Combining Texts

All the ideas for 'Elements of Geometry', 'What is Art?' and 'Truth'

expand these ideas     |    start again     |     specify just one area for these texts

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]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
14965 Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
3. Truth / F. Semantic Truth / 2. Semantic Truth
14968 A weakened classical language can contain its own truth predicate [Gupta]
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 / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
14964 The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
14969 Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
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]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
8122 True works of art transmit completely new feelings [Tolstoy]
8121 Art is when one man uses external signs to hand on his feelings to another man [Tolstoy]
8124 The highest feelings of mankind can only be transmitted by art [Tolstoy]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
8123 The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
22710 People estimate art according to their moral values [Tolstoy]
8125 The upper classes put beauty first, and thus freed themselves from morality [Tolstoy]
8064 We separate the concept of beauty from goodness, unlike the ancients [Tolstoy]