more from this thinker
|
more from this text
Single Idea 10699
[filed under theme 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
]
Full Idea
Is there, in addition to the 200 Cheerios in a bowl, also a set of them all? And what about the vast number of subsets of Cheerios? It is haywire to think that when you have some Cheerios you are eating a set. What you are doing is: eating the Cheerios.
Clarification
From the context, we can take Cheerios to be a breakfast cereal!
Gist of Idea
Does a bowl of Cheerios contain all its sets and subsets?
Source
George Boolos (To be is to be the value of a variable.. [1984], p.72)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.72
A Reaction
In my case Boolos is preaching to the converted. I am particularly bewildered by someone (i.e. Quine) who believes that innumerable sets exist while 'having a taste for desert landscapes' in their ontology.
The
23 ideas
with the same theme
[objections to the whole idea of set theory]:
|
8745
|
Classes are logical fictions, and are not part of the ultimate furniture of the world
[Russell]
|
|
6436
|
I gradually replaced classes with properties, and they ended as a symbolic convenience
[Russell]
|
|
10044
|
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element
[Russell/Whitehead, by Shapiro]
|
|
18208
|
We regard classes as mere symbolic or linguistic conveniences
[Russell/Whitehead]
|
|
11064
|
Classes can be reduced to propositional functions
[Russell, by Hanna]
|
|
7548
|
Classes, grouped by a convenient property, are logical constructions
[Russell]
|
|
13536
|
Skolem did not believe in the existence of uncountable sets
[Skolem]
|
|
10304
|
Very few things in set theory remain valid in intuitionist mathematics
[Bernays]
|
|
3355
|
Von Neumann wanted mathematical functions to replace sets
[Neumann, by Benardete,JA]
|
|
9920
|
Two objects can apparently make up quite distinct arrangements in sets
[Goodman, by Burgess/Rosen]
|
|
3336
|
Two things can never entail three things
[Quine, by Benardete,JA]
|
|
10699
|
Does a bowl of Cheerios contain all its sets and subsets?
[Boolos]
|
|
8972
|
What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}?
[Inwagen]
|
|
9570
|
In Field's Platonist view, set theory is false because it asserts existence for non-existent things
[Field,H, by Chihara]
|
|
6548
|
Physicalism requires the naturalisation or rejection of set theory
[Lycan]
|
|
13481
|
Maybe sets should be rethought in terms of the even more basic categories
[Hart,WD]
|
|
7035
|
God does not create the world, and then add the classes
[Heil]
|
|
10207
|
Anti-realists reject set theory
[Shapiro]
|
|
8758
|
We could talk of open sentences, instead of sets
[Chihara, by Shapiro]
|
|
18151
|
Could we replace sets by the open sentences that define them?
[Chihara, by Bostock]
|
|
9563
|
A pack of wolves doesn't cease when one member dies
[Chihara]
|
|
10108
|
As a reduction of arithmetic, set theory is not fully general, and so not logical
[George/Velleman]
|
|
10687
|
Maybe we reduce sets to ordinals, rather than the other way round
[Hossack]
|