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It seems the majority of scientists hold for a the hyper-effectiveness of mathematics in natural sciences as a sign that nature is deeply mathematical. Although I believe that some mathematisism is necessary to tackle the description of the world, I can't find the intuition behind the mathematical intelligibility of the univers to be grounded outside of a belief and the modern success of the "hard sciences", nothing really goes to prove that mathematics are embedded in Nature.

The opposite point of view, that which aligns with a selective-effectiveness of mathematics, is more reasonable as a stance. Mathematics is only efficient in that it chooses its field of effectiveness, it focus on structure, extracts it and deals with it. Here, one can go as far as imagining that Mathematics is a branch of psychology: we "conceive" Mathematics as we further harmonize our mental behavior and the world's (matter's ?) behavior. One can imagine that a real structure in the Univers is no truer than the effect of such an harmonization, it is only because we can picture the behavior of the world by way of the behavior of our mind (and vice-versa) that we project structure in the world.

My goal in the post is three fold: 1) to see if some scientistics have constructed a smiliar reasonning and how it influenced their work, 2) find out about philosophers who have persued with some depth the perspective of Mathematics as a branch of psychology, 3) get your take on it.

Thanks for your time.

P.S: I have not read the book with the title, just went for the expression as it seems to cristallize the stance very well.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Geoffrey Thomas ♦
    Feb 11, 2020 at 10:49
  • Mathematics is clearly not a branch of psychology since it can be automatized. en.wikipedia.org/wiki/Symbolic_Manipulation_Program
    – puppetsock
    Feb 11, 2020 at 17:18
  • @puppetsock: we have to take the conversation to the chat (above) for further exchange, however, manipulating symbols is not mathematics. Mathematics is not going to be automized, at least in as far as Gödel's result apply.
    – Gloserio
    Feb 11, 2020 at 18:15

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When studying nature we often study the relationships between various forms of energy. These relationships are the origin of the structures which we use mathematics to describe. This method works quite well but the idea that we are projecting structure onto the universe based upon our current understanding of mathematics is inescapably true. We usually frame understanding within a context we already understand. Also an inescapable truth. The challenge for an honest scientist is to remember that the effectiveness of mathematics doesn’t actually guarantee that mathematics alone will correctly describe nature. It is possible to construct a mathematical description which gives answers that seem completely consistent with observations and yet are fallacious in their construction. Only repeated experiments intended to disprove the thesis can reveal the fallacious structure or assumptions. But not in every case, sometimes you may never know that you are mischaracterizing nature. I also hear mathematicians claim that the beauty and elegance of their conceptions are final and authoritative indicators of the validity of a theory. My question in that case is, how can you possibly know that there is not a still more beautiful and elegant solution which you are currently incapable of conceiving? You couldn’t, by definition. So that metric is not a dependable guide to the truth!

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  • Thank your for the answer. I take the point that a scientist tries to build a mathematical depiction which has some root in experience, you can see how many theories deploy mathematics, but only one (or many) survive, that's the one (or many) with the easiest (a.k.a: most elegant) math and best experimental back-up. I would feel more comfortable with this method if it was made clear that all mathematic can describes is what mathematics "could" describe, it is the jump to assertion that "all reality is mathematical in nature" which I am having a hard time with.
    – Gloserio
    Feb 9, 2020 at 20:45
  • Nope. In many cases we can know that there is exactly one answer. en.wikipedia.org/wiki/Uniqueness_theorem en.wikipedia.org/wiki/Existence_theorem
    – puppetsock
    Feb 11, 2020 at 17:08
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The mathematization of science is a lot stronger a movement than just: "the modern success of the hard sciences". it is actually a reasonable inference from material reductionism. This is because matter appears, at the quantum scale to not really be material, but mathematical. The rationale behind the dominant view of QM, the Copenhagen Interpretation, s "shut up and calculate" -- IE the implications and framework and rationale of the model do not matter, it just IS because the math works!

Meanwhile the second most popular interpretation, the Many Worlds interpretation, is defended by Sean Carroll, because the many worlds are just there in the math. Therefore they should be assumed to exist!!!! http://www.preposterousuniverse.com/blog/2014/06/30/why-the-many-worlds-formulation-of-quantum-mechanics-is-probably-correct/

So -- most theoretical physicists basically think that QM, and the universe, are derivative from mathematics. They reduce to math.

There is one major thinker I have read who is pushing back against this and that is Lee Smolin. Here is my review of a book he co-wrote in an effort to rescue physics from mathematization: https://www.amazon.com/gp/customer-reviews/R16VWWZ5I5SC8Q?ref=pf_vv_at_pdctrvw_srp

Here is an essay Smolin wrote on his alternate approach to mathematics. https://arxiv.org/pdf/1506.03733.pdf Note most mathematicians are platonists, and would disagree with his presumption that math is derived from some hidden property of matter and space.

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  • Thanks for the answer, you are right in pointing out the underlying material reductionism (which have taken mathematics to be its language). I recall Sean Carroll saying that most of today's physicist are not inclined to argue the philosophical side of the fondamental questions, they would rather go for the math and hope for the experience to guide. Susskind pointed that in 30 years time, much of the experimental validation will be impossible due to financial issues, hence we will be forced to trust the mathematics, something Einstein will be glad to hear.
    – Gloserio
    Feb 10, 2020 at 10:38
  • Hmmm. Smolin pointed out in "The Trouble with Physics" that the first three efforts to unify GR and QM all worked mathematically, but then failed experimentally. That happened with M-theory (meta string theory) initially too -- it predicted only negative or zero CC, but then we found we had a positive CC -- but then its property of infinite flexibility and therefore irrefutability was invoked, negative branes were invented, and positive CCs were then easily produced. With the infinite space of math to work with, Susskind's approach will lead physics further astray.
    – Dcleve
    Feb 10, 2020 at 13:47
  • Susskind's approach is maybe one choice left to attack the foundational questions, unless you start imagining some different mathematics or re-introduce some non-material aspects to the natural sciences. Would you agree that physics in some ways should be a large though experiment formulated in Math and aided by experiment (in opposition to a large experimentation formulated in Math and aided by thought experiment) ?
    – Gloserio
    Feb 11, 2020 at 9:26
  • Hope this is not out of place here, but this discussion, for me,, fulfills all of the reasons that I belong to the SEP. Capable thinkers who clearly have spent the requisite amount of time and effort to become informed are in discussion about a topic, the nature and role of mathematics in science, which is being discussed calmly and with full respect to each contributor. Plus the input is very helpful. Thanks to all involved! Charles M Saunders
    – user37981
    Feb 11, 2020 at 18:43
  • @Gloserio -- I endorse a Popperian approach to science -- assume indirect realism, observe, then speculate, then test, then revise. In Popper's metaphysics math is part of world 3, and math is among the useful category of hypotheses our world 2 consciousness engages, to help us deal with world 1 of matter. Note Popper and Quine, the two 20th century giants of Phil of Science, were platonists about ideas, after extending empirical indirect realism to ideas.
    – Dcleve
    Feb 12, 2020 at 4:24

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