On 08 Feb 2017, at 04:02, Brent Meeker wrote:
On 2/7/2017 2:16 AM, Telmo Menezes wrote:
Yes. The relation of mathematics to facts in the world is one of
description. That a dx/dt = -x has a decaying exponential as a
solution is
not a fact about the world. As any engineer will tell you, it
means that if
the differential equation is a good description of something about
the world
then the decaying exponential will be a good description of
something about
the world. The analogy with Godel's theorem is that if we create
an AI
system to prove theorems, no matter how fast or long it runs it
will not be
able to prove all true theorems.
And, importantly, it will not be able to prove its own consistency.
If
we are machines ourselves, this also applies to us, right?
One cannot prove his own consistency as a formal axiomatic inference
machines - but very little of our reasoning is in that form. Even
that which is in that form may not rely on axioms of infinity.
Finite mathematics can certainly be consistent - every computer
implements it. And nothing precludes someone else from proving
your consistency.
No problem with this. Notice that the scheme of TOEs I gave does not
mention any theory having the axiom of infinity. Mechanism is a
finitist theory. Judson Web wrote a very nice book on this.
Now, incompleteness applies on any machine reasoning about itself
correctly (no matter how they reason), and we limit ourselves to such
machine, which is all we need to extract physics from the sum of their
"dreams" which exists in arithmetic (by Church-Thesis and "yes
doctor", although we could use the weaker strong AI thesis, here).
It is the believer in Matter which have to explain how Matter
interfere with the computation so as making the immaterial machine non
conscious. Just invoking MATTER is not valid. We can always add a God
to make any theory wrong, which is typically what the creationist are
doing. Scientists prefer to use Occam instead, especially if that
provides a testable theory, like with Mechanism.
Bruno
Brent
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