display all the ideas for this combination of philosophers
2 ideas
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
Full Idea: Various authors have argued that identity statements arising in the context of the 'Julius Caesar' problem in philosophy of mathematics constitute category mistakes. | |
From: Ofra Magidor (Category Mistakes [2013], 1.1 n1) | |
A reaction: [She cites Benacerraf 1965 and Shapiro 1997:79] |