[FOM] extramathematical notions and the CH

[Timothy Y. Chow]

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.

Tim