Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'The Logical Structure of the World (Aufbau)' and 'Towards a Critique of Hegel's Philosophy'

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23 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19441 All philosophies presuppose their historical moment, and arise from it [Feuerbach]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19442 I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach]
2. Reason / C. Styles of Reason / 1. Dialectic
19444 Each proposition has an antithesis, and truth exists as its refutation [Feuerbach]
19445 A dialectician has to be his own opponent [Feuerbach]
3. Truth / A. Truth Problems / 3. Value of Truth
19443 Truth forges an impersonal unity between people [Feuerbach]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
19446 To our consciousness it is language which looks unreal [Feuerbach]
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
19447 The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach]
14. Science / B. Scientific Theories / 1. Scientific Theory
18699 Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button]
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
12131 All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody]