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Topic: Matheology § 224
Replies: 84   Last Post: Apr 20, 2013 4:43 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 224
Posted: Apr 13, 2013 1:17 PM

On 4/13/2013 11:19 AM, Nam Nguyen wrote:
> On 12/04/2013 6:59 PM, fom wrote:

<snip>

>>
>> With the first two definitions technically being
>> axioms because the symbols may not be eliminated
>> through substitution. That is why the signature
>> is formally introduced initially as
>>
>> <<M, |M|>, <c, 2>, <e, 2>>
>>
>> Obviously, I cannot specify an infinite domain.

>
> Exactly, fom. You, I, et al. don't seem to have a disagreement here.
>
> What we seem to have is a difference in understanding in where we
> _can_ go from here, i.e., from one "cannot specify an infinite
> domain"!
>

Constructive mathematics.

> My presentation over the years is that it does _not_ matter
> what, say, Nam, fom, Frederick, Peter, ... would do to
> "specify an infinite domain", including IP (Induction Principle),
> a cost will be exacted on the ability to claim we know, verify,
> or otherwise prove, in FOL level or in metalogic level.
>
> The opponents of the presentation seem to believe that with IP
> we could go as far as proving/disproving anything assertion,
> except it would be just a matter of time. Which sounds like
> Hilbert's false paradigm of a different kind.
>
> That's the difference on the two sides.
>

The *paradigm* of first-order logic involves an
ontology and a metaphysics with which you disagree.
This is why I say that you are probably not using
first-order logic in what you are trying to do. This
is why I interpret what I have already seen as trying
to take advantage of partiality. Partiality is not
part of the *paradigm* of first-order logic.

That is not to say that what you are doing would
not be interesting. It is to say that it is hard
for people to have you say that you are using a
certain set of principles but then also make statements
incoherent with that set of principles.

First-order logic is not really about "truth verification".

Although "truth" is part of the jargon, it is, at
this point, almost meaningless to talk of it as such.

In fact, I recently ran across an article where the
model theorist Wilfred Hodges commented on the difference
between Tarski's 1933 paper and his 1956 paper. In the
article, Hodges condoned the greater abstraction that
was concomitant with the generality of application of
mathematical systems. The problem, of course, is that
model theory professes to be about "truth" and
"satisfaction". If model theory is to be about
something else, then it should be using phrases like

"... is applicable"

for

"... is true"

and

"... is justifiably applicable by ..."

for

"... is a consequence of ..."

In the modern debate between "ideal language theory" and
"natural language theory" what is at issue is the notion
of meaning. The "ideal language theory" bases the meaning
of language symbols solely on semantic truth assignments.
The "natural language theory" bases the meaning of language
symbols on pragmatic considerations that inform the
content by which a truth assignment may occur.

In other words, the only real meaning of "truth" is that
it facilitates the representation of details for the
transformation

uninterpreted syntax -> interpreted syntax

Just yesterday I summarized how I now understand
these matters in a correspondence:

------------------------------------------------------

So, mathematics has reached this curious place where
the meaning of statements is given by semantic truth
conditions based upon an indeterminable ontology presumed
through purported denotation in relation to the descriptive
introduction of names eliminable through representation
within the uninterpreted syntax by means of Goedel
arithmetization.

------------------------------------------------------

But, then, my views are non-standard. I am certain
that everyone else is "actually" speaking about
"actual truth" and that I am simply condemned to
my own "private language".

You think I do not understand how you are trying to
say something that may be relevant. I am trying to
get you to understand that it will be difficult
to succeed if you do not try to figure out what
paradigm of logic you may be trying to apply. Once
things. And, again, I direct you to

http://plato.stanford.edu

as a good resource to try to figure out a different
way of explaining yourself.

Date Subject Author
4/12/13 Alan Smaill
4/12/13 namducnguyen
4/12/13 Frederick Williams
4/12/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Peter Percival
4/14/13 fom
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/16/13 namducnguyen
4/16/13 namducnguyen
4/16/13 Jesse F. Hughes
4/16/13 namducnguyen
4/16/13 fom
4/17/13 namducnguyen
4/17/13 fom
4/17/13 namducnguyen
4/17/13 Jesse F. Hughes
4/17/13 Jesse F. Hughes
4/17/13 namducnguyen
4/20/13 namducnguyen
4/17/13 Frederick Williams
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 fom
4/18/13 namducnguyen
4/18/13 Frederick Williams
4/18/13 namducnguyen
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Peter Percival
4/15/13 Peter Percival
4/14/13 namducnguyen
4/14/13 namducnguyen
4/13/13 Frederick Williams
4/13/13 Peter Percival
4/13/13 Peter Percival
4/13/13 namducnguyen
4/15/13 Peter Percival
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Frederick Williams
4/14/13 Frederick Williams
4/14/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 namducnguyen