Combining Philosophers

All the ideas for Richard Cumberland, Euclid and Sarah Bakewell

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20 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
21238 Later phenomenologists tried hard to incorporate social relationships [Bakewell]
21237 Phenomenology begins from the immediate, rather than from axioms and theories [Bakewell]
2. Reason / A. Nature of Reason / 7. Status of Reason
6222 If a decision is in accord with right reason, everyone can agree with it [Cumberland]
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 / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
6217 Natural law is supplied to the human mind by reality and human nature [Cumberland]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
6221 If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
6218 The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland]
6220 The happiness of all contains the happiness of each, and promotes it [Cumberland]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
6216 Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]