Single Idea 23441

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

Full Idea

Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone.

Gist of Idea

Logical truth is true in all models, so mathematical objects can't be purely logical

Source

Øystein Linnebo (Philosophy of Mathematics [2017], 2)

Book Reference

Linnebo,Øystein: 'Philosophy of Mathematics' [Princeton 2017], p.21


A Reaction

Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that).