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Single Idea 10560
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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Full Idea
Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set.
Gist of Idea
Set-theoretic imperialists think sets can represent every mathematical object
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
Book Ref
-: 'Philosophical Studies' [-], p.367
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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