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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 7, 2013 1:28 PM
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On 7/6/2013 10:49 PM, Shmuel (Seymour J.) Metz wrote:
> In <Rt-dna0-mbsy7ErMnZ2dnUVZ_rmdnZ2d@giganews.com>, on 07/05/2013
> at 08:23 PM, fom <fomJUNK@nyms.net> said:
>

>> modern mathematics differentiates ordinal numbers from cardinal
>> numbers.

>
> Modern Mathematics treats cardinals as special cases of ordinals.
>


Coming from one who slipped in a few references
to New Foundations in other threads, this is surprising.
New Foundations uses Fregean number classes, does it
not?

The source of that assertion in the sense I used
it can be found in William Tait's "Frege vs. Cantor
and Dedekind" reprinted in a Blackwell anthology
(2002) edited by Jacquette. ISBN: 0-631-21869-6

============================================

I posted once that my foundational studies had
led me to mathematical systems in which the
distributivity laws did not necessarily hold
or required modification.

I remarked in that post, that I believed this
arose from the use of canonical representatives
within classes of terms. This mathematical
practice is not "represented" in logic.

Also, I directed attention to Lawvere's discussion
of the category of pointed sets in which the
distributive laws do not hold.

Fregean number classes cannot form sets in the
usual set theories to which your remarks seem
to relate. One way to interpret von Neumann
cardinals, however, is as a canonical representative
from its given Fregean number class. It is
in this way that a cardinal number is representable
as a set.

So, if one asks "What is a number?" does the question
of identity include consideration of pointed classes?
Or, relative to a model, pointed sets?

???





Date Subject Author
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
Shmuel (Seymour J.) Metz
7/7/13
Read Re: Ordinals describable by a finite string of symbols
Peter Percival
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/8/13
Read Re: Ordinals describable by a finite string of symbols
Shmuel (Seymour J.) Metz
7/8/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/5/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/6/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/6/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/6/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/8/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/7/13
Read Re: Ordinals describable by a finite string of symbols
LudovicoVan
7/7/13
Read Re: Ordinals describable by a finite string of symbols
fom

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