Five observations concerning the intended meaning of the intuitionistic logical constants

Journal of Philosophical Logic 29 (4):409-424 (2000)
This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of 'proof'; (2) Kreisel's explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of → can be easily and safely ameliorated; (4) the definition of → in terms of 'proofs from premises' results in a loss of the inductive character of the definitions of ∨ and ∃; and (5) the same occurs with the definition of ∀ in terms of 'proofs with free variables'
Keywords intuitionistic semantics  logical constant  construction  proof  intended meaning
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DOI 10.1023/A:1004881914911
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A. S. Troelstra (1988). Constructivism in Mathematics: An Introduction. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..

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