Combining Texts

All the ideas for 'fragments/reports', 'Inexpressible Properties and Propositions' and 'Russell's Mathematical Logic'

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15 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Since properties have properties, there can be a typed or a type-free theory of them [Hofweber]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]