Combining Texts

All the ideas for 'Truly Understood', 'Completeness of Axioms of Logic' and 'The Structure of Paradoxes of Self-Reference'

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15 ideas

4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
17751 Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
5. Theory of Logic / L. Paradox / 1. Paradox
13373 Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / b. König's paradox
13368 The 'least indefinable ordinal' is defined by that very phrase [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
13370 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
13369 By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
13366 The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
13367 The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
13371 If you know that a sentence is not one of the known sentences, you know its truth [Priest,G]
13372 There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
12608 Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
12605 A sense is individuated by the conditions for reference [Peacocke]
12607 Fregean concepts have their essence fixed by reference-conditions [Peacocke]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
12609 Concepts have distinctive reasons and norms [Peacocke]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
12604 Any explanation of a concept must involve reference and truth [Peacocke]
19. Language / C. Assigning Meanings / 4. Compositionality
12610 Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke]