Bruno Marchal wrote:

>
> UDA is an argument showing that COMP + "there exist a physical running
> UD" entails the reduction of physics to number theory/computer science.
>
> So with OCCAM you can already eliminate the hypothesis that there is
> physical running UD, and thus that there is any need for a physical
> universe.
>

Excellent, Bruno, excellent.  I agree.  Number is fundamental, physical
domain is secondary.

One might be able to carry things further by asking what is
information/number though?  Then it may be the case that (at least in
the case of discrete math) you could reduce mathematics to 'cognition'
(where 'cognition' is defined as 'perception, integration and
reflection on knowledge').

That is to say, one might be able to reduce mathematical Information to
*variance* (or difference, or statistical complexity aka Shannon),
which could be shown to equivalent in some sense to *perception*.

Then one might be able to reduce mathematical Forms/Logical
Propositions to *associations* (or knowledge or Bayesian links aka
Markov chains), which could be shown to be equivalent in some sense to
*integration* (knowledge integration or intelligence)

Finally one might to able to reduce mathematical self-references
(possibly certain combinations of Category Theory with Modal Logic) to
*Cognitive Reflections* .

Then all of (discrete) mathematics could be shown to be equiavlent to
*cognition*.  Thus (discrete) mathematics and cognition should perhaps
no longer be treated as seperate subjects and instead combined into a
single category called *Mathematico-Cognition* ;)


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