Saturday, June 20, 2009

Tarski's (T) schema

Tarski's (T) schema says that:

  1. X is true if, and only if, p
in every case in which X is a "name" for the sentence p. Elsewhere, Tarski makes it clear that every definition of p counts as a "name" for p. So, here's something fun. While, necessarily, every instance of the (T) schema is true, it is not the case that every instance of the (T) schema is necessarily true. For instance, if the first sentence that Janet uttered today is "Snow is white", then the following is an instance of the (T) schema:
  1. The first sentence that Janet uttered today is true if, and only if, snow is white.
Indeed, (2) is true. But (2) is, plainly, not a necessary truth, since Janet's first sentence today could have been different.

Were the (T) schema Tarski's definition of truth, this could be the start of a criticism. For we do expect instances of definitional sentences to be necessary truth. E.g.,

  1. Patrick's best friend is a bachelor if, and only if, Patrick's best friend is a never-married, marriageable man
is an instance of the definition of a bachelor, and it is a necessary truth. The issue here is that standard definitions are of the form:
  1. F(X) if, and only if, G(X)
where X occurs in the definiendum and the definiens. Not so in the (T) schema. But, again, that seems to be alright because the (T) schema, while a material condition that any definition of truth must satisfy, is not taken by Tarski to be a definition of truth.

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2 comments:

  1. ryanbJune 20, 2009 at 9:35 AM

    It seems weird to me to call 'the first sentence Janet uttered today' a NAME for her sentence 'snow is white'. Isn't it, rather, a definite description? Is this why you put "name" in scare quotes?

    Second, I thought that the part which fills in the X in the T schema was supposed to be a complete sentence. But, 'the first sentence Janet uttered today' isn't. It is a subject without a predicate.

    Perhaps these reasons are part of the explanation of the difficulty you find.

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  2. Alexander R PrussJune 20, 2009 at 10:09 AM

    One fills in a complete sentence for p, but X is a "name". Tarski himself gives an example of a definite description for a "name", so it's clear that by "name" he simply means an expression referring to the sentence.

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