Combining Texts

All the ideas for 'Leibniz', 'Cantorian Abstraction: Recon. and Defence' and 'The Theory of Logical Types'

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11 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]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
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 / 8. Abstractionism Critique
9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]