Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Mirror Mirror - Is That All?' and 'The Philosophy of Mathematics'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
9327 Organisms understand their worlds better if they understand themselves [Gulick]
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 / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186 First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
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
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
11. Knowledge Aims / A. Knowledge / 2. Understanding
9325 In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick]
11. Knowledge Aims / A. Knowledge / 6. Knowing How
9326 Knowing-that is a much richer kind of knowing-how [Gulick]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
9319 Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
9320 Higher-order theories divide over whether the higher level involves thought or perception [Gulick]
9321 Higher-order models reduce the problem of consciousness to intentionality [Gulick]
9322 Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick]
27. Natural Reality / G. Biology / 2. Life
9324 From the teleopragmatic perspective, life is largely an informational process [Gulick]