Despite the title of this blog, I have made it clear that I reject any form of Platonism, from the original idea of “Forms” to the mathematical variety. This is something I’ve given quite a bit of thought to, and one of those instances were I can document having changed my mind, from a positive position to a negative one. But of course I’m neither a metaphysician nor a philosopher of mathematics, so my opinions in this area are simply those of a scientist and philosopher with a general background in both disciplines.

Nonetheless, there is yet another type of Platonism about which I can claim more expertise: Andreas Wagner’s biological Platonism. I have known Andreas for years (we met a couple of times, but I am very familiar with his writings in biology), and I can say without hesitation that he is one of the most interesting and provocative theoretical developmental biologists out there. Last year, he published an essay in Aeon magazine entitled “Without a library of Platonic forms, evolution couldn’t work.” I beg to differ, and I’ll explain why in this essay.

Andreas tells us that a fundamental unit in biological classification is the species. We, for instance, belong to the species Homo sapiens, which is distinct from our closest relative, the chimpanzee, known scientifically as Pan troglodytes. (The full name of our species is actually Homo sapiens sapiens, because we can’t be too modest about our own wisdom; and by the way, it is controversial whether humans really belong to a different genus than chimpanzees. Some biologist have proposed renaming ourselves Pan sapiens. That would be a rare example of human humility, as well as good scientific practice.)

It is true that species are a more crucial level in the taxonomic hierarchy of living things than both levels below (sub-species, races) and above (genus, family, order, etc.), and have been so since Linnaeus. But Andreas begins to veer off the main course of modern biology when it talks about “boxes” (the species) and “hierarchies” in too rigid a fashion. Ever since the mid-60s, modern systematics is based on what is known as a cladistic approach, which organizes biological forms in nested, highly branching trees (“clades”) that do not actually correspond, if not in a vague and imprecise manner, to the Linnaean boxes. This makes sense: evolution is a continuous process that produces all sorts of patterns and gradations, which makes systematics a hell of a lot more challenging than, say, stamp collecting.

It is therefore even weirder when Andreas talks about the “essence” of species, and links the concept directly to Platonism: “A systematist’s task might be daunting, but it becomes manageable if each species is distinguished by its own Platonic essence. For example, a legless body and flexible jaws might be part of a snake’s essence, different from that of other reptiles. The task is to find a species’ essence. Indeed, the essence really is the species in the world of Platonists. To be a snake is nothing other than to be an instance of the form of the snake.”

No, definitely not. To begin with, modern biology has long since rejected any talk of “essence.” Indeed, Darwin himself was what we might call a species anti-realist, as he thought that species are arbitrary boundaries drawn by humans for their own convenience, not reflective of any deeper metaphysical reality. Sure enough, biologists still don’t agree on a universal definition of species (see my essay and modest proposal here), a good reason being that, say, a “species” of bacteria has nothing whatsoever to do with a species of plants, and the latter has little similarity — as a category — to a species of invertebrates, and the latter… You get the point.

Second, no, snakes cannot reasonably be thought of as “nothing other than an instance of the Form of the snake.” Not only that simply doesn’t help (how do we study these Forms? Where are they?), it is a way of seeing things that is in serious tension with the whole idea of evolution. Snakes are a group of reptiles that likely evolved from burrowing lizards back in the Cretaceous. This means that they acquired their supposed Platonic Form gradually, first by passing through a two-legged stage (e.g., in the fossil known as Najash rionegrina), or species with hind-limbs but lacking connection between the pelvic bones and the vertebrae (as in Haasiophis, Pachyrhachis and Eupodophis). And who knows what future evolution has in store for the descendant of current snakes. So to say that what we see now somehow represents the Platonic terminus of an evolutionary process is entirely groundless.

Of course Andreas is aware of this sort of objections, and indeed brings up the so-called “glass lizard,” a legless lizard that is indistinguishable from a snake, and yet is classified among lizards on the basis of a number of other anatomical traits. He also mentions the Cretaceous “snakes” with rudimentary hindlegs. It is because of these cases that the famed 20th century evolutionary biologist Ernst Mayr called Plato “the great anti-hero of evolutionism.”

But Andreas insists that Plato will have the last word, we just need to dig deeper. His first move, though, is odd. He quotes the 1905 biologist Hugo De Vries, one of the re-discoverers of Mendel’s work that established the modern science of genetics, and who was skeptical of Darwin. De Vries famously said: “Natural selection can explain the survival of the fittest, but it cannot explain the arrival of the fittest.”

This is odd because the reconciliation of genetics and Darwinism is one of the crowning achievements of 20th century biology, taking the form of the so-called Modern Synthesis, a complex articulation of the Darwinian insight, incorporating the ideas of common descent, natural selection, mutation and recombination into a general mathematical theory of how evolution works. Harking back to De Vries is a dead-end.

Undeterred, Andreas introduces a metaphor to clarify what he calls a “problem” (and which I don’t think is any such thing). Presumably taking inspiration from Jorge Luis Borges, he invites us to imagine a gigantic library containing all possible sequences of letters in the English alphabet (the specific language doesn’t matter, really). Most of the books in the library are nonsensical, but from time to time you will find an exact replica of the works of Shakespeare, or Darwin’s Origin of Species. If you pick up a volume at random, however, the chances you’ll happen on something valuable are minute.

If we imagine a library containing instead all possible sequences of DNA, it will describe all functional proteins, as well as a bunch that will never work. The question is: since mutation is random, how does natural selection “know” how to find its way in the very, very large library of possible forms?

Developing the metaphor, Andreas suggests that we could find our way into the English texts library if the books were organized so that neighbor books would have some of their text changed, but retained the original meaning. Some of the neighbors may actually change the meaning of a word, while still be readable in sensible English, for instance with a “mutation” changing GOLD into MOLD.

Andreas sees the genomic equivalent of the library arranged in the same way: all DNA sequences that maintain the same functional protein, or all sequences that change amino-acids in the protein while retaining functionality, are connected by single steps, so that one can traverse the entire library without having to make huge jumps across a bunch of sequences that would be non-functional and therefore fatal.

He adds: “Let me put this point as strongly as I can. Without these pathways of synonymous texts, these sets of genes that express precisely the same function in ever-shifting sequences of letters, it would not be possible to keep finding new innovations via random mutation. Evolution would not work.”

Well, yes, and that’s precisely where natural selection comes in! While mutations are random with respect to their fitness value, natural selection is not at all a random process, but one that statistically picks valuable mutations and keeps them in the population’s gene pool, while at the same time eliminating any mutation that turns out to be significantly deleterious or fatal. That is, natural selection does the work of “walking” a population through the library, and it is the combination of a random process (mutation) and a non-random one (selection) that yields evolutionary change. There is no mystery here, and there hasn’t been for about a century now.

Andreas doesn’t appear to be as puzzled by how natural selection can find its way through the library, though, as by a different question: “So nature’s libraries and their sprawling networks go a long way towards explaining life’s capacity to evolve. But where do they come from? You cannot see them in the glass lizard or its anatomy. They are nowhere near life’s visible surface, nor are they underneath this surface, in the structure of its tissues and cells. They are not even in the submicroscopic structure of its DNA. They exist in a world of concepts, the kind of abstract concepts that mathematicians explore. Does that make them any less real?”

Yes, of course it does. If by “real” one means that the sequences in question have some kind of substantive ontology, they “exist” somewhere, though obviously not in standard 4-dimensional spacetime. But if not there, where? What does it mean for an abstract concept, or a possibility, to “exist”? These are the very same questions faced by mathematical Platonists, and biological Platonism — like its math counterpart — simply seems to conjure up a problem where none exists, proceeding then to offer a solution that is no solution at all.

If one is short on arguments, one can still resort to name dropping, which is a temptation to which Andreas too succumbs: “Some believe with the Austrian philosopher Ludwig Wittgenstein that mathematical truths are human inventions. But others believe with Plato that our visible world is a faint shadow of higher truths. Among them are many mathematicians and physicists, including Charles Fefferman, winner of the Fields medal, the equivalent of a Nobel Prize in mathematics. He expressed his experience when breaking new mathematical ground this way: ‘There’s something awe-inspiring. You aren’t creating. You’re discovering what was there all the time, and that is much more beautiful than anything that man can create.’ In physics, the Nobel laureate Eugene Wigner called it ‘the unreasonable effectiveness of mathematics.’ And indeed, it is not clear why Newton’s law of gravitation should apply to so much more than the falling apple that might have inspired it, why it should describe everything from accreting planets to entire solar systems and rotating galaxies. Except that it does. For whatever reason, reality appears to obey certain mathematical formulae.”

Okay, let’s break this down a bit. To begin with, for every pro-Platonist quote by an eminent scientist or mathematician or philosopher one can easily come up with an equally strident counter-quote by a skeptic of equal rank. (Try it out as a Google game with your friends.) Second, Newton’s law is actually wrong, so it is a little bizarre to use it as an example. It turns out to be an approximation of General Relativity, valid only under certain specific circumstances. And we already know that GR is in some sense wrong or incomplete in turn. (And by the way, Newton made up the story of the falling apple to embellish his own scientific insight.) Third, reality doesn’t “obey” mathematical formulae. Rather, mathematical formulae are human inventions (Wittgenstein docet) that more or less accurately describe reality.

Which leads me to conclude with one of those anti-Platonism quotes alluded to above, by none other than Albert Einstein: “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? […] In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” (from J.R. Newman, The World of Mathematics, Simon & Schuster, 1956)