Combining Texts

All the ideas for 'Conspectus libelli (book outline)', 'Mathematics: Form and Function' and 'Continuity and Irrational Numbers'

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9 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18189 ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
17611 We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10572 A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
17612 Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18087 If x changes by less and less, it must approach a limit [Dedekind]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
12699 A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
12700 Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
12736 If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
12698 Every body contains a kind of sense and appetite, or a soul [Leibniz]