26 Feb 2009

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

[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.




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

No comments:

Post a Comment