Combining Philosophers

All the ideas for Euclid, Michael Williams and Henry E. Kyburg Jr

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47 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 / C. Correspondence Truth / 3. Correspondence Truth critique
3593 The only way to specify the corresponding fact is asserting the sentence [Williams,M]
3. Truth / D. Coherence Truth / 1. Coherence Truth
3585 Coherence needs positive links, not just absence of conflict [Williams,M]
3584 Justification needs coherence, while truth might be ideal coherence [Williams,M]
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 / A. Overview of Logic / 3. Value of Logic
3599 Deduction shows entailments, not what to believe [Williams,M]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / e. The Lottery paradox
6368 If my ticket won't win the lottery (and it won't), no other tickets will either [Kyburg, by Pollock/Cruz]
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 / a. Beliefs
3591 We could never pin down how many beliefs we have [Williams,M]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
3582 Propositions make error possible, so basic experiential knowledge is impossible [Williams,M]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
3592 Phenomenalism is a form of idealism [Williams,M]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
3579 Sense data avoid the danger of misrepresenting the world [Williams,M]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
3581 Sense data can't give us knowledge if they are non-propositional [Williams,M]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
3564 Is it people who are justified, or propositions? [Williams,M]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8851 Coherentists say that regress problems are assuming 'linear' justification [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
3595 What works always takes precedence over theories [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
8849 Traditional foundationalism is radically internalist [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
3580 Experience must be meaningful to act as foundations [Williams,M]
8853 Basic judgements are immune from error because they have no content [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
3578 Are empirical foundations judgements or experiences? [Williams,M]
8855 Sensory experience may be fixed, but it can still be misdescribed [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
3576 Foundationalists are torn between adequacy and security [Williams,M]
3577 Strong justification eliminates error, but also reduces our true beliefs [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
3589 Why should diverse parts of our knowledge be connected? [Williams,M]
3590 Coherence theory must give a foundational status to coherence itself [Williams,M]
13. Knowledge Criteria / C. External Justification / 1. External Justification
3571 Externalism does not require knowing that you know [Williams,M]
3574 Externalism ignores the social aspect of knowledge [Williams,M]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
3569 In the causal theory of knowledge the facts must cause the belief [Williams,M]
3567 How could there be causal relations to mathematical facts? [Williams,M]
3586 Only a belief can justify a belief [Williams,M]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
3573 Externalist reliability refers to a range of conventional conditions [Williams,M]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
3565 Sometimes I ought to distrust sources which are actually reliable [Williams,M]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
3566 We control our beliefs by virtue of how we enquire [Williams,M]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
8852 In the context of scepticism, externalism does not seem to be an option [Williams,M]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3594 Scepticism just reveals our limited ability to explain things [Williams,M]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
3575 Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M]
14. Science / A. Basis of Science / 1. Observation
3587 Seeing electrons in a cloud chamber requires theory [Williams,M]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
3588 Foundationalists base meaning in words, coherentists base it in sentences [Williams,M]