Vergauwen, A Metalogical Theory of Reference, Introduction, §18

by Corry Shores
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Roger Vergauwen

A Metalogical Theory of Reference: Realism and Essentialism in Semantics

Chapter 1.1 Introduction: Truth Definition and Semantics

§18 Tarski's form for Truth Definitions and Compositionality

We saw Tarski's form for Truth definitions:

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

And we took an example:

"Brussels is in Belgium" is true (in English) if and only if Brussels is in Belgium.

To be adequate, we would need one such truth definition for every possible sentence in our object language. But there are infinitely many sentences we can make in any natural language. So it is impossible to give a complete list. We may solve this by means of making recursive definitions. In this way, the meaning of the whole is built-up from the meaning of all its parts. We call this the Fregean principle of compositionality. This principle is central to Montague's model theoretic semantics.

We see that for Tarski, truth and meaning are closely interrelated. Still, we cannot so far see from Tarksi's theory how we might regard a truth definition's reference.

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