[FOM] constructivism and physics

John McCarthy jmc at steam.Stanford.EDU
Tue Feb 7 16:22:20 EST 2006

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 

> 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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