Single Idea 15369

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

The nonconservativeness of set theory over first-order arithmetic has done much to establish set theory as a substantial theory indeed.

Clarification

'Nonconservative' means it enables new proofs

Gist of Idea

Set theory is substantial over first-order arithmetic, because it enables new proofs

Source

Leon Horsten (The Tarskian Turn [2011], 07.5)

Book Reference

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.93


A Reaction

Horsten goes on to point out the price paid, which is the whole new ontology which has to be added to the arithmetic. Who cares? It's all fictions anyway!