Re: Raatikainen's critique of Chaitin

From: Timothy Murphy (tim_at_birdsnest.maths.tcd.ie)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 15:20:58 +0100

Aatu Koskensilta wrote:

>
>> If you accept that there are proofs outside the formal system,
>> aren't you getting quite close to Chaitin's position?
>
> How? Accepting this seems quite trivial since the proofs important to
> mathematicians never take place in formal systems, unless the
> mathematician happens to be a proof theorist.

Is that true?
Although proofs are not written formally, out of kindness,
I imagine most proofs eg in group theory
could be written formally if one were forced to do that.

But I wonder if Chaitin's apparent statement
that some theorems might be true "for no reason"
is not being taken too seriously.
(I haven't actually seen this remark,
although I've read quite a lot of Chaitin's work.)

I would interpret the remark as meaning
that if one pairs off propositions in a formal system
with finite strings
then a random string in Chaitin's sense,
ie a string with high algorithmic entropy,
would correspond to a "random" proposition in some sense.

In other words, I suspect he was being a little mischievous.
  

-- 
Timothy Murphy  
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland

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