Platonism After Darwin: Mathematical Potentiality and the Creative Advance

Reflections on this discussion, which is part of the Symposium on Platonic Space.

I’ve only listened to the first 20 minutes or so of this session. These are preliminary reflections, and I expect I’ll have more to say once I’ve heard the rest. I also plan to participate live in another meeting of this symposium group, to which dozens of researchers are contributing. What follows is really just me riffing and trying to get my bearings so as to frame what I think is at stake.

Chris Fields mentions the shift that crystallizes in the nineteenth century and then intensifies into the early twentieth: the emergence of non-Euclidean geometries, the foundations problem in mathematics, and the proliferation of rival programs for grounding mathematical knowledge—logicism, formalism, intuitionism/constructivism, set theory in its various axiomatizations, and later category-theoretic approaches. Whatever one’s preferred genealogy, the contemporary philosophy of mathematics has been blown wide open into a plurality of metaphysical possibilities.

Levin is drawn to a broadly “Platonic” picture of mathematical reality, which is not easy to argue against, at least not decisively, and certainly not without paying a metaphysical price somewhere else. I haven’t looked at the most recent polls, but anecdotally it is no secret that many practicing pure mathematicians are Platonists by default. That doesn’t mean they’ve all signed onto a worked-out metaphysical doctrine. But in the lived practice of mathematical work, the experience feels like contact with something that has its own necessity, something participated in, rather than something merely invented. No doubt others push hard in the opposite direction and try to give an explicitly Darwinian evolutionary or “ontogenetic” account of mathematics—something my friend Tim Jackson is likely to emphasize when he joins the discussion—where mathematical cognition is continuous with biological development and the historical emergence of quasi-invariants.

But as Levin suggests, science discovers that physical processes instantiate patterns that can be described using mathematics. Constants, symmetries, ratios and other invariants are not themselves empirical objects but mathematically formulated relations. Their success in application to physics forces the philosophical question of why nature exhibits such profound mathematical order. Why is nature mathematically intelligible at all, and what does that intelligibility commit us to metaphysically?

Chris Fields then brought in the mystery of time. In many physical formalisms, time enters equations as a quantifiable variable. But the undeniable usefulness of treating time as a parameter for coordinate analysis does not mean temporality is ultimately measurable by clocks. Whatever clocks measure, lived temporality is obviously not simply identical with that measurement, since there’s no way to measure or read a dial except while already living through the flow of time. Atomic clocks are extremely precise instruments for correlating periodic processes, but the precision of the instrument doesn’t settle the ontological question of what time is.

Bergson is relevant here. He wasn’t right about everything in his dispute with Einstein. But he was right to insist that duration or lived temporality—the irreversible, qualitative passage of nature, the thickness of becoming—is not reducible to what clocks quantify. All physical parameterizations sit within this deeper temporal context. The special sciences can never fully encompass this with formal models, because the models presuppose the very becoming they attempt to represent. Models are invaluable abstractions, but abstractions cannot explain living temporality.

Metaphysics is the critic of the abstractions of the special sciences. It asks what has been left out, what has been smuggled in, and what has been unduly reified by misplaced concreteness. At the same time, metaphysics has no other data to work with than what all the specialized modes of experience provide. Its categories must remain corrigible: they must be adjusted and refined in light of what the sciences disclose. Whitehead’s project is to propose a matrix of categories adequate to what has been revealed across the whole range of inquiry—physics, chemistry, biology, psychology, sociology, and so on.

But there’s a further Jamesian-Peircean move we cannot avoid: radical empiricism means we don’t get to arbitrarily exclude domains of experience that don’t fit the narrow epistemic limits of physicalism. Religious experience, aesthetic experience, moral experience are part of the data any metaphysical scheme even pretending to adequacy (if not completeness) must interpret, not because they are infallible sources of insight, but because they are part of what an honest, comprehensive account of human experience includes.

If we’re going to do metaphysics and cosmology, if we’re trying to think seriously about the nature of life, the universe, and everything, we eventually have to face the weighty questions. We might even need to get our hands dirty and do some theology. Is this an intelligent universe? Well, it certainly seems intelligible. Physics gains purchase on reality by applying mathematics and technique to nature. The success of mathematical physics is not self-explanatory. Metaphysics is, among other things, an attempt to articulate the conditions that make intelligibility possible. Of course, the irreversibility of evolutionary time does put certain limits on that intelligibility. And mathematics can and had misled the scientific imagination of nature.

For Goethe, the human organism, with its suite of healthy sense organs, is not a subjective impediment to objectivity but the most refined instrument for nature’s self-disclosure. That view is rooted in the older hermetic and Platonic idea of the human being as microcosm: a miniature universe, a recapitulation of the whole. And it is precisely because we are such a recapitulation that we can, in some measure, participate intellectually and imaginatively in the same patterns that produce the physical world.

Schelling’s phrase autophysis philosophia (“nature itself philosophizing”) captures what Goethe is on about. The philosophy of nature is not a spectator sport. It is nature coming to reflective expression in and through the human being. Newtonian and Copernican science accomplished something essential by dislocating us from the center—by taking, as it were, a sun’s-eye view. That decentering was historically necessary. But now we have to rediscover ourselves as a “moving center” (Richard Tarnas’ phrase), not in the sense of a simple return to medieval anthropocentrism, but in the sense that the knowing subject is itself a participatory event in nature.

The goal of science should not be to pretend we can stand outside the world and see it from nowhere. That “view from nowhere” is a residue of a certain deistic ideal of objectivity that was historically useful but metaphysically distorting when absolutized. The point is rather that a human being—as a microcosm—can, through self-reflexive participation, cultivate a more inclusive, more comprehensive, more “divine” mode of feeling and understanding. Not a God’s-eye view from outside, but through intimate participation, a widening of concern, a refinement of attention, a disciplined receptivity to mathematical form and to moral and aesthetic value.

An analogy to with the cellular collective composing us may be helpful. My sense of selfhood—the continuity of my conscious identity—can be imagined as the emergent achievement of the monotheistic religion of my cells. Through morphogenesis, metabolism, and maintenance, my cellular collective sustains a whole that no one cell can comprehend. Their bioelectrically and morphogenetically coordinated activities (hemoglobin flowing through my veins, the rhythms of my heart, the synchronous waves of my neurons) is something like a ritual practice: patterned repetitions that sustains a living unity. They worship the whole they serve without consciously intending me. Cells are like spiritual practitioners participating in the divine life by performing prayer and ritual without intellectually understanding why.

If you scale this intuition up, you get something like the process theological image: the divine is not at the beginning as a cosmic engineer with a blueprint, but at the end as an emergent fulfillment. Max Scheler quipped that traditional theology imagined God at the beginning, but it turns out God is at the end. In other words, there is something about the nature of the divine that emerges in and with the universe as it evolves. That doesn’t mean the beginning is “pure chaos.” In fact, I think it’s important to say there is no such thing as pure chaos (though I’m not getting into that here). But it does mean we should resist any picture in which the world is merely the mechanical execution of a pre-written script. The universe is still being created. And God needs our help in that effort.

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