Combining Philosophers

All the ideas for Euclid, Kretzmann/Stump and W Wimsatt/W Beardsley

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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]
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]
14. Science / A. Basis of Science / 2. Demonstration
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
20400 Intentions either succeed or fail, so external evidence for them is always irrelevant [Wimsatt/Beardsley, by Davies,S]
7266 The author's intentions are irrelevant to the judgement of a work's success [Wimsatt/Beardsley]
7268 The thoughts of a poem should be imputed to the dramatic speaker, and hardly at all to the poet [Wimsatt/Beardsley]
7267 Poetry, unlike messages, can be successful without communicating intentions [Wimsatt/Beardsley]
7269 The intentional fallacy is a romantic one [Wimsatt/Beardsley]
7271 Biography can reveal meanings and dramatic character, as well as possible intentions [Wimsatt/Beardsley]