Combining Philosophers

Ideas for Richard Cumberland, Leon Horsten and Irenaeus

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15364

English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

10885

Computer proofs don't provide explanations [Horsten]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

10881

The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]

15360

ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]

15369

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

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

15370

Predicativism says mathematical definitions must not include the thing being defined [Horsten]