On 12 Sep 2014, at 07:31, Richard Ruquist wrote:
Liz,
As far as I know, Max does not have a theory. He just has a
hypothesis with nothing theoretical to back it up.
One aspect of his hypothesis is that the creation of matter requires
math that is both consistent and complete.
Whereas Godel has seemingly to me proven that such math does not
exist. Is that true?
Gödel showed that you cannot have an effective (checkable theory)
which is both consistent and complete. But you can have a theory
consistent and complete. It will just be non effective. The theorems
will not be recursively enumerable, and you will be unable to check
mechanically if a proof is valid, or if a true proposition is provable.
A simple example is just the set of all true arithmetical
propositions. Only a logician can call that a theory. usually the
theories have to be effective to be considered as genuine theory.
usually, the non effective structure related to truth is called a
"model" in logic (but the set of sentences true in that model is also
called "theory" by logicians, but those are most of the time non
effective (non Recursively enumerable).
Bruno
Rich
On Thu, Sep 11, 2014 at 10:19 PM, meekerdb <[email protected]>
wrote:
On 9/11/2014 6:36 PM, LizR wrote:
Obviously I haven't read the PDF file with Chs 1-8, which may take
me a while - but I do (mildly) take issue with this assertion.
Mathematics is merely a description of nature. Nature can operate
mathematically (adverb), but cannot be claimed to 'be' the
mathematics. Being predictive with/using mathematics does not prove
nature is made of it. I deal with nature itself. Not maths. When
you realise this you end up with dual aspect science. A 3 tiered
epistemic framework practical for science
This is of course the position that science has taken for the past
few centuries without realising that there was any alternative.
However, now that Max Tegmark (and of course Bruno) have argued
that there is an alternative, simply claiming that nature cannot be
made of maths no longer cuts the mustard. It's true that maths
being predictive doesn't "prove that nature is made of maths"
because as we know, science doesn't set out to prove anything,
especially not sweeping ontological claims. But it still seems
quite possible to me, at least, that Max may be onto something,
because as he points out his theory explains the "unreasonable
effectiveness" of maths in physics - so I will be interested to
hear some counter arguments that explain this effectiveness on a
non universe-is-maths basis. So far I've seen a bit of handwavium,
but generally I've been underwhelmed by the alternatives presented
to explain this, which leaves Max's theory out in front in terms of
explanatory power, as far as this particular issue is concerned.
Not that there aren't problems with Max's theory, of course. (It's
mind boggling for a bear of little brain like me to attempt to
grasp how it could possibly actually work....) But it does seem
plausible enough to deserve decent counter-arguments.
One counter argument is to note that math has been "unreasonably
effective" in Ptolemaic astronomy, Newtonian physics, fluid
dynamics, non-relativistic quantum mechanics, and other theories
which we now think were mere approximations. This seems much more
consistent with mathematics being descriptive rather than
prescriptive.
I'd say mathematics is just a matter of being very precise about
axioms and what you infer from them so that you find lots of
interesting consequences but don't fall into contradiction.
Brent
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