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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

[objections to the whole idea of set theory]

23 ideas
Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Shapiro on Russell/Whitehead]
We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
Classes can be reduced to propositional functions [Hanna on Russell]
Classes, grouped by a convenient property, are logical constructions [Russell]
Skolem did not believe in the existence of uncountable sets [Skolem]
Very few things in set theory remain valid in intuitionist mathematics [Bernays]
Von Neumann wanted mathematical functions to replace sets [Benardete,JA on Neumann]
Two objects can apparently make up quite distinct arrangements in sets [Burgess/Rosen on Goodman]
Two things can never entail three things [Benardete,JA on Quine]
Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}? [Inwagen]
In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Chihara on Field,H]
Physicalism requires the naturalisation or rejection of set theory [Lycan]
Maybe sets should be rethought in terms of the even more basic categories [Hart,WD]
God does not create the world, and then add the classes [Heil]
Anti-realists reject set theory [Shapiro]
We could talk of open sentences, instead of sets [Shapiro on Chihara]
Could we replace sets by the open sentences that define them? [Bostock on Chihara]
A pack of wolves doesn't cease when one member dies [Chihara]
As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman]
Maybe we reduce sets to ordinals, rather than the other way round [Hossack]