Combining Texts

All the ideas for 'Concerning the Author', 'The Essence of Reference' and 'Russell's Mathematical Logic'

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20 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
14767 The demonstrations of the metaphysicians are all moonshine [Peirce]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
14764 I am saturated with the spirit of physical science [Peirce]
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 / F. Referring in Logic / 1. Naming / e. Empty names
10429 It is best to say that a name designates iff there is something for it to designate [Sainsbury]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10425 Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
10438 Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
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]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14768 Infallibility in science is just a joke [Peirce]
12. Knowledge Sources / D. Empiricism / 2. Associationism
14765 Association of ideas is the best philosophical idea of the prescientific age [Peirce]
14. Science / B. Scientific Theories / 1. Scientific Theory
14766 Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
10432 A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury]
19. Language / B. Reference / 5. Speaker's Reference
10434 Even a quantifier like 'someone' can be used referentially [Sainsbury]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
10431 Things are thought to have a function, even when they can't perform them [Sainsbury]