Combining Texts

All the ideas for 'Universals and Particulars', 'Elements of Geometry' and 'Explanation and Reference'

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19 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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
17505 Using proper names properly doesn't involve necessary and sufficient conditions [Putnam]
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 / D. Universals / 6. Platonic Forms / c. Self-predication
4442 Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]
9. Objects / D. Essence of Objects / 5. Essence as Kind
11908 Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam]
14. Science / B. Scientific Theories / 2. Aim of Science
17508 Science aims at truth, not at 'simplicity' [Putnam]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
17506 I now think reference by the tests of experts is a special case of being causally connected [Putnam]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
17507 Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam]
11904 Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P]