Combining Philosophers

All the ideas for Herodotus, JP Burgess / G Rosen and Kenneth Kunen

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28 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
9921 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9924 Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
9933 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
4. Formal Logic / G. Formal Mereology / 1. Mereology
9928 Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
9926 A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9932 The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9923 We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925 Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9934 Number words became nouns around the time of Plato [Burgess/Rosen]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9918 Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen]
9929 Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9927 Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen]
9930 Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen]
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]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9919 The old debate classified representations as abstract, not entities [Burgess/Rosen]
27. Natural Reality / C. Space / 2. Space
9922 If space is really just a force-field, then it is a physical entity [Burgess/Rosen]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]