Combining Texts

All the ideas for 'Classical Cosmology (frags)', 'Set Theory and Its Philosophy' and 'Art and Its Objects'

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31 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]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
20339 Classes rarely share properties with their members - unlike universals and types [Wollheim]
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]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
20338 We often treat a type as if it were a sort of token [Wollheim]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
20343 A love of nature must precede a love of art [Wollheim]
20342 Interpretation is performance for some arts, and critical for all arts [Wollheim]
21. Aesthetics / B. Nature of Art / 1. Defining Art
20348 A criterion of identity for works of art would be easier than a definition [Wollheim]
21. Aesthetics / B. Nature of Art / 2. Art as Form
20347 If beauty needs organisation, then totally simple things can't be beautiful [Wollheim]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20331 It is claimed that the expressive properties of artworks are non-physical [Wollheim]
20345 Some say art must have verbalisable expression, and others say the opposite! [Wollheim]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
20336 Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim]
20337 The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20333 If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim]
20334 The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim]
20335 The ideal theory of art neglects both the audience and the medium employed [Wollheim]
20340 A musical performance has virtually the same features as the piece of music [Wollheim]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
20341 An interpretation adds further properties to the generic piece of music [Wollheim]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
20332 A drawing only represents Napoleon if the artist intended it to [Wollheim]
27. Natural Reality / E. Cosmology / 1. Cosmology
5994 Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]