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Single Idea 17821

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory ]

Full Idea

We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'.

Gist of Idea

You can ask all sorts of numerical questions about any one given set

Source

Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering')

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.358

A Reaction

This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set.

Related Ideas

Idea 17819 A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege]

Idea 17820 If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege]

The 14 ideas with the same theme [denial that mathematics is just set theory]:

16896 If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge]
18161 The theory of classes is superfluous in mathematics [Wittgenstein]
8697 Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend]
8304 No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe]
9906 If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf]
17821 You can ask all sorts of numerical questions about any one given set [Yourgrau]
17815 We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
10560 Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
10222 Mathematical foundations may not be sets; categories are a popular rival [Shapiro]
17827 Sets exist where their elements are, but numbers are more like universals [Maddy]
17830 Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
9643 Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
9644 When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]