Single Idea 21648

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

Full Idea

A major flaw of the neo-Fregean program is that it is more impressed by the technical result that Peano Arithmetic can be interpreted by second-order logic plus Hume's Principle, than empirical considerations about how numbers come about.

Gist of Idea

Neo-Fregeans are dazzled by a technical result, and ignore practicalities


Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3)

Book Reference

Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.159

A Reaction

This doesn't sound like a problem that would bother Fregeans or neo-Fregeans much. Deriving the Peano Axioms from various beginnings has become a parlour game for modern philosophers of mathematics.