By Richard Montague
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Extra info for Formal Philosophy: Selected Papers
That is, Ext^C^-f P(a)-K) is linked by a semantic rule to Int^(T(a)'). It is a remarkable feature of Frege's work that it 39 INTRODUCTION can be incorporated so readily into a model theoretic account of intensional phenomena. Since extension and intension are interdefinable, we can choose to define either notion recursively. To do this for intensions, we first stipulate the following assignment of semantic types to the syntactic categories of 9l 4 . (C-5) Syntactic category IC IV IC 2C FOR Semantic type
Indeed, the aim of the program is to produce a mathematically elegant semiotic theory of natural language, and in view of examples of influence such as this it would be unwise to allow any phase of the theory to develop in isolation. The methodology of the program, then, should consist in developing stronger and stronger fragments of the language under study, each fragment being furnished with a syntax and a semantic and pragmatic interpretation. Under no circumstances should syntactic research proceed far in advance of such interpretation, since there is great risk that the results of such research might have to be discarded because of semantic inadequacies.
We can legitimately expect any semantic theory to provide answers to these questions. 45 'Walk' and 'run', for instance, and 'unicorn' and 'zebra' certainly do differ in meaning, and we require a dictionary of English to tell us how. But the making of a dictionary demands considerable knowledge of the world. The task of explaining the particular meanings of various basic expressions will obviously presuppose, if not factual information, at least a minutely detailed terminology for classifying things of all kinds.