Combining Philosophers

All the ideas for Euclid, Gonzalo Rodriguez-Pereyra and Mirabeau and committee

expand these ideas     |    start again     |     specify just one area for these philosophers

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]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
18435 Resemblance Nominalists say that resemblance explains properties (not the other way round) [Rodriquez-Pereyra]
18436 Entities are truthmakers for their resemblances, so no extra entities or 'resemblances' are needed [Rodriquez-Pereyra]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
19855 The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
19856 The law expresses the general will, and all citizens can participate [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 3. Constitutions
19861 There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee]
25. Social Practice / A. Freedoms / 2. Freedom of belief
19858 No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee]
25. Social Practice / A. Freedoms / 3. Free speech
19859 Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee]
25. Social Practice / B. Equalities / 2. Political equality
19857 All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee]
25. Social Practice / C. Rights / 4. Property rights
19862 Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee]
25. Social Practice / E. Policies / 4. Taxation
19860 Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee]