Combining Texts

All the ideas for 'works', 'Essays on Intellectual Powers 3: Memory' and 'Principles of Arithmetic, by a new method'

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23 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
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]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]