Combining Texts

All the ideas for 'How the Laws of Physics Lie', 'Set Theory and Its Philosophy' and 'Russell's Ontological Development'

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34 ideas

2. Reason / D. Definition / 12. Paraphrase
21699 Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine]
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 / E. Categories / 4. Category Realism
16185 Causality indicates which properties are real [Cartwright,N]
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]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
16182 Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
16184 An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
16167 Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N]
16169 Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N]
16176 Covering-law explanation lets us explain storms by falling barometers [Cartwright,N]
16177 I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N]
16180 You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N]
16171 The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
16183 In science, best explanations have regularly turned out to be false [Cartwright,N]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
21700 Taking sentences as the unit of meaning makes useful paraphrasing possible [Quine]
21701 Knowing a word is knowing the meanings of sentences which contain it [Quine]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
16175 A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
6781 There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird]
16166 Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
16179 Good organisation may not be true, and the truth may not organise very much [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
16170 To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N]
16181 Simple laws have quite different outcomes when they act in combinations [Cartwright,N]
16178 There are few laws for when one theory meets another [Cartwright,N]