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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 10:06 PM

On 7/4/2013 11:42 PM, apoorv wrote:
> My understanding is very imprecise, but the compactness/ completeness theorems
> ' A theory is consistent iff it has a model'. -
> The model itself is a theory in some other language,
> So, should it be, ' a theory is consistent iff it has a Consistent model'.
> Which really means that semantic consistency is somewhat of a regress.

This is not quite accurate.

Although one may argue as to how to
view certain modern presentations, the
transition from syllogistic logic to
modern compositional forms of logic had
been accomplished by Frege. In Frege's
writings, he refers to intensional logicians
and how his views disagree with those
positions.

Frege's language seems to reflect the Aristotelian
arrangement from "Posterior Analytics" where the
definition of an object (its "essence") had been
fundamentally associated with "substance".

However, the abstractness of mathematical objects
creates a problem in this regard. Frege, himself,
viewed his theories of arithmetic as grounded on
a "logical object" taken to be substantive. He
eventually retracted those views.

Having said that, I agree with your analysis and
do not think that there is any real advantage to

Still, there are few choices:

http://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

Take your pick: circularity, infinite regress, or
meaningless syntax.

I personally think that you throw them into a blender
and hit the switch to make a smoothie.

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