David Deutsch's claim about "mathematicians' misconception"

[Sam Sanders]

Dear Lew,

>>> Actually it's the other way around -- apparently the laws of physics are derived from earlier, abstract mathematical concepts of inference.
>> 
>> That sounds a little exaggerated: what abstract concepts of inference were at the basis of e.g. quantum mechanics or relativity?  What concepts did Newton base himself on?
> 
> Well, consider Aristotle's syllogism BARBARA:
> 
> All objects fall down.
> Apple is an object.
> Therefore, Apple falls down.
> 
> Similar inferences are used in natural sciences while seeking for general laws in the material world.

One could perhaps make a case for this in principle.  In practise, it goes a little more like this:  

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).  


> As well as in logic and mathematics (re: formulas) ever since ancient times, thus prior to Newton. 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.  

Best,

Sam