25 Feb 2009

Vergauwen, A Metalogical Theory of Reference, Introduction, §9

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

Roger Vergauwen

A Metalogical Theory of Reference: Realism and Essentialism in Semantics

Introduction: the Temperature of a Hot Topic

§9 Putnam's Anti-Realist Critique of Model-Theoretic Semantics

This text's second chapter will discuss Putnam's critique of realism.

One important result of model-theoretic semantics has been the Löwenheim-Skolem Theorem. From this we derived the concept of a non-standard (or non-intended) model for a theory. Putnam uses this theorem to demonstrate that we cannot supply a unique standard model for our model-theoretic semantics. He shows that there cannot be a unique satisfaction relation between the theory and the world. If Putnam is correct, then we would not be able to use an interpretation of the semantic metalanguage (the intensional logic) to unambiguously determine the reference relation with external reality. Putnam argues instead that only use can determine this relation. He calls it 'internal realism'. For, both language and reality are considered to be internal to us.

But we will find that neither Putnam's critique nor his alternative solution holds.
He points out that it is impossible to select one model to represent the real relation between language and the world.
His alternate view depends on a difference between two views of logic and language.
1) One view sees logic as a specific instance of the universal medium of language, and
2) the other view sees language as merely an uninterpreted logical calculus.

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

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