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Single Idea 17815
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
]
Full Idea
Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move.
Gist of Idea
We can't use sets as foundations for mathematics if we must await results from the upper reaches
Source
Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two')
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.356
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
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The theory of classes is superfluous in mathematics
[Wittgenstein]
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8697
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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
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If ordinal numbers are 'reducible to' some set-theory, then which is which?
[Benacerraf]
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17821
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You can ask all sorts of numerical questions about any one given set
[Yourgrau]
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17815
|
We can't use sets as foundations for mathematics if we must await results from the upper reaches
[Yourgrau]
|
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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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10222
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Mathematical foundations may not be sets; categories are a popular rival
[Shapiro]
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17827
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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]
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