Combining Philosophers

All the ideas for Wilson,G/Schpall,S, Stilpo and George Boolos

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47 ideas

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 / 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]
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]
20. Action / A. Definition of Action / 1. Action Theory
20014 Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall]
20. Action / A. Definition of Action / 4. Action as Movement
20019 Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall]
20021 Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
20022 To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall]
20023 If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall]
20025 We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
20031 On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / d. Group intentions
20028 Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall]
20027 If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall]
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
20016 Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall]
20017 Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall]
20018 Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
20012 Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
20029 Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall]
20013 It is generally assumed that reason explanations are causal [Wilson/Schpall]
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]