Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'On 'The Beginning of Philosophy'' and 'The Nature of Mental States'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
19456 Philosophy is distinguished from other sciences by its complete lack of presuppositions [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]
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]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2590 Dispositions need mental terms to define them [Putnam]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
2591 Total paralysis would mean that there were mental states but no behaviour at all [Putnam]
17. Mind and Body / C. Functionalism / 1. Functionalism
2588 Is pain a functional state of a complete organism? [Putnam]
2589 Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam]
2592 Functional states correlate with AND explain pain behaviour [Putnam]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
2587 Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
6376 Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam]
2330 If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim]