Combining Texts

All the ideas for 'Philosophy of Mathematics', 'fragments/reports' and 'fragments/reports'

expand these ideas     |    start again     |     specify just one area for these texts


6 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero]