert, judgment etc. The operator 'it is true' replaces the assertoric component again to give us back the sentence (although the main verb is now the 'is' of 'it is true' rather than the verb of the operated-on sentence).

Thus the expression 'it is true that' is a sentence-operator that contains two operators, namely 'is true' and 'that'. The operator 'that' operates on sentences to produce a that-clause:a noun-phrase that names a content, a possible object of belief and judgment. It does this by removing the assertoric element from the sentence. The operator 'it is true' operates upon that-clauses, to form whole sentences. Such sentences have the same truth-conditions as the original sentence. Thus:

(1) Snow falls

is a sentence that asserts something, via the assertoric component embedded in the main verb 'falls'.

(2) that snow falls

is a that-clause naming a possible object of judgment or belief, such as in the sentence 'John believes that snow falls', which we parse as 'John / believes / that snow falls' to clarify its relational form 'X believes Y'. Note that in the belief sentence the verb 'falls' is no longer the main verb. The truth or falsity of 'John believes / that snow falls' no longer depends on whether snow does fall or not. Rather it depends on whether John believes this or not. Finally

(3) It is true that snow falls

Gets us back to a sentence with the same truth-conditions as (1), but with a different semantics. The main verb is now the 'is' of 'it is true', and the verb 'falls' is a subordinate verb. The assertoric component of (3) lies in the 'is' of 'it is true', the assertoric component of (1) lies in 'falls'. We can parse (3) as 'It is true / that / snow falls' to make it clear that there are two operators rather than one (Frege's mistake was to think there is only one). Or we can parse it as 'It is true that / snow falls' to make it clear that the combination of 'it is true' and 'that' gives us a further operator.

This may remove the temptation to suppose that there are such things as 'truthmakers'. (Well it won't, I imagine the supporters of truthmaking will continue in the deep error of their ways, but that is the way). The operator approach is of course consistent with a thoroughgoing nominalist program. I wonder whether, if ordinary language had the right synactic structure so that operators and existence-verbs and the like were clearly identified, the users of that language would be so committed to realist semantics. Could we even 'do' metaphysics in such a language?