David Deutsch's claim about "mathematicians' misconception"

[Timothy Y. Chow]

Jose Manuel Rodriguez Caballero wrote:
>  Reading [1], I found the following claim, due to David Deutsch, about the
> relevance of the laws of physics in foundations of mathematics:
>
>> there was a widespread assumption -- which I shall call the 
>> mathematicians' misconception -- that what the rules of logical 
>> inference are, and hence what constitutes a proof, are a priori logical 
>> issues, independent of the laws of physics.
[...]
> What could be the status of what David Deutsch calls the 
> "mathematicians' misconception" in the framework of foundations of 
> mathematics? Could be in the same category as Platonism, Formalism, and 
> Intuitionism?

Very interesting...thanks for mentioning this.

The following link might work better:

https://arxiv.org/pdf/1210.7439.pdf

To quote a little bit more:

    The theory of computation was originally intended only as a
    mathematical technique of studying proof (Turing 1936), not a branch of
    physics.  Then, as now, there was a widespread assumption---which I
    shall call the mathematicians' misconception---that what the rules of
    logical inference are, and hence what constitutes a proof, are a priori
    logical issues, independent of the laws of physics.  This is analogous
    to Kant's (1781) misconception that he knew with certainty what the
    geometry of space is.  In fact proof and computation are, like
    geometry, attributes of the physical world.  Different laws of physics
    would in general make different mathematical assertions provable.  (Of
    course that would make no difference to which mathematical assertions
    are *true*.)  They could also make different physical states and
    transformations simple---which determines which computational tasks are
    tractable, and hence which logical truths can serve as rules of
    inference and which can only be understood as theorems.

I don't feel like dissecting Deutsch's view in detail here---I have voiced 
objections to similar ideas in the context of discussions of 
hypercomputation [*]---but will just say that the misconceptions seem to 
me to be on Deutsch's part and not on the mathematicians' part.  If we 
want to attach an "ism" then I would attach it not to the "mathematicians' 
misconception" itself, but rather to Deutsch's own misconceptions; I'd 
propose the term "Deutschism" since I don't think his views on this point 
are widely shared.

[*] See for example https://cstheory.stackexchange.com/a/4838 and
     https://cs.nyu.edu/pipermail/fom/2004-February/007932.html

Tim