# Comment on Nicolas Gisin "Intuitionistic Mathematics"?

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• Fra
In summary, the author seems to be critiquing the real numbers and proposing intuitionistic mathematics in order to solve some of the problems with classical mathematics.
Fra
I noticed this https://www.physicsforums.com/forums/quantum-interpretations-and-foundations.292/ about Indeterminism in Physics and "Intuitionistic Mathematics" but it was already closed.

I just wanted to add that, although the value of these ideas are aren't clear from abstract of quick skimming, I immediately acknowledge some questions and subproblems that I think is important and quite deep and too important to be lost. The paper could perhaps have been written differently in order to not reject people. (quotes are from the paper https://arxiv.org/abs/2011.02348v1)

"scientific determinism would only be an illusion due to the timeless mathematical language scientists use."

This is also the essence of Smolins argument in "time reborn", the power of mathematics is because it's limited. The timeless laws and timeless mathematics are really just a limiting case, of describing a small subsystem from a dominant environment.

"To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We argue that intuitionistic mathematics provides such a language and we illustrate it in simple terms."

Smolin in his book also goes on at lenght in books and videos with examples and discussions on howto understand evolution of law, without resorting to "meta laws" in a meta state space. Smolins proposed solution was "evolution", in analogy to biological evolution (thereof his CNS hypothesis)

Gisins proposed solution here seems to be "intuitionistic mathematics", and critique agfainst real numbers. I must admitt that while the discussion has too much of a "human angle", I share the critiqued against the real numbers. most foundations of probability theory also takes this for granted.

The one thing that made to react to this, is that "intuitionistic mathematics" emphasies that the "operator/observer/agent" (I refuse to say human) shares analogies with intrinsic measures, where the idea is that an agents "meausre" must be constructable from what is available to the agent, and if the information capacitry is limited, then so is the set of possible instrinsice measures (or mathematics).

But this is very fuzzy, and for myself the motivation for such a programme is connected to finetuning, renormalization and unification (which would related to SR and GR of course), I wish I could understand the motivation (in terms of open question in phyusics, rather than merely philosophical terms) of the "intuitionistic mathematics".

I totally understand that this is difficult, so I haven en open mind, and aren't quite ready to judge this. Does anyone know another paper where the author connects these ideas of open problems or unification? This motivation should I think come first, in order to motivate readers.

So smolins constrasts the "newtonian paradigm" with "evolution of law and reality of time".
This author seems to constrast classical mathematics, with "intuitionistic mathematics"?

I think the two contrasting scenarios seem to have a common abstraction.

But there are differences. Smolin has no critique against real numbers in his books as far as I can remember.
The main problem I have is that "intuitionistic mathematics" seem to refer to humans? I wonder what Gisin would think about instead referring the construction beein "intuitionistic" relative to an abstract agent? This i would like to see more about if there is a paper.

/Fredrik

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