Vergauwen, A Metalogical Theory of Reference,1.2, §19

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 1.2 Primitive Reference and Satisfaction

§19 Tarski's Truth Definition and Predicates

Truth, for Tarski, is a metalanguage predicate over object language sentences. We should draw our truth definitions from a formal language L. For Tarski, a language contains a finite number of undefined or primitive predicates.

We will now consider a simple example language L. It contains two primitive predicates:

a) "is the moon" and

b) "is blue."

Now consider any predicate P and also consider the sentence

P refers to x.

In our truth-conditional semantics, we will take this sentence to mean

P is true of x.

Now suppose that P is the predicate "is the moon." We would then make the truth-conditional sentence:

"is the moon" refers to x if and only if x is the moon.

Or, perhaps P is the predicate "is blue." Hence

"is blue" refers to x if and only if x is blue.

Let's now place this in more general terms. We will speak of the simple language L along with its finite number of predicates:

P primitively refers to x if and only if

(a) P is the expression "is the moon" and x is the moon

(b) is the expression "is blue" and x is indeed blue.

We construct the non-primitive predicates using such things as truth functional connectors and quantifiers. We may define a primitive reference by giving a list such as the one above.

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