Combining Texts

All the ideas for 'Introduction to Russell's Theory of Types', 'Philosophy of Mathematics' and 'Scientific Thought'

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10 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
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 / E. Objects over Time / 4. Four-Dimensionalism
A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad]
If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
The present and past exist, but the future does not [Broad, by Dummett]
We could say present and past exist, but not future, so that each event adds to the total history [Broad]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
We imagine the present as a spotlight, moving across events from past to future [Broad]