Combining Texts

All the ideas for 'The Architecture of Mathematics', 'What is Analytic Philosophy?' and 'The Structure of Paradoxes of Self-Reference'

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13 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
22334 Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock]
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]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22332 German and British idealism is not about individual ideas, but the intelligibility of reality [Glock]
18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
22336 We might say that the family resemblance is just a consequence of meaning-as-use [Glock]
22335 The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock]