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The purpose ol' this paper is to make clear the difference bet・ween Hey. ting, who was a represent・atiire scholar of the int,uitionist school and who first introduced the intuit・ionistic formal logic and arithmetic, and Gentzen, who was a representative schular of t・he Hilbertiait finiList school, by a close look at their const・ructive interpretatioris of logical connecl・ives. "'e show that although both Gentzen and }Ieyting proposed very sirnilaT' construci,ivc int・erpretations for logical connectives of intuitionistic: logic: uiathernatically, thcir interpretations were based on very. different standpoints philosophically. : Ceritzen used ttie logical positivisL way, of verification theory of meaning, while Heyting ernphasized the Husscrlian phenomenologica] way of verification theory of meaning. in addit,ion, we shal! poiut out that although both Heyting and Centzen einphasized similar forins of constructive interpretation for the intuitionistic mplication in terms of "proof-construction;7, the not・ieii of "proof" here was taken very differently, by, Gentzell and Heyting, resulLed in the diff'erent attitudes towards t,he intuitionistic log. ic.

Some Remarks on a Difference between Gentzen's Finitist and Heyting's Intuitionist Approaches toward Intuitionistic Logic and Arithmetic