Combining Texts

All the ideas for 'Natural Kinds and Biological Realism', 'Letters to Des Bosses' and 'Set Theory'

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27 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12780 We can grasp the wisdom of God a priori [Leibniz]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
12774 Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz]
12777 Monads do not make a unity unless a substantial chain is added to them [Leibniz]
12782 Monads control nothing outside of themselves [Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
12778 There is active and passive power in the substantial chain and in the essence of a composite [Leibniz]
12783 Primitive force is what gives a composite its reality [Leibniz]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12775 Things seem to be unified if we see duration, position, interaction and connection [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
12776 Every substance is alive [Leibniz]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
12753 A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz]
9. Objects / D. Essence of Objects / 12. Essential Parts
12781 A composite substance is a mere aggregate if its essence is just its parts [Leibniz]
10. Modality / B. Possibility / 1. Possibility
12779 There is a reason why not every possible thing exists [Leibniz]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
12785 Truth is mutually agreed perception [Leibniz]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
17371 Some kinds are very explanatory, but others less so, and some not at all [Devitt]
27. Natural Reality / G. Biology / 5. Species
17372 The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt]
17373 Species pluralism says there are several good accounts of what a species is [Devitt]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
12784 Allow no more miracles than are necessary [Leibniz]