Re: Cantor Confusion

On 19 Nov 2006 03:43:04 -0800, imaginatorium@xxxxxxxxxxxxx wrote:


David Marcus wrote:
imaginatorium@xxxxxxxxxxxxx wrote:
David Marcus wrote:
imaginatorium@xxxxxxxxxxxxx wrote:
*** T. Winter wrote:
In article <1163602667.089204.113210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> *** T. Winter schrieb:
...
> > In
> > principle no axiom is necessary. But you need a few to have some start
> > to work with.
>
> That's the question. By means of axioms you can produce conditional
> truth at most. I am interested in absolute truth. Axioms will not help
> us to find it. I don't think we need any axioms.

If you want to find absolute truth you should not look at mathematics.

Really? There are two groups of order 4; could any truth be more
absolute than that?

I think it depends on what the words mean. If the axioms are correct in
your model, then the theorems are correct in your model.

Well, model-schmodel, really. (This stuff is a bit beyond me,
actually...)

It's not entirely clear what the notion of "absolute truth" refers to.
Suppose you think it is a matter of absolute truth that all men are
created equal. Then you go to Venus and discover that in their language
the word 'All' means flying, 'men' means pigs, 'are' means eat,
'created' means chocolate, and 'equal' means icecream.* Moreover the
atmosphere of Venus turns out to be full of flying pigs, but is of such
chemical composition that icecream of any flavour self-combusts
explosively. Well, has absolute truth varied? I think the reasonable
answer is 'No', because a truth is _about_ something, not merely a
string of formal symbols.

: * Language doesn't work like this - I know, but I haven't time to
assemble grammars and whatnot
: just to make the same point. Anyway, see the Hilary Putnam stuff
about horses and schmorses
: (which I have only read secondhand in Dennett).

Why did you pick the statement you did, rather than something like 2 + 2
= 4?

Because as far as I know there is no (normal, sane) interpretation of
the _words_ of my statement about groups of order 4 other than the
standard one. Whereas, for example, in other contexts 2 + 2 = 1, so
while the truth to which "2+2 = 4" refers is absolute, it takes longer
to write, because you have to spell out the full context, and in
present crank company even saying "integers" may take 2-3 lines.

You say this depends on my axioms and my model; but are there such that
make my claim about groups of order 4 untrue?

I don't know.

You claim to have a PhD in mathematics, and you "don't know"? What a
feeble answer. So disappointed was I when I saw it, that I was tempted
to say I begin to understand where Lester gets his "ideas" from, though
mercifully I overcame that temptation, seeing it would probably start
him off again.

Well, Brian, the problem is that you and others get into mathematics
to find some kind of absolute truth then for answers you get shuffled
off into models, axioms, and theorems nonsense. The difficulty is you
are asking the wrong people. You're asking the models, axioms, and
theorems people and all they can do is engage in a professional
recitativo of the status quo. That's all they know. What else could
you expect? As far as they're concerned there is no truth. If you
really want truth the skip truth police like David and if you really
don't want to get me started again try figuring it out for yourself.

I think I see that there could be a set of rather weak axioms that
formed something called groupette theorino, which were simply powerless
to prove the existence of two groups of order 4, but my suggestion is
that no-one would accept such a miniature as being grownup group
theory.

Brian Chandler
http://imaginatorium.org

~v~~
.

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