## Abstraction and set theory.(English)Zbl 1014.03014

Summary: The neo-Fregean program in the philosophy of mathematics seeks a foundation for a substantial part of mathematics in abstraction principles – for example, Hume’s Principle: The number of $$F$$s = the number of $$G$$s iff the $$F$$s and $$G$$s correspond one-one – which can be regarded as implicitly definitional of fundamental mathematical concepts – for example, cardinal number. This paper considers what kind of abstraction principle might serve as the basis for a neo-Fregean set theory. Following a brief review of the main difficulties confronting the most widely discussed proposal to date – replacing Frege’s inconsistent Basic Law V by Boolos’s New V which restricts concepts whose extensions obey the principle of extensionality to those which are small in the sense of being smaller than the universe – the paper canvasses an alternative way of implementing the limitation of size idea and explores the kind of restrictions which would be required for it to avoid collapse.

### MSC:

 03A05 Philosophical and critical aspects of logic and foundations 00A30 Philosophy of mathematics 03E99 Set theory
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### References:

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