Combining Texts

All the ideas for 'Three Varieties of Knowledge', 'The Artworld' and 'Elements of Geometry'

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20 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
8868 Objective truth arises from interpersonal communication [Davidson]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
8867 A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
10347 Objectivity is intersubjectivity [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
8866 If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
10346 Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett]
19. Language / F. Communication / 4. Private Language
8870 Content of thought is established through communication, so knowledge needs other minds [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
8869 The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
20328 A thing is only seen as art in an 'artworld', which has a theory and a history [Danto]