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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 31 ideas from George Boolos

10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
10483 Mathematics and science do not require very high orders of infinity [Boolos]
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
8693 An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos]
13547 Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
18192 Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
10833 Many concepts can only be expressed by second-order logic [Boolos]
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
13671 Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
7806 Boolos invented plural quantification [Boolos, by Benardete,JA]
10225 Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
7785 The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
10736 Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
10780 Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
10699 Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
10700 First- and second-order quantifiers are two ways of referring to the same things [Boolos]