An Introduction to the Philosophy of Time and Space by Bas C. Van Fraassen

By Bas C. Van Fraassen

An introductory, old survey of philosophical positions on area and time, during the detailed thought of relativity and the causal thought of time.

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In order to bring out the apparent analogy between a programmatic interpretation for a non-classical logic and an in­ terpretation in classical two-valued semantics, we considered the stipu­ lations governing the classical logical constants as being framed in a similar straightforward manner. Such stipulations of course give an impression of being totally unexplanatory: an understanding of the stipulation governing a logical constant of the object-language de­ pends upon knowing the meaning of the corresponding logical con­ stant in the metalanguage.

In order to see the answer to this, we have to look more closely at the non-classical case. The standard two-valued semantics is so firmly entrenched for classical logic that it is unnecessary to qualify any prop­ osition concerning the completeness of a fragment of classical logic: if it be said, of any such fragment, that it is complete or incomplete, we know with respect to what notion of validity the assertion is meant, since it is taken for granted that the two-valued semantics is the in­ tended one.

The only answer we can give is 'a proposition'. But this answer is quite unspecific; in this context it means only 'whatever is to be taken as being the semantic value of a sentence in an intuitionistic language'. And it is precisely this lack of any specific notion of what the semantic value of a sentence is to be that shows that the notion of an internal interpretation is not a genuinely semantic one at all. The replacement of the word 'set' by the word 'species' was not a mere shift in favoured terminology.

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