Forms at Home in the Universe: On Two Problems of Body

The mind-body problem we are familiar with, so let us not tally with this too much; at least, not yet.

There is another problem of body, most famously formulated by Eugene Wigner, in his oft cited paper on the “unreasonable effectiveness of mathematics” in the physical sciences. How comes it that mathematical concepts such as complex numbers, for instance, have such a ready application in the physical sciences, and without which the physical world is unintelligible to us?

There is a kind of miracle at work here; in Wigner’s terms

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.

What we have here is a problem of body, what I’ll call a form-body problem; why do the forms of mathematics so frequently and so fundamentally crop up in the physical world?

What is interesting is that it is recent historical developments that enabled us to formulate this problem in a deep way. It was in the 19th century that mathematics really took its modern shape as an abstract and pure discipline, “a world unto itself” to use the expression of Amir Alexander in his wonderful Dual at Dawn: Heroes, Martyrs and the Rise of Modern Mathematics.

Prior to this, through the supremacy of geometry handed down to us from Euclid, mathematics was firmly grounded in the natural world. It was not a world unto itself. For most of Western intellectual history astronomy was the queen of the sciences, where geometrical techniques had a ready and eminently intelligible application. The relationship between mathematics and the world is nowhere near as mysterious or miraculous here. It is not so hard to see how one could argue that geometry emerges from the relationship of things in the world or of things in space.

In the 19th century not only did a pure, abstract, mathematics emerge that was a world unto itself but also astronomy was displaced as the queen of the sciences. Now physics became king, to borrow the expression of Iwan Morus.

This dual intellectual movement, of the rise of pure mathematics and the elevated ontological status attached to the physical, then leads to Wigner’s problem; how does the physical world emerge from the abstract world?

One can see how this is a dilemma for those versed in the analytic-synthetic distinction. How do truths of the physical world depend upon truths of the analytical if there be a hard and fast distinction between the two?

My own view is that the development of modern mathematics and the rise of physics to cognitive sovereignty played a very important role in the emergence of logical positivism as an attempt to reconcile these two intellectual revolutions within a single, empiricist and physicalist, worldview.

But Wigner’s problem, despite all that, remained, and remains, a deep mystery.

So we have two problems of body; the mind-body problem and the form-body problem. I agree with Chomsky’s position on the former, namely until a proper account of the physical or body can be given there isn’t much hope of dealing with the mind-body problem indeed even addressing it. The same applies for the latter.

Chomsky himself in What Kind of Creatures are We? makes an argument for panpsychism. That, somehow, mental attributes inhere in the physical; that is, physical entities have mental attributes like consciousness. This renders the emergence of mind from body wholly less mysterious than it would otherwise be.

Why not the same for Wigner’s problem? That the physical inheres in the abstract world of pure mathematics, that complex numbers and so on have physical attributes? One could argue for this from analogy.

I suspect, that is wildly speculatively suspect, that the issue of form looms large here. Form played a critical, although in different ways, role in the philosophies of Plato and Aristotle to which everything that came after are mere footnotes.

I suspect that Plato was right about Forms, and its relation to the physical, only his view needs to be purged of the error of transcendence. Forms are not out *there* in a pure Platonic heaven they are in *here* at home in the universe.

This is my off the beaten track hunch.