Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Russell's Mathematical Logic' and 'Draft Statement of Human Obligations'

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26 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 / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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 / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
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 / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
23814 Every human yearns for an unattainable transcendent good [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23824 Where human needs are satisfied we find happiness, friendship and beauty [Weil]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
23815 We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil]
23. Ethics / F. Existentialism / 4. Boredom
23823 Life needs risks to avoid sickly boredom [Weil]
24. Political Theory / B. Nature of a State / 4. Citizenship
23822 We all need to partipate in public tasks, and take some initiative [Weil]
24. Political Theory / D. Ideologies / 3. Conservatism
23817 We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil]
25. Social Practice / A. Freedoms / 3. Free speech
23819 Deliberate public lying should be punished [Weil]
25. Social Practice / A. Freedoms / 6. Political freedom
23818 We have liberty in the space between nature and accepted authority [Weil]
25. Social Practice / C. Rights / 4. Property rights
23820 People need personal and collective property, and a social class lacking property is shameful [Weil]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
23821 Crime should be punished, to bring the perpetrator freely back to morality [Weil]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
23816 Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil]