Posted by
glen ep ropella on
URL: http://friam.383.s1.nabble.com/The-society-of-mind-tp585264p586882.html
Ken Lloyd wrote:
> The gist of the Gödel / Hilbert conflict is that it changed the nature of
> science from a search for the truth to "separating what is probably true
> from the demonstrably false". From H. Pollack -- Uncertain Science,
> Uncertain World.
I'm not sure who I'm disagreeing with, here, you or Pollack [grin]; but
I do have to disagree with what I think that statement means.
The gist of the Goedel/Hilbert thing (I don't think it's appropriate to
call it a conflict) isn't really about what's true or false (probable or
determined). It's about language and expressibility.
This is clearer if you set Goedel's work aside and look closer at
Tarski's work in the same area, which separates languages into at least
two sets, those simple enough to tolerate a solid definition of "truth"
and those too complex to tolerate it.
Now, I suppose one might say that if languages simple enough to tolerate
a well-defined "truth" are always easy to distinguish from reality (the
theorems formed are unsound), then that's evidence that reality is more
well-described by complex languages. Hence, if complex languages don't
have a well-defined "truth" and reality is best described by complex
languages, then, perhaps reality doesn't contain a well-defined truth.
And, if we jump to that conclusion, then, sure, the Goedel/Hilbert thing
might ultimately be about real truth and real falsity. But that's an
awfully large jump.
And I also think it's a bit aggressive to claim that the Goedel/Hilbert
thing impacted science. It certainly impacted how we reflect on
scientific progress. But does it really impact science? Have any
scientists changed their methods (i.e. the methods sections of their
published papers) citing the GIT? Would I use different beakers or dig
in different locations if the GIT were false? Would I change my
experimental subjects from baboons to rats? Granted, at the boundaries
between physics and metaphysics (string theory, GUTs, speculative
cosmology, etc.), the GIT rises to play a very important role. But for
most of what we call "science", the GIT's irrelevant.
(Please note that I'm playing Devil's Advocate to some extent because I
do believe Rosen's hand-waving claims that ambiguity is key in causal
entailment and (largely) absent from inferential entailment, and that
these claims are important to science. So, if we're right in our
premature conclusion that reality contains ambiguity, then that's
further justification for thinking that the GIT has a real correlate ...
i.e. that the GIT impacts science.)
--
glen e. p. ropella, 971-219-3846,
http://tempusdictum.com============================================================
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