Combining Texts

All the ideas for 'Understanding', 'Substance and Individuation in Leibniz' and 'What is Cantor's Continuum Problem?'

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21 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
8. Modes of Existence / A. Relations / 1. Nature of Relations
13076 Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
13102 If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne]
13103 Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
13104 Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
13100 Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13068 We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
13069 The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13072 Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne]
17080 Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne]
9. Objects / E. Objects over Time / 12. Origin as Essential
13101 Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13081 Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne]
11. Knowledge Aims / A. Knowledge / 2. Understanding
19691 Unlike knowledge, you can achieve understanding through luck [Grimm]
19690 'Grasping' a structure seems to be modal, because we must anticipate its behaviour [Grimm]
19692 You may have 'weak' understanding, if by luck you can answer a set of 'why questions' [Grimm]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
13071 We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne]