Re: What sci.logic is like

Ross A. Finlayson wrote:
Nam D. Nguyen wrote:
MoeBlee wrote:
On Apr 14, 3:16 pm, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:

With a possible exception of Torkel
Franzen, perhaps? (Not only he seemed to have an in-depth of formal
reasoning, he also exhibited certain appreciation of difficult
"subtleties" associated with it.

I love Torkel Franzen, but it's clear to me that there are still
posters active who have both an extensive technical understanding and
also a fine appeciation of informal nuances.

What I meant is that TF seemed (occasionally) to be *willing to discuss*
subtleties beyond what a typical text book would do. (If not in this
forum then maybe elsewhere, like FOM forum.) I've not seen one in this forum
who would like to discuss in-depth the foundational problems of FOL, with
an intention to improve it.



Hi Nam,

When you say, "discuss in-depth the foundational problems of FOL", I hope you might explain what you see as being "foundational problems of FOL."

Thanks, Ross, for the question. I certainly won't be able to list
all details in one post, and some of what I'm going to list
may overlap each other (they're related to the foundation of FOL
anyway), but here's a list of what I think I know or suspect:

(1) Overuse (if not outright abuse) the power of intuition.
The evidence is exemplified by Godel's work in Incompleteness:
Godel never *explicitly* stated/admitted that we must assume
the syntactical consistency of the encoding formal system
at hand. All that is in the matter was just a mere silent
assumption that such formal system exist viz-a-viz the intuitive
standard model of arithmetic, namely the natural numbers,
which is of course a circular proof.

This isn't an attack on the use of the natural numbers in the
foundation per se. But by not properly formalizing the limitation
of such assumption, we've in effect violated the intended rigidity
of syntactical proof machinery of FOL.

(2) Current FOL framework is incapable of admitting that w.r.t. to a particular
formula F, and a collection K of formal systems, it's entirely
conceivable - and quite possible - that it's unknowable if F is
decidable in any system in K.

(3) As the expressing tool for natural sciences, FOL framework is inadequate
to faithfully key scientific concepts: relativity, uncertainty, and AI.


Thanks,

Ross F.



.