Combining Philosophers

All the ideas for Aeschylus, Euclid and Jeremy Bentham

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25 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]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
5901 Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
5271 Prejudice apart, push-pin has equal value with music and poetry [Bentham]
5934 Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
3777 Pleasure and pain control all human desires and duties [Bentham]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
3554 Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham]
3781 The value of pleasures and pains is their force [Bentham]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
20977 Natural rights are nonsense, and unspecified natural rights is nonsense on stilts [Bentham]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
3778 The community's interest is a sum of individual interests [Bentham]
25. Social Practice / C. Rights / 1. Basis of Rights
21003 Only laws can produce real rights; rights from 'law of nature' are imaginary [Bentham]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
7810 The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling]
25. Social Practice / F. Life Issues / 6. Animal Rights
20280 Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham]
26. Natural Theory / A. Speculations on Nature / 1. Nature
3779 Unnatural, when it means anything, means infrequent [Bentham]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
3780 We must judge a thing morally to know if it conforms to God's will [Bentham]