Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Logicism Revisited' and 'On the Reality of Accidents'

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11 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic guides thinking, but it isn't a substitute for it [Rumfitt]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
The If-thenist view only seems to work for the axiomatised portions of mathematics [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]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
Abstracta are abbreviated ways of talking; there are just substances, and truths about them [Leibniz]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]