Combining Philosophers

All the ideas for Roderick Firth, Alan Musgrave and Peter Unger

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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
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
Logical truths may contain non-logical notions, as in 'all men are men' [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 is a bulwark of logical positivism [Musgrave]
Formalism seems to exclude all creative, growing mathematics [Musgrave]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Vague predicates lack application; there are no borderline cases; vague F is not F [Unger, by Keefe/Smith]
9. Objects / A. Existence of Objects / 5. Simples
There are no objects with proper parts; there are only mereological simples [Unger, by Wasserman]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
We are not conscious of pure liquidity, but of the liquidity of water [Firth]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
The meaning of 'know' does not change from courtroom to living room [Unger]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
No one knows anything, and no one is ever justified or reasonable [Unger]
13. Knowledge Criteria / D. Scepticism / 4. Demon Scepticism
An evil scientist may give you a momentary life, with totally false memories [Unger]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]