Combining Texts

All the ideas for 'works', 'Representative Government' and 'Elements of Geometry'

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21 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
6806 Do not multiply entities beyond necessity [William of Ockham]
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
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
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]
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 / D. Universals / 5. Universals as Concepts
22132 Species and genera are individual concepts which naturally signify many individuals [William of Ockham]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
20508 How people vote should be on public record, so they can be held accountable [Mill, by Wolff,J]
20507 Voting is a strict duty, like jury service, and must only be aimed at the public good [Mill]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
20505 Direct democracy is inexperience judging experience, and ignorance judging knowledge [Mill]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
20504 People can only participate in decisions in small communities, so representatives are needed [Mill]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
19381 The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
8010 William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham]
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
16679 Even an angel must have some location [William of Ockham, by Pasnau]