Logic & Philosophy of Science Colloquium

Analytic Philosophy is replete with claims that "A's are just B's" or that "talk about A's is just talk about B's". Such claims are promissory notes drawn on the Bank of Logic and it would be a good plan to have a clear conception of what they amount to should anyone try to cash them in. The only nontrivial claim of this flavour of whose logical underpinnings it is possible to give a comprehensive account in under an hour is the claim that facts about cardinal numbers are just facts about sets. This I propose to do. A similar claim about ordinal arithmetic can be made and a thorough analysis of the underlying logic leads to an unravelling of the Burali-Forti paradox.