[FOM] extramathematical notions and the CH
Timothy Y. Chow
tchow at alum.mit.edu
Thu Jan 31 14:44:37 EST 2013
On Thu, 31 Jan 2013, Joe Shipman wrote:
> We would "know" the mathematical statement in question because we
> believe our physical theories to be true
Yes, this is the crucial point. In what sense do we "know" or "believe"
our physical theories to be true? Do we know that general relativity is
true? Do we know that quantum field theory is true? All we know is that
they seem to be experimentally valid within certain parameter ranges. We
don't know with any *mathematical* certainty that future experiments won't
turn out differently and force us to revise our physical theories. This
is especially true when we extrapolate the theories beyond the parameter
ranges that we already have experimental verification for, which is what
is going on in all the hypercomputation proposals that anyone has ever
come up with.
You have not really addressed my crucial question: How do you rule out the
possibility that your proposed experiment, instead of giving us new
mathematical knowledge, simply serves to disprove the physical theory?
The answer, of course, is that you can't. All you can do is stubbornly
insist that you believe the physical theory. This is no different in
principle from stubbornly insisting *right now* that ZFC is consistent.
In both cases you're just looking at a finite amount of evidence and
dogmatically extrapolating outside well-confirmed parameter ranges. And
as soon as you condone an attitude of dogmatic allegiance to a physical
theory, there's nothing to stop dogmatic allegiance to silly green-cheese
theories as well.
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