Combining Texts

All the ideas for 'On Sufficient Reason', 'Constructibility and Mathematical Existence' and 'Paradoxes of the Infinite'

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8 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
19404 Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
8758 We could talk of open sentences, instead of sets [Chihara, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
19403 Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz]