โ Scribed by Neil Tennant
No coin nor oath required. For personal study only.
In his paper 'The Philosophical Basis of Intuitionistic Logic 'l, Dummett argues towards a justification of intuitionistic logic from a broad Wittgensteinian thesis about meaning: that every aspect of meaning must be such that one's grasp thereof is capable of being manifested eventually and implicitly in observable behaviour. His argument is intricate; it would take us too far afield here even to sketch its general route. 2 I am concerned rather with charting a different passage from the broad thesis just stated to the claim that it is intuitionistic logic which correctly reflects graspable meanings of the logical operators.
This new route takes as its point of departure the game theoretic semantics for first order languages which has recently been made better known by Hintikka in exegetical application to what Wittgenstein said about language games. 3 I shall first try to improve upon Hintikka's explanation of the (classical) language game for first order interpreted languages; then examine his claim that these serve a Wittgensteinian purpose in capturing or conveying the forces of the logical operators; and finally describe a modified game which, given the broad nieaning thesis above, serves this purpose better and confers Upon the logical operators intuitionistic rather than classical meanings. II 1 shall call the whole, consisting of language and the actions into which it is woven, the 'language game'. (para. 7) Our clear and simple language games are not preparatory studies for a future regularization of l a n g u a g e -a s it were first approximations, ignoring friction and air-resistance. The language games are rather set up as objects of comparison which are meant to throw light on the facts of our language by way not only of similarities but also of dis-similarities (para. 150) (Wittgenstein: Philosophical Investigations, Part I)
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