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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 3:44 PM
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On 7/7/2013 8:02 AM, Julio Di Egidio wrote:
>
> I have tried and re-read the thread: I fail to see all the connections,
> but that's good. :)
>


It is in Kant that one finds precisely the
remark that compares the relationship of a
universal judgement to a singular judgement
as being that of infinity to unity.

Apoorv attaches the introduction of infinity
into mathematics as related to the universal
quantifier.

Not grasping the sense of the quote (which is
fine -- who wants to read this anyway?), he
asked additional questions that introduce even
greater complexity.

I believe you have read "Tractatus Logico-Philosophicus"

Wittgenstein rejects Leibniz' principle of identity
of indiscernibles and proposes that the sign of
equality is eliminable on the basis of each object
having a unique name.

Modern model theory "extends languages" with constants
without definitions. This is an algebraic approach (in
the sense of universal algebra), and, is thus relevant
to the perspectives of Skolem.

But, it is in the nature of definitions that symbols are
introduced with respect to properties. This is an application
of Leibniz' principle of identity of indiscernibles.

So one is confronted with the relationship of uninterpreted
symbols of a language as treated in model theory and the
defined symbols which Apoorv hopes to use to reasonably
restrict notions in set theory.

Does that help?

It just gets worse...





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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