Evolution as an Argument for Intelligent Design

The presentation of evolution and intelligent design as competing approaches to the same scientific evidence is as useful as it is facile. The typical juxtaposition insinuates, at least in the popular imagination, that evolution invites with it not merely methodological but metaphysical naturalism, while intelligent design is inseparable from Theism (and, perhaps, religion). While this presentation has the prima facie advantages of providing an apparently clean distinction between science and pseudoscience along with being easily comprehended by anyone lacking intimate familiarity with the issue, explorations of any depth into the anatomy of the controversy reveal this picture of things to be superficial. It is at least complicated, for instance, by the fact that evolution and naturalism are arguably incompatible beliefs (in the sense that their conjunction implies a defeater for the belief in the reliability of our cognitive faculties, which in turn provides a defeater for the belief in that conjunction). This point has been elaborately argued by Alvin Plantinga1 and has gained indirect support recently from the work of Hoffman (et al.).2 Not to mention that intelligent design is compatible with both methodological and metaphysical naturalism, for intelligent design says only that we can, under certain (presently satisfied) conditions, make a justified inference to design (usually at the bio-chemical or genetic levels), and such unconventional views as directed panspermia,3 for example, could provide a naturalistic framework licensing the kind of design-inferences which figures like Behe4 and Meyer5 wish to make.6 To make matters worse, metaphysical naturalism is compatible with intelligent design on certain anti-realist readings of science, and even on realism there are design inferences which pose no challenge to contemporary scientific consensus (such as, for instance, the inference to which some fine-tuning arguments invite us). Thus, ironically, I think that while naturalism and evolution appear to be ideological siblings, on closer inspection we find that naturalism is more compatible with intelligent design than it is with evolution.7

Having sufficiently muddied the waters, I now intend to jump in. However, the obligatory preliminary caveat must be added at this point that I find the theory of evolution theologically unobjectionable, even in its so-called neo-Darwinian form. I find evolution more than theologically conscionable (even, and especially, in light of Humani Generis), and any residual (and recurring) doubts I may have about it come from philosophical and/or scientific considerations. There are some noteworthy doubts to survey here, including the criticism from Fodor and Piattelli-Palmarini to the effect that evolution by ‘natural selection’ is not a properly scientific theory at all,8 or Kalevi Kull’s suggestion that there are now, in light of epigenetics, viable evolutionary theories which operate without natural selection,9 not to mention some of the better arguments from intelligent design theorists,10 in particular from the difficulty of finding a mathematically viable model of neo-Darwinian evolution.11 As the provocative title of Thomas Nagel’s book, Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False,12 suggests, the intellectual tide may be turning on this question.

Nevertheless, I remain for the moment cautiously committed to the (neo-Darwinian) theory of evolution, though I have become much less militant about this commitment over the years. Ever since I was made to really understand the theory of evolution (largely thanks to Kenneth R. Miller in a spectacular presentation here), I have been unable to shake a sense of awe at its elegance. The stunning beauty of the theory, its ability to explain so much with so simple a mechanism, impels my belief. This is more than just unhinged sentimentalism; there is some reason to think that beauty or elegance are indications of truth, even in the hard sciences. I have quoted the following passage from Robin Collins before, but it bears repeating;

To say that the beauty of the mathematical structure of nature is merely subjective, however, completely fails to account for the amazing success of the criterion of beauty in producing predictively accurate theories, such as Einstein’s general theory of relativity.”13

If beauty is a signpost of truth, a sort of ‘trademark of reality,’ then that provides at least some reason to think that the theory of evolution, in virtue of its captivating loveliness, is at least approximately true. At least we can say that given any two scientific theories which are otherwise empirically indistinguishable (or, less strictly, where neither one is empirically preferable to the other), the more beautiful of the two is more likely to be true. I continue to think that the neo-Darwinian theory of evolution best exemplifies, on balance, the desiderata we look for in scientific theories (e.g., explanatory scope, predictive and retrodictive power, elegance, etc.). At least it does so, best I can tell, better than any currently available alternative view.

In any case, I am not here to defend any typical version of intelligent design proposed as an alternative to standard evolutionary theory. I want to do something much more interesting than that. I want to briefly explore whether, as I suspect, evolution lends credence to intelligent design. I think that it does, but in order to explain how it does I need to introduce the reader to an idea put forward recently by the philosopher Alvin Plantinga. In a recent best-selling popular-level book Plantinga gave an astonishing defence of Michael Behe’s case for intelligent design. It was astonishing because it offered a completely novel and innovative reading of Behe. In short, he suggests that we can form a properly basic belief in design which, while not indefeasible, may not be threatened by evolution. It may not be threatened by evolution because instead of being an inference to design, Plantinga suggests that our apprehension of design in nature is rather more like a perception.

“In many cases, so the thought goes, the belief that something or other is a product of design is not formed by way of inference, but in the basic way; what goes on here is to be understood as more like perception than like inference.”14

On his view, a person whose cognitive faculties are operating correctly while being appropriately connected to the external world can perceive design. Now, the astute reader will have noticed a tension here, since intelligent design as I previously defined it was supposed to be an inference. However, if we relax our definition of intelligent design a little bit, we can see a way to take evolution as evidence, in some loose sense, for intelligent design. Define intelligent design roughly as:

Intelligent Design =def. the justified/warranted belief in design in the natural world.

How, though, could evolution possibly provide any support for intelligent design thus defined? Well, I have already hinted at how; the evolutionary process itself may give us the impression of design. Notice that I am not merely saying that the products of the evolutionary process give the impression of design, but that the evolutionary process itself bespeaks intelligence.

Ever since seeing the beauty and elegance in the theory of evolution, I have had a difficult time understanding how anyone who believed in it could avoid what seemed to me to be the obvious conclusion; namely, that the process of evolution seemed an intelligent orchestration. I am, on this point, in strong agreement with the quasi-heretic Pierre Teilhard de Chardin, who could not help but read (perhaps too much) religious significance into evolution. Those who do not see this have, in my opinion, not sufficiently reflected upon the apparent design of the evolutionary process itself. How odd would it be if a universe fundamentally comprised of unintelligent elements and forces with no intelligently designed fundamental structure (laws, etc.) just happened to give rise to the overwhelming appearance of design? It seems nearly unconscionable to me. Some unscrupulous thinkers dismiss this intuition as naïve, suggesting that the mechanisms responsible for the appearance of design are comprehensible without any appeal to intelligence. In one sense, they are quite right. In a deeper sense, I think they are the ones being naïve. Judgments about design (i.e., teleological judgments) are similar to judgments of the good, and the beautiful in that they are profoundly subjective (more so than, say, mathematical judgments, or judgments relying on logical intuitions). How, then, can I expect to convey this sense of ‘perceived design’ to those who do not apprehend it as readily as I do? Perhaps an illustration will be helpful here.

People often chuckle irreverently when first learning of the philosophical views of several pre-Socratics, including, for instance, Diogenes Apolloniates who argued that air is intelligent. I often chuckle just as irreverently when I compare those views to the currently fashionable materialism adopted unthinkingly by so many people today. The pre-Socratics were attempting to explain why the world appears to be intelligently structured, and the answers they came up with almost invariably posited some underlying intelligence (usually in an element, or some other alleged fundamental ingredient of reality). By contrast, the materialist strangles intelligence out of the picture entirely, insisting instead that the fundamental elements of the world are unintelligent, and the complex underlying structure of the natural order (with all its laws and constants) is an inexplicable accident. Sure, they express hope that one day it will become an explicable accident (unconsciously committing a sort of materialism-of-the-gaps fallacy), but in this they have already missed the point. What makes their view so odious is that it suggests that ‘unintelligence’ is the best explanation for order (and, ultimately, even order enough to instantiate intelligence itself). In other words, their view is that unintelligent matter guided by no intelligence at all just happens to organize itself into highly complex structures (from sub-atomic particles all the way up to galaxies), including (eventually) the human brain (the paradigmatic locus of intelligence). This seems incredible, to put it mildly. I, for one, can more easily see the sense in thinking that if matter arranges itself into complex end-directed structures it must be intelligent than I can in thinking that matter arranges itself into complex structures with the appearance of being designed for a purpose under no intelligent impulse or direction at all. To put it somewhat poetically: the view that matter is intelligent is much less crazy than the view that intelligence is matter.

Evolution provides a microcosm of this general phenomena; it, too, involves matter arranging itself in ways which give the appearance of design, and by a process (namely natural selection operating upon phenotypically relevant gene-expression profiles which are engineered to replicate themselves in ways open to the editing power of mutation) which appears intelligent. The indelible impression I am left with when pondering the evolutionary process itself, then, is that it must be intelligently designed. That it, in other words, requires an explanation involving some deeper more fundamental intelligence.

I remain entirely conscious that this impression is not very widely shared, but to assume, as does the materialist, that unintelligent matter guided by no intelligence whatsoever can arrange itself in ostensibly intelligent ways has always seemed, to me, to be nothing short of insane. We aren’t merely speaking about gravity being a sufficient explanation for matter organizing itself into roughly spherical shapes; we’re talking about the very structure of DNA, the chemical structures of carbon and water, the structure and precise calibration of the fundamental laws governing our universe, and the process by which, beginning with one modest single-celled organism, a veritable explosion of life into kingdoms of wildly intelligent structures can succeed. Hardly anything seems more forcefully evident to me than that intelligence went into the world. What Plantinga has done for me is to clarify that my impression need not be cashed out in terms of an inference, but may be more appropriately regarded as a perception. This opens up some new avenues to explore philosophically, in particular by removing ‘intelligent design’ from debates about evolution altogether.

This line of reasoning, if it has the potential I think it does, may even restore credibility to other arguments in the near neighbourhood. For instance, the argument presented and developed in Immanuel Kant’s much neglected third installment of his famous critiques, namely, theCritique of the Power of Judgment, may be recuperable. This critique was largely discarded in the wake of On the Origin of Species, in particular because the thesis seemed to depend on the impossibility of a theory like Darwin’s. One particularly damning but famous line reads as follows:

“For it is quite certain that we can never adequately come to know the organized beings and their internal possibility in accordance with merely mechanical principles of nature, let alone explain them; and indeed this is so certain that we can boldly say that it would be absurd for humans even to make such an attempt or to hope that there may yet arise a Newton who could make comprehensible even the generation of a blade of grass according to natural laws that no intention has ordered; rather, we must absolutely deny this insight to human beings.”15

It was after Kant’s declaration (that there would never be a Newton for the blade of grass) that God (or whatever cosmic force is responsible for sublime irony) gave the world Darwin. However, I think there is a more profound reading of Kant’s argument throughout the Critique of the Teleological Power of Judgment (the second part of the third critique) which isn’t susceptible to so casual a dismissal. Upon closer inspection, we find Kant’s claim to be more nuanced; his argument, precisely, is about our teleological power of judgment, and not about alleged teleology in the world.

“There is thus left nothing but a proposition resting only on subjective conditions, namely those of a reflecting power of judgment appropriate to our cognitive faculties, which, if one were to express it as objectively and dogmatically valid, would say: There is a God; but all that is allowed to us humans is the restricted formula: We cannot conceive of the purposiveness which must be made the basis even of our cognition of the internal possibility of many things in nature and make it comprehensible except by representing them and the world in general as a product of an intelligent cause (a God).”16

As always with Kant, there is much here to unpack (and I will not even attempt to do so here), but, in effect, Kant is arguing that while we cannot justify any claim of intelligent design about the world we must nevertheless axiomatically presuppose intelligent design, otherwise we will be ultimately unable to comprehend the natural world. We might call this methodological intelligent design, as opposed to metaphysical intelligent design. In Kant’s view, intelligent design is not a perception so much as a presupposition which serves as a necessary precondition for our teleological judgments.

This critique of the teleological power of judgment may have as much going for it as Thomas Aquinas’ fifth way. In fact, rereading the last of the Quinque viæ through this lens also lends it enormous credibility. Although it is also readily dismissed by modern thinkers, St. Thomas’ teleological argument may be no worse for ware given the assumption that design is perceived. Aquinas’ fundamental point is that nothing which lacks intelligence can move itself, with any considerable consistency or regularity, toward a beneficial end.

The argument can be briefly outlined as follows:

  1. Anything which acts “always, or nearly always, in the same way, so as to obtain the best result”17is either intelligent or being directed by a being “endowed with knowledge and intelligence”18
  2. Natural bodies act always, or nearly always, in the same way, so as to obtain the best result.
  3. Natural bodies are not intelligent.
  4. Therefore, natural bodies are directed to their ends by a being endowed with knowledge and intelligence

Et hoc omnes intelligent Deum. The crucial assumption here is that “whatever lacks intelligence cannot move [itself] towards an end.”19 Thus, if the fundamental ingredients of the world are unintelligent, they will not be able to conspire to combine themselves or work together towards an intelligent end of any kind, including the development of intelligent creatures, or even creatures whose parts are intelligently ordered so as to take aim towards the ends beneficial to the organism as a whole.

Although this argument could be interpreted inferentially (i.e., as suggesting that design is an inference to the best explanation of end-directedness, or suggesting that it attempts to infer by analogy (e.g., because C has features {a,b,c} and things with features {a,b,c} are known to usually be designed, so C is probably designed, etc.)), I want, here, to suggest that this argument could be interpreted as proposing that we perceive design when observing teleological behaviour.

Although one could retort that it is logically possible that something appear designed without a designer, possibilities are renowned for coming cheap, we are all naturally (and appropriately) epistemic conservatives (and, given our psychological predisposition to believe in design, we would need some very good argument to persuade us otherwise unless we abandoned epistemic conservatism altogether), and ultimately, in the absence of some very good argument for thinking we are mistaken about our impression of design, the retort has no more force than the power of suggestion. I’m sure a more responsible and elaborate development of the reasoning here would repay the inquiring mind, but I will leave my exploration here for now in the hope that I will, in future, return to these thoughts and finesse them appropriately.

1 Platinga, Alvin. “An evolutionary argument against naturalism.” Disputatio philosophica 1, no. 1 (1999): 50-69.

2 Mark, Justin T., Brian B. Marion, and Donald D. Hoffman. “Natural selection and veridical perceptions.” Journal of Theoretical Biology 266, no. 4 (2010): 504-515.

3 Crick, Francis HC, and Leslie E. Orgel. “Directed panspermia.” Icarus 19, no. 3 (1973): 341-346.

4 Behe, Michael J. Darwin’s black box: The biochemical challenge to evolution. Simon and Schuster, 1996.

5 Meyer, Stephen C. Signature in the Cell: DNA and the Evidence for Intelligent Design. Zondervan, 2009.

6  As could time travel scenarios or other outrageous science fiction scenarios which would still, in principle, be compatible with Naturalism.

7 As an aside, I note that while it may seem ridiculous to combine intelligent design with (metaphysical) naturalism, I think that the fault here lies more with naturalism than with intelligent design. It continues to baffle and scandalize me that anyone continues to put any credence in naturalism as a viable vision of reality. Philosophy, at least in metaphysics, is supposed to be about making as good a sense as it is possible to make of the world around us. The idea is supposed to be to come up with a systematic and synoptic eagle’s eye view of reality which makes more sense, on balance, than any other competing views. In no way does Naturalism appear to me to achieve this. It fails to explain consciousness, it fails (even in principle) to explain the existence of the world as a whole, it fails to explain the efficacy of science (on a realist reading of science), it fails to do justice to our moral and aesthetic experiences, it fails to explain how there could be mathematical and analytic truths, it seems to get the extension of possibility wrong, the whole philosophy is just a hopeless mess. What’s worse, I cannot think of a single halfway decent argument for it and I’m doubtful that this is due to my lack of philosophical imagination. If intelligent design is ‘problematic,’ then Naturalism is beyond the pale.

8 Fodor, Jerry, and Massimo Piattelli-Palmarini. What Darwin got wrong. Profile books, 2011.

9 Kull, Kalevi. “Adaptive evolution without natural selection.” Biological Journal of the Linnean Society 112, no. 2 (2014): 287-294.

10 For a good collection of such arguments and counter-arguments, see: Dembski, William A., and Michael Ruse, eds. Debating design: from Darwin to DNA. Cambridge University Press, 2004.

11 See Dembski, William A. “The logical Underpinnings of Intelligent Design.” Debating design: from Darwin to DNA, Cambridge (2004): 311-440. And Meyer, Stephen C. “The Cambrian Information Explosion.” In Debating Design: From Darwin to DNA (2004): ??-??.

12 Nagel, Thomas. Mind and cosmos: why the materialist neo-Darwinian conception of nature is almost certainly false. Oxford University Press, 2012.

13 Robin Collins, The Case for Cosmic Design, (2008), http://infidels.org/library/modern/robin_collins/design.html

14 Alvin Plantinga, “Where the Conflict Really Lies: Science, Religion and Naturalism,” (New York: Oxford University Press, 2011): 245.

15 Kant, Immanuel. Critique of the Power of Judgment. Edited by Paul Guyer. (Cambridge University Press, 2009): 270-271.

16 Kant, Immanuel. Critique of the Power of Judgment. Edited by Paul Guyer. (Cambridge University Press, 2009): 270.

17 Summa Theologica, Prima Pars, Question 2, Article 3.

18 Summa Theologica, Prima Pars, Question 2, Article 3.

19 Summa Theologica, Prima Pars, Question 2, Article 3.

Brief Reflections on the Condemnations of 1277

Among the 219 condemnations issued in 1277[1] at the Université de Paris, we find the following one:

“91. That there has already been an infinite number of revolutions of the heaven, which it is impossible for the created intellect but not for the first cause to comprehend”[2]

This is extremely interesting, for it appears to endorse a key controversial premise of the Kalam cosmological argument with which such thinkers as St. Thomas Aquinas disagreed; namely, that the universe cannot have an infinitely long history. While Aquinas believed in creatio ex nihilo a finite amount of time ago, he thought this to be an article of faith which reason, left to its own devices, could never strictly establish.

However, Aquinas cannot be accused of committing himself to this condemned article, for (i) the article only condemns the proposition that there have been (and not that there ‘could have been’) infinitely many revolutions of the heavens, and(/or) (ii), more precisely, that there has been an infinite number of revolutions which (a) is impossible for the created intellect to comprehend, and (b) is not impossible for the first cause to comprehend. Thus, if one maintained that there were an infinite number of revolutions which the created intellect could possibly comprehend one could have avoided the charge of being committed to the view condemned in the 91st article of condemnations issued in 1277 (in letter if not in spirit).

Article 191 comes closer to posing a problem for Aquinas (or, since he passed away in 1274, for his reputation and doctrines):

“191. That the natural philosopher has to deny absolutely the newness of the world because he bases himself on natural causes and natural reasons, whereas the faithful can deny the eternity of the world because he bases himself on supernatural causes.”[3]

Yet even this fails to proscribe Aquinas’ doctrine, for Aquinas allowed the philosopher to believe in the newness of the world by arguing that no argument could demonstrate the impossibility of such a position, even if no argument could establish its truth. Interestingly, at least some of Thomas Aquinas’ own doctrines were thought to conflict with at least some of the condemnations issued on the list (I do not know which ones), and the Church apparently annulled these after this was discovered.[4]

Also interesting, the Catholic Encyclopedia notes:

“…hence it was that the theologians of Paris declared erroneous the opinion maintaining that God Himself could not give the entire universe a rectilinear motion, as the universe would then leave a vacuum behind it, and also declared false the notion that God could not create several worlds.”[5]

So, it was declared that God could have created multiple worlds, and it was also implied that God could have created an aether (or any physical analogue which would account for absolute motion). This has interesting implications for the intersection of Catholic theology and the philosophy of physics, implying that even if the Einsteinian or Minkowskian interpretations of relativity are correct (insofar as they dispense with the aether), something like the neo-Lorentzian interpretation could have been correct (i.e., is correct in some logically possible world). I’m not sure about this because if we accept that the neo-Lorentzian interpretation of relativity logically entails an A-theory of time then Catholicism (or, at least, this list of condemnations) commits me (and others) to the view that there is at least one logically possible world in which the A-theory is true, so it better not turn out that the A-theory conflicts logically with doctrines like God’s simplicity or immutability (for those properties are not contingent). Maybe there’s some way to wiggle out of this, but I’m not very confident of any of the attempts to do so with which I have become familiar (e.g., can there really be an aether without a preferred reference frame?).

It is worth noting that I’m not entirely sure how much authority these condemnations carry. After all, some of them were annulled, which indicates to me that they clearly didn’t require the assent of faith, nor is it reasonable to assume that they required religious assent (which is an extension of the assent of faith). Indeed, these condemnations were not issued with full papal authority, but issued instead by the (at the time) Bishop of Paris, Etienne Tempier, and issued on his own authority (and not Pope John XXI’s). It is true that Tempier was instructed by the Pope to investigate the matter of controversies rocking the world of academic theology at the time, and that those whose teaching was found to be condemned by any of the articles were excommunicated – but these amount to mere practices. They are possible (and harsh) configurations of canon law with no direct and perspicuous implications for Catholic dogma.

That concludes my register of thoughts and initial reactions to this list of condemnations, only recently made known to me. I will conclude, somewhat self-deprecatingly, with the first two condemned articles, just as a reminder to myself (and others like me):

 “1. That there is no more excellent state than to study philosophy.
2. That the only wise men in the world are the philosophers.”[6]

[1] According to the preface translated here: http://faculty.fordham.edu/klima/blackwell-proofs/MP_C22.pdf these condemnations were issued in 1276. Is it possible I’m confusing one list of condemnations with a different list?

[2] http://faculty.fordham.edu/klima/blackwell-proofs/MP_C22.pdf

[3] http://faculty.fordham.edu/klima/blackwell-proofs/MP_C22.pdf

[4] https://en.wikipedia.org/wiki/Condemnations_of_1210%E2%80%931277#Condemnation_of_1277

[5] Pierre Duhem, “History of Physics,” in The Catholic Encyclopedia Vol. 12., (New York: Robert Appleton Company, 1911), accessed June 20, 2016. http://www.newadvent.org/cathen/12047a.htm

[6] http://faculty.fordham.edu/klima/blackwell-proofs/MP_C22.pdf

Math, therefore God?

“Monsier! (a+bn)/n=x, donc Dieu existe; répondez!”[1]

Thus (allegedly) spoke the mathematician Leonard Euler when, at the invitation of Russian Empress Catherine the second, he confronted Denis Diderot in a (very short) debate on the existence of God. Diderot, who was not very good at math, was dumbstruck; he had absolutely no idea how to even begin responding to such an argument. In fact, he couldn’t even understand the argument, and Euler knew it! The court laughed him literally out of town (he promptly asked the Empress for leave to return to France). The formula, of course, is entirely meaningless, and may have been sleight of hand on Euler’s part (making his argument mathemagical rather than mathematical). Additionally, the anecdote has survived only in sparse notes (of dubious historical relevance) here and there with probably varying degrees of accuracy, so it is anyone’s guess what Euler actually meant. This amusing anecdote does, however, invite us to think about what arguments there could be, in principle, from mathematics for the existence of God.[2] Without offering much commentary on how promising these arguments are, I want to distinguish three viable (or, at least, viably viable) types of arguments which could be constructed.

The Argument from Mathematical Beauty

Although the formula Euler originally spouted off didn’t signify anything of mathematical (or philosophical) consequence, the beauty of Euler’s equation, eiπ + 1 = 0, gave rise to the apocryphal anecdote that Euler argued “eiπ + 1 = 0, therefore God exists.” There is (mathematicians tell us) a sublime mathematical beauty in this equation, and there is no obvious or intuitive reason why it is true. What is so special about this equation? One savvy commentator I ran across online put it so nicely I feel compelled to quote him:

“It’s a sort of unifying identity in mathematics, containing each of the fundamental operations (additive, multiplicative, exponential) and each of the fundamental constants (e, i, pi, 1, 0) combined in a theorem that united trigonometry, analysis, and algebra and geometry. It’s really an amazing identity, and the proofs for it are diverse and fascinating…”[3]

It has, thus, been called the origin of all mathematics. Keith Devlin is purported to have said:

“like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.”[4]

Its elegance cries out for an explanation, but that explanation has proved so elusive that a desperate appeal to God begins to look almost reasonable, even to (some) mathematicians.

What should we make of this sort of argument? It seems on its face to be about as prima facie (in)admissible as any other argument from beauty. However, this argument may have more to recommend it than meets the eye. In particular, mathematical beauty has an uncanny predictive ability, at least in the sense that the more beautiful the mathematical formula, the more likely it is to describe the fundamental structure of the real world. Robin Collins has noted, for instance, that:

“To say that the beauty of the mathematical structure of nature is merely subjective, however, completely fails to account for the amazing success of the criterion of beauty in producing predictively accurate theories, such as Einstein’s general theory of relativity.”[5]

John Polkinghorne, in a lecture I recently had the pleasure of listening to (via podcast), said something similar though with less economy of words:

“It isn’t just [to satisfy] an aesthetic indulgence that theoretical physicists look for beautiful equations; it is because we have found, time and again, that they are the ones which actually do describe… a true aspect of the physical world in which we live. I suppose the greatest physicist I’ve known personally was Paul Dirac, (who held Newton’s old chair… in Cambridge for more than 30 years, who was one of the founding figures of quantum theory, [and] unquestionably the greatest British theoretical physicist of the twentieth century) and he made his great discoveries by a relentless and highly successful lifelong quest for mathematical beauty. Dirac once said ‘it is more important to have beauty in your equations than to have them fit experiment.’ Now he didn’t mean by that that it didn’t matter at the end of the day whether your equations fit the experiments (I know no physicist could possibly mean that), but what he meant was this: ok, you’ve got your new theory, and you use the solution and you find it doesn’t seem to fit what the experimentalist is telling you – now there’s no doubt that’s a setback, but it’s not absolutely necessarily fatal. Almost certainly, you will have solved the equations in some sort of approximation, and maybe you’ve just made the wrong approximation, or maybe the experiments are wrong (we have [known that] to happen even more than once in the history of physics – even in my lifetime I can think of a couple examples of that), so at least there’s some sort of residual hope that with a bit more work and a bit more luck you might have hit the jackpot after all. But, if your equations are ugly, there’s no hope. The whole 300-year history of theoretical physics is against you. Only beautiful equations really describe the fundamental structure of the world. Now that’s a very strange fact about the world… What I am saying to you is that some of the most beautiful (mathematical) patterns that our pure mathematical friends can think up in their studies just thinking abstractly… are found actually to occur, to be instantiated, in the structure of the world around us.”[6]

So mathematical beauty satisfies the empirical desideratum of predictive power in the sense that the more beautiful the mathematical expression, the more likely it is to describe reality.

Interestingly I think this kind of consideration can motivate a scientist (and perhaps even a die-hard empiricist, and/or a naturalist) to believe in the objectivity of aesthetic properties. In fact, unless they find a plausible evolutionary account for why our brains should be calibrated so as to recognize more beauty in the abstract mathematical equations which, it turns out, describe reality, than we find in other equations, there will be a residual mystery about the eerie coincidence of mathematical beauty and accurate mathematical descriptions of physics. An eerie coincidence the queerness of which can perhaps be mitigated by admitting the objectivity of aesthetic qualities.

However, the puzzling queerness of that eerie coincidence can only be (or can most plausibly be) ultimately alleviated if the universe is seen as the product of a (trans-)cosmic artist. If behind the fundamental structure of the universe there lies an intellect with aesthetic sensibilities (in some sense), then that would explain why the world showcases the mathematical-aesthetic qualities it does at the level of fundamental physics even when there is no (obvious?) reason why it should have. That, though, begins to look quite a lot like Theism.

The Argument from the Applicability of Mathematics

This segues into the next kind of argument from mathematics, which concerns the applicability of mathematics to accurate descriptions of the fundamental structure of the physical world. For the purposes of this argument beauty is entirely irrelevant. What is surprising, and in need of an explanation (according to this argument), is that the physical world would turn out to be describable in the language of mathematics (and here we are not simply referring to the basic truths of arithmetic, which are true across all logically possible worlds). William Lane Craig has become the most well-known proponent of this argument, and his articulation of it is relatively succinct.

“Philosophers and scientists have puzzled over what physicist Eugene Wigner called the uncanny effectiveness of mathematics. How is it that a mathematical theorist like Peter Higgs can sit down at his desk and by pouring over mathematical equations predict the existence of a fundamental particle which experimentalists thirty years later after investing millions of dollars and thousands of man-hours are finally able to detect? Mathematics is the language of nature. But, how is this to be explained? If mathematical objects are abstract entities causally isolated from the universe then the applicability of mathematics is, in the words of philosopher of mathematics Penelope Maddy, “a happy coincidence.” On the other hand, if mathematical objects are just useful fictions, how is it that nature is written in the language of these fictions? In his book, Dr. Rosenberg emphasizes that naturalism doesn’t tolerate cosmic coincidences. But the naturalist has no explanation of the uncanny applicability of mathematics to the physical world. By [contrast], the theist has a ready explanation. When God created the physical universe, he designed it on the mathematical structure he had in mind. We can summarize this argument as follows:

  1. If God did not exist, the applicability of mathematics would be a happy coincidence.
  2. The applicability of mathematics is not a happy coincidence.
  3. Therefore, God exists.”[7]

I am not sure of this argument’s philosophical quality, since it seems to me that it may be a metaphysically necessary truth that a logically possible world be amenable to mathematical description of some kind. For instance, it certainly seems true that whatever the geometry of space happens to be, there’s no necessary fact of the matter, but it also seems true that if the geometry of space isn’t Euclidean, it may be hyperbolic, or elliptic, (or maybe something else, je ne sais quoi) but it has got to be something, and what it happens to be may, therefore, not cry out for any more explanation than any other quaint contingent fact about the world.[8] However, maybe I’m mistaken about this; maybe the argument is, in fact, just as viable as other teleological or ‘fine-tuning’ arguments are.

Argument from Mathematical Truth

Finally, the third kind of argument I can think of would go something like this: mathematical truths, like all truths, have truth-makers. These truth-makers will have to be metaphysically necessary on pain of mathematical truths being contingent – but it seems obvious that mathematical truths are necessary truths, that they hold across all logically possible worlds. Now, Nominalism about mathematical objects is incompatible with the commitments we just outlined (unless one adopts Nominalism about modal properties as well), and so seems implausible (or, at least, less plausible than it otherwise would have been in virtue of this incompatibility). Platonism also, however, seems to be problematic. Between Platonism and Nominalism, there is a wide range of views including Divine Conceptualism (according to which mathematical objects exist as necessary thoughts in the necessary mind of God), Theistic Activism, Scholastic Realism[9] and many others besides. In fact, a variety (and perhaps a majority) of the accounts of abstract objects on offer today presuppose the existence of God in different ways.

This opens the way to at least two arguments we could construct for the existence of God. First, we could argue that one of these accounts in particular is most plausibly correct (such as Greg Welty’s Theistic Conceptual Realism),[10] and work our way up from there to the implication that God exists. Second, we could take the disjunction of all the accounts of abstract objects which require the existence of God and argue that (i) if any of them is correct then God exists, but (ii) it is more plausible than not that at least one of them is correct, from which it follows (iii) it is more plausible than not that God exists.

So, there we have it, three kinds of arguments from mathematics for the existence of God; a transcendental argument (from beauty), a teleological argument (from applicability), and an ontological argument (from necessity). Could there be others? Maybe, but I suspect that they will all end up falling into one or another (or maybe at least one) of the general categories I tried to outline here. I admit that I didn’t outline them as general categories very well, but that exercise will have to wait for another day when I have more time to blog to my heart’s content.

As a quick post scriptum; if Euler had any substantive argument in mind and wasn’t merely mocking Diderot for his lack of mathematical aptitude, which of these three kinds of arguments would he most likely have had in mind? It’s hard to say, of course, but my best guess is that if he had anything in mind at all, it would fall into the third category. He may have been thinking that the fact that mathematical and purely abstract (algebraic) ‘structural’ truths exist at all requires some explanation, and this explanation must be found in God. This is just a guess, and I make no apologies for it – I am happy to think that Euler was just teasing Diderot, but I am equally happy to entertain the thought that if Diderot had not immediately asked to leave (because of his embarrassment), Euler may have been able to elucidate his point.

[1] Gillings, Richard J. “The so-called Euler-Diderot incident.” The American Mathematical Monthly 61, no. 2 (1954): 77-80. http://www.fen.bilkent.edu.tr/~franz/M300/bell2.pdf

[2] Notice that these are not to be confused with mathematical arguments per se; they are merely arguments from mathematics, in the same way as you might have arguments from physics (the argument from cosmological fine-tuning, the Kalam, etc.) for the existence of God which are not intended to be scientific proofs of God’s existence, but scientifically informed philosophical proofs/arguments for God’s existence.

[3] Russel James, Why was Euler’s Identity Supposed to be a Proof for the Existence of God, https://www.quora.com/Why-was-Eulers-identity-supposed-to-be-a-mathematical-proof-for-the-existence-of-God; Note that he finishes the quoted paragraph with the words “but It has nothing to do with god whatsoever.” I have left this out not because I think he is wrong, or to misrepresent his position, but because it has nothing to do with the formula and everything to do with the propositional attitude he adopts with respect to the question of whether the formula is any kind of reason to think there is a being like God.

[4] Paul J. Nahin, Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills, (Princeton University Press, 2011), 1. https://books.google.co.uk/books?id=GvSg5HQ7WPcC&pg=PA1&redir_esc=y#v=onepage&q&f=false

[5] Robin Collins, The Case for Cosmic Design, (2008), http://infidels.org/library/modern/robin_collins/design.html

[6] John Polkinghorne, Science in the Public Sphere, http://www.veritas.org/science-public-sphere/

[7] William Lane Craig, Is Faith in God Reasonable? William Lane Craig vs. Dr. Rosenberg, http://www.reasonablefaith.org/debate-transcript-is-faith-in-god-reasonable

[8] I am really, honestly, no more sure of this counter-argument than I am of the argument. For those interested, please do check out the debate between Craig and Daniel Came on the Unbelievable? Podcast, which you can also find here: https://www.youtube.com/watch?v=nn4ocx316dk

[9] J.T. Bridges defends this view: https://www.youtube.com/watch?v=eFU1BKxJf1k

[10] See: Greg Welty, “Theistic Conceptual Realism,” in Beyond the Control of God: Six views on the Problem of God and Abstract Objects, ed. Paul Gould, (New York: Bloomsbury Academic, 2014), 81-96.

Mlodinow’s Euclidean Equivocation

Leonard Mlodinow, who with Stephen Hawking co-authored The Grand Design, wrote the following passage in another book he wrote titled Euclid’s Window:

“By 1824, Gauss had apparently worked out an entire theory. On November 6 of that year, Gauss wrote to F. A. Taurinus, a lawyer who dabbled quite intelligently in mathematics, “The assumption that the sum of the three angles [of a triangle] is less than 180° leads to a special geometry, quite different from ours [Le., Euclidean], which is absolutely consistent, and which I have developed quite satisfactorily for myself. . ..” Gauss never published this, and insisted to Taurinus and others that they not make his discoveries public. Why? It wasn’t the church Gauss feared, it was its remnant, the secular philosophers.
In Gauss’s day, science and philosophy hadn’t completely separated. Physics wasn’t yet known as “physics” but “natural philosophy.” Scientific reasoning was no longer punishable by death, yet ideas arising from faith or simply intuition were often considered equally valid. One fad of the day which particularly amused Gauss was called “table-rapping,” in which a group of otherwise intelligent people would sit around a table with their hands placed in an arched position upon it. After a halfhour or so, the table, as if bored with them, would start to move or tum. This was supposedly some sort of psychic message from the dead. Exactly what message the ghouls were sending is unclear, although the obvious conclusion is that dead people like to position their tables against the far wall. In one instance, the entire Heidelberg law faculty followed for some time as their table moved across the room. One pictures a bunch of bearded, black-suited jurists pacing alongside, struggling to keep their hands in their appointed spot, attributing the locomotion to occult animal magnetism rather than their push. This, to Gauss’s world, was reasonable; the thought that Euclid had erred was not.”[1]

Ignoring the snide and historically fantastical notes about scientific reasoning ever having been punishable by death,[2] this passage is meant to set Gauss up as the champion of science, and his work is meant to signal the victory of science over philosophy. Mlodinow means to show how Euclid’s fifth postulate (concerning parallel lines), which was believed to be as philosophically secure as anything could be, was proven to be incorrect by the discovery, in modern physics, that space is non-Euclidean; in other words, it is not true that for any straight line L, and any point P not on L, there is only one line which can be drawn through P parallel to L. It may seem to be true, but our study of the physical world shows us that it isn’t (so the story goes). This, I will suggest, is just rhetorical slight of hand on Mlodinow’s part. In fact, it is worse; I believe that this represents a genuine antinomy in Mlodinow’s view of the nature of science itself, given what he has committed himself to in print elsewhere. I’ll develop this shortly below.

Shortly after the passage about Gauss trembling in fear of the indomitable secular philosophers (all of whom were apparently busy pushing tables around faculty lounges trying to communicate with the dead) Mlodinow introduces the character of Immanuel Kant. He chooses to portray Kant as the philosopher par excellence, and as the antagonist of scientific progress. He takes special care to note:

 “In Critique of Pure Reason, Kant calls Euclidean space “an inevitable necessity of thought.””[3]

It is worth saying a few words in defense of Kant, before we move on. Mlodinow provided no (precise) citation for the quote, so I searched through the Critique of Pure Reason for myself and could find no such statement. A quick glance at some Kant scholars indicates to me that there are some mixed signals here. On the one hand, never once does Kant refer to Euclid, or Euclidean geometry, or the fifth postulate, or even parallel lines (apart from one brief comment about immediately perceiving that the opposite angles of a parallelogram are equivalent) throughout the Critique of Pure Reason, so that the attribution to him of the saying above must, at best, be justified by reading between the lines. On the other hand, it is not unlikely that when Kant made statements about space, he was presupposing something like Euclidean space. It is true that Kant thought that the conception of space, like that of time, was an a priori intuition which was inalienable to the rational intellect. Instead of saying, with the empiricists, that our conception of space came come from the five senses, Kant thought that our conception of space was a precondition for our having intelligible empirical experiences at all. He writes:

“Space is not a conception which has been derived from outward experiences. For, in order that certain sensations may relate to something without me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as without, of, and near to each other, but also in separate places, the representation of space must already exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself only possible through the said antecedent representation. Space then is a necessary representation a priori, which serves for the foundation of all external intuitions.”[4]

Although Kant’s student, Schultz, was apparently interested in the treatment of parallel lines, Kant never talked about Euclid’s fifth postulate in his published works at all (though there are comments sprinkled about in his unpublished works). In any case, what Kant says about our a priori intuition is hardly undermined by the discovery that the geometry of space is non-Euclidean (i.e., hyperbolic or elliptic). Andrew Janiak observes:

“Kant highlights the accepted fact that we represent space as an infinite Euclidean magnitude—this can be widely accepted, despite the dispute concerning space’s ontology. […] We do not have a sensation of an infinite Euclidean magnitude.”[5]

Wes Alwan also writes:

“If we discover that the universe is actually, objectively (in the Kantian sense) non-Euclidean when our spatial intuition suggests it is Euclidean, then there is a conflict here between the faculties of understanding and intuition. If you’ve studied non-Euclidean geometry you’ll readily see what this means: the denial of the parallel postulate violates our intuition (unless we model the new geometry within Euclidean geometry but as occurring on a hyperbolic surface); but it does not produce any logical inconsistency. And in fact this is the whole point of Kant calling our perception of Euclidean space “intuition”: I have no other basis for the parallel postulate — I cannot argue for it as following from a principle of logic or arithmetic; nor can I argue about it from some a posteriori discovery in physics about the nature of the world.”[6]

Mlodinow quizzaciously continues:

“Kant, noting that geometers of the day appealed to common sense and graphical figures in their “proofs,” believed that the pretense of rigor ought to be dispensed with, and intuition embraced. Gauss held the opposite view-that rigor was necessary, and most mathematicians were incompetent.”[7]

Nevermind that Kurt Gödel essentially reiterated the very same point as Kant’s, and offered (what he thought was) a demonstration of it in what we now know as the incompleteness theorem (though, to be entirely fair, Mlodinow acknowledges this later on in the book); the point, for Mlodinow, is for us to recognize in the confrontation between Kant and Gauss a microcosmic confrontation between philosophy and science. A conflict from which science emerged victorious over philosophy, physics over common sense, and observation over intuition. The empiricist’s wet dream could not have been better narrated.

Reminiscent of Friedrich Nietzsche’s famous statement that “God is dead!”[8] Mlodinow and Hawking write, in the opening passage of their book The Grand Design, that “Philosophy is dead.”[9] Somewhat ironically,[10] they mean the very same thing, which is that metaphysics is dead. Metaphysics has been confused for a great many things which it is not, so it is worth calling attention to its definition; metaphysics is nothing other than the study of the extra-mental, extra-linguistic, model-independent, objective nature and structure of reality. What the metaphysician wants to know is what the fundamental furniture of reality includes. Where the construction worker is happy to use bricks, metaphysicians want to know what bricks are really made of, and where the mathematician is happy to use numbers the metaphysician wants to know what numbers are. From the perspective of the metaphysician, all the physicist does is offer empirically adequate models of space-time phenomena. That’s it. No amount of empirical data can definitively settle the matter of whether those models are literally accurate, nor can any of those models be the complete story because scientific models (if interpreted literally) presuppose countless philosophical assumptions which cannot be scientifically explored.

Accordingly, Hawking and Mlodinow sketch out, in the book, a view which they call model-dependent realism about science. They write:

“According to model-dependent realism, it is pointless to ask whether a model is real, only whether it agrees with observation.”[11]

In fact, they boldly exclaim that one of the central conclusions of their book is that “there is no picture-independent concept of reality.”[12] In one of the most tantalizing passages of their book they give some indication of just how radical their view really is, and it is worth quoting at some length.

“Model-dependent realism can provide a framework to discuss questions such as: If the world was created a finite time ago, what happened before that? An early Christian philosopher, St. Augustine (354–430), said that the answer was not that God was preparing hell for people who ask such questions, but that time was a property of the world that God created and that time did not exist before the creation, which he believed had occurred not that long ago. That is one possible model, which is favored by those who maintain that the account given in Genesis is literally true even though the world contains fossil and other evidence that makes it look much older. (Were they put there to fool us?) One can also have a different model, in which time continues back 13.7 billion years to the big bang. The model that explains the most about our present observations, including the historical and geological evidence, is the best representation we have of the past. The second model can explain the fossil and radioactive records and the fact that we receive light from galaxies millions of light-years from us, and so this model—the big bang theory—is more useful than the first. Still, neither model can be said to be more real than the other.”[13]

Although somewhat cryptic, it is important that we do not gloss over what’s being said in this passage. What Hawking and Mlodinow are saying is that while some people believe that the big bang theory is true, and six-day creationism is false, and other people believe that the big bang theory is merely closer to being true than the story of six-day creationism, none of these people are correct. As a matter of fact, the big bang hypothesis happens to be a more useful model (given certain hypothetical goals) than six-day creationism and this is the only reason we adopt it in preference to the latter. Although they claim that their view circumvents debates between scientific realists and scientific anti-realists, in reality their model-dependent realism is just a thinly-veiled version of scientific anti-realism!

Now, my chief problem with Mlodinow is not his philosophy of science; he can be an anti-realist until the cows come home and it won’t be any skin off my back. My problem with him isn’t that he thinks we should be empiricists instead of rationalists with respect to objects of intuition like Euclid’s fifth postulate. My problem isn’t even that he thinks that science can license the claim that Euclid’s fifth postulate was literally incorrect (though I do find the suggestion annoying). My real problem with Mlodinow is that I see no way for him to put all of these beliefs together coherently. He cannot on the one hand say that science has shown us that Euclid’s geometry is objectively incorrect, and on the other hand say that no scientific model is ever objectively ‘real’ (by which he means model-independently true). The best he can do, I think, is argue that we ought to abandon Euclid’s fifth postulate when operating within models of geometry which better account for the curvature of space than Euclidean geometry. That’s it, end of story. He cannot even say that Euclid’s fifth postulate was wrong, because the parallel postulate is true within a Euclidean model of geometry! For Mlodinow to say anything which is one iota more philosophically committing than that we should abandon Euclid’s fifth postulate for the same reasons we should abandon Euclidean geometry is for him to wander into utter incoherence.

I want to finish by saying a word or two about this now typical attitude of dismissiveness, condescension, derision and contempt for philosophy among professional scientists, exemplified especially by people like Mlodinow. Although I have no doubt that Mlodinow is a great physicist, it is unfortunate that he has added his (incredibly shrill) voice to the cacophonous choir of scientists grossly overestimating their philosophical aptitudes. What makes his comments particularly irksome is not that I and other philosophers find them disagreeable, but that they are logically irreconcilable. That, to a philosopher, is like hearing the sound of forks scrapped across a chalk board. It really is true what they say; the man who thinks he has no need of philosophy is the one who will be in most need of it.[14] Einstein, whose best friend, it is worth remembering, was none other than Kurt Gödel, was absolutely right when he wrote:

“It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophizing?”[15]

There is one possible reprieve for Mlodinow; although he insinuates fairly strongly throughout his book that Euclid, Kant, et alia were literally wrong about the parallel postulate, he could perhaps backpedal and defend himself by insisting that he never committed himself to the statement that the parallel postulate is literally false. If this is the case, then I owe him an apology for today’s blogging exercise.

[1] Leonard Mlodinow, Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace (New York: Simon and Schuster, 2010), 116.

[2] It is remarkably silly to say, as people often do, that Galileo was burnt at the stake, or that Marco Antonio Dominis was persecuted for his scientific ideas instead of his vitriolic attacks on the papacy, or that Cecco d’Ascoli was burnt alive for saying that there were people on the other side of the planet instead of his attempt to determine the nativity of Christ by reading his horoscope. There is a modernist myth that the man of science was persecuted in the age of the Church, but this sounds like a phantasmagorical persecution complex. It wasn’t only men of science who got into trouble with the church (it was also artists, writers, poets, theologians, and philosophers), and when men of science did get into trouble it was almost never on account of their scientific work (Galileo is the very notable exception; and serves as the exception which proves the rule). Notice that the same is not true for Theologians. It was, in fact, much more dangerous to do Theology than it ever was to do Science. It is approximately as puerile to say that scientists were, in general, afraid of the Church as to say that Gauss was afraid of secular philosophers.

[3] Leonard Mlodinow, Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace (New York: Simon and Schuster, 2010), 117.

[4] Immanuel Kant, The Critique of Pure Reason, http://www.gutenberg.org/files/4280/4280-h/4280-h.htm

[5] Andrew Janiak, “Kant’s Views on Space and Time,” in The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), ed. Edward N. Zalta, http://plato.stanford.edu/archives/win2012/entries/kant-spacetime/.

[6] https://www.partiallyexaminedlife.com/2013/10/30/why-non-euclidean-geometry-does-not-invalidate-kants-conception-of-spatial-intuition/

[7] Leonard Mlodinow, Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace (New York: Simon and Schuster, 2010), 117.

[8] Friedrich Nietzsche, The Gay Science, section 125, transl. Walter Kaufmann (1974).

[9] Stephen Hawking and Leonard Mlodinow, The Grand Design, (Random House Digital, 2010): 5.

[10] Ironic because where Nietzsche as a continental philosopher treated systematic thinking with scorn, Hawking and Mlodinow, as scientists, revel in rigor.

[11] Stephen Hawking and Leonard Mlodinow, The Grand Design, (Random House Digital, 2010): 46.

[12] Stephen Hawking and Leonard Mlodinow, The Grand Design, (Random House Digital, 2010): 42.

[13] Stephen Hawking and Leonard Mlodinow, The Grand Design, (Random House Digital, 2010): 49-50.

[14] In particular because to think that one doesn’t need a philosophy is already to have a philosophy (though it is a very bad one).

[15] Quote from Howard, Don A., “Einstein’s Philosophy of Science”, The Stanford Encyclopedia of Philosophy (Winter 2015 Edition), ed. Edward N. Zalta http://plato.stanford.edu/archives/win2015/entries/einstein-philscience/; “Physik und Realität.” Journal of The Franklin Institute 221: 313–347. English translation: “Physics and Reality.” Jean Piccard, trans. Journal of the Franklin Institute221: 348–382. Reprinted in Einstein 1954, 290–323. Note that when taking this quote in its full context it isn’t nearly as complimentary of philosophers, but I’m not sure that Einstein was right about the rest of what he wrote on the matter; I’m merely saying that he was right about this comment.

An Argument for Analogy

I have heard some atheists and skeptics about God’s existence claim that the Thomistic doctrine of analogy (i.e., that we can only speak about God by analogy, since we form our concept about God under the influence of empirical impressions of creatures, and so cannot possibly form a univocal concept of God’s essence as such), cannot be right because there is nothing about which we can only speak by analogy. In other words, if we can speak about anything by analogy, then we can speak about that thing univocally as well (followers of Duns Scotus will often press this point).[1] In this post I want to explore a way in which I think the multiverse hypothesis, which is popular among naturalists today, implies that there are some things, after all, about which we can speak, write and think, only by way of analogy, or at least by way of analogy alone.

There are a few different definitions of the multiverse hypothesis, but I will here take the multiverse hypothesis to be the thesis that there is an ensemble of universes, including our own, all of which have their own entirely separate spaces and times. On this hypothesis other space-times exist, but, it turns out, their spaces and times are incommensurable with our own. Everything may seem fine so far, but an interesting thing happens when we reflect more deeply on this (hypothetical) situation. It turns out that, in a rather straightforward way, the space and time of any alternative universe isn’t really what we refer to as space, or what we refer to as time. It makes no sense to ask ‘how far away’ an object in the space of another universe is, or ‘how long ago’ an event in another universe was, precisely because those universes do not share our time, or our space. It makes no sense to ask how old another universe is compared to ours, or how large another universe is compared to ours, for they cannot stand in such relations to each other. Those comparisons break down at this level because they become semantically vacuous. Such relations simply do not obtain between different universes.

This makes clear that our time is what we refer to when we talk about time, and our space is what we refer to when we talk about space. We are, when conceiving of other universes, taking our concepts of time and space and saying of a reality actually incommensurable with our own that it is ‘like this.’ That, however, is just to say that we are using our concepts of space and time analogously, and this is precisely the way in which the Thomist thinks we can, and must, speak about God. These other universes do not literally or univocally have any space, or any time, where these words are understood in their literal senses. You can satisfy this for yourself by thinking through some obvious considerations; for instance, consider that anything extended in time is, by logical necessity, earlier, later, or simultaneous with all other events in time. In the case of another universe this is not so, for anything extended in the ‘time’ of another universe is not earlier, later, or simultaneous with all other events in time. The same can be said of space, since any two (non-identical, non-overlapping) things extended in space are, necessarily, some distance apart from each other, but objects extended in different spaces are no distance apart from each other. The only way to make sense of talk of spaces and times incommensurable with our own is by analogy; we can speak about other space-times only by adopting a propositional attitude according to which we recognize our statements to be predicated by way of analogy. Our terms are inherited from the world with which we are familiar, and we are using them to speak about realities which we otherwise (than by analogy) cannot speak or think about at all. Nevertheless, the multiverse hypothesis can be both coherent and even true.

If I am right, then what this shows is that analogous predication is coherent and legitimate after all, at least if the multiverse hypothesis is a coherent hypothesis (it may not be, of course, but at least the naturalist/skeptic who takes it to be a coherent hypothesis will not be able to turn around and say that the Thomistic doctrine of analogy must be wrong because there isn’t anything about which we can speak only by analogy). Perhaps the naturalist will recoil at this point and argue that even if different universes have incommensurable times and spaces, that doesn’t mean that there is no way to predicate anything univocally about these different universes. For instance, perhaps two universes can stand in some real relation (for instance of similarity) to one another, or perhaps we can say that both exist in exactly the same sense of ‘exist.’ In response, I want to say that I am doubtful that any two universes can stand in any real relation to each other at all (I think this is ultimately a linguistic confusion), and even if many different universes could be said to exist in a univocal sense, their spaces and times considered as such could only be described and conceived of by analogy with our own. Perhaps it is not inappropriate to point out, as well, that existence is not a first-order predicate anyway (a point with which the naturalist will almost certainly agree), so that the fact that it can be applied apparently univocally shouldn’t worry us precisely because it isn’t a property. As such, it contributes absolutely nothing to the idea of the thing in question, and the doctrine of analogy maintains that it is our idea of the thing which can be formed exclusively by analogy.

Another objection may be that space and time are complex ideas which are conceptually formed by putting together combinations of simpler ideas, each of which can, as it turns out, be used univocally as applied to our universe and to others. For instance, somebody could suggest that time is nothing other than the direction of increasing entropy, and that ‘entropy,’ ‘direction’ and ‘increasing’ are concepts which can be applied univocally across different universes.[2] I think that this is wrong for a few reasons. First, ‘direction’ doesn’t seem to be univocally applied across different space-times (maybe it is, but it isn’t clear to me that it is). Second, I see no reason to think that time is defined by the direction in which entropy increases. In fact, the only reason we think of entropy increasing over time is because as time passes we observe an increase in entropy, but had it been the other way around we would have defined time as the direction in which entropy decreases, and, indeed, there are presumably some (at least possible) universes in the multiverse in which, as time goes on, entropy does decrease – and if this is even possible, given the multiverse hypothesis, then time cannot mean merely the direction in which entropy increases. If time simply meant the direction in which entropy increases then a universe in which entropy decreases over time would be physically impossible, but that, as far as I know, is not the case (perhaps someone could raise a quibble here about the second law of thermodynamics, but that is articulated precisely with the presumption that it is about our universe). Moreover, if one simply defines time as the direction in which entropy increases then I think it follows trivially that in no universe is it physically possible for entropy to decrease over time, but there is no good reason at all to accept this definition of time, and there are some very deep philosophical reasons for rejecting such a definition.[3] In any case I think our concept of time is more primitive and basic than our concept of entropy; we discovered that entropy increases as time passes, but we did not and could not have discovered the reverse.

In conclusion then, it seems to me that the naturalist faces a dialectical dilemma here. Either analogous predication is coherent and legitimate, in which case we can countenance both the doctrine of analogy and the multiverse hypothesis, or else it isn’t, in which case we cannot. If the naturalist wants to appeal to the multiverse hypothesis, even as a merely coherent hypothesis (for instance, as a possible explanation of the appearance of fine-tuning), then they will have to concede to the Thomist that we can, in principle, speak about God by analogy alone (not to be confused with the concession that we can only speak about God by analogy).


[1] See: Thomas Williams, “John Duns Scotus,” in The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), Edited by Edward N. Zalta, http://plato.stanford.edu/entries/duns-scotus/#NatThe

[2] My thanks to a friend for bringing this point to my attention.

[3] For more on this topic please visit: http://www.reasonablefaith.org/questions-on-the-arrow-of-time


Theism, Evolution and Randonmess

A good friend of mine with experience lecturing neophyte philosophy students as a Teacher’s Assistant (at the university of Western Ontario) has reported to me that many, if not most, of his students believed that the theory of evolution and the existence of God each entail each other’s negations. This is a depressing report, especially to a theistic evolutionist such as myself. Since the compatibility of both the theory of evolution and the existence of God is so conspicuously obvious to me, it continues to baffle me that anyone should think them contradictory. Perhaps one of the reasons for this naïve assessment is that evolution’s being ‘random,’ is thought (rather unreflectively) to be incompatible with the notion that it has been divinely guided. Ignoring the fact that God’s existence doesn’t, on its own, logically entail his divine involvement in the world, there still doesn’t seem, on the face of it, to be any incompatibility between God’s existence (and divine involvement in the world) and the biological theory of evolution. However, perhaps these people are reasoning in the following way:

  1. If God exists & evolution is true, then God (must have) guided evolution.
  2. If evolution is true, then it was ‘random’ (which is stipulated as part of the theory itself).
  3. If evolution was random, then it could not have been guided.
  4. Evolution is true.
  5. Therefore, God does not exist.

4.* God exists.
5.* Therefore, Evolution is not true.

Where is the problem with this reasoning? I think the problem is clearly with premise 3, though my critique is going to focus on sharpening, through analysis, the (so far) vague concept of randomness which makes its first appearance in the second premise. Here the work of Dr. Craig is useful; he has argued that what all biologists mean by saying that mutations occur ‘randomly’ is that they occur without a view to the benefit of the organism. Craig takes his cue from a prominent biologist, Francisco Ayala, according to whom:

“The meaning of “random” that is most significant for understanding the evolutionary process is… that mutations are unoriented with respect to adaptation; they occur independently of whether or not they are beneficial or harmful to the organisms.”[1]

Elliott Sober reiterated the same point when he explained:

“Let me talk about this idea of ‘guided’ mutations. This has been a kind of lightning-rod term. Creationists and Theists in the United States often hear biologists say that mutations are ‘unguided,’ ‘random,’ and they think that biologists are denying that God has any role in the natural process, and they think ‘well, if your theory says that [then] I reject it because I think that God is involved in everything that happens…’ what I want to describe now is what Biologists actually mean by ‘mutations being unguided.’ What I just described [above] is, I think, a misunderstanding of the biology. The idea that mutations are unguided says nothing about whether God plays a role in nature one way or another. So let me explain what biologists mean, or ought to mean, by ‘unguided mutations.’ When they say that mutations are unguided they do not mean that they have no causes; we all know that mutations have causes. Radiation causes mutations, smoking causes mutations, there are plenty of causes [of mutations] so [that] when you say they’re unguided or random it doesn’t mean that they are uncaused. What it means is that mutations have their causes, but they do not happen because they would be good for the organism in which they occur. Most mutations are deleterious, and the good ones that occasionally come along, the adaptive ones that fuel the evolutionary process, they have their causes too but they do not occur because they would help organisms to survive in their environments.”[2]

All biologists mean by stipulating that mutations are ‘random,’ therefore, is that the mutations do not aim toward (or away from) adaptive advantage. The biologist is clearly using the term ‘random’ in a very technical sense, just as the mathematician might use the term ‘random’ in a technical sense to characterize a certain set/series of numbers, and what the biologist means by this technical-theoretical term doesn’t seem to entail randomness in any sense which would preclude God’s providentially directing evolution. So, the question is, is there some deeper reason why this technical sense of ‘randomness’ does, after all, preclude God’s having a providential hand in evolution? Can this modest statement about biological randomness really purchase the metaphysically rich thesis that evolution was not (and could not have been) ‘guided’ by God? How could one cash-out such an incredible claim? Dr. Craig offers his thoughts:

“[Evolutionary creationists] would say that God has so set up the process that by chance alone these organisms will have evolved. Now… these folks would see the evolutionary process as under the superintendence of God and therefore is a guided process in that God allows it to function so as to arrive at his predetermined ends. Now, why can’t evolution be guided in that sense, in the sense that… the theistic evolutionist thinks of it? There the chance mutations and natural selection are within the broader purposes of God.

Well, what you discover when you read the evolutionary biologist is that of course they don’t deny that the process could be guided in that sense. That’s a metaphysical conclusion to which scientific evidence is irrelevant. What they simply mean is that the production of offspring does not occur with a view toward what will make these offspring survive better in the future, that there isn’t a kind of mechanism that produces offspring that will be well-suited to survival. Well, that’s perfectly within the purview of progressive creationism or theistic evolution. That’s a very limited, narrow, sense of guidedness that doesn’t need to be denied by the theistic evolutionist or progressive creationist. Suppose, for example, the [evolutionary] creationist thinks that the reason that God allows certain types of offspring to be produced is so that they will [become] easy prey for some other predator which he wants to flourish. Well in that sense, yes, it’s not guided with a view toward the survivability of the offspring – quite the contrary – the purpose is that they become prey for some other species or some predator. But the whole process is guided in this broader sense. So the problem here is that Miss Kirby [who thinks there is an incompatibility here] just has a philosophically superficial understanding of what it is to be guided, and the sense in which the evolutionary process is unguided is one that the theologian could affirm.”[3]

This seems pretty airtight to me, and nevertheless not everyone is convinced (on the far right or the far left). Casey Luskin, for instance, writes:

“Generally speaking, I find myself nearly always agreeing with Dr. Craig’s arguments. A few years ago I had the pleasure of watching Dr. Craig offer a compelling debate performance against Christopher Hitchens on “Does God Exist.” But on this issue of the nature of Darwinian theory, I find myself in a rare situation where I disagree with Dr. Craig.”[4]

I find this to be a frustrating situation; why aren’t these new atheists, or these evangelical creationists, convinced, as I am, by this reasoning? To answer that, I supposed I’d have to be a psychologist or a sociologist, or both. What I can do, as a philosopher, is try to come up with additional arguments which might help to change these people’s minds. Here is one such argument I’d like to present:

  1. If the theory of evolution were true, then physical determinism would be possibly true.
  2. If physical determinism were (even) possibly true, then God’s providential control over evolution would be possible.
  3. Evolution is true.
  4. Therefore, God’s providential control over evolution is possible.

It seems obvious to me that the theory of evolution is compatible with the theory of physical determinism; in fact, many naturalists who are strictly materialists or physicalists (and even some naturalists who aren’t) affirm both that physical determinism is true, and that the theory of evolution is true (which further reinforces what has already been said, namely that the technical sense in which evolutionary biologists use the word ‘random’ is compatible with other senses in which evolution might be guided or deterministic). However, suppose for the sake of argument that physical determinism is true (at least, if you like, up to the point of the appearance of the first creatures with libertarian free will), and that evolution is also true; why couldn’t God have so arranged the initial conditions under which the universe began to exist that he deterministically brings it about that evolution produces exactly what he intended it to?

Notice here that I am not claiming that physical determinism is in fact true (it seems to me rather dubious), but that it is possibly true, and that this possibility is enough to demonstrate the logical compossibility of evolutionary theory and God’s divine providential hand in directing the precise course of evolution. This seems to me to be a knock ‘em down drag ‘em out argument – I cannot even imagine what a (reasonable) critical rejoinder would look like, at least presuming that people are reasoning in approximately the way I imagined at the beginning of this post. I suspect that if some person remains unpersuaded by this argument, they won’t be persuaded by any argument, so that this is about as good as we can ever hope to do.

It may be worth saying a brief word about possible alternative arguments for the logical incompatibility of theism and evolution. Perhaps somebody could argue as follows:

  1. If God (being a maximally good, powerful and intelligent/rational being) had to choose between two different ways to bring about an effect, He would, ceteris paribus, elect to use the more efficient of the two means.
  2. Evolution is a means which is less efficient than other means which would have been options for God.
  3. Evolution is true.
  4. Therefore, God did not choose to actualize evolution.
  5. If God exists and Evolution is true, then God did choose to actualize evolution.
  6. Therefore, God does not exist.

The thought here is that a rational being always prefers, all things being equal, the more efficient of any two methods for achieving a given goal. This is a popular definition in economic theory, and sometimes makes an appearance in political philosophy. For instance, in his magnum opus,A Theory of Justice,” John Rawls characterized his idealized denizens of the ‘original position’ as rational in the following sense:

“… rationality must be interpreted as far as possible in the narrow sense, standard in economic theory, of taking the most effective means to given ends.”[5]

The trouble with this definition is well noted by William Lane Craig, to whom I will turn again. Craig has made the point numerous times that ‘efficiency’ can only be a value for a being with either (or both) limited time, or limited resources.[6] As God has neither limited time, nor limited resources, there is no reason to think God could value efficiency. So, as well as this definition may work in economic or political theory, it isn’t very useful theologically or philosophically.

Strictly speaking, I disagree with Craig, but I take his point to be a useful one to show that the presumption of the first premise in this argument seems to be false. I am inclined to think that God could value efficiency for aesthetic reasons, which would help to explain why parsimony, for instance, appears to be indicative of the truth of a theory, and not merely of its usefulness. There are puzzles in the philosophy of science about why parsimony would, on naturalism, make a theory any more likely to be true, whereas on Theism, at least if God values the aesthetic quality of simplicity, it may not be so surprising after all.[7] By analogy, consider that the elegance or beauty of a theory often seems to point to its truth, which seems an odd coincidence unless one is a Theist. Robin Collins has pointed out that beauty itself has been a seemingly useful indication of a scientific theory’s truth. He writes:

“To say that the beauty of the mathematical structure of nature is merely subjective, however, completely fails to account for the amazing success of the criterion of beauty in producing predictively accurate theories, such as Einstein’s general theory of relativity.”[8]

Admittedly parsimony needs to be carefully defined, and even if God does value parsimony it would presumably be in competition with other aesthetic values God might have (as any good engineer will tell you, the simplest way, on the face of it, is not always the best way). However, if God does value parsimony (and hence ‘efficiency’ in at least some cases) for aesthetic reasons, that may provide Him with a good reason to elect the more efficient of two otherwise equally good methods. Efficiency would only be valued to the degree that it allows for an optimal balance between itself and other aesthetic values. This caveat of mine does nothing, however, to take away from the effectiveness of Craig’s response in the case at hand. There simply is no reason whatever to think that evolution is not parsimonious enough that God might have elected to use it (and this is never-minding the theological/apologetic justifications for God’s allowing evolution).

Another argument might go as follows:

  1. Evolution is a process which involves gratuitous evil (evil for which there is no morally sufficient reason which God has for allowing in the world).
  2. God exists if and only if gratuitous evil does not.
  3. Evolution is true.
  4. Therefore, God does not exist.


3.* God exists.
4.* Therefore, evolution isn’t true.

The trouble with this argument is that it is simply a version of the problem of evil, which comes in two forms; there is the so-called ‘logical’ problem of evil, and the ‘evidential’ problem of evil. As it stands today nobody thinks that the ‘logical’ problem of evil, which suggests that the existence of any evil is logically incompatible with the existence of God, stands any hope of being correct. Second, although there are significant problems with the evidential argument from evil, it is worth pointing out that if the above argument is intended to be a version of the logical problem of evil then it incontrovertibly fails, and if it is intended to be a version of the evidential problem of evil then it can be dealt with in all the standard ways in which all versions of the evidential problem of evil are dealt with. In other words, because ‘evolution’ as such is not an essential feature of this argument, but an accidental one, evolutionary theory plays no special role in the argument, implying that evolution as such poses no special challenge.

What other arguments could there be? Although there is always the possibility that there is some other clever argument to think that God’s existence and the theory of evolution are not compossible, an argument which I have never heard or thought of, still it seems unlikely that any such arguments exist or are forthcoming (and even more unlikely that they would be unanswerable). So, I think we can conclude with tremendous confidence that the theory of evolution is not only compatible with the existence of God, but also his divine providence.

[1] Francisco J. Ayala, “Darwin’s greatest discovery: Design without designer,” in Proceedings of the National Academy of Sciences USA, 104, no. Suppl 1 (2007): 8567-8573.

[2] Elliott Sober, “Darwin and Intelligent Design,” Lecture, the Sydney Ideas Lecture Series, The University of Sydney, Sydney Australia, April 22, 2010. http://fora.tv/2010/04/22/Elliott_Sober_Darwin_and_Intelligent_Design

[3] “Is Evolution a Threat to Christianity?” Narrated by William Lane Craig and Kevin Harris, ReasonableFaith Podcast, ReasonableFaith, December 5, 2011. http://www.reasonablefaith.org/is-evolution-a-threat-to-christianity#ixzz3RSURRy2s

[4] Casey Luskin, “Unguided or Not? How Darwinian Evolutionists Define their Theory,” http://www.evolutionnews.org/2012/08/unguided_or_not_1063191.html

[5] Rawls, John. “A Theory of Justice, rev. ed.” Cambridge, MA: Belknap 5 (1999): 12.

[6] See: “UFO’s” Narrated by William Lane Craig and Kevin Harris, ReasonableFaith Podcast, ReasonableFaith, August 17, 2008. http://www.reasonablefaith.org/ufos

[7] See Pruss: http://alexanderpruss.blogspot.ca/2014/03/simplicity-as-sign-of-design.html; http://alexanderpruss.blogspot.ca/2013/08/explaining-simplicity-of-theories.html; http://alexanderpruss.blogspot.ca/2013/07/why-prefer-simple-and-elegant-theories.html;

[8] http://infidels.org/library/modern/robin_collins/design.html

Does Micro-indeterminism entail Macro-indeterminism?

A professor of mine, with whom I habitually disagree (much to his pretended ‘chagrin’ and our mutual amusement), has argued previously, and again recently, that even if indeterminism were true at the micro-level, for instance at the level of quantum mechanics, that would do nothing to make macro-determinism infeasible, where macro-determinism means something like: for every macro-physical event E, either (i) there is always exactly one macro-physical event E* from which E followed deterministically, or at least (ii) E, if it is not preceded by any physical events, deterministically entails all proceeding macro-physical events. I have previously expressed my skepticism about the thesis that if quantum indeterminacy were really true, then it would yield no consequences for the thesis of physical determinism on the macro (i.e., ‘observable’) level. It seemed to me that if quantum indeterminacy were really true, then it would always in principle be metaphysically and even nomologically possible for some macro-physical event of type E (which, with law-like regularity, causally brings about some subsequent macro-physical event type E*), to obtain without E* subsequently obtaining. To fail to recognize this, I thought, was just not to take quantum indeterminacy seriously. Even if the probability that macro-physical event E occurred without bringing it about that E* occurred is vanishingly small, so small as to be reputed practically impossible (say something in the order of, or less than, one chance in ten to the power of fifty, or something like that), it would still be physically possible for E to occur and E* not to occur. I argued that although there are some properties for which it is false to say ‘if one part of a whole has property P, then the whole has property P’ – for instance, if a song on an album has the property of being under three minutes long, it does not follow that the album has the property of being under three minutes long[1] – there are other properties for which it is true to say that ‘if one part of a whole has property P, then the whole has property P.’ For instance, suppose one part of a whole has the property of being extended in space; it does clearly follow from that that the whole has the property of being extended in space.[2] We call it a ‘fallacy’ because the inference from part-to-whole isn’t always and everywhere truth-preserving, but that doesn’t entail that it is never anywhere truth-preserving, and it is intuitively obvious that it is an inference immune to the problem of truth-preservation in at least some instances. Thus I argued that the property of being indeterminate was one of these instances, so that if some part of a whole (say, where the ‘whole’ is the continuous space-time, and the part in question is the quantum foam) has the property of being indeterminate, then the whole has the property of being indeterminate.

However, more recently I had been considering revising my view, and in trying to revise it I had to think through some of the considerations which I want to explore in this article. I will, here, lay out a case for defending my professor’s contention, and then subsequently argue that while I can imagine a possible world in which micro-indeterminism and macro-determinism were both true, such a world is not part of the set of physically possible worlds. What has to be denied, in order to reconcile micro-indeterminism and macro-determinism is, I think, too much.

First, the case in defense of the thesis that micro-indeterminism does not entail macro-indeterminism could go something like this: there is some finite set of possible and indeterminate quantum mechanical events [Q1, Q2,… Qn], and nothing determines which of these events will occur. This is sufficient for micro-indeterminism. Now suppose that each member of the set [Q1, Q2,… Qn] would either (i) (along with the set of macro-physical events preceding it) bring some macro-physical event P about necessarily, or else (ii) at least would do nothing to impede P’s coming about deterministically from some set of antecedent macro-physical events. So, on the first story Q1 ⊃ P, and Q2 ⊃ P, and so on, so that (Q1 v Q2 v … Qn) ⊃ P. On the second story there is causal closure of the macro and/or micro physical levels, so that each of these levels is entirely causally autonomous from the other. If either of these two stories worked, then one could safeguard macro-determinism even while conceding micro-indeterminism.

Do either of these stories work? I was, for a time, tempted to think that the first one could work in principle. After all, it seemed logically possible. The second is a little more queer because it is hard to imagine that micro-physical events could be called genuinely ‘physical’ events if they were not in any sense causally connected to the observable physical realm – what would it mean to call them ‘physical’ if they were not part of one single physical plenum? However, maybe the second story deserves more sympathy than that. Perhaps the word ‘physical’ has a wider use, so that we can even refer to universes in a multiverse ensemble (if such an ensemble exists) as physical, and the events occurring in them would be genuinely physical events, even if they were causally sealed off from our observable physical world. However, something is obviously wrong, in fact, with both of these stories, as I intend now to illustrate.

Suppose that there is a macro-physical brain-state event B1 which is caused by some ‘observation’ of an (indeterministic) quantum mechanical event (of course this wouldn’t be direct observation, but just suppose that all the appearances where such that, given my scientific paradigm, it appears to me that some quantum mechanical indeterminate micro-physical event has occurred – i.e., I can ‘detect’ it). Suppose that the set of all macro-physical events prior to B1 is symbolized by ‘S’, where each event in S is either entailed by all the events prior to it, or at least, if there is a ‘first event’ in the set, that it will entail all of the events subsequent to it in the set. Let this world with S & B1 be symbolized as W. Now, there is a logically possible world W’ which is maximally ‘close’ or ‘near’ to W, in which S obtains, but B1 does not obtain. Instead, S obtains along with B2, where B2 is the observation of a different quantum mechanical event (or none at all). Here, since both B1 and B2 are macro-physical events (i.e., observable brain states), it seems as though micro-indeterminism has led to macro-indeterminism. Notice that our logically possible worlds (W: [S&B1], and W’:[S&B2]) are both metaphysically possible, and nomologically possible given our currently best understanding of physics (at least to the best of my knowledge, and accepting for the sake of argument that an indeterministic model of quantum mechanics is correct insofar as it is indeterministic).

Consider the fact that observable brain states can be caused by (indeterministic) quantum mechanical events – if this is true, then neither of the stories we told work in fact. Quantum mechanical events, if they are really indeterminate, and if they really can, under certain conditions, cause different brain-states to actualize, and the actualization of brain-states is a macro-physical event, then clearly micro-indeterminism of the kind attested to in the standard Copenhagen view of quantum mechanics really can (and necessarily can) bring about some macro-physical observable event which would otherwise mutatis mutandis not have occurred. (I should add here a quick caveat lector: I do not endorse or believe in indeterminism of this kind, I mean only to accept that there is such indeterminism for the sake of argument – to see what would follow). For either story to work, we need micro-physical indeterminacy to be in principle undetectable to science. So, we can conclude that if detectable micro-physical indeterminacy exists, then micro-indeterminacy does entail macro-indeterminacy. In other words: detectable micro-indeterminacy entails macro-indeterminacy. Even in a world where micro-indeterminism were true and macro-determinism were never observationally disconfirmed, macro-determinism would, given ‘detectable’ micro-indeterminism, not in fact be true.

This same conclusion could be derived if we accepted the doctrine of mereological supervenience, according to which, as Jaegwon Kim explains, “[the] properties of wholes are fixed by the properties and relations that characterize their parts.”[3] If the set of properties and relations which characterize the physical world at the most basic level include indeterminacy then it seems to follow from mereological supervenience that the properties of the observable physical world include indeterminacy, even if nothing we bear witness to on the observable level would lead us to suspect its indeterminacy.

The intuition of my professor, I assume, is something like this: whatever happens at the quantum level, if we suspend an 18-wheeler 30 feet off the ground and then let it go, it will fall; come what may on the quantum mechanical level, that 18 wheeler is necessarily going to fall to the ground. Is this true? I’m not sure. I can imagine a set of quantum mechanical events all conjunctively occurring (however unlikely) such that the truck just disappeared, but this might just be my failure to distinguish science from science fiction.

Macro-physical determinism (Macro-determinism for short) is true if and only if every single macro-physical event either follows deterministically from others, or else at least deterministically entails all successive macro-physical events. If micro-physical events are indeterministic and observable or detectable by creatures whose brain-states are macro-physical, then macro-determinism is false. Even in a world where there are no observers at all, if there are indeterministic events which, counterfactually, would be observable were an observer appropriately situated, then that world is (macro-)indeterministic. The difference between the micro- and the macro- physical, after all, is purely anthropomorphic. There just is, in reality, no causal separation between events which are not observable to us, given the human organism as, in the words of Bas C. van Fraassen, “a certain kind of measuring apparatus,”[4] and those events which are observable to us. Our being organisms for whom some physical events are directly observable, and for whom others are merely detectable, does not give us any reason at all to think that unobservable physical events have no causal efficacy for bringing about macro-physical events. The atomic bomb is evidence enough of that. The idea is that the world really is a causal plenum. Imagine, by analogy, that each event in the physical world hooks up to all other physical events so as to make the whole aggregate different then it otherwise would have been without it, in the same way that the meaning holist thinks that each belief in a web of beliefs determines the character of all of the beliefs in that particular web.

This seems to settle the case pretty definitively, since a difference in the brain states of some observer can plausibly bring about a very different causal chain of macro-physical events. Thus, even if there is a logically possible world in which both micro-indeterminism and macro-determinism are true, it certainly isn’t our world, nor any worlds near enough to ours where there are detectable indeterministic events of any kind.

Is there a way out of this? Perhaps; for one thing, all somebody needs in order to claim that micro-indeterminism does not entail macro-indeterminism is that there be some logically/metaphysically possible world in which micro-indeterminism and macro-determinism are both true. I can imagine somebody arguing that when an observer ‘observes’ (mediately) a quantum mechanical event, the observer determines (by observing) what would otherwise have been an indeterminate event. Here the suggestion is that observation has the effect of making a macro-physical event deterministically cause a micro-physical event, but that no unobserved micro-physical events ever bring about a different macro-physical event. Is this possible? We are putting to one side the question of whether this gets the science right (I make no pretensions to understand the dynamics of quantum theory, since I am a philosopher and adamantly not a physicist); the question is rather ‘if this did get the science right, if this were really how the world were, then would it follow that micro-indeterminism could be conjoined with macro-determinism?

This would have to deny Heisenberg’s uncertainty principle, the cornerstone of chaos theory (which, contrary to folk-science, is actually a deterministic theory). The intuition behind chaos theory in general is just that every event, no matter how seemingly insignificant, has an impact on the whole causally-continuous world. A butterfly flaps it’s wings twice, as opposed to once, within some finite span of time, in central park, and a hurricane is set to hit the shore of Australia where it otherwise (keeping all else besides the extra butterfly-wing-flap the same) would not have. However, that’s no surprise – after all, chaos theory is built on the assumption that the world is a causal plenum, and this is perhaps the very thing being denied. If one is sincere in her commitment to the indifference micro-indeterminism makes for macro-(in)determinism then it seems there has to be causal closure of the micro-indeterminate level, such that no micro-physical event can even in principle bring about an observational difference, which would mean that no indeterminism could, in principle, be observed. If it were observed, (at least if it were observed by physical creatures whose brain states could be observed) then by that very fact it would have caused a macro-physical event.

It would have to be that the micro- and macro- levels were causally sealed off from each other, or causally indifferent to each other; at least that either the indeterminacy of the one was causally impotent with respect to the other, or that the determinacy of one was causally indifferent to the indeterminacy of the other. To be truly indifferent, though, the indeterminacies would have to be in principle unobservable – or at least they could not be observable/detectable in principle by beings whose observational apparatus was significantly physical. This, however, raises a troubling conundrum for the philosophy of science. Since the range or set of nomologically possible worlds is determined by our best scientific theories, and since those are birthed by methodologically empirical observation, it seems odd, and perhaps even incoherent full stop, to say that there is a nomologically possible world where physical events occur in such a way that they could not, in principle be detected or figure into our theories born of empirical observation. Perhaps there is a metaphysically possible world where materialism/physicalism is correct, and this case-scenario obtains, but it would not be a nomologically possible world. In fact, it seems a necessary truth that such a world would not be nomologically possible!

Is it metaphysically possible to have a causal quarantine of the micro-physical indeterminate level? If it is, then micro-indeterminism does not strictly entail macro-indeterminism. Moreover if that kind of quarantine is possible, then why not a quarantine of a certain set of macro-physical events? Maybe there are some macro-physical events which are deterministic in the sense that they will follow each other ‘come what may’ elsewhere (even come what brain-state events may). For instance, if the universe is expanding at escape velocity and thus faces imminent heat-death, then (plausibly) no combination of quantum mechanical events (or macro-physical brain-state events), however unlikely, will steer the universe clear of this apocalyptic course. This kind of macro-determinacy would be weaker than the macro-determinacy we have had in mind (pace the definition I offered above), but it would still be some kind of macro-determinism.

Therefore, micro-indeterminism nomologically entails macro-indeterminism just in case both (i) micro-indeterminism is observable in principle by creatures whose brain-states are macro-physical, and (ii) no set of macro-physical events is causally quarantined from the rest of the macro-physical order. The cost of denying (ii) is no less than the presumption that the world is a causal plenum (an assumption upon which some of our scientific theories, like Chaos theory, are built), along with mereological supervenience. The cost of denying (i) is to abandon the view that the range of nomologically possible worlds is set by what would be in principle empirically verifiable by observers situated appropriately/idyllically  in the logically possible world in question. Maybe this second option isn’t as bad as it looks; perhaps we can imagine, given our best science, a logically possible world within the range of nomologically possible worlds set by our best science, where the same regularities held in fact, and where we would only ever and always observe (even in principle, we could only ever and always observe) phenomena which would proscribe the construction of our best scientific model(s). Whether it is coherent to talk about nomologically possible worlds where no observers idyllically situated could in principle, using the scientific method, come to apprehend the nomic regularities which held in fact is an issue which I will leave for further exploration another time, when/if I decide to dig deeper into the relationship of modal discourse and the philosophy of science.

To recapitulate, so far I have argued that the ‘fallacy of composition’ objection against inferring macro-indeterminism from micro-indeterminism doesn’t seem to work, just as it doesn’t work to object that way to the inference from some thing’s part being extended in space to the thing as a whole being extended in space (note that having the property of being extended in space as a whole does not imply that there is nothing more to a thing than it’s spacial extension). This argument is tenuous though, as it will rely in part on one’s intuitions, and could in principle be defeated given a better understanding of the science involved. I argued that the cost of denying the legitimacy of this inference would be (no less than) the doctrine of mereological supervenience, and the doctrine that the physical world is a causal continuum from top to bottom. I also argued that there cannot in principle be a nomologically possible world were observers with a physical apparatus could not in principle detect indeterminacy if indeterminacy were a nomic reality. This is because it seems to me that to say that something is undetectable to physical science in principle is plausibly just to say that it is not physical. I have also conceded, however, that perhaps there is a more modest form of macro-determinism, call it weak macro-determinism, according to which there is some subset of macro-physical events which follow deterministically from each other come what may elsewhere. The universe’s facing heat death is one example of something which, come what brain-states may, seems physically inevitable. This, however, is not strong enough for macro-determinism as such, and thus has nothing, or in any case very little, to do with the present discussion. If observers can in principle stand in a ‘detecting’ relation to nomic indeterminacy (whether of the macro or micro variety), then macro-indeterminism follows of nomological necessity.


[1] I am here adapting an example I first read here: Is The Universe Contingent? (http://www.philosophyofreligion.info/theistic-proofs/the-cosmological-argument/the-argument-from-contingency/is-the-universe-contingent/)

[2] I gave this example previously on my Undergraduate Blog, in an article called: The Fallacy of “The Fallacy of Composition” Objection (http://thirdmillennialtemplar.wordpress.com/2013/02/03/the-fallacy-of-the-fallacy-of-composition-objection/)

[3] Jaegwon Kim, Mind in a physical world: An essay on the mind-body problem and mental causation. (MIT press, 2000), 18.

[4] Bas. C. van Fraassen, “Empiricism and Scientific Realism” in Philosophy of science: The central issues. Second Edition, edited by Curd, Martin, and Jan A. Cover. (WW Norton, 1998): 1070.