Re: Carlo Rovelli's critique of Platonism

[Bruno Marchal]

On 08 Jun 2017, at 03:34, Bruce Kellett wrote:

I have just come across this paper from a year or so ago. Rovelli  
essentially summarizes many of my own negative feelings about  
mathematical platonism.


https://arxiv.org/pdf/1508.1.pdf


Exercise. Show that the Church-Turing-Post-Kleene thesis refutes  
Rovelli's  idea that "if it is little, it depends on us". In fact the  
question is "who us?", But you don't need mechanism to refute Rovelli.  
The CT part of "YD + CT" is enough .  Sorry for the exercise, but I am  
under the june torture time (exams, corrections).


Mechanism, and Occam, says that the sigma_1 platonism is enough. It is  
the Brouwer separable part of mathematic, where classical  
mathematicians and intuitionist mathematicians "agree" (extensionally).


The interesting things are invariant for the choice of the phi_i. The  
choice of Fortran-phi_i, or the LISP-phi_i, or -phi_i will  
be locally circumstancial, but the laws of mind and matter are  
independent of that base, and their truth-notion are equivalent. This  
needs no more than the common arithmetical realisim needed to make  
sense of the Church-Turing thesis and of any Turing universal system.


That minimal number realism is conceptually interesting (cf. Number  
Theory, the Music of the primes or the crazy partitions of natural  
numbers (Ramanujan), etc.), and familiar, to humans since long (taught  
in primary school). There are also arithmetic problem in newspapers,  
and not much lambda expression problem, nor combinators one.


But the theology (mind and matter) is independent of the basic choice,  
the "initial church-turing universal reality.


A measure of the complexity of universal computability in  
"provability" scale is the sigma completeness. It is the ability to  
search the numbers and find those having a verifiable provable  
(decidable) property. A sigma1, or simply sigma formula has the shape  
EnP(n) with P decidable.  With the Matiyasevich-Robinson-Davis-Putnam  
result this amounts to the belief in the existence of solution or non  
solution to diophantine polynomial equations!


That part assumed is very small compared to basically all theories,  
especially in metaphysics. But it does not depend on us more than it  
depends on all universal numbers.


In category theory you can see them as cartesian closed categories  
with a natural numbers object, the literature is very rich on this.


We can limit the use of the excluded middle to the "EnP(n)".

That is where I stop to be platonist, and I do not assume the  
induction principle at the ontological level. Indeed at that level  
"observer/believer"' dream, made by machine having much richer belief,  
like including many induction axioms, can be proven to exist (in  
infinitely many histories).


Little does not mean it depends on us, except if you meant by us:  us  
the universal numbers.


Bruno

PS I will comment your other post, at some time, as it is a busy  
period of time, but in one word: you don't take the absence of  
collapse enough into account.
I want take some time to read the post. You might try to avoid the  
patronizing insulting tone which is the tool of those who does not  
believe themselves in their own arguments.









Bruce

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http://iridia.ulb.ac.be/~marchal/



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Re: Carlo Rovelli's critique of Platonism

[David Nyman]

On 8 Jun 2017 2:35 a.m., "Bruce Kellett"  wrote:

I have just come across this paper from a year or so ago. Rovelli
essentially summarizes many of my own negative feelings about mathematical
platonism.


Interesting paper, Bruce. However AFAICS he is in effect making the case
for the computationalist mode of explanation, which is indeed related to
the notion of Michelangello's stone or Borges's library. The crucial
difference is in the definition of the observer and its 'interest' or
interpretation as intrinsic rather than imposed from without. Of course,
the not inconsiderable task of explicating the precise consequences of such
intrinsic perceptual filtering remains. But the mode of explanation relies
on the computationalist Babel as its inferential basis, which is the extent
to which it need be said to 'exist'. It is precisely *eludes* reification
because it is the unique assumptive basis upon which the provenance of
'things' is subsequently to be inferred. It's not a thing in itself; its
role is explanatory, not substantial.

Again in effect Rovelli alludes to the deeper import of this approach to a
'theory of everything'. In essence it 'out-Darwins Darwin' by proposing, in
principle, how the appearance of creativity, from the emergent perspective
of an intrinsic interpretation, could indeed come about without the need to
appeal to a creator.

https://arxiv.org/pdf/1508.1.pdf

Bruce

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