Combining Philosophers

All the ideas for Stilpo, Michael Williams and Brian Clegg

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55 ideas

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 / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
3599 Deduction shows entailments, not what to believe [Williams,M]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
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]
28. God / C. Attitudes to God / 5. Atheism
3029 Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius]