Combining Texts

All the ideas for 'fragments/reports', 'Logicism Revisited' and 'The Nature of Existence vol.2'

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19 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 / B. Change in Existence / 1. Nature of Change
How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
Change is not just having two different qualities at different points in some series [McTaggart]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]