Single Idea 9876

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

Full Idea

The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one.

Gist of Idea

Set theory isn't part of logic, and why reduce to something more complex?

Source

Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.224


A Reaction

Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental.