Combining Texts

All the ideas for 'Rationality', 'Thought and Responsibility' and 'Russell's Mathematical Logic'

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16 ideas

2. Reason / A. Nature of Reason / 1. On Reason
You can be rational with undetected or minor inconsistencies [Harman]
2. Reason / A. Nature of Reason / 6. Coherence
A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
2. Reason / D. Definition / 8. Impredicative Definition
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
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 / 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]
14. Science / C. Induction / 1. Induction
Enumerative induction is inference to the best explanation [Harman]
14. Science / C. Induction / 3. Limits of Induction
Induction is 'defeasible', since additional information can invalidate it [Harman]
14. Science / C. Induction / 4. Reason in Induction
All reasoning is inductive, and deduction only concerns implication [Harman]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Ordinary rationality is conservative, starting from where your beliefs currently are [Harman]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
A man is a responsible agent to the extent he has an intention, and knows what he is doing [Hampshire]