Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'Critique of Judgement I: Aesthetic'

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30 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 / 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 / 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]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
12157 Kant gave form and status to aesthetics, and Hegel gave it content [Kant, by Scruton]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
20346 The aesthetic attitude is a matter of disinterestedness [Kant, by Wollheim]
18547 Only rational beings can experience beauty [Kant, by Scruton]
24172 It is hard to see why we would have developed Kant's 'disinterested' aesthetic attitude [Cochrane on Kant]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
20408 With respect to the senses, taste is an entirely personal matter [Kant]
20409 When we judge beauty, it isn't just personal; we judge on behalf of everybody [Kant]
20411 Saying everyone has their own taste destroys the very idea of taste [Kant]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
24170 Kant thinks beauty ignores its objects, because it is only 'form' engaging with mind [Cochrane on Kant]
22711 The beautiful is not conceptualised as moral, but it symbolises or resembles goodness [Kant, by Murdoch]
4025 Kant saw beauty as a sort of disinterested pleasure, which has become separate from the good [Kant, by Taylor,C]
20412 Beauty is only judged in pure contemplation, and not with something else at stake [Kant]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
22046 The mathematical sublime is immeasurable greatness; the dynamical sublime is overpowering [Kant, by Pinkard]
21458 The sublime is a moral experience [Kant, by Gardner]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
5643 Aesthetic values are not objectively valid, but we must treat them as if they are [Kant, by Scruton]
20410 The judgement of beauty is not cognitive, but relates, via imagination, to pleasurable feelings [Kant]
28. God / C. Attitudes to God / 3. Deism
1558 Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]