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Single Idea 9932
[filed under theme 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
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Full Idea
Recent commentators have de-emphasised the set paradoxes because they play no prominent part in motivating the most articulate and active opponents of set theory, such as Kronecker (constructivism) or Brouwer (intuitionism), or Weyl (predicativism).
Gist of Idea
The paradoxes no longer seem crucial in critiques of set theory
Source
JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b)
Book Ref
Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.223
A Reaction
This seems to be a sad illustration of the way most analytical philosophers have to limp along behind the logicians and mathematicians, arguing furiously about problems that have largely been abandoned.
The
15 ideas
from 'A Subject with No Object'
9918
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Abstract/concrete is a distinction of kind, not degree
[Burgess/Rosen]
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9919
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The old debate classified representations as abstract, not entities
[Burgess/Rosen]
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9921
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'True' is only occasionally useful, as in 'everything Fermat believed was true'
[Burgess/Rosen]
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9922
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If space is really just a force-field, then it is a physical entity
[Burgess/Rosen]
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9923
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We should talk about possible existence, rather than actual existence, of numbers
[Burgess/Rosen]
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9924
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Modal logic gives an account of metalogical possibility, not metaphysical possibility
[Burgess/Rosen]
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9925
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Structuralism and nominalism are normally rivals, but might work together
[Burgess/Rosen]
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9926
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A relation is either a set of sets of sets, or a set of sets
[Burgess/Rosen]
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9928
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Mereology implies that acceptance of entities entails acceptance of conglomerates
[Burgess/Rosen]
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9927
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Mathematics has ascended to higher and higher levels of abstraction
[Burgess/Rosen]
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9929
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Much of what science says about concrete entities is 'abstraction-laden'
[Burgess/Rosen]
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9930
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Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas
[Burgess/Rosen]
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9933
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The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set
[Burgess/Rosen]
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9932
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The paradoxes no longer seem crucial in critiques of set theory
[Burgess/Rosen]
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9934
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Number words became nouns around the time of Plato
[Burgess/Rosen]
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