[FOM] Mumford on the foundations of Mathematics

[Frank Waaldijk]

John, the `disproof' of the continuum hypothesis that you mention seems to 
show a fundamental lack of understanding of the problems associated with 
stochastical experiments.

what does the statement: `pick a random real number' mean?

we still don't know what: `pick a random natural number' means, or do we?

the `experiment' described could certainly be carried out in the real world, 
but it is clear that then one of the appropiate variables would be the 
diameter of the darts. and this is the most prominent failing of the 
argument given: it does not indicate the foundation of the belief that the 
hitting of exactly one real number can be modelled statistically.

in my article on the foundations of constructive mathematics, i argue a 
little in favor of giving these issues some real attention. because i do 
agree with mumford that statistics is a very important tool with regard to 
the mathematical modeling of our physical world, and also i think we do not 
clearly understand the mathematical nature of our universe.

so yes, i agree these are foundational issues, but they are most commonly 
evaded probably for their unfamiliarity and difficulty.

i can only hope that this message will get past the moderator, since my 
previous message which was related to this issue (a real statistical 
experiment to test whether our world is deterministic) was blocked 
repeatedly.

interested greetings,

frank waaldijk


----- Original Message ----- 
From: "Baldwin, John T." <jbaldwin at uic.edu>
To: "foundations of mathematics" <fom at cs.nyu.edu>
Sent: Monday, August 28, 2006 3:15 PM
Subject: [FOM] Mumford on the foundations of Mathematics


> Fom members may be interested in the following article.  In addition
> to the tenditious account of logic vrs stochasticity, there is a
> intriguing `disproof' of the continuum hypothesis on page 13.
>
> D. Mumford, "The Age of Stochasticity"
> <http://www.dam.brown.edu/people/mumford/Papers/Dawning.pdf>
> http://www.dam.brown.edu/people/mumford/Papers/Dawning.pdf
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