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All the ideas for 'Russell's Mathematical Logic', 'Propositional Objects' and 'How the Laws of Physics Lie'

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30 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / E. Categories / 4. Category Realism
16185 Causality indicates which properties are real [Cartwright,N]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
18969 How do you distinguish three beliefs from four beliefs or two beliefs? [Quine]
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 / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
18967 A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine]
19. Language / D. Propositions / 6. Propositions Critique
18968 The problem with propositions is their individuation. When do two sentences express one proposition? [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]
27. Natural Reality / C. Space / 3. Points in Space
18970 The concept of a 'point' makes no sense without the idea of absolute position [Quine]