Combining Texts

All the ideas for 'Logicism Revisited', 'On the Source of Necessity' and 'Letters to Lelong'

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12 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron]
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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Force in substance makes state follow state, and ensures the very existence of substance [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron]