Combining Texts

All the ideas for 'works (fragments)', 'Philosophy of Mathematics' and 'Rationality and Virtue'

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13 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Possessing the virtue of justice disposes a person to good practical rationality [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Calling a knife or farmer or speech or root good does not involve attitudes or feelings [Foot]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
The essential thing is the 'needs' of plants and animals, and their operative parts [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Observing justice is necessary to humans, like hunting to wolves or dancing to bees [Foot]