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All the ideas for 'Russell's Mathematical Logic', 'A Free Will' and 'Vagueness and Contradiction'

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36 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / e. Late classical philosophy
23326 In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M]
23335 In late antiquity nearly all philosophers were monotheists [Frede,M]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9136 The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen]
2. Reason / B. Laws of Thought / 1. Laws of Thought
9131 Two long understandable sentences can have an unintelligible conjunction [Sorensen]
2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
3. Truth / B. Truthmakers / 6. Making Negative Truths
9139 If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
9140 Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen]
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 / D. Assumptions for Logic / 1. Bivalence
9119 No attempt to deny bivalence has ever been accepted [Sorensen]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
9135 We now see that generalizations use variables rather than abstract entities [Sorensen]
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]
5. Theory of Logic / L. Paradox / 3. Antinomies
9125 Denying problems, or being romantically defeated by them, won't make them go away [Sorensen]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
9137 Banning self-reference would outlaw 'This very sentence is in English' [Sorensen]
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]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
9116 Vague words have hidden boundaries [Sorensen]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9132 An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
9128 It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen]
9130 Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
9118 The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen]
12. Knowledge Sources / B. Perception / 5. Interpretation
9124 We are unable to perceive a nose (on the back of a mask) as concave [Sorensen]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
9126 Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
9121 Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen]
16. Persons / F. Free Will / 2. Sources of Free Will
23334 For Christians man has free will by creation in God's image (as in Genesis) [Frede,M]
23333 The idea of free will achieved universal acceptance because of Christianity [Frede,M]
23337 The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
9134 The negation of a meaningful sentence must itself be meaningful [Sorensen]
19. Language / D. Propositions / 4. Mental Propositions
9133 Propositions are what settle problems of ambiguity in sentences [Sorensen]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
23336 There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M]
25. Social Practice / A. Freedoms / 4. Free market
9129 I can buy any litre of water, but not every litre of water [Sorensen]
28. God / A. Divine Nature / 4. Divine Contradictions
9122 God cannot experience unwanted pain, so God cannot understand human beings [Sorensen]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
23313 The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M]