David Deutsch's claim about "mathematicians’ misconception"

[José Manuel Rodríguez Caballero]

Dear FOM members,
  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.


It is well-known that logical inference is formally rather similar to
causality in spacetime, in the sense that both relations are reflexive,
antisymmetric, transitive. Using this analogy it is possible to develop a
common framework for special and general relativity on the one hand and
proof theory on the other hand [3]. But even in this case, the logical
inference is considered as independent of the laws of physics
(mathematicians’ misconception according to David Deutsch).

Rather close to David Deutsch's approach was William Rowan Hamilton's
proposal [4] that Algebra is the science of pure time [2]. Indeed, Hamilton
defined the real numbers of ratios of steps between moments of time and
derived some properties of the real numbers in this way.

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?

Kind regards,
Jose M.

References:
[1] Deutsch, David. "Constructor theory." Synthese 190.18 (2013): 4331-4359.
URL =
http://constructortheory.org/portfolio/the-philosophy-of-constructor-theory/

[2] Ohrstrom, Peter. "WR Hamilton's view of algebra as the science of pure
time and his revision of this view." Historia Mathematica 12.1 (1985):
45-55.
URL = https://www.sciencedirect.com/science/article/pii/0315086085900679

[3] J. Gorard, "Some Relativistic and Gravitational Properties of the
Wolfram Model," Complex Systems, 29(2), 2020 pp. 599–654.
URL = https://www.complex-systems.com/abstracts/v29_i02_a03/

[4] William Rowan Hamilton, "Theory of Conjugate Functions, or Algebraic
Couples; with a Preliminary and Elementary Essay on Algebra as the Science
of Pure Time."  Transactions of the Royal Irish Academy, volume 17 (1837),
pp. 293-422.
URL =
https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/PureTime/PureTime.pdf
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