It's
often asked whether or not Kurt Gödel's theorems can be applied outside
mathematics. John Horgan certainly applies them to the theories of
physics. Or, more accurately, he writes that

“Kurt Gödel's incompleteness theorem denies us the possibility of constructing a complete, consistent mathematical description of reality” (6).

Clearly
there's a jump here from Gödel's mathematical incompleteness
theorems to physical reality. Or, more accurately, from Gödel's theorems to a
“consistent mathematical description of reality”. Is that jump
justified?

Well,
for a start, physics is utterly dependent on mathematics. Thus if all descriptions of reality in physics
involve mathematics, and mathematics is subject to Gödel's theorems,
then that must pass over to the descriptions of reality which are
offered by physicists. In other words, if a mathematical system must
be incomplete (or not entirely provable), then that description of
reality must be incomplete (or not entirely provable). The two must
fall and rise together.

More
meat is put on this idea of whether or not Gödel's theorems are
applicable to theories about reality when John Horgan says that the
“British physicist John Barrow argued that Gödel's incompleteness
theorem undermines the very notion of a

*complete*theory of nature” (69). We move again from mathematical systems to the incompleteness of a “complete theory of nature”. It can be said here that Barrow is simply transferring the incompleteness of mathematics to the incompleteness of a “complete theory of nature”. Again, does the former necessarily pass over to the latter?
In
more detail: Godel established that "any moderately complex system
of axioms inevitably raises questions that cannot be answered by the
axioms". Then Horgan moves onto to say that the “implication
is that any theory will always have loose ends”.

Many
scientists accept this application of Godel's theorems to physics,
including Moravec, Roger Penrose and Freeman Dyson. The latter says:

“

**Since we know the laws of physics are mathematical, and we know that mathematics is an inconsistent system, it's sort of plausible that physics will also be inconsistent.” (254)**
Thus what
we have here is a logical argument:

i)
Physics is mathematical.

ii)
Mathematics is an inconsistent system.

iii)
Therefore physics must be an inconsistent system (or simply
incomplete).

The
only problem here is seeing the entirety of mathematics as a single
system (which itself incorporates systems). Perhaps it is.

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