### Single Idea 16345

#### [catalogued under 7. Existence / C. Structure of Existence / 2. Reduction]

Full Idea

The observation that Peano arithmetic is relatively interpretable in ZF set theory is taken by many philosophers to be a reduction of numbers to sets.

Gist of Idea

That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction

Source

Volker Halbach (Axiomatic Theories of Truth [2011], 23)

Book Reference

Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.330

A Reaction

Nice! Being able to express something in a different language is not the same as a reduction. Back to the drawing board. What do you really mean by a reduction? If we model something, we don't 'reduce' it to the model.