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All the ideas for 'fragments/reports', 'Logicism in the 21st Century' and 'Cantorian Abstraction: Recon. and Defence'

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12 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
9148 I think of variables as objects rather than as signs [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787 The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
9152 If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9149 To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K]
9150 We should define abstraction in general, with number abstraction taken as a special case [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8786 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]