AtD pg 675

[Lawrence Bryan]

The only thing I would add is that a simple consequence of the theorem  
that might be easier to understand is that Godel showed that there  
exist legitimate statements (by legitimate I mean the lexicon and  
syntax is valid within that system) in any system that's at least as  
rich as arithmetic whose truth cannot be determined from the axioms of  
that system and even if the axiom system is extended there will still  
be such unprovable statements.

Lawrence

On Jan 6, 2008, at 4:43 PM, Page wrote:

> Mark,
>
> My request was for further elucidation of your thoughts vis a vis  
> the Incompleteness Theorem and TRP, not the Theorem itself. Anyone  
> who has studied formal logic is well-acquainted with Godel. Your  
> comments are helpful, though I want to think through your comment  
> about intentionality.
>
> Page
> ----- Original Message -----
> From: Mark Kohut
> To: Page
> Cc: pynchon -l
> Sent: Sunday, January 06, 2008 9:32 AM
> Subject: Re: AtD pg 675
>
> Page has asked me to elaborate on Godel's Theorem and it
> has occurred to me that I should have elaborated more in the  
> original post.
>
> Page:
> Here are Godel's incompleteness theorems presented (adequately for  
> my purposes ) by wikipedia. (If any
> more knoweldgeable, more disciplined p-listers think wikipedia does  
> it up wrong, enlighten please.)
> Some p-lister's seem to have read the bestseller about Godel's  
> theorems. I have not.
> Gödel's incompleteness theorems
>
> From Wikipedia, the free encyclopedia
>
> (Redirected from Gödel's incompleteness theorem)
> Jump to: navigation, search
> In mathematical logic, Gödel's incompleteness theorems, proved by  
> Kurt Gödel in 1931, are two theorems stating inherent limitations of  
> all but the most trivial formal systems for arithmetic of  
> mathematical interest.
>
> The theorems are also of considerable importance to the philosophy  
> of mathematics. They are widely regarded as showing that Hilbert's  
> program to find a complete and consistent set of axioms for all of  
> mathematics is impossible, thus giving a negative answer to  
> Hilbert's second problem. Authors such as J. R. Lucas have argued  
> that the theorems have implications in wider areas of philosophy and  
> even cognitive science as well as preventing any complete Theory of  
> Everything from being found in physics, but these claims are less  
> generally accepted.
>
>
> Hilbert (from AtD) is herein contained.
>
>
> For my purposes in trying to explicate AtD, I might be arguing that  
> Pynchon uses the "n + 1 indefinitely" notion fromn Kit to state in  
> another way his
>
> belief that science/;math can never provide any complete Theory of  
> Everything.
>
>
> A-and, as I put out there, perhaps TRP was showing the open- 
> endedness, the "freedom" of consciousness....infinitely renewable  
> "intentionality" to use a concept some philosophers use........
>
>
> OK, tell me I'm stretching it.........
>
>
> Mark
>
>
>
>
>
>
> ----- Original Message ----
> From: Page <page at quesnelbc.com>
> To: Mark Kohut <markekohut at yahoo.com>
> Sent: Saturday, January 5, 2008 7:39:20 PM
> Subject: Re: AtD pg 675
>
> Mark-- Please elaborate on Godel's theorem. There is something  
> there, but, like Locke, I know not what. Thanks, Page
> ----- Original Message -----
> From: Mark Kohut
> To: pynchon -l
> Sent: Saturday, January 05, 2008 8:27 AM
> Subject: Fw: AtD pg 675
>
>
> So, is this "seeing' perspective, Pynchon recognizing human  
> consciousness
> in 'grasping the cosmos?
>
> His way of, once more, indicating that the "answers" lie outside of  
> pure math and
> scientific measurements? Always another step?
>
> Is this a kind of metaphoric Godel's theorem?
>
>
>
>
> ----- Original Message ----
> From: Michael J. Hußmann <michael at michael-hussmann.de>
> To: pynchon-l at waste.org
> Sent: Saturday, January 5, 2008 9:37:10 AM
> Subject: Re: AtD pg 675
>
> Richard Fiero (rfiero at gmail.com) wrote:
>
> > ". . . he understood that this zigzagging around [yo-yoing?] around
> > through four-dimensional space-time might be expressed as a vector  
> in
> > five dimensions.  Whatever the number of n dimensions it inhabited,
> > an observer would need one extra n+1, to see it and connect the end
> > points to make a single resultant."
> > Why does Kit seem to think that n+1 dimensions are needed?
>
> Good question. You don't need an extra dimension just for the  
> resultant
> vector, and you might just add up the individual vectors to draw the
> resultant, all within n dimensions. But insofar as "seeing it"  
> requires
> an outside observer -- you cannot "see" a path on a two dimensional
> surface unless you rise above this surface in a third dimension --,
> another dimension becomes necessary.
>
> - Michael
>
>
> Michael J. Hußmann
>
> E-mail: michael at michael-hussmann.de
> WWW (personal): http://michael-hussmann.de
> WWW (professional): http://digicam-experts.de
>
>
>
>
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