Vergauwen, A Metalogical Theory of Reference, Introduction, §17

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Logic & Semantics, Entry Directory]
[Vergauwen's Metalogical Theory of Reference, Entry Directory]

[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

§17 Tarski's Truth Definition and Adequacy

Previously we noted that Tarski's truth definition can be formalized and generalized as:

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

We are using "if and only if." Hence this is a "material equivalence." It has two parts.

1) The left side is the definiendum. It contains the name 'X.'

2) This name 'X' stands for a sentence in the object language, which we name L; and 'p' is a translation of this sentence 'X' in some given metalanguage.

We will later see that we must clearly differentiate the metalanguage from the object language.

Now suppose that we take every true sentence in our object language L. Then suppose we link each of these true sentences to a translation 'p' in the metalanguage. Further assume that we link the true L sentences with 'p' translations according to Tarski's above formulation:

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

If all the above conditions are met, then our truth definition is adequate.

Tarski is concerned mainly with formal languages. Hence we may use axiomatic logic to construct our truth definitions.

We will give an example of

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

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

We see that both the object and metalanguage are in English. Later we will see the problems with this. But we could easily solve that by rendering one in another language such as French or Russian.

[Other Entries in this Series]

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