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Full Idea
Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?
Gist of Idea
We can have a series with identical members
Source
William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.51
A Reaction
The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 9984 | We can have a series with identical members [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |