Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Logicism Revisited' and 'Intuitionism'

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13 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism seems to exclude all creative, growing mathematics [Musgrave]
Formalism is a bulwark of logical positivism [Musgrave]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
If there are intuited moral facts, why should we care about them? [Dancy,J]
Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J]
Obviously judging an action as wrong gives us a reason not to do it [Dancy,J]
Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]