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Single Idea 10565
[filed under theme 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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Full Idea
There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new.
Gist of Idea
There is no stage at which we can take all the sets to have been generated
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
Book Ref
-: 'Philosophical Studies' [-], p.372
The
14 ideas
from 'Replies on 'Limits of Abstraction''
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10569
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If you ask what F the second-order quantifier quantifies over, you treat it as first-order
[Fine,K]
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10565
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There is no stage at which we can take all the sets to have been generated
[Fine,K]
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10564
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We might combine the axioms of set theory with the axioms of mereology
[Fine,K]
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10560
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Set-theoretic imperialists think sets can represent every mathematical object
[Fine,K]
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10563
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A generative conception of abstracts proposes stages, based on concepts of previous objects
[Fine,K]
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10561
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Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object
[Fine,K]
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10562
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We can combine ZF sets with abstracts as urelements
[Fine,K]
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10567
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We can create objects from conditions, rather than from concepts
[Fine,K]
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10571
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Concern for rigour can get in the way of understanding phenomena
[Fine,K]
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10568
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Logicists say mathematics can be derived from definitions, and can be known that way
[Fine,K]
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10570
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Assigning an entity to each predicate in semantics is largely a technical convenience
[Fine,K]
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10573
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Dedekind cuts lead to the bizarre idea that there are many different number 1's
[Fine,K]
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10575
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Why should a Dedekind cut correspond to a number?
[Fine,K]
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10574
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Unless we know whether 0 is identical with the null set, we create confusions
[Fine,K]
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