[FOM] "Hidden" contradictions
Prof. Ranjit Nair
director at cpfs.res.in
Sat Aug 17 06:01:16 EDT 2013
Let's not
forget that Hilbert’s 6th problem was the mathematical
treatment of the axioms of physics. Also that the question of
the
completeness of physics in 20 years has been the subject
of bets by
Stephen Hawking. He conceded his first such bet in
his Dirac lecture
in
2002 using Gödel's theorem to argue
that if mathematics is
'incomplete', physics has to be so too.
The same bet offered in
Delhi in
2001 was taken up by me and
since the earlier concession
was generic in
nature, it follows
that the later bet stands conceded
too. However it
appears
that Hawking has reneged, after recovering
his optimism about the
possible completeness of physics, in work with
Hertog, Hartle and
others. It is true that physics often employs theories
that are
literally false, such as recovering the classical limit by
setting
Planck's constant equal to zero (the correspondence principle of
Niels Bohr), when in fact the constant is what it is, a non-zero
constant.
The use of counterfactual approximations evident in e.g.
the
"effective field theory" approach to quantum field
theory. No
further elaboration is required.
/>_______________________________________
Professor Ranjit
Nair
Director
Centre for Philosophy & Foundations of
Science
P.B. No. 4017, Malaviya Nagar P.O.
New Delhi
110017
/>India
Tel. +91 11 65951738 / 46170795
Cell +91
9810332846 / 8826585999
e-mail:
director at cpfs.res.in
href="mailto:irector.cpfs at gmail.com">irector.cpfs at gmail.com
/>president at wias.in
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href="http://www.cpfs.res.in/">http://www.cpfs.res.in/
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/>
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/>/>From:"Timothy Y. Chow"
To:"Foundations of
/>Mathematics"
Date:Thu, August 15, 2013 8:05 am
/>/>Subject:Re: [FOM] "Hidden" contradictions
/>/>> On Wed, 14 Aug 2013, Mark Steiner wrote:
>> I
/>appreciate this response. However, my physicist
friends tell me that
/>/>>> the theory known as QED is
thought to be inconsistent, but
people use it
>>
anyway, with great success in
predictions. I
think what this
means is
>> the claim
that there is no way to
formalize QED in a consistent
>>
axiomatic system. If
this is
right, then there is a sense in which
>>
formal systems do
play some kind of role in physics.
>
> The alleged
inconsistency of QED is a
complicated topic that has been
>
discussed in great
detail
before on FOM and I don't think we want to
/>>
rehash it all
here, but I'll just say that even if we grant the
(somewhat
/>> debatable) propositions that (1) "QED is
thought
to be
inconsistent" and
> (2) this means
that "there is
/>no way to formalize QED in a consistent
> axiomatic
system",
then really all this shows is
the exact opposite:
/>> namely, that
formal systems *do
not* play an important role
in physics.
> If
they
did, then the physicists would be
compelled to abandon QED. The
/>> only role formal systems are
playing here is in framing
certain
/>> philosophical
discussions *about* physics.
>
>
Tim
>
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