Combining Philosophers

All the ideas for Euclid, Hamid Vahid and Leopold Kronecker

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23 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 / 1. Mathematics
12427 All of mathematics is properties of the whole numbers [Kronecker]
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 / c. Priority of numbers
10091 God made the integers, all the rest is the work of man [Kronecker]
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]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
19712 Maybe there is plain 'animal' knowledge, and clearly justified 'reflective' knowledge [Vahid]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
19703 Epistemic is normally marked out from moral or pragmatic justifications by its truth-goal [Vahid]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19705 'Mentalist' internalism seems to miss the main point, if it might not involve an agent's access [Vahid]
19706 Strong access internalism needs actual awareness; weak versions need possibility of access [Vahid]
19707 Maybe we need access to our justification, and also to know why it justifies [Vahid]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
19709 Internalism in epistemology over-emphasises deliberation about beliefs [Vahid]
13. Knowledge Criteria / C. External Justification / 1. External Justification
19704 Externalism may imply that identical mental states might go with different justifications [Vahid]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
19710 With a counterfactual account of the causal theory, we get knowledge as tracking or sensitive to truth [Vahid]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
19711 Externalism makes the acquisition of knowledge too easy? [Vahid]