Combining Philosophers

All the ideas for Augustin-Louis Cauchy, George Boolos and Robert Merrihew Adams

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46 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 / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18085 Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18084 When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14508 A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM]
14511 There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM]
16463 Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker]
9. Objects / D. Essence of Objects / 9. Essence and Properties
12031 Essences are taken to be qualitative properties [Adams,RM]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12034 If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM]
14510 Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM]
16455 Black's two globes might be one globe in highly curved space [Adams,RM]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14507 Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
11964 Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
16451 Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker]
11901 Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P]
14512 Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM]
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 / B. Reference / 3. Direct Reference / a. Direct reference
12032 Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM]