Combining Philosophers

All the ideas for Thrasymachus, Euclid and Andrew Dobson

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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]
24. Political Theory / C. Ruling a State / 4. Changing the State / b. Devolution
23429 The environment needs localised politics, with its care for the land [Dobson]
24. Political Theory / D. Ideologies / 1. Ideology
23424 An ideology judges things now, and offers an ideal, with a strategy for reaching it [Dobson]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
23426 Ecologism is often non-liberal, by claiming to know other people's best interests [Dobson]
24. Political Theory / D. Ideologies / 8. Socialism
23427 Socialism can be productive and centralised, or less productive and decentralised [Dobson]
24. Political Theory / D. Ideologies / 12. Feminism
23428 Difference feminists say women differ fundamentally from men [Dobson]
24. Political Theory / D. Ideologies / 13. Green Politics
23430 A million years is a proper unit of political time [Dobson]
23425 Ecologism says growth must be reduced, and efficiency is not enough [Dobson]
23422 For the environment, affluence and technology matter as much as population size [Dobson]
23423 We currently value the present fourteen times more highly than the future [Dobson]
28. God / C. Attitudes to God / 3. Deism
1558 Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]