Predicative foundations of arithmetic
نویسندگان
چکیده
منابع مشابه
Predicative foundations of arithmetic
Predicative mathematics in the sense originating with Poincaré and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithm...
متن کاملChallenges to Predicative Foundations of Arithmetic
Introduction. This is a sequel to our article “Predicative foundations of arithmetic” (1995), referred to in the following as [PFA]; here we review and clarify what was accomplished in [PFA], present some improvements and extensions, and respond to several challenges. The classic challenge to a program of the sort exemplified by [PFA] was issued by Charles Parsons in a 1983 paper, subsequently ...
متن کاملA Note on Finiteness in the Predicative Foundations of Arithmetic
In a sequence of two papers, Solomon Feferman and Geoffrey Hellman ([FH95], [FH98]) introduced formal contexts in which they established the existence and categoricity of a natural number structure by predicative means given the primitive notion of a finite set of individuals and given also that these individuals have some structure as built up by ordered pairs (Peter Aczel had a crucial contri...
متن کاملPredicative fragments of Frege Arithmetic
Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity in...
متن کاملPredicative Logic and Formal Arithmetic
After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell’s Principia Mathematica with the axiom of infinity but without the axiom of reducibility. 1 Historical introduction After discovering the inconsistency in Frege’s Grundgesetze der Arithmetik, Russell proposed two changes: first, dropping the assumption that to every h...
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ژورنال
عنوان ژورنال: Journal of Philosophical Logic
سال: 1995
ISSN: 0022-3611,1573-0433
DOI: 10.1007/bf01052728