Combining Texts

All the ideas for 'Academica', 'Elements of Geometry' and 'Internalism Exposed'

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

24 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
2661 Dialectic is speech cast in the form of logical argument [Cicero]
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
2673 There cannot be more than one truth [Cicero]
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 / D. Assumptions for Logic / 2. Excluded Middle
2669 Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero]
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]
12. Knowledge Sources / B. Perception / 1. Perception
2664 If we have complete healthy senses, what more could the gods give us? [Cicero]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
2665 How can there be a memory of what is false? [Cicero]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
6871 We can't only believe things if we are currently conscious of their justification - there are too many [Goldman]
6872 Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman]
6874 Internal justification needs both mental stability and time to compute coherence [Goldman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
6873 Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6875 Reliability involves truth, and truth is external [Goldman]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
20800 Every true presentation can have a false one of the same quality [Cicero]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
2672 Virtues must be very detached, to avoid being motivated by pleasure [Cicero]