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By J (Ed.) Barwise

ISBN-10: 3540042423

ISBN-13: 9783540042426

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Tbe consequences of viewiDg quantifiers from a model-theoretical vantage point - and thc importancc of doing so - are illustrated further by the followiDg observation. In a game-theoretical approach, among the safest assumptions one can make in logic are equivalenccs one can set up between a sentencc and its higher-order translation. Tbe following is a case in point: (3) (VxX 3y)R(x. y] .. (3f)( Vx)R(x,f(x)] This equivalenee ought to be UDobjectionable for a constructivist. He or she would of course restrict the values of the function variable as the right-hand side of (3) to constructive functions (in some sense or other).

Those aspects that arguably are merely special cases of certain features of rational and even scientific methodology in general are unaffected by any criticisms. For instance, there is no need of interpreting truth as disclosedness as Heidegger does, but a certain (not necessarily vicious) circle can be argued to be present even in sober scientific inquiry, rightly understood. In other respects, too, my results have to be understood correctly. I am not saying that we should disregard the thoughts of those philosophers who have believed in the ineffability of semantical and conceptual matters or that they 18 LINGUA UNIVERSALlS VS.

Universal) must be ~ought of as involving a choice of IS TRUTH INEFFABLE? 31 individuals that may depend on earlier choices. " Moreover, the "cash value" (operational value) of a quantified proposition like (1) for a mathematician is precisely the possibility of such dependent choices. A Fregean believer in the universality of language and its logic must nevertheless look away from the idea of such choices as a mere misleading illustration of the true immutable relations between concepts, perhaps in the same spirit as Plato's criticism of all the talk of "constructions" in geometry.

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The Syntax and Semantics of Infinitary Languages by J (Ed.) Barwise


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