Combining Philosophers

All the ideas for Aenesidemus, Euclid and Hugo Grotius

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22 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]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
7404 Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
6040 There is no universal goal to human life [Aenesidemus, by Photius]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
7402 Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
21938 Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius]
25. Social Practice / A. Freedoms / 7. Freedom to leave
19845 A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
22133 Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD]
7406 A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
7403 Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck]
25. Social Practice / E. Policies / 1. War / b. Justice in war
23585 It is permissible in a just cause to capture a place in neutral territory [Grotius]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
6892 Moral principles have some validity without a God commanding obedience [Grotius, by Mautner]