It seems that prominent physicist Max Born (https://en.wikipedia.org/wiki/Max_Born) believed in some kind of Platonism.

We can infer this, for example, from the book "The Innermost Kernel" (https://epdf.pub/the-innermost-kernel.html):

In a letter to Bohr in 1953, Max Born suggested that it is the mathematical structures that constitute the reality behind the ‘subjective’ physical phenomena. Mathematics reproduces the hidden structures that form the core of reality. Moreover he identified these structures with the structures of pure thinking.

Does this mean that Max Born, much like e.g Max Tegmark (https://en.wikipedia.org/wiki/Max_Tegmark), believed that there were infinitely many universes each one corresponding to a mathematical structure?

  • It appears to me that Max was agreeing with Kant that the source of complexity and order is Mind. I cannot see why this implies multiple universes. It is likely that only one basic structure works. – user20253 Aug 23 '19 at 11:18

The answers to both "some kind of platonism" and "infinitely many universes instantiating mathematical structures" is no. Born is closer to Hegel than to Plato, and even further from Tegmark than from Plato.

His views are described more systematically in the book Physics in My Generation (1966), the chapter Symbol and Reality:

"In every field of experiences this correspondence of sense impressions with symbols has been established... I wish to speak only about the exact sciences which I know. There mathematical symbols are used, and they have a particularity: they reveal structures.

Mathematics is just the detection and investigation of structures of thinking which lie hidden in the mathematical symbols... These are structures of pure thinking. The transition to reality is made by theoretical physics which correlates symbols to observed phenomena. Where this can be done hidden structures are coordinated to phenomena; these very structures are regarded by the physicist as the objective reality lying behind the subjective phenomena."

First, the second paragraph indicates that Born, unlike Tegmark, separates physical from "platonic"/mental existence, and has no need to instantiate his structures as physical universes. Second, Born espouses what is now called mathematical structuralism. This does mean that mathematical claims carry objective truth, but it does not mean that what they are about (like structures) exists even platonically. Structuralism is certainly compatible with platonism, but it does not compel it, it is even compatible with some forms of nominalism. The structures can supervene on something else (like actions or communal practices), and the mathematical talk of them can be expressing that in a different guise. For Born, being objective stems from being "communicable, controllable", and is more of a Hegelian than platonic variety (a la Tegmark), perhaps with a Peircean twist, see SEP Peirce's View of the Relationship Between His Own Work and German Idealism. Another parallel is to Poincare's structural realism with a Kantian flavor.

Born himself invokes Kant and Hegel to clarify his position, and even adapts Hegelian take on Kant's thing-in-itself to his own conception. He goes even further than necessitarian Hegel in admitting:

"The experimentalist has the choice which of them to employ. Thus a subjective trend is reintroduced into physics and cannot be eliminated. Another loss of objectivity is due to the fact that the theory makes only probability predictions".

Nonetheless, the following passages suggest that a purely nominalistic structuralism, where the structures are "empty abstracta", is not for Born either:

[...] The assumption that the coincidence of structures revealed by using different sense organs and communicable from one individual to the other is accidental, is improbable to the highest degree... The concept of causality is a residue of former ways of thinking and is replaced today by the process of coordination as described before. This procedure leads to structures which are communicable, controllable, hence objective. It is justified to call these by the old term 'thing in itself.' They are pure form, void of all sensual qualities. That is all we can wish and expect...

If the object of modern physics, in particular those of atomic physics, are identified with KANT'S 'thing in itself' one can agree with HEGEL that they are a 'perfect abstractum.' But that they are perfectly empty, something from a world beyond, does not fit the facts. Remember what practical use can be made of them in the production of things like engines, aeroplanes, nuclear reactors, plastics, electronic computers and so on ad infinitum. It might happen that nuclear research leads to our being transfered to 'the other world.' Yet HEGEL did not mean this and could not foresee it.'

As usual, it is disputable what Hegel meant or foresaw (steam engines were already around, and there is nothing, in principle, preventing abstracta from being useful in practice). The kind of thin but real existence of abstracta, along with their supervenience on actions and "habits" as the objectively real patterns in them, is reminiscent of Peirce's "extreme realism", derived from merging Kant and Hegel with Duns Scotus, see What is existence and how far does it extend? Although it is unlikely that Born was familiar with it. The reference in the quote is to Hegel's Encyclopedia of Philosophy, §44:

"The thing in itself... means the object as far as everything referring to consciousness, feeling, emotion as well as to all notions is abstracted. It is easy to see what is left - the perfect abstractum, the complete emptiness, just something from 'the other world (Jenseits)...'".

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Based on the quoted passage, Max Born claimed that mathematics reproduces the hidden structures of reality. This reproduction would be a way to see those structures perhaps more clearly like a photograph might allow us to see details of scenery that we missed. It does not suggest that this reproduction is the reality it reproduces.

The most one can say from this is that Born believed the universe is real, not that he believed the universe was identical to that mathematical structure or that the scenery was identical to the photograph. They aren't the same, but one reproduces the other.

Max Tegmark on the other hand believes that every consistent mathematical structure is itself a universe. Our universe is a mathematical structure. Consider this quote from "The Multiverse Hierarchy" (page 10).

It means that mathematical equations describe not merely some limited aspects of the physical world, but all aspects of it. It means that there is some mathematical structure that is what mathematicians call isomorphic (and hence equivalent) to our physical world, with each physical entity having a unique counterpart in the mathematical structure and vice versa.

This goes beyond reproducing the hidden structures of the universe. Because of that there need not be a multiverse of universes from Born's perspective. Each mathematical theory need not be a separate universe.

Tegmark, M. (2009). The multiverse hierarchy. arXiv preprint arXiv:0905.1283. Retrieved on August 22, 2019 from arXiv.org at https://arxiv.org/pdf/0905.1283.pdf

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