Combining Philosophers

All the ideas for Euclid, Jeremiah and Bernecker / Dretske

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25 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]
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 / 1. Knowledge
3756 Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske]
12. Knowledge Sources / B. Perception / 7. Causal Perception
3757 Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
3759 You can acquire new knowledge by exploring memories [Bernecker/Dretske]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
3752 Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3753 Foundationalism aims to avoid an infinite regress [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
3754 Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske]
13. Knowledge Criteria / C. External Justification / 1. External Justification
3755 Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3761 Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
3760 Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske]
18. Thought / C. Content / 6. Broad Content
3758 Semantic externalism ties content to the world, reducing error [Bernecker/Dretske]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
7346 Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P]
28. God / A. Divine Nature / 3. Divine Perfections
22920 Do I not fill heaven and earth? saith the Lord [Jeremiah]
28. God / C. Attitudes to God / 3. Deism
22089 Am I a God afar off, and not a God close at hand? [Jeremiah]