Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Jody Azzouni and Kenneth Kunen

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34 ideas

3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
12442 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
12439 Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
12437 Truth lets us assent to sentences we can't explicitly exhibit [Azzouni]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
12452 Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
12446 Names function the same way, even if there is no object [Azzouni]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247 Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451 Scientific laws largely rest on the results of counting and measuring [Brouwer]
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454 Intuitionists only accept denumerable sets [Brouwer]
12453 Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
12447 That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni]
7. Existence / D. Theories of Reality / 7. Fictionalism
12445 If fictional objects really don't exist, then they aren't abstract objects [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
12449 Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
12440 If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
12438 In the vernacular there is no unequivocal ontological commitment [Azzouni]
12441 We only get ontology from semantics if we have already smuggled it in [Azzouni]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
9. Objects / A. Existence of Objects / 4. Impossible objects
12448 Things that don't exist don't have any properties [Azzouni]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10117 Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
27. Natural Reality / F. Chemistry / 3. Periodic Table
12450 The periodic table not only defines the elements, but also excludes other possible elements [Azzouni]