Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'On Concept and Object'

expand these ideas     |    start again     |     specify just one area for these texts

24 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 / E. Structures of Logic / 1. Logical Form
4975 A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9949 There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18995 Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
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 / B. Properties / 10. Properties as Predicates
10317 It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10535 Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
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]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9839 Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
4973 As I understand it, a concept is the meaning of a grammatical predicate [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
9167 Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
4974 For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]