Combining Texts

All the ideas for 'A Résumé of Metaphysics', 'Letters to Des Bosses' and 'Knowledge and the Philosophy of Number'

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24 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 / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
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]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
5049 Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]
28. God / A. Divine Nature / 3. Divine Perfections
5048 Perfection is simply quantity of reality [Leibniz]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
12784 Allow no more miracles than are necessary [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5050 Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz]