Combining Philosophers

All the ideas for Anaxarchus, George Boolos and Michael Williams

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66 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 / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
18192 Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
7785 The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13547 Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10699 Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
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 / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10225 Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
10736 Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
10780 Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13671 Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806 Boolos invented plural quantification [Boolos, by Benardete,JA]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
10700 First- and second-order quantifiers are two ways of referring to the same things [Boolos]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
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]
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8693 An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos]
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]