Combining Texts

All the ideas for 'fragments/reports', 'Elements of Geometry' and 'Externalist Theories of Empirical Knowledge'

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20 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]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / e. The Lottery paradox
4261 The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
4255 Externalist theories of knowledge are one species of foundationalism [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
4257 The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
4256 The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour]
13. Knowledge Criteria / C. External Justification / 1. External Justification
4258 Extreme externalism says no more justification is required than the truth of the belief [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
4259 External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
4260 Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5996 Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]