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Topic: Ordinals describable by a finite string of symbols
Replies: 27   Last Post: Jul 8, 2013 9:56 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: Ordinals describable by a finite string of symbols
Posted: Jul 5, 2013 9:23 PM

On 7/4/2013 11:42 PM, apoorv wrote:
>
>
> But ordinals form a chain in their natural order,

One of WM's finitist supporters (I believe he
posts as Albrecht) wrote the following:

"Numbers count themselves"

I have thought about that statement in several
contexts. Since you bring up the subject of
"names" through mention of nameability, consider
my restatement:

"Numbers name their counts"

"Numbers count their names"

In my opinion this properly reflects the
relation between ordinality and cardinality.

That is, I find myself unable to differentiate
the ordinal relation of numbers from the
semiotics of naming.

Do not misunderstand me. I realize how the
philosophical investigation of 'names' is
far removed from the nature of number. However,
the idea of a logical foundation for mathematics
mandates consideration on how that philosophy
manifests itself in the foundations of mathematics.

If forced to consider "intuitive representations
of number" corresponding with the Kantian schema
of a sequence of homogeneous representations placed
side by side, then I transform Albrecht's statement
to my own. This is because modern mathematics
differentiates ordinal numbers from cardinal
numbers.

It is only with respect to consideration of
Cantor's completed infinities that these concepts
are clearly different, however.

But, to have that theory, limit ordinals must be
assumed to exist (in the abstract). They cannot
be constructed. But, they can extend the chain
which is their natural configuration.

(assuming the logic did not have some fatal
error with which I have no particular concern).

Date Subject Author
7/5/13 fom
7/5/13 fom
7/6/13 Shmuel (Seymour J.) Metz
7/7/13 Peter Percival
7/7/13 fom
7/8/13 Shmuel (Seymour J.) Metz
7/8/13 fom
7/5/13 fom
7/5/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/8/13 apoorv
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom