Journal of Philosophical Logic 24 (1):1 - 17 (1995)
|Abstract||Predicative mathematics in the sense originating with Poincar´ e 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 arithmetic itself.1 It is the main purpose of this paper to show that this appearance is illusory: as will emerge, a predicatively acceptable axiomatization of the natural number system can be formulated, and both the existence of structures of the relevant type and the categoricity of the relevant axioms can be proved in a predicatively acceptable way.|
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