Combining Philosophers

All the ideas for Hesiod, Hastings Rashdall and Alan Musgrave

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14 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]
16. Persons / B. Nature of the Self / 2. Ethical Self
Morality requires a minimum commitment to the self [Rashdall]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
All moral judgements ultimately concern the value of ends [Rashdall]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
23. Ethics / E. Utilitarianism / 6. Ideal Utilitarianism
Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall]
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall]
Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG]