Validity and quantification in intuitionism

Harrie de Swart; C.J. Posy

doi:10.1007/BF00253915

Validity and quantification in intuitionism

Harrie de Swart, C.J. Posy

Department of Philosophy

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Abstract

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

Original language	English
Pages (from-to)	117-126
Journal	Journal of philosophical logic
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF00253915
Publication status	Published - 1981

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abstract = "We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.",

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AB - We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

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JO - Journal of philosophical logic

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Validity and quantification in intuitionism

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