Combining Texts

All the ideas for 'fragments/reports', 'Substitutional Classes and Relations' and 'Remarks on axiomatised set theory'

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9 ideas

2. Reason / D. Definition / 7. Contextual Definition

21560

Any linguistic expression may lack meaning when taken out of context [Russell]

2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes

21561

'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879

Axiomatising set theory makes it all relative [Skolem]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

18130

Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

8. Modes of Existence / A. Relations / 1. Nature of Relations

21562

There is no complexity without relations, so no propositions, and no truth [Russell]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]