25 Feb 2009

Vergauwen, A Metalogical Theory of Reference, Introduction, §7

[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

§7 Tarski, Kripke, Montague, Models, and Intensional Logic

Alfred Tarski was a 20th century Polish logician. He offered the first definition for truth in formal languages.

We first consider a language we want to study. We call it our 'object language.'

Then we try to establish the conditions under which sentences are true in the object language. We call this other language the "metalanguage."

But, this method does not explain the referential nature of formal languages.

The first chapter is concerned with Richard Montague's Model-theoretical or Possible Worlds semantics. Kripke further developed this field.

Model theoretical semantics looks at the circumstances that make a sentence true. These they consider to constitute the meaning of a sentence. Such theories try to understand how a sentence's truth is determined by the meanings of its smallest components: its words. They define meaning as intension. And they understand intension to be a function of possible worlds to extensions.

Frege first distinguished intension and extension, with his Sinn-Bedeutung distinction.

Models are abstract structures of entities. We use them to interpret a logical calculus.

Montague's model-theoretic semantics sets-up a semantic metalanguage for natural language. This metalanguage takes the form of a logical language. This logical language is an Intensional Logic. We translate natural language into this intensional logic. Then we use models to interpret the translated statements. These interpretations then are the representations of the sentence's meaning.

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

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