Single Idea 13896

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism]

Full Idea

We shall endeavour to see whether it is possible to follow through the strategy adumbrated in 'Grundlagen' for establishing the Peano Axioms without at any stage invoking classes.

Gist of Idea

The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes

Source

Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi)

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.131


A Reaction

The key idea of neo-logicism. If you can avoid classes entirely, then set theory paradoxes become irrelevant, and classes aren't logic. Philosophers now try to derive the Peano Axioms from all sorts of things. Wright admits infinity is a problem.

Related Idea

Idea 13899 The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]