Combining Texts

All the ideas for 'Philosophy of Mathematics', 'The Source of Necessity' and 'thirty titles (lost)'

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


11 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 / B. Unity of Objects / 2. Substance / c. Types of substance
Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Explanation of necessity must rest on something necessary or something contingent [Hale]
Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Concept-identities explain how we know necessities, not why they are necessary [Hale]
28. God / C. Attitudes to God / 5. Atheism
Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]