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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
]
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
with the same theme
[denial that mathematics is just set theory]:
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16896
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If numbers can be derived from logic, then set theory is superfluous
[Frege, by Burge]
|
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18161
|
The theory of classes is superfluous in mathematics
[Wittgenstein]
|
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8697
|
Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them
[Benacerraf, by Friend]
|
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8304
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No particular pair of sets can tell us what 'two' is, just by one-to-one correlation
[Benacerraf, by Lowe]
|
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9906
|
If ordinal numbers are 'reducible to' some set-theory, then which is which?
[Benacerraf]
|
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17821
|
You can ask all sorts of numerical questions about any one given set
[Yourgrau]
|
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17815
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We can't use sets as foundations for mathematics if we must await results from the upper reaches
[Yourgrau]
|
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10560
|
Set-theoretic imperialists think sets can represent every mathematical object
[Fine,K]
|
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10222
|
Mathematical foundations may not be sets; categories are a popular rival
[Shapiro]
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17827
|
Sets exist where their elements are, but numbers are more like universals
[Maddy]
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17830
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Number theory doesn't 'reduce' to set theory, because sets have number properties
[Maddy]
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9643
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Set theory may represent all of mathematics, without actually being mathematics
[Brown,JR]
|
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9644
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When graphs are defined set-theoretically, that won't cover unlabelled graphs
[Brown,JR]
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23621
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Numbers are properties, not sets (because numbers are magnitudes)
[Hossack]
|