David Deutsch's claim about "mathematicians' misconception"

[Lew Gordeew]

Dear Sam,

Am Mo., 23. Nov. 2020 um 21:19 Uhr schrieb Sam Sanders <sasander at me.com>:

> The fundamental procedure of the natural science seems to be to  
> formulate theories which are then
> tested against experimental data.  If the data are consistent with  
> the predictions, this counts towards the
> theory being (more) reliable.  If the data contradicts the theory,  
> the latter needs adjustment (or rejection
> in worst case).  What and where adjustment (or rejection) is needed  
> is part of the “magic” of science and
> will never be cast into logical rules (in my opinion).

>> Also note that many abstract mathematical objects are more  
>> sophisticated than "real" objects currently investigated
>> in physics or elsewhere in natural sciences.

> This greatly depends on what you mean by “sophisticated”:

> On one hand, infinite objects have nice closure properties, allowing  
> for a nice, smooth, and elegant theory. Bigger and bigger infinite  
> structures can be build, with ever more complicated properties.

> On the other hand, if by “sophisticated” one would mean “mirrors the  
> physical world”, the math shall become
> very finite and very messy rather quickly.

What I kept in mind is a more sophisticated treatment of infinity. In  
the set theory we consider infinite inner models, ordinals and  
cardinals, etc. Where are physical counterparts? They consider only  
plain, pre-Cantor, infinity of the space-time. My naive question: what  
is beyond black holes?  Maybe something comparable to ordinals beyond  
omega? Or take proof theory. There are infinite ordinals, too. For  
example what could be physical evidence of Friedman's generalization  
of Kruskal theorem that deals with simple physical objects like finite  
trees labeled with natural numbers (which also are easily  
interpretable in a finite physical world). We know that logical proofs  
require infinite ordinals ...

Best,
Lew