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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

Date: Thu Dec 9 06:35:25 1999

Jerry Clark wrote:

Chris Maloney answered:

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:

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

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