Combining Texts

All the ideas for 'fragments/reports', 'Logicism Revisited' and 'Individuation'

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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]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Not all predicates can be properties - 'is non-self-exemplifying', for example [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Neither mere matter nor pure form can individuate a sphere, so it must be a combination [Lowe]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
If the flagpole causally explains the shadow, the shadow cannot explain the flagpole [Lowe]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Properties are facets of objects, only discussable separately by an act of abstraction [Lowe]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]