Re: Cantor Confusion

On 18 Nov 2006 21:33:39 -0800, 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.

So why not start off with a simpler question, Brian? What does it mean
to be absolutely false?

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.

The difficulty with categorical assumptions of truth of this kind,
Brian, is that they're only assumptions. You're still trying to get at
the idea of truth by assumption. You need to be able to demonstrate
"truth" and not just assume it.

: * 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?

Brian Chandler
http://imaginatorium.org

~v~~
.