On 01 Aug 2015, at 03:08, meekerdb wrote:
-------- Forwarded Message --------
Michelangelo's Stone: an Argument against Platonism in Mathematics
ROVELLI, Carlo (2015) Michelangelo's Stone: an Argument against
Platonism in Mathematics. [Preprint]
If there is a €œplatonic world€ M of mathematical facts, what does M
contain precisely? I observe that if M is too large, it is
uninteresting, because the value is in the selection, not in the
totality; if it is smaller and interesting, it is not independent
from us. Both alternatives challenge mathematical platonism. I
suggest that the universality of our mathematics may be a prejudice
hiding its contingency, and illustrate contingent aspects of
classical geometry, arithmetics and linear algebra.
http://philsci-archive.pitt.edu/11595/1/Platonism.pdf
I agree with the author, except for arithmetic (his last section) when
we postulate comp. And there, the analytical and the physical truth is
indeed in the eye of the beholder, but the beholder is a precise
arithmetical notion, the universal machine, and the FPI detrivialize
the analytical and physical reality.
Rovelli's critics is close to my critics of Tegmark: "all mathematical
structure" is a too big concept, which when made precise is either
inconsistent, or not all of mathematics.
Rovelli only ignores the mind-body problem, and the fact that we can
have a theory of mind in which to formulate that problem
mathematically. Then when it uses comp, we need no more that a simple
countable reality, which can be show to be the same in all models of
ZF, for example, or even the same in classical and intuitionistic
mathematics, and comp explains how the laws of physics emerge from
that *phenomenologically*.
With computationalism, arithmetic is not more trivial than
Schroedinger equation or Everett Universal Wave. In fact comp makes
physics as much universal than arithmetic: it explains why there are
physical *laws* at the base of all possible geographies.
Bruno
PS I have to go now, more on this perhaps later.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
