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All the ideas for 'fragments/reports', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'The Structure of Paradoxes of Self-Reference'

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18 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733 Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874 Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
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 / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18252 Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271 We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10623 Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
9975 Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165 My Basic Law V is a law of pure logic [Frege]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9190 A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
13665 Frege took the study of concepts to be part of logic [Frege, by Shapiro]