Combining Philosophers

All the ideas for Euclid, 3rd Earl of Shaftesbury and Ernest Nagel

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21 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]
7. Existence / C. Structure of Existence / 2. Reduction
3425 Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
18545 The disinterested attitude of the judge is the hallmark of a judgement of beauty [Shaftesbury, by Scruton]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6237 Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
6234 If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6233 A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
6236 People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury]
23. Ethics / A. Egoism / 1. Ethical Egoism
6235 Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
6232 Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
5642 For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton]