Combining Texts

All the ideas for 'fragments/reports', 'Defending the Axioms' and 'Essays on Intellectual Powers 3: Memory'

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24 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
9. Objects / E. Objects over Time / 1. Objects over Time
1350 Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid]
9. Objects / E. Objects over Time / 13. No Identity over Time
21322 We treat slowly changing things as identical for the sake of economy in language [Reid]
9. Objects / F. Identity among Objects / 1. Concept of Identity
21320 Identity is familiar to common sense, but very hard to define [Reid]
1367 Identity can only be affirmed of things which have a continued existence [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
23644 Without memory we could have no concept of duration [Reid]
23643 We all trust our distinct memories (but not our distinct imaginings) [Reid]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
1356 A person is a unity, and doesn't come in degrees [Reid]
16. Persons / A. Concept of a Person / 2. Persons as Responsible
1359 Personal identity is the basis of all rights, obligations and responsibility [Reid]
16. Persons / A. Concept of a Person / 3. Persons as Reasoners
21319 I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
21323 The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
21321 Memory reveals my past identity - but so does testimony of other witnesses [Reid]
21324 If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid]
21325 Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid]
21327 If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid]
1366 If consciousness is personal identity, it is continually changing [Reid]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
1352 Thoughts change continually, but the self doesn't [Reid]
28. God / A. Divine Nature / 1. God
6011 There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara]