[FOM] constructivism and physics

Charles Silver silver_1 at mindspring.com
Wed Feb 8 09:26:16 EST 2006

	In one of David Deutsch's papers, he unveils a quantum
mechanical "machine" which he calls "the square root of not".
One machine can produce any result, but when two of them
are hooked together, the reverse of the initial input of the
first machine is produced.   (I.e., 1 |--> 0, and 0 |-->1.)
He bemoans the inadequacy of logicians to arrive at such
a "not" and challenges them to do so.   He says logic as
presently constructed is empty, but needs to be useful in
reflecting reality.

Charlie Silver

On Feb 7, 2006, at 3:22 PM, John McCarthy wrote:

> Physics has often gone in the opposite direction.  Rather than
> confining itself to a subclass of "core mathematics", physicists and
> engineers have introduced techniques that "core mathematicians"
> considered unsound but later treated.  Oliver Heaviside's operational
> calculus was deemed unsound but later blessed via (if I remember
> correctly) the Laplace transform.  The Dirac delta function and its
> extensions were considered unsound but later blessed by Laurent
> Schwartz's theory of distributions.  I recall that Feynmann's
> integration over spaces of paths went far beyond what Norbert Wiener
> and his successors in integration over function spaces had been able
> to justify.
> I wouldn't be surprised if chaos theory got itself into non-measurable
> sets.
>> Dear FOM'ers,
>> Can someone please provide some references on connections between
>> constructivism in mathematics and mathematical physics?  There must
>> be some literature on this topic.
>> Thanks,
>> Steve Awodey
>> Carnegie Mellon
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