26 Feb 2009

Vergauwen, A Metalogical Theory of Reference, Introduction, §16

by Corry Shores
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[The following is summary. Paragraph headings are my own.]

Roger Vergauwen

A Metalogical Theory of Reference: Realism and Essentialism in Semantics

Chapter 1.1 Introduction: Truth Definition and Semantics

§16 Tarski's Truth Definition

For Tarski, semantics is no different than logical semantics. Thus semantics for him is a part of logic. It discusses
a) the relations between such linguistic objects as sentences, and
b) what is expressed by these objects.

Tarski's concept of truth dates back to Aristotle. In his Metaphysics, he writes

"To say of what is that it is not, or of what is not that it is, is false; but to say of what is that it is and of what is not that it is not, is true."

This sort of truth theory is inherent to correspondence theory. For Tarski, "the truth of a sentence consists in its conformity with (or correspondence to) the reality." But this formulation raises numerous problems. To solve them, we will need to thoroughly revise the concept of meaning and its model-theoretic representation.

Nonetheless, the concept of truth remains a core semantic concept. It uses asserted truth conditions to directly relate to our understanding of sentences. For, to understand a sentence means also to understand the conditions that would make it true. Thus if we give the truth definition for some semantic system, we may obtain an understanding of all formalized sentences in that system.

But Tarski is not satisfied with Aristotle's formulation. He offers the following as the general form for truth definitions:

The sentence X is true (in L) if and only if p.

Vergauwen, Roger. A Metalogical Theory of Reference: Realism and Essentialism in Semantics. London: University Press of America, 1993.

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