Combining Texts

All the ideas for 'Commentary on 'De Anima'', 'works' and 'Set Theory and Its Philosophy'

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22 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
13445 Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
16774 Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
12. Knowledge Sources / B. Perception / 3. Representation
7400 Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck]
16. Persons / F. Free Will / 4. For Free Will
4310 We have inner awareness of our freedom [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
6553 Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan]
22. Metaethics / B. Value / 2. Values / e. Death
16764 The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19676 Nature is devoid of thought [Descartes, by Meillassoux]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
6518 Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes]