Re: The Game of Life

From: Marchal <marchal.domain.name.hidden>
Date: Thu Dec 9 06:35:25 1999

Jerry Clark wrote:

>> I don't believe in infinite sets. But I'd accept
>>a rephrasing along the
>> lines of "the probability of being in a universe
>>like ours is very close
>> to 100%". Still like to see the reasoning though.
>>(Or perhaps a reference).


Chris Maloney answered:

>What does this mean, "I don't believe in infinite sets?" Do you
>believe in the number 42? Do you believe in green? Do you believe
>in (pick any human)?

Yes Chris. You should known that awfull truth: some people
doesn't believe in the infinite !
In philosophy of math they are called FINITIST.
The worst thing is that it is a perfectly respectable and
consistent philosophy of math.

Note that Schmidhuber is also a sort of finitist.

We can distinguish different sort of finitism. Two extremes are:
1) The ultrafinitist. This one does not even believe in big
numbers. He believes in 42, but will not believe in 42^42^42^...^42
(42 times) for exemple. The ultrafinitist can not even say that
he does not believe in the infinite. He just give no meaning at all
to such a word.
2) The intuitionist. He can be seen as a open minded finitist. He
does not believe in actual infinite sets, but he does believe in
ever growing finite sets. Nevertheless he does not believe in
non continuous functions, nor in non computable functions!
He considers mathematical objects as his own creation, and he believe
in a mathematical object only when he has been able to construct it.

There is a huge variety of finitism between them.
Note that my UDA argument and my chapter
5 can be comprehend by a intuitionnist, but not by an ultrafinitist.

People should realise that there is almost as many philosophy
of math as there are mathematicians! That is why "the whole math"
is a very bad defined expression.

It is amazing that a finitist is interested in the EVERYTHING idea!
But why not ? Welcome to Jerry the finitist!

Tell me, Jerry, are you nearer the ultrafinitist or the intuitionnist?
Do you believe in the standart meaning of the sequence:

I II III IIII IIIII IIIIII IIIIIII IIIIIIII ... ?

Also, you wrote:

>Once you start talking about transfinite measures I give up. The Bayesian
>arguments
>that underpin all these anthropic arguments are based on *probability* and
>therefore on *natural* numbers, counting etc.

Such "therefore" is a little hard to accept for me. After all
Lebesgue measure theory has been invented mostly for the founding
of probability in the continuum frame. The same with the continuous
Fourier transform, which are so usefull and down to earth.


Bruno
Received on Thu Dec 09 1999 - 06:35:25 PST