Combining Texts

All the ideas for 'The Theory of Logical Types', 'Outline of a System of Utilitarianism' and 'Truth'

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11 ideas

3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
3. Truth / F. Semantic Truth / 2. Semantic Truth
A weakened classical language can contain its own truth predicate [Gupta]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Negative utilitarianism implies that the world should be destroyed, to avoid future misery [Smart]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
Any group interested in ethics must surely have a sentiment of generalised benevolence [Smart]