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Single Idea 10567
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects.
Gist of Idea
We can create objects from conditions, rather than from concepts
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
Book Ref
-: 'Philosophical Studies' [-], p.373
A Reaction
The point is that no particular object is now required to make the abstraction.
The
14 ideas
from 'Replies on 'Limits of Abstraction''
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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10575
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Why should a Dedekind cut correspond to a number?
[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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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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