Combining Philosophers

All the ideas for Hippolytus, Euclid and John L. Pollock

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24 ideas

2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
3. Truth / A. Truth Problems / 1. Truth
8820 Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
8819 We need the concept of truth for defeasible reasoning [Pollock]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
8822 Statements about necessities need not be necessarily true [Pollock]
11. Knowledge Aims / A. Knowledge / 4. Belief / f. Animal beliefs
8818 Defeasible reasoning requires us to be able to think about our thoughts [Pollock]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
8811 What we want to know is - when is it all right to believe something? [Pollock]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
8817 Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8814 Epistemic norms are internalised procedural rules for reasoning [Pollock]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8823 Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8813 If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock]
13. Knowledge Criteria / C. External Justification / 1. External Justification
8812 Norm Externalism says norms must be internal, but their selection is partly external [Pollock]
8816 Externalists tend to take a third-person point of view of epistemology [Pollock]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
8815 Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock]