Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'Free Will Defence' and 'Logicism Revisited'

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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]
9. Objects / D. Essence of Objects / 4. Essence as Definition
Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
19. Language / B. Reference / 1. Reference theories
Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
Moral evil may be acceptable to God because it allows free will (even though we don't see why this is necessary) [Plantinga, by PG]
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
It is logically possible that natural evil like earthquakes is caused by Satan [Plantinga, by PG]