Against biological Platonism

A rendition of the Library of Babel, by J.L. Borges

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)

296 thoughts on “Against biological Platonism

  1. Seth Leon

    Thanks for clarifying David. I was reading the 2nd quote in ordinary language, and don’t buy into the idea that structural relations are real objects.

    Is the idea that using math in the form of say complex systems theory or some other approach one in principle could approximate an ideal tunnel for some given conditions by plugging in the data should the important data from the other important variables be available? This just suggests that actual physical systems exists and that we can identify some regularity in component’s we have identified from the system. I agree with DanK and Massimo, that this does not imply that the mathematical relations are real in the same sense as identified objects.


  2. synred

    still don’t understand the distinction. If someone says “A is true but might not have been true, and B is true and could not possibly have not been true”, isn’t “true” used in the same sense each time in the sentence? If not then how can we link the clauses in this sentence?

    Seems reasonable to me. One is still asserting something to be true, though the quality of the evidence varies or in some cases is completely lacking. Still whoever asserts something is making a ‘truth claim’ — right or wrong… It seems like a Wittgenstein type issue.


  3. Robin Herbert

    Hi synred,

    To clarify, are you saying that “true” has a different meaning in the first clause of the sentence:““A is true but might not have been true, and B is true and could not possibly have not been true” to the one it has in the second?

    Liked by 1 person

  4. synred

    The mouse’s tunnel is likely not optimal anyway. Good enough is all evolution can achieve. And likely the environment and predators vary enough to make the concept of an ‘optimal tunnel’ meaningless.

    And if some god adapted the mouse to be perfect his snakes would die out.


  5. Robin Herbert

    I will tell you why I don’t think it makes sense. If the word “true” in the sentence:

    “A is true but might not have been true, and B is true and could not possibly have not been true”

    has a different meaning in the first clause to the one it has in the second, then we could use two separate words for these different concepts, say a-true and b-true. So it would become:

    “A is a-true but might not have been a-true, and B is b-true and could not possibly have not been b-true”

    So what would be the difference between “a-true” and “b-true”? If you say that “a-true” sentences are sentences that are true, but might not have been the case then you have the first clause saing “A is true, but might not have been the case but it might not have been the case that A was true and might not have been the case”

    In other words the first clause is implying that it might have been that A had to be the case. And that would in turn imply that A had to be the case, full stop.

    So it doesn’t make sense to me that different modalities, scope and certainty about something means that we have different types of truth. It makes more sense to say that we mean one thing by the truth and the modalities, scope and levels of certainty are qualifiers about that concept.


  6. Thomas Jones

    Robin, the first seems to imply something relative while the second an absolute. A is true today but might not have been yesterday and B is true today and could not have not been true yesterday.


  7. brodix


    ” if some god adapted the mouse to be perfect his snakes would die out.”

    No snakes, etc. and the mice overpopulate.

    Life is linear; Toward good, away from bad. Nature is cyclical; What goes round, comes round.

    Liked by 1 person

  8. Robin Herbert

    When you qualify a concept, you don’t change that concept, rather you create a new concept which consists of the base concept plus the qualifier.

    If you say that qualifying a concept changes the concept that it qualifies then you get the shift in meaning of the type that I point out. Worse, you end up in an infinite regress.

    So the word “true” means the same thing in that sentence each time it is used.


  9. Robin Herbert

    Presumably the “optimal tunnel” is the one which will lead to the highest probability in some environment that the particular genetic configuration will be passed on.


  10. synred

    No. think I said exactly, almost the opposite. The both assertions are assertions something is true, the evidence different.


  11. synred

    Robin, the first seems to imply something relative while the second an absolute. A is true today but might not have been yesterday and B is true today and could not have not been true yesterday.

    Thomas I think robin is referring to the truth or falsehood of the statements, nor the quality of the evidence, but just the meaning of the word ‘true.’

    Liked by 1 person

  12. synred

    Evolution is anything but linear. I don’t know what life is linear means, but it does involve a lot of non-linear processes.


  13. Robin Herbert

    Let me quickly address why “simplistic and intellectually lazy” does not constitute a valid critique of a position.

    Say Jill makes a particular claim and provides her reasons and then John says that it is simplistic and intellectually lazy.

    Firstly, if there was some invalidity or lack of soundness in Jill’s reasoning, John could have simply pointed it out and then the charges of being simplistic and lazy would be superfluous.

    Does the claim that she has been simplistic and intellectually lazy help Jill see why she is wrong? How? She knows that John thinks that there is some complexity she has failed to address or some more thinking that she ought to do. But if John cannot identify this complexity or give a hint to what sort of extra thinking she ought to be doing then how does he know that there in any? On the other hand if John can identify the complexity or the areas in which she should be doing more thinking, then he could just do that.

    Finally, suppose Jill didn’t do the extra thinking due to laziness. That does not imply, in itself, that there was extra thinking necessary.

    If there is some CCTV footate of known gangsters leading someone by gunpoint into a warehouse and later of them carrying out his dead body in a blanket, then the simplistic and intellectually lazy conclusion would be that they had murdered him. But it would probably be true.

    If the police had come to this conclusion because they were lazy and simplistic, then that would not imply that the conclusion was any less true.

    If the police had been complex and intellectually industrious they might have arrived at a number of ingenious alternative theories, but, let’s face it, those would probably have been wrong.


  14. synred

    Presumably the “optimal tunnel” is the one which will lead to the highest probability in some environment that the particular genetic configuration will be passed on.

    Which means that an optimal tunnel only exist in a non-existent perfectly uniform environment.

    Even in a reasonably uniform environment evolution will not find the ‘optimal tunnel.’ It hunts around at random. It ‘search’ can be restricted by previous history of the species or it’s ancestor species. Evolution copples together a good enough solution (or quite often doesn’t and then every body dies)., it does not seek the ideal.


  15. synred

    If the police had been complex and intellectually industrious they might have arrived at a number of ingenious alternative theories, but, let’s face it, those would probably have been wrong

    However, it doesn’t mean the police were right either They are quite often wrong. That’s why we have defense lawyers.


  16. Robin Herbert

    Say there is a particular population of deer mice in a particular environment. For them to build a better tunnel there needs to be some shape, size or configuration of tunnel which would better serve the purpose and increase the probability that they survive to procreate. There also needs to be some plausible set of mutations that would create a deer mouse that builds that better tunnel.

    For that population, in that environment, there is a fact of the matter about whether or not both these conditions held before any mutation occurs in that population, in that environment.

    But those facts don’t have to be encoded anywhere else, because they are encoded in the state of that population and that environment. Having them encoded anywhere else would be superfluous.

    Liked by 2 people

  17. synred

    Presumably the “optimal tunnel” is the one which will lead to the highest probability in some environment that the particular genetic configuration will be passed on.

    Even that is not clear. Evolution can’t find that highest probability a particular will be passed on. It finds a combination that happens to be past on more frequently than the others in the gene pool. If conditions old steady for a few generations that combination will come to dominate the pool. If conditions change it may prove a dead end after some initial success.`

    There may be an ‘optimal’ in the sense of most likely to reach the next generation (however, generation is defined). It’s also a statistical truth that evolution will almost never hit on this combination and if did it wouldn’t matter as things change.


  18. Robin Herbert

    “However, it doesn’t mean the police were right either They are quite often wrong. That’s why we have defense lawyers.”

    Yes, but the defense lawyers would have to do better than point out that it was a very simple conclusion or claim that the police didn’t think hard enough about alternative solutions.


  19. Robin Herbert

    Also, don’t overlook the positive aspects of laziness. There is a lot of unnecessary activity in this world due to the fact that people were not lazy enough. I once took over as IT manager in a chain of jewelry stores. The previous manager arrived at 5:30 am each and every business day and downloaded reports from each of the 150 stores nationwide and manually compiled them into reports for the region and product managers.

    He was certainly not lazy and his way of doing it was certainly complex. Me, being the lazy and simplistic fellow I am, wrote a program that automated the whole process and the same reports were delivered to the managers’ mailboxes by 5:40 am each day, while I happily arrived at 8:30 am having had a leisurely morning.


  20. synred

    claim that the police didn’t think hard enough about alternative solutions.

    which of course precisely what defense lawyers do and they a often right!

    If scientist collected evidence the way police do we’d still be in the dark ages.

    Your example of the known gangsters and the video is straw. Things are rarely that simple and hence simple minded is often (but not always) wrong.

    What the hell? Even a broken clock is right twice a day…


  21. synred

    In the USA it’s ‘innocent ;until proven guilty’, the burden of proof is on the police. The lawyers need merely show the cops ignored plausible alternatives to get there client off (who may be guilty).

    Lazy policing results in injustice both ways: the innocent go to jail and the guilty get off.

    In the case of the central park 5 lazy policing (and outright bias) not only put 5 innocent kids sin jail, it left a rapist murder on the loose and lead directly to more rape and murder.


  22. Robin Herbert

    My example of the gangsters and the video is not straw, it is a real life case that just recently happened in Australia. Actually things usually really are that simple. It is usually only on the telly and in books that it turns out the gangsters had gone straight and were preventing the man from killing someone, but another person, lurking in the shadows had shot the person and they, each thinking the other had done it were covering up for each other, not realising they were both innocent and then the defense lawyer breaks the story of the man who we had all thought completely innocent of anything.

    No, they had killed him and were disposing of the body. They are both in jail now.

    We had another case where the police did not accept the simplistic and intellectually lazy option. A woman claimed a dingo had taken her baby. But they knew better. She had taken the baby to Uluru in order to kill it for some mysterious but perhaps religiously motivated reason. We had highly respected forensic experts talk about the characteristic spray pattern of the blood stain in the car (which turned out to be a sort of rust retardant that is found in all Holden Sunbird of that year)

    No simplistic intellectually lazy solution for them.

    But it turned out that a dingo had taken her baby.


  23. Robin Herbert

    But I go back to my original point. If John ignores Jill’s specific reasoning and says “that is simplistic and intellectually lazy” then what does it add? If John cannot identify the complexities he is claiming that Jill has overlooked, then how does he know this? On the other hand if he does know of these complexities then he could simply point them out.

    It may be that he is right and those complexities are there – but simply claiming they are their adds nothing. Implying that Jill has missed these complexities through laziness sounds like ad hominem

    Liked by 1 person

  24. Robin Herbert

    I don’t know whether lazy policing or over industrious policing leads to more injustices. A friend of mine was picked up by the police because he was carrying an expensive looking boom box and they assumed he had stolen it. They spent two full days interrogating him and eventually he signed a confession.

    That does not sound like lazy policing. At his trial he simply had the shop assistant, who was a respected member of the community and knew him well and testified that he had bought the boom box. He recalled well how he had taken my friend through all of the options and his chat with him.

    The judge asked the police why they had not simply gone and spoken to this man in the first place. They could not answer. That would have been much simpler than two days of interrogation. That doesn’t sound like lazy policing to me.


  25. Robin Herbert

    Yet another friend was arrested by the police at a demo where some of the others had become unruly. The were very industrious in trying to break his story that he was a mild mannered department head in the civil service who had exercised his right to demonstrate and had broken no law. They found out all sorts of things. Turns out he was gay. Who knew? Even the judge said “Oh for goodness sake, what possible relevance?”


  26. Thomas Jones

    Hi, Robin, “I don’t think you are understanding what I am saying.”

    The thought did occur to me. 🙂 And I was too lazy to trace it back. But I wrote my comment before I saw your later post above mine. Which helped. But not much. Anyway, I’ll defer to you since you are the staff logician here and let you and synred follow the optimal tunnel. I’ll be waiting on the other side. 🙂


  27. Robin Herbert

    “Even that is not clear. Evolution can’t find that highest probability a particular will be passed on. It finds a combination that happens to be past on more frequently than the others in the gene pool. ”

    I don’t get it. Isn’t the thing that got passed on more frequently than the others in the gene pool the thing that had the greatest probability of being passed on?


Comments are closed.