Combining Philosophers

All the ideas for Crawford L. Elder, Peter Koellner and J Pollock / J Cruz

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33 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
8. Modes of Existence / B. Properties / 1. Nature of Properties
13795 Properties only have identity in the context of their contraries [Elder]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
13798 Maybe we should give up the statue [Elder]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
13797 The loss of an essential property means the end of an existence [Elder]
9. Objects / D. Essence of Objects / 9. Essence and Properties
13794 Essential properties by nature occur in clusters or packages [Elder]
13796 Essential properties are bound together, and would be lost together [Elder]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
6346 The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
6351 Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz]
6374 To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
6355 Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
6359 Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz]
12. Knowledge Sources / B. Perception / 1. Perception
6366 Perception causes beliefs in us, without inference or justification [Pollock/Cruz]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
6362 Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
6371 Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
6373 Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
6353 People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz]
6361 Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
6357 Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
6363 Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
6365 Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
6354 Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz]
6367 Coherence theories isolate justification from the world [Pollock/Cruz]
13. Knowledge Criteria / C. External Justification / 1. External Justification
6370 Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
6358 One belief may cause another, without being the basis for the second belief [Pollock/Cruz]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
6364 We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz]
14. Science / C. Induction / 1. Induction
6352 Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz]
14. Science / C. Induction / 6. Bayes's Theorem
6372 Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
6360 Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz]