论文信息 - Iteration One More Time

Iteration One More Time

There are (at least) two reasons for investigating abstraction principles for set theory. The first concerns the technical feasibility of a neo-logicist foundation for all of mathematics. The second concerns the connection between the theory of Fregean extensions (as codified in various restrictions of Basic Law V) and the mathematical notion of set (as codified in various axiomatic set theories, such as ZFC).2 Neo-logicists argue that we can reproduce (the most important parts of) mathematics using abstraction principles. An abstraction principle is any second-order formula3 of the form: (∀P)(∀Q)[@(P) = @(Q) ↔ E(P, Q)]

Roy T. Cook

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