Combining Texts

All the ideas for 'works', 'Philosophy of Mathematics' and 'Letters to Frege'

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


9 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]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
If parallelism is true, how does the mind know about the body? [Crease]
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]