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Switch to: References
Citations of:
Banishing the rule of substitution for functional variables
Journal of Symbolic Logic 18 (3):201-208 (1953)
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This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first (...) |
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The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few rudimentary facts (...) |
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This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak K\"onig's (...) |
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Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his articles with (...) |
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By the standards presented in the Introduction, CMFC2 is deficient on at least one ontological ground: ‘∀’ is a syncategorematic expression and so CMFC2 is not an ideal language. To some there may be an additional difficulty: any two wffs provably equivalent in the classical sense are provably identical. We hope in sequel to present systems free of these difficulties, free either of one or the other, or perhaps both.This work was done with the aid of Canada Council Grant S74-0551-S1. |
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