Combining Philosophers

All the ideas for Brad W. Hooker, Jrgen Habermas and A.George / D.J.Velleman

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60 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
20962 Habermas seems to make philosophy more democratic [Habermas, by Bowie]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
15670 The aim of 'post-metaphysical' philosophy is to interpret the sciences [Habermas, by Finlayson]
1. Philosophy / H. Continental Philosophy / 5. Critical Theory
15665 We can do social philosophy by studying coordinated action through language use [Habermas, by Finlayson]
2. Reason / A. Nature of Reason / 4. Aims of Reason
20573 Rather than instrumental reason, Habermas emphasises its communicative role [Habermas, by Oksala]
2. Reason / D. Definition / 7. Contextual Definition
9955 Contextual definitions replace a complete sentence containing the expression [George/Velleman]
2. Reason / D. Definition / 8. Impredicative Definition
10031 Impredicative definitions quantify over the thing being defined [George/Velleman]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10098 The 'power set' of A is all the subsets of A [George/Velleman]
10099 The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman]
10101 Cartesian Product A x B: the set of all ordered pairs in which a∈A and b∈B [George/Velleman]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
10103 Grouping by property is common in mathematics, usually using equivalence [George/Velleman]
10104 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10096 Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10097 Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10100 Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
17900 The Axiom of Reducibility made impredicative definitions possible [George/Velleman]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
10109 ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10108 As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
10111 Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10129 A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10105 Differences between isomorphic structures seem unimportant [George/Velleman]
5. Theory of Logic / K. Features of Logics / 2. Consistency
10119 Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
10126 A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]
5. Theory of Logic / K. Features of Logics / 3. Soundness
10120 Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10127 A 'complete' theory contains either any sentence or its negation [George/Velleman]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
10106 Rational numbers give answers to division problems with integers [George/Velleman]
10102 The integers are answers to subtraction problems involving natural numbers [George/Velleman]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10107 Real numbers provide answers to square root problems [George/Velleman]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
9946 Logicists say mathematics is applicable because it is totally general [George/Velleman]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
10125 The classical mathematician believes the real numbers form an actual set [George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
17899 Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10128 The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17902 A successor is the union of a set with its singleton [George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10133 Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10130 Set theory can prove the Peano Postulates [George/Velleman]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
10089 Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10131 If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10092 In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman]
10094 The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman]
10095 Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman]
17901 Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
10114 Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman]
10134 Much infinite mathematics can still be justified finitely [George/Velleman]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
10123 The intuitionists are the idealists of mathematics [George/Velleman]
10124 Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
20961 What is considered a priori changes as language changes [Habermas, by Bowie]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
10110 Corresponding to every concept there is a class (some of them sets) [George/Velleman]
19. Language / A. Nature of Meaning / 1. Meaning
15667 To understand a statement is to know what would make it acceptable [Habermas]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
15668 Meaning is not fixed by a relation to the external world, but a relation to other speakers [Habermas, by Finlayson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
15666 To understand language is to know how to use it to reach shared understandings [Habermas]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
15677 Moral right is linked to validity and truth, so morality is a matter of knowledge, not an expression of values [Habermas, by Finlayson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
2854 Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
15672 Actions norms are only valid if everyone possibly affected is involved in the discourse [Habermas]
23. Ethics / B. Contract Ethics / 2. Golden Rule
2856 Universal moral judgements imply the Golden Rule ('do as you would be done by') [Hooker,B]
23. Ethics / B. Contract Ethics / 9. Contractualism
15671 Move from individual willing of a general law, to willing norms agreed with other people [Habermas]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
20883 Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
20884 Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
15669 People endorse equality, universality and inclusiveness, just by their communicative practices [Habermas, by Finlayson]
25. Social Practice / B. Equalities / 2. Political equality
23416 Political involvement is needed, to challenge existing practices [Habermas, by Kymlicka]
25. Social Practice / F. Life Issues / 2. Euthanasia
20885 Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
20882 Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]