Combining Texts

All the ideas for 'Dthat', 'Formal and Material Consequence' and 'Russell's Mathematical Logic'

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17 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 / 4. Pure Logic
14187 If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
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 / B. Logical Consequence / 1. Logical Consequence
14188 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
14182 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
14183 Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
14184 In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
14186 Logical connectives contain no information, but just record combination relations between facts [Read]
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]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
14185 Conditionals are just a shorthand for some proof, leaving out the details [Read]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
14080 Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]