|Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 73 (1999), pp. 151-180|
|Paper - Abstract|
- Frege's logicism in the philosophy of arithmetic consisted, au fond, in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference.
- Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the arithmetic of the finite cardinals.
- 'In my Grundlagen der Arithmetik, I sought to make it plausible that arithmetic is a branch of logic, and need not borrow any ground of proof whatever from either experience or intuition. In the present book this shall now be confirmed, by the derivation of the simplest laws of cardinal number by logical means alone'.
- Thus Frege, at the outset of his Grundgesetze der Arithmetik.
- In my contribution to today's symposium, I wish to consider what he meant by the claim that arithmetic is a branch of logic, and to assess this claim's prospects of eventually being confirmed.
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2019
- Mauve: Text by correspondent(s) or other author(s); © the author(s)