Abstract
Intuitionists and classical logicians use in common a large number of the “logical” axioms, even though they supposedly “mean different things” by the logical connectives and quantifiers — conquans for short. But Wittgenstein says “The meaning of a word is its use in the language”. We prove that in a definite sense the intuitionistic axioms do indeed characterize the “logical” conquans, both for the intuitionist and the classical logician.
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References
H. Enderton, A Mathematical Introduction to Logic, Academic Press, New York-London, 1972.
A. Margaris, First Order Mathematical Logic, Blaisdell, Waltham, Massachusetts, 1967.
E. Mendelson, Introduction to Mathematical Logic, van Nostrand, Princeton, New Jersey, 1964.
L. Wittgenstein, Philosophical Investigations, Basil Blackwell, Oxford, 1968.
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Harris, J.H. What's so logical about the “logical” axioms?. Stud Logica 41, 159–171 (1982). https://doi.org/10.1007/BF00370342
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DOI: https://doi.org/10.1007/BF00370342