Theos-Talk Archives (January 1997 Message tl00155)

theos-l@vnet.net wrote:


> ------------------------------
> 
> Date: Wed, 8 Jan 1997 10:39:29 -0700 (MST)
> From: JRC <jrcecon@selway.umt.edu>
> To: Multiple recipients of list <theos-l@vnet.net>
> Subject: Re: The Limits of Free Will
> Message-ID: <Pine.OSF.3.95.970108095723.9681A-100000@selway.umt.edu>
> 
> On Wed, 8 Jan 1997, Tom Robertson wrote:
> > >>
> > >> The laws of mathematics are eternal and changeless.  Like the laws of
> > >> morality and physics, they can be discovered, but never invented.
> > >>
> > >If you can demonstrate this with something other than just an assertion
> > >of your belief, you will have refuted Godel's Theorem. While you may take
> > >comfort in the belief that the laws of mathematics are "eternal and
> > >changeless", no working mathematician has given serious credibility to
> > >that idea in close to half a century ... its seen in the field as a
> > >charming, if unsophisticated, superstition from the past. Myself, as
> > >well as several friends, would be most interested to see a formal proof of
> > >your statement ... as it would likely be worth a Nobel Prize.
> >
> > I would be curious to know the name of the individual who arbitrarily
> > decided that 2+2=4.  But I'm flattered that you told my idea to several of
> > your friends.  I'd like to see a "formal proof" that 2+2 might not be 4,
> > also.  When might 2+2 become 5?
> >
> I didn't tell my friends - the ones I have in mind are mathematicians whom
> I consult when I need advice about the nuances of econometrics ... and
> whom I 've had discussions with concerning Godel's thought. The notion of
> "formal proof" that you quote as though it is suspect in some way is a
> concept from mathematics - it has very definite meaning. Godel's formal
> proof is several dozen pages of brilliant and tightly argued mathematical
> logic. If your statement, which is a virtually direct refutation of his
> argument, is to be accepted as true, it *would* win you a Nobel Prize, but
> you'll have to actually construct one of those "rational arguments" you
> are so famous for ... and if you can do so, I will gladly show my friends
> the argument, and if the argument was actually something containing
> substance, they would gladly submit your name to the Nobel Committee.

The Nobel Committee does not award prizes in mathematics, and no one has 
ever been a Nobel Laureate in Mathematics.  However, there is a 
prestigious award in Mathematics which is known as the "Field Medal" I 
believe.

The Nobel Committee does award prizes in physics; however physicists (as 
physicists) are disinterested in questions of logic and pure mathematics 
discussed here.


> However, the delightful and transparent attempt to detract attention from
> the idiocy of your first statement by demanding proof that 2+2 might not
> equal four is hardly an argument.

Whitehead and Russel did prove that 1+1=2 starting only from pure logic. 
 (This took hundreds of pages of difficult formulae).  And with a little 
more work (I hesitate to say just a little more work), I am sure that 
they could have gotten 2+2=4 as well.

But there are algebraic structures in which a.(b+c)=(a.b)+c; very 
different from the law in ordinary algebra in which a.(b+c)=(a.b)+(a.c).
But I'm afraid that's another game entirely.


> 
> You made a definative statement about the nature of mathematical laws.
> This is a claim that has been extensively discussed in the field, and is
> widely agreed to have been fully resolved earlier in the century. I asked
> for *proof* of the rationality of that statement ... the step by step
> logic you use to not just present the idea as an opinion, but as a fact.
> As I *have* read Godel's proof, 

Godel's proof is built entirely on the structure of logic created by 
Whitehead and Russell.  This concerns the formal undecidability of 
certain propositions.  But I wonder if we were to leave Whitehead and 
Russell alone, and reformulate the matter in a different way, if Godels 
result would still obtain?

>I would be most interested to compare
> your chain of reasoning to his. The question is not whether 2+2=4 ... it
> is whether Godel's proof, considered in the field to be one of the most
> brilliant pieces of mathematics in the history of the field, and one that
> in the rarefied circles of pure mathematics is considered an event equal
> in stature to the creation of the calculus, is *wrong*. You (clearly not
> even realizing it), are claiming that it is.
> 
> And it is this kind of thing I meant when in another post I said you used
> "freshman logic". Your statement about the nature of mathematical laws is
> nothing but your opinion, yet it is framed as though it is a "rational
> fact". Even further, it has been *proved* wrong by a man using logical and
> mathematical reasoning at a level probably beyond your ability to even
> begin to grasp, let alone refute. You use, once again, the tactic you
> often do, which is that when someone actually challenges one of your
> statements, and demands the "rational argument" you so often demand others
> use, you do not respond by doing so, but instead try to introduce some
> different question. It won't work. You made a statement. According to the
> field of mathematics, persuaded by a magnificent and elegant piece of work
> by Godel, your statement is just simply *wrong*. And judging by the level
> of your response, it seems likely you don't have the intellectual capacity
> to even understand why ... however, if you'd care to read Godel's proof,
> and offer your criticism of even a single statement, a considerable number
> of people would be quite interested in seeing you do so.
>                                                                 -JRC

JRC, Godel's work is an absolutely beautiful result, we all agree.  But 
to what extent is its universality limited by being tied to the formal 
structure created by Whitehead and Russell?

Now on this last point, I'm afraid that the only relevance to theosophy 
might be that Russell's brother Frank was a Buddhist, with whom he might 
have discussed once or twice some points of Buddhist logic.


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