Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Letters to Frege' and 'Morality as system of hypothetical imperatives'

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13 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]
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism
Morality is inescapable, in descriptive words such as 'dishonest', 'unjust' and 'uncharitable' [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Reason is not a motivator of morality [Foot, by Hacker-Wright]
Rejecting moral rules may be villainous, but it isn't inconsistent [Foot]
23. Ethics / D. Deontological Ethics / 1. Deontology
Saying we 'ought to be moral' makes no sense, unless it relates to some other system [Foot]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
Morality no more consists of categorical imperatives than etiquette does [Foot]