Combining Philosophers

All the ideas for Euclid, John Haldane and Joseph Butler

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20 ideas

2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9603 An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
9894 A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
22278 Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
8673 Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
10250 Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
1600 Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
9. Objects / F. Identity among Objects / 5. Self-Identity
3144 Everything is what it is, and not another thing [Butler]
9. Objects / F. Identity among Objects / 9. Sameness
21315 A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
21317 Despite consciousness fluctuating, we are aware that it belongs to one person [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
21313 If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
21314 Consciousness presupposes personal identity, so it cannot constitute it [Butler]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
21318 If the self changes, we have no responsibilities, and no interest in past or future [Butler]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
8066 Butler exalts conscience, but it may be horribly misleading [Anscombe on Butler]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
22251 Liberalism may fail because it neglects the shared nature of what we pursue and protect [Haldane]