Unreasonably Effective

In a much quoted academic paper, Eugene Wigner once wrote:

The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. [1]

Wigner dubbed the amazing success of mathematics in accurately describing and predicting the physical world, “the unreasonable effectiveness of mathematics” [2]. It is quite astonishing. Why should it be that, for example, when Einstein was looking for some mathematical description of his theory of general relativity, he discovered that Riemann’s non-Euclidean geometry, invented about half a century earlier, was the perfect fit?

How is it that recent experiments to measure the magnetic moment of an electron should so precisely match the predictions of quantum electrodynamics, even when measured at a precision of eight parts in a trillion? One of the inventors of the theory of quantum electrodynamics, Freeman Dyson, said, “I’m amazed at how precisely Nature dances to the tune we scribbled so carelessly fifty-seven years ago, and at how the experimenters and the theorists can measure and calculate her dance to a part in a trillion.” [3]

Mario Livio writes:

In the late 1960s, physicists Steven Weinberg, Sheldon Glashow, and Abdus Salam developed a theory that treats the electromagnetic force and weak nuclear force in a unified manner. This theory, now known as the electroweak theory, predicted the existence of three particles (called the W+, W-, and Z bosons) that had never before been observed. The particles were unambiguously detected in 1983 in accelerator experiments (which smash one subatomic particle into another at very high energies) led by physicists Carlo Rubbia and Simon van der Meer. [4]

As Einstein put it, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” [5]

First, we might question the claim that mathematics is “independent of experience”. Sir Michael Atiyah wrote:

If one views the brain in its evolutionary context then the mysterious success of mathematics in the physical sciences is at least partially explained. The brain evolved in order to deal with the physical world, so it should not be too surprising that it has developed a language, mathematics, that is well suited for the purpose. [6]

This seems to accord with the latest research by cognitive scientists:

The cognitive scientists base their conclusions on what they regard as a compelling body of evidence from the results of numerous experiments. Some of these tests involved functional imaging studies of the brain during the performance of mathematical tasks. Others examined the math competence of infants, of hunter-gatherer groups such as the Mundurukú, who were never exposed to schooling, and of people with various degrees of brain damage. Most of the researchers agree that mathematical capacities appear to be innate. For instance, all humans are able to tell at a glance whether they are looking at one, two or three objects (an ability called subitizing). A very limited version of arithmetic, in the form of grouping, pairing, and very simple addition and subtraction, may also be innate, as is perhaps some very basic understanding of geometrical concepts (although this assertion is more controversial). Neuroscientists have also identified regions in the brain, such as the angular gyrus in the left hemisphere, that appear to be crucial for juggling numbers and mathematical computations, but which are not essential for language or the working memory. [7]

This explains only how it is that we come to have the ability to grasp the mathematical nature of the world: it does not explain why the world is, to such an impressive extent, mathematical. It is quite conceivable that the world should not exhibit regularities at all. It is even easier to conceive of a world which, although regular, exhibits a particular regularity rather than the universal regularity that we observe.

Why is it that the same law governs the motion of the heavens and the falling of an apple? As Sir Isaac Newton described it:

“Nature is very consonant and conformable to herself.” [8]

This was not always believed to be the case. The Scholastic philosophers, following Aristotle, believed that each thing behaves as it does because of its own nature. Thus it is the nature of the Moon that makes it orbit the Earth, it is the nature of the sea that causes it to rise and fall in tides, and it is the nature of an apple to fall toward the centre of the Earth. According to such a view, natural philosophy consists of determining and describing the various different natures of different entities. Newton’s great insight was that the universe is governed by universal laws: the orbit of the Moon, the rise and fall of the tides, and the falling of an apple are all the result of a universal law of gravitation. This was a revolutionary realisation:

This principle of nature being very remote from the conceptions of Philosophers, I forbore to describe it in that book, least I should be accounted an extravagant freak and so prejudice my Readers against all those things which were the main designe of the book. [9]

So not only is it possible to conceive of a world exhibiting local, particular regularity but no universal laws, that is indeed how the world was perceived for many centuries.

It also seems possible to conceive of a world that exhibits regularities which are nevertheless not mathematical: such a possibility is described by George Coyne and Michael Heller in their book A Comprehensible Universe [10]. However, if we accept the thesis that our mathematics is an evolutionary adaptation to the regularity of the world, then perhaps such a world could not exist in practice. If we found ourselves in a regular world then necessarily those regularities would be mathematical, as what we mean by mathematics would depend on the regularities whose nature our brains had evolved to accommodate.

If Atiyah is correct, then it is not ultimately the mathematical nature of the world that is surprising, but rather the universal regularity of the world. On the other hand, it is far from obvious that Atiyah is correct. Richard Hamming wrote:

If you pick 4,000 years for the age of science, generally, then you get an upper bound of 200 generations. Considering the effects of evolution we are looking for via selection of small chance variations, it does not seem to me that evolution can explain more than a small part of the unreasonable effectiveness of mathematics. [11]

The only answer to Hamming appears to be that, long before the age of science, we evolved, as the research of cognitive scientists mentioned above appears to tell us, an innate faculty for very rudimentary mathematics. We must then appeal to the nature of mathematics itself, what Atiyah calls the “abstract hierarchical nature of mathematics” [12], to explain how this rudimentary mathematics can be so remarkably successful when extended to every level from the subatomic to the galactic. Unfortunately, appealing to the nature of mathematics as we know it does seem to rather beg the question.

Nevertheless, whether we accept Atiyah’s evolutionary explanation or not, we are still left with the mystery of why it should be that the world exhibits universal regularities — regularities which, whether necessarily or contingently, we can express with astonishing accuracy in the language of mathematics. Coyne and Heller quote Einstein:

The very fact that the totality of our sense experiences is such that by means of thinking it can be put in order, this fact is one which … we shall never understand. One may say “the eternal mystery of the world is its comprehensibility”. [13]

Why is there order rather than chaos? Of course, this question cannot be answered rationally, for it is the validity of rationality that we are trying to explain. Coyne and Heller quote Sir Karl Popper:

Neither logical argument nor experience can establish the rationalist attitude; for only those who are ready to consider argument or experience, and who have therefore adopted this attitude already, will be impressed by them. That is to say, a rationalist attitude must be first adopted if any argument or experience is to be effective, and it cannot therefore be based upon argument or experience. So rationalism is necessarily far from comprehensive or self-contained. [14]

Coyne and Heller continue:

Why then should we not adopt irrationalism? Because when one confronts rationalism with irrationalism, one immediately sees that rationalism is a value. Therefore, “the choice before us is not simply an intellectual affair, or a matter of taste. It is a moral decision”. Indeed, the choice of value is the moral decision. Popper calls this kind of rationalism critical rationalism, the one “which recognizes the fact that the fundamental rationalist attitude results from an (at least tentative) act of faith — from faith in reason”. [15]

So there is a sense in which this mystery — this fundamental mystery about the world — cannot be answered, at least not rationally. As Einstein said, “we shall never understand” [16].

But the inquiring philosopher, who cannot help attempting to explain, is unlikely to be satisfied by this. As Coyne and Heller put it, “The principal tenet of rationality is that one is never allowed to cease asking questions if there remains something to be sought.” [17]

It seems clear to me that there is indeed something remaining to be sought.

[1] Wigner, E. P. 1960. Communications in Pure and Applied Mathematics, vol. 13, no. 1. Reprinted in Saatz, T. L., and Weyl, F. J., eds. 1969. The Spirit and the Uses of the Mathematical Sciences (New York: McGraw-Hill).

[2] Ibid.

[3] Livio, M. 2009. Is God a Mathematician? (New York: Simon & Schuster). p. 223.

[4] Ibid. p. 224

[5] Einstein, A. 1934. “Geometrie und Erfuhrung” in Mein Weltbild (Frankfurt am Main: Ullstein Materialien).

[6] Atiyah, M. 1995. Times Higher Education Supplement, 29th of September. Quoted in Livio, M. op. cit. p. 243.

[7] Livio, M. op. cit. p. 232

[8] Newton, I. 1704. Opticks (London: Smith & Walford)

[9] Ibid. The book to which he refers is his Philosophiae Naturalis Principia Mathematica, 1687 (London: Pepys)

[10] Coyne, G. and Heller, M. 2008. A Comprehensible Universe: The Interplay of Science and Theology (Springer)

[11] Hamming, R. W. 1980. The American Mathematical Monthly, 87(2), 81. Quoted in Livio, M. op. cit. p. 246.

[12] Atiyah, M. op. cit.

[13] Einstein, A. 1936. “Physics and Reality” in Journal of the Franklin Institute 221. pp. 349 – 382. Quoted in Coyne, G. and Heller, M. op. cit. p. 3

[14] Popper, K. P. 1974. The Open Society and Its Enemies: Volume 2 (London: Routledge & Kegan Paul) p. 224. Quoted in Coyne, G. and Heller, M. op. cit. p. 9

[15] Coyne, G. and Heller, M. op. cit. p. 9. In which they quote from Popper, K. P. op. cit. pp. 230 – 232

[16] Einstein, A. op. cit.

[17] Coyne, G. and Heller, M. op. cit. p. xiv

Published in: on July 26, 2009 at 9:39 pm  Leave a Comment  


I still don’t completely understand why it is that thousands of people can wander around wearing clothing emblazoned with the image of Che Guevara and it is considered completely acceptable; whereas if one person were to walk around displaying an image of a Nazi in a positive light he would, quite rightly, be excoriated.

Here are some of the wise sayings of Ernesto “Che” Guevara:

If the missiles had remained we would have used them against the very heart of America including New York. We must never establish peaceful coexistence. In this struggle to the death between two systems we must gain the ultimate victory. We must walk the path of liberation even if it costs millions of atomic victims.

– Quoted in The Nuclear Deception: Nikita Khrushchev and the Cuban Missile Crisis by Servando Gonzales (Spooks Books, 2002, p. 111)

To send men to the firing squad, judicial proof is unnecessary. These procedures are an archaic bourgeois detail. This is a revolution! And a revolutionary must become a cold killing machine motivated by pure hate.

– Quoted in The Cuban Revolution: Years of Promise by Teo A. Babun and Victor Andres Triay (University Press of Florida, 2005, p. 57)

The situation was uncomfortable for the people and for [Eutimio], so I ended the problem giving him a shot with a .32 pistol in the right side of the brain, with exit orifice in the right temporal [lobe]. He gasped for a little while and was dead. Upon proceeding to remove his belongings I couldn’t get off the watch tied by a chain to his belt, and then he told me in a steady voice farther away than fear: “Yank it off, boy, what does it matter.” I did so and his possessions were now mine.

– Diary entry quoted in Che Guevara: A Revolutionary Life by Jon Lee Anderson (Bantam Books, 1997)

In the future individualism ought to be the efficient utilization of the whole individual for the absolute benefit of a collectivity.
Published in: on July 21, 2009 at 3:41 pm  Comments (1)  


Since I read Atheism and Theism [1], J.J.C. Smart has become something of a philosophical hero for me. I really admire both his philosophical acumen and his attitude towards philosophy and other philosophers in general. If only all atheists exhibited his combination of sharp logic and respect for those that disagree with him (and all theists were a bit more like J.J. Haldane) then the philosophy of religion would be a lot more respectable.

I mentioned Smart only because I wanted to refer to his claim that there are few knockdown arguments in philosophy [2], which I think is important. However, I note that I have inadvertently produced another basis for my segue into a discussion of a talk by Richard Dawkins.

In July 2005, Richard Dawkins gave a talk at TED entitled “Queerer than we can suppose: the strangeness of science” [3]. Much of the talk is taken up by Dawkins’ theory that our ideas about what really exists, or what is normal, are the result of our evolution in what he calls Middle World. The “middle” refers to our position in the scale of things between the very small, the level of particle physics and quantum theory, and the very large, the level of astronomy and general relativity.

Thus, for example, we perceive rocks to be hard and impenetrable because at our level, the level of humans, rocks are indeed impenetrable. I cannot walk through, or pass my hand through, solid rock. However, at the quantum level, both rocks and humans are of course mostly empty space. A neutrino-sized being that had evolved a brain in its neutrino-sized world would perceive rocks to be mostly space. Similarly, we have evolved to possess an intuitive understanding of motion at the sort of middling speeds that things, such as animals, in our middling world of everyday experience tend to exhibit. If we had evolved to move through the cosmos at speeds nearing the speed of light, we would have a better intuitive of understanding of Einstein’s theories of relativity.

Dawkins refers to Feynman’s description of quantum theory:

Richard Feynman compared the accuracy of quantum theory’s experimental predictions to specifying the width of North America to within one hair’s breadth of accuracy. This means that quantum theory has got to be in some sense true. Yet the assumptions that quantum theory needs to make in order to deliver those predictions are so mysterious that even Feynman himself was moved to remark, “If you think you understand quantum theory, you don’t understand quantum theory.” [4]

The difficulty that we have understanding the way the world works at very small and very large scales is, according to Dawkins, due to our having evolved in a world of medium-scale entities.

Dawkins goes further than this, to speculate about the way the world might appear to other species:

“Really”, for an animal, is whatever its brain needs it to be in order to assist its survival. And because different species live in different worlds, there will be a discomforting variety of “really”s. What we see of the real world is not the unvarnished world but a model of the world, regulated and adjusted by sense-data, but constructed so it’s useful for dealing with the real world.

The nature of the model depends on the kind of animal we are. A flying animal needs a different kind of model from a walking, climbing or swimming animal. A monkey’s brain must have software capable of simulating a three-dimensional world of branches and trunks; a mole’s software for constructing models of its world will be customised for underground use; a water strider’s brain doesn’t need 3D software at all since it lives on the surface of the pond in an Edwin Abbott flatland.

I’ve speculated that bats may see colour with their ears. The world model that a bat needs in order to navigate through three dimensions catching insects must be pretty similar to the model that any bird, a day-flying bird like a swallow, needs to perform the same kind of tasks. The fact that the bat uses echoes in pitch darkness to input the current variables to its model while the swallow uses light is incidental. Bats, I’ve even suggested, use perceived hues such as red and blue as labels, internal labels, for some useful aspect of echoes — perhaps the acoustic texture of surfaces: furry or smooth and so on — in the same way as swallows, or indeed we, use those perceived hues, redness and blueness etc., to label long and short wavelengths of light. There’s nothing inherent about red that makes it long wavelength. [5]

It is interesting that Dawkins draws such a strong distinction between the way the world objectively is and the way it subjectively appears to us, even going so far as to claim that another species may see “red” in quite different circumstances from those that would cause a human to see red. His description of “redness” and “blueness” could be a textbook description of qualia. He certainly appears to be saying that there is something that it is like to be a bat. This seems to contradict his own self-description as an austere mechanist:

Most scientists today subscribe to a mechanistic view of the mind. We’re the way we are because our brains are wired up as they are and our hormones are the way they are. We’d be different, our characters would be different, if our neuro-anatomy and our physiological chemistry were different.

But we scientists are inconsistent. If we were consistent, our response to a misbehaving person like a child murderer should be something like, “This unit has a faulty component, it needs repairing.” That’s not what we say. What we say, and I include the most austerely mechanistic among us, which is probably me, what we say is, “Vile monster! Prison is too good for you!” Or worse we seek revenge, in all probability thereby triggering the next phase in an escalating cycle of counter-revenge, which we see of course all over the world today.

In short, when we’re thinking like academics, we regard people as elaborate and complicated machines like computers or cars. But when we revert to being human, we behave more like Basil Fawlty, who you remember thrashed his car to teach it a lesson when it wouldn’t start on Gourmet Night.

The reason we personify things like cars and computers is that just as monkeys live in an arboreal world and moles live in an underground world and water striders live in a surface-tension dominated flatland, we live in a social world. We swim through a sea of people, a social version of Middle World. We are evolved to second-guess the behaviour of others by becoming brilliant, intuitive psychologists.

Treating people as machines may be scientifically and philosophically accurate but it’s a cumbersome waste of time if you want to guess what this person is going to do next. The economically useful way to model a person is to treat him as a purposeful, goal-seeking agent with pleasures and pains, desires and intentions, guilt, blame-worthiness.

Personification and the imputing of intentional purpose is such a brilliantly successful way to model humans, it’s hardly surprising the same modelling software often seizes control when we’re trying to think about entities for which it’s not appropriate, like Basil Fawlty with his car or like millions of deluded people with the universe as a whole. [6]

There is some confusion here. Is it or is it not accurate to describe people as purposeful? Dawkins appears to be saying that it is never accurate to describe anything as purposeful but that it is sometimes useful to pretend that certain things, such as other people, are purposeful. He does not say that treating other humans as purposeful is deluded, he says it is useful. But in that case the millions of people who believe the universe is purposeful cannot be deluded either: it is merely the case that their belief is not as useful as it is when applied to humans.

Dawkins cannot have it both ways. Either humans genuinely are purposeful, in which case “treating people as machines” is neither scientifically nor philosophically accurate, or people who impute purpose to the universe are not deluded. Dawkins seems to switch between correspondence and pragmatist truth theories as it suits him, which makes his philosophical position rather incoherent.

But let us ignore his snide comment about the deluded masses. There is still a problem with the claim that although people are really just machines, it is more useful for us to pretend that they are not.

Even those who, like Dawkins, claim that the world is purposeless cannot help both experiencing the sensation of having purposes themselves and treating others as if they genuinely are “purposeful, goal-seeking agent[s] with pleasures and pains, desires and intentions, guilt, blame-worthiness.” Indeed, the latter segment of Dawkins’ talk is an attempt to explain why it is that we cannot help believing that humans are purposeful.

But if we cannot help believing it, we should surely demand some damn good evidence that it isn’t real. Dawkins does not present any such evidence: all he does is attempt to explain how it could be the case that we believe it even if it isn’t real. He does not present any rational reason for believing that it isn’t real.

What could such a reason be? Elsewhere, particularly when arguing about the existence of God, Dawkins makes reference to the idea that a simple or parsimonious explanation is better than one that introduces unnecessary complexity or leaves yet more to be explained [7]. So it may be that he would like to remove purpose from our understanding of the world because he believes that everything can be adequately explained without it.

However, there are two flaws in this approach. The first is that it is not at all clear that everything can be adequately explained without it. We experience the sensation of having purpose and we believe we perceive purpose in the actions of others. The obvious explanation is that our perceptions are correct: we really do have purpose and so do other people. Dawkins’ alternative is that purpose is illusory, an artifact of the way that our brains predict the actually mechanistic behaviour of others. But denial is not explanation. Dawkins has not demonstrated that purpose is illusory, he has just stipulated that it is so and then conjectured some way in which such a stipulation might accord with our apparently contradictory experience.

Furthermore, this conjecture does not even account for all the evidence. Perhaps it could explain why we treat other people as “goal-seeking agent[s] with pleasures and pains, desires and intention” but it does not explain why it is that we ourselves feel pain and desire. Regardless of its origin, artifact of simulation or otherwise, I have first-hand experience of pain, desire, intention and so forth. Dawkins offers no explanation for this.

Second, earlier in his talk he seemed to postulate the existence of qualia, which throws doubt on any claim he might make that his explanation is more parsimonious than the obvious one. It is hard to make sense of this, since the existence of qualia would presumably refute his mechanistic philosophy, the support of which appears to be the sole motivation for his denial that purpose is real. Moreover, even if there is some way in which Dawkins’ position could be stated coherently, it is still not clear that his explanation in terms of simulations of “a social Middle World” is simpler than just accepting the reality of purpose.

Finally, perhaps there is a pragmatic reason for claiming that purpose is illusory. We have already seen that Dawkins vascillates between pragmatism and a concern for objective truth: perhaps in this case he is being pragmatic. However, Dawkins himself admits that humans cannot help thinking in terms of purpose, in which case it would be bizarre to claim that it is more pragmatic to think in some other way. Indeed, one might reasonably claim in such circumstances that the most pragmatic option would be to accept the reality of purpose, even if other considerations cause one to doubt its reality.

On the basis of this talk, there does not seem to be any rational reason for rejecting the common sense view that humans are purposeful, that they have intentions and desires, experience pleasures and pains and so on.

Dawkins appears to have chosen a theory, a philosophy of mind known as eliminative materialism, and then tried to explain how our contradictory experiences might be shoehorned into this theory. In both science and philosophy, it is generally considered bad form to pick a conclusion then attempt to explain away any data that contradicts it. In general, one should attempt to begin with the data and then seek the theory that best explains it. One can only assume that Dawkins has an ideological motivation to do otherwise.

[1] Atheism and Theism, J.J.C. Smart and J.J. Haldane, Wiley-Blackwell, 2003.

[2] ‘Why Philosophers Disagree’, J.J.C. Smart, in Reconstructing Philosophy: New Essays in Metaphilosophy, J. Couture and K. Nielsen (editors), University of Calgary Press, 1993, pp. 67-82.

[3] The talk can be viewed on YouTube: http://www.youtube.com/watch?v=1APOxsp1VFw

[4] Ibid. 00:54 – 01:28

[5] Ibid. 11:29 – 13:28

[6] Ibid. 19:03 – 21:26

[7] Dawkins frequently complains that a creator God would have to be at least as complex as that which He created, thus any attempt to explain the universe as God’s creation is useless because we are left with the equally or more difficult task of explaining God. I deduce from this that Dawkins doesn’t really understand what theologians mean when they say that God creates and sustains the world. Until recently I did not understand what they meant either but, having read a couple of books, I now have a much better idea. It is clear to me that Dawkins has not bothered to do even a cursory amount of research into his opponents’ theses, which is remarkable given the scorn he pours on those who dare to question scientific theories without first studying science. I really enjoy his books on biology, which makes his hypocrisy in philosophical matters deeply saddening. See Dawkins versus Swinburne at the Maverick Philosopher for a very restrained response to one of Dawkins’ exercises in double standards.

Published in: on July 17, 2009 at 12:21 am  Leave a Comment  

The Unchanged Changer

Over on the aptly named McCabism blog, Gordon McCabe recently wrote about Christopher Hart’s review of Karen Armstrong’s new book, The Case for God: What Religion Really Means. Dr McCabe wrote:

Hart’s proposition that God is not a being, but Being itself, is the familiar doctrine of pantheism, which is inconsistent with the personal nature of God enshrined in Christianity, Judaism and Islam.

However, the proposition that God is Being itself is not the same as pantheism. In fact, pantheism and “God is Being” are mutually exclusive. To explain this — or, more accurately, to explain my understanding of this issue: the whole thing is too damn convoluted and confusing for me to claim to understand it completely — I thought I would attempt to produce my own exposition of the famous “Unmoved Mover” argument.

We start with two premises. The first is pretty uncontroversial so I’ll get it out of the way now: we observe change in the world. Things change.

The second premise is really an attempt to provide an explanation of change. This is rather typical of philosophers: whereas a normal person might quite happily accept that things change and leave it at that, a philosopher cannot help but ask why: why do things change? What is it that makes them change? Can we explain change?

Philosophy is basically an attempt to explain things. I think it revealing that some modern philosophers “solve” the traditionally difficult problems of philosophy not by producing an actual solution but instead by declaring that such and such does not really require an explanation. It smacks of intellectual dishonesty, or at the least a lack of imagination and curiosity unworthy of a philosopher, but that is a cantankerous complaint for another day.

What is change? It is the phenomenon whereby an entity ceases to be in one state and is henceforth in another state, at least until it changes again. There are two extreme views about change, which have come to be associated with two early Greek philosophers: Heraclitus and Parmenides.

Heraclitus held that change is all there is. He claimed that there are no entities, just flux. Even if we can make sense of this idea (which is not easy: one intuitively assumes a substrate when considering flux) it has an obvious problem. We observe entities all the time. If everything is just flux, then how do we explain the fact that we appear to be surrounded by identifiable entities?

Modern science does not help us. The entities of quantum physics may not be much like the everyday entities with which most people are familiar but they are nevertheless things, not pure flux. A quantum state is still a state, whether mixed or pure, so we cannot get away from the fact that there appear to be things that change. Indeed, I suspect the difficulty we have trying to make sense of the notion of pure flux is due to its incompatibility with our experience, both our everyday experience and the most bizarre experiences of esoteric science, in which change is not something that exists alone but is rather something that things do.

Parmenides overshoots in the other direction: he claims that there is no change. All the apparent change that we observe in the world is, according to him, an illusion. The usual interpretation of his argument goes something like this: everything that exists is a part of existence; anything that changes must be changed by something else; but the only thing other than existence is non-existence, i.e. nothing, which obviously can’t change anything because it doesn’t exist; therefore nothing changes.

Well, it’s something like that anyway. To be honest, I don’t really understand Parmenides (and there is considerable controversy among those who claim that they do) but that doesn’t matter for now: it’s not as if my description of the philosophy of Heraclitus was at all fair to the complexities of his thought. For the purposes of this argument, I just want to set up two extremes concerning change: everything is change and there is no change.

This allows me to portray Aristotle’s views on change as a welcome return to common sense, a reasonable middle ground between the two self-evidently absurd extremes. The problem is this: we need to explain how it is that things can change. We can’t just follow Heraclitus and say that change is all there is, because that doesn’t allow for the existence of the things that we see doing the changing. But we can’t follow Parmenides either because then we can’t explain the change that we see the things undergoing.

Aristotle solves this conundrum by proposing that things are both actually in some state and potentially in some other state (or states). Now we can describe change as the process by which a thing moves from its current actual state to one of its potential states. We now have a notion of potential existence. The matches in my matchbox are not actually alight at this moment but they have the potential to be alight, if, for example, I were to strike them.

Instead of one monolithic thing we call existence — which cannot change because the only thing that isn’t existence is non-existence, and something that doesn’t exist can’t change anything — we have many different entities that vary in their actual and potential existence. Because these entities have both actual and potential properties, and the potential can become the actual via the process of change, we can accommodate both the existence of things and the fact that they change. This answers both Heraclitus and Parmenides.

Now, nothing changes unless something causes it to change. A match lights when you strike it and not if you don’t. If a match appeared to spontaneously burst into flame we would look for an explanation — perhaps it was being heated by some other heat-source — and we wouldn’t be satisfied unless we could find some explanation for its ignition. Whenever anything changes we expect there to be something else that caused that change: that is why the change happened then and not at some other time.

But only something that actually exists can cause change. I cannot light my pipe with an unlit match regardless of the fact that the match has the potential to be lit. The match must be actually alight before it can cause change in other things as a result of its burning.

So we arrive at our second premise: change is the phenomenon whereby something that actually exists causes something else to actualise its potential.

It is important to note that this is an immediate effect. We are not talking about causes happening before an effect: that does not make sense in this context. Changes occur precisely when they are caused. The cause precedes the effect only in the sense that it is logically antecedent, not temporally antecedent. To go back to striking matches, it is precisely when the combustible chemicals on the head of the match reach their ignition temperature that they begin to burn. Here the friction caused by striking the match is the cause of the heat that ignites the match head and it all happens at the same time.

The stock example in philosophy textbooks is that of someone pushing a stone along the ground using a stick. The stone is moving because the stick is moving and the stick is moving because the person is moving, but obviously they are all moving at the same time. The movement of the person is logically antecedent to the movement of the stone but not temporally so.

Well, then. According to our first premise, things change. We observe change in the world. According to our second premise, the change that we observe involves the actualisation of potentialities by things that actually exist.

However, there is an obvious danger of infinite regress here. If A was changed by B which was changed by C which was changed by D which was changed by E… where does it end? How can it end?

Obviously the end of the chain cannot be something that can itself be changed. If it were, then it wouldn’t be the end of the chain. So the end of the chain cannot have the potential to be in any way other than the way that it is. So it has no potentiality. But it must, as we have seen, actually exist or it would not be able to cause change. So the end of the chain is purely actual.

You have probably guessed by now that the end of the chain is, as Aquinas would put it, what we call God (et hoc dicimus Deum). You can deduce lots of stuff about the Unchanged Changer, such as that there can only be one of them, but I don’t intend to attempt any of that now. I just want to point out the silliness of a couple of common refutations of this argument.

First, there is this one: “If everything has a cause then what caused God?” As should be evident from the above argument, it is not necessary to suppose that everything has a cause. We only suppose that change has a cause. God, as pure actuality, does not (indeed, by definition, cannot) change and therefore does not need a cause. That is the whole point of the argument.

Second, there is this: “If God caused everything, what came before God?” Again, it should be obvious from the above argument that temporal precedence has nothing to do with it. How or if or when the universe came into being is completely irrelevant. We are talking here only about logical antecedence. As Edward Feser wrote about Aquinas’ proofs:

His aim is to show that given that there are in fact some causes of various sorts, the nature of cause and effect entails that God is necessary as an uncaused cause of the universe even if we assume the universe has always existed and thus had no beginning. The argument is not that the world wouldn’t have got started if God hadn’t knocked down the first domino at some point in the distant past; it is that it wouldn’t exist here and now, or undergo change… here and now unless God were here and now

I also rather like this metaphor:

The world is not an independent object in the sense of something that might carry on if God were to “go away”; it is more like the music produced by a musician, which exists only when he plays and vanishes the moment he stops.

[The Last Superstition, St Augustine’s Press, 2008, pp. 86 & 88]

Embarrassingly, I realised as I was coming to the end of the argument that I’d done the wrong one. I did the one that ends with Pure Actuality and not the one that ends with Being Itself. It is similar but is based on existence rather than change: roughly, contingent existence takes the place of potentiality and necessary existence takes the place of actuality; thus rather than ending up with something that actually exists and has no potential, you end up with something that necessarily exists and is not contingent on the existence of anything else.

Anyway, the point was merely to demonstrate that when theologians say things like “God is Being” they are, or at least might be, referring to the conclusion of a rational argument rather than just spouting mytho-poetic metaphor. Certainly, in that particular instance they are not referring to the doctrine of pantheism. It is also not true to claim that such a statement is “inconsistent with the personal nature of God enshrined in Christianity”, as it is actually a rather old proof, one of many, from which various attributes of God including his personality are deduced at great length by Aquinas and other Scholastic philosophers.

Finally, is the argument sound? I think it is valid. I think if you wish to refute the argument your best bet would be to have a go at the second premise: Aristotle’s metaphysics of change.

Published in: on July 6, 2009 at 6:25 pm  Leave a Comment  

My Friend’s Philosophy

Whenever I am uncertain about a philosophical issue, especially when I am on the verge of changing my mind about something that I deem important, I like to run my ideas past a certain friend of mine. This man is extremely sceptical and cynical, in the contemporary meanings of those words. We used to joke, or perhaps half-joke, that he worshipped Richard Dawkins. So when I am considering something decidedly non-scientific, especially something concerning religion or the like, I find it very helpful to discuss the matter with him. He always makes short work of any nonsense or inconsistencies in my arguments.

Some time ago, we argued about the nature of morality. He believes that his sense of right and wrong does not correspond to any objective, external measure of morality. He believes that no system of morality can be said to be correct or incorrect but rather that all moral systems are equally valid or invalid. Indeed, on his account objective validity is not a concept that can be coherently applied to morality.

This understanding of morality seems to accord with current scientific opinion. The origin of our moral sense appears to be explicable solely in terms of biological and cultural evolution. However, since no normative conclusions can be drawn from such a genealogy (as we have seen) we are left with moral nihilism. Morality is revealed to be a convenient fiction.

In the interests of honest disclosure, I must admit that my dissent from this view is motivated in part by my disgust at the above conclusion. I find moral nihilism utterly repellent. However, if that is the truth of the matter then so be it. I am unable to believe something that I know to be false. But it seems likely to me that there is an error in his argument: if morality exists then it is surely not a physical thing, which means that our inability to scientifically deduce a system of morality from physical truth is irrelevant, or at least inconclusive. My friend’s reply is that morality does not exist in any meaningful sense.

He divides reality into the objective and the subjective. That which is objective is the same for everyone, whereas that which is subjective may differ from person to person. He then declares that the objective exists but the subjective does not. He further declares that we may define the objective as that which can be independently observed by different people (or that which different people can logically deduce from independent observations). Thus the truths of physics are objective, whereas the truths of morality are subjective (and hence not really truths at all).

If we were to encounter an alien civilisation, composed of beings utterly different from our own, we could be sure that we would agree on the mathematics of the physical world. If any of our physical or mathematical theories were contradictory, we could resolve the contradiction through observation and logical analysis. In contrast, we should not expect our moral systems to be similar — indeed, we have many wildly divergent moral systems here on Earth — and there is no scientific procedure by which we could resolve our moral differences. It is in this respect that my friend distinguishes between the objective and subjective. The former can be determined by reference to an external, independent reality, while the latter is purely personal.

I am also happy to define the objective as that which is the same for everyone and the subjective as that which might differ for each person. However, I do not see why there could not be something objective that is nevertheless not amenable to scientific enquiry. My friend replies that he does not think it makes sense to talk about the existence of something that cannot be independently observed.

But surely that is begging the question. If you define existence as the potential to be independently observed, then of course that which cannot be independently observed does not exist. But why choose that definition of existence in the first place?

The one thing that I know exists is my personal, subjective experience. No coherent philosophy can deny that. Solipsists may deny that anything else exists but even they cannot deny that thought or personal experience exists. Everything else is a deduction, abstraction or extrapolation from that primary fact which is that I experience.

If we grant ontological validity to the distinction between the subjective and the objective, as my friend would like to do, then we are surely left with either some form of substance dualism or solipsistic idealism. The one thing we cannot coherently do is to define existence as a property that does not belong to the only thing that we cannot deny exists.

Given that both substance dualism and idealism have their own significant problems, I am led to believe that my friend’s distinction between the objective and the subjective is epistemological rather than ontological. This should not really be surprising, since he defined those two categories in terms of the means by which one acquires knowledge about them.

Thus we are forced to accept the existence of some things, or some properties of things, that cannot be identified through independent observation of physical reality, i.e. scientific experimentation. But how do we come to have knowledge of such things?

My friend would say that there is no valid means of acquiring knowledge besides the scientific method, simply because without recourse to independent observation of an external reality we have no means of differentiating between competing claims. I have one moral system, you have another, how can we possibly determine whose is right? This inability to “objectively” distinguish between competing claims is the reason he would deny reality to any such claims.

It is rather a stumbling block. It does not seem necessary, or indeed rational, to deny reality to something merely because it is not amenable to the methods of scientific enquiry. However, it is not unreasonable to declare that there’s no point talking about something if we can never be sure whether what we say is true or false.

But here my friend’s argument becomes circular once again. He has implied a theory of truth whereby “true” and “false” are to be determined by empirical observation and logical deduction therefrom alone. He has taken Sir Karl Popper’s maxim that potential falsifiability differentiates science from non-science and elevated it to a criterion that differentiates between the meaningful and the meaningless. But there is really no rational reason to do this, it is merely the indulgence of an aesthetic preference for “hard science and logic”.

Popper himself preferred Alfred Tarski’s semantic theory of truth. He believed that Tarski had rehabilitated Aristotle’s correspondence theory of truth. Indeed, as Malachi Haim Hacohen writes in Karl Popper – The Formative Years (Cambridge University Press, 2002, pp. 281-282), it is hard to see how one can make sense of falsifiability without some form of correspondence theory of truth.

In the Stanford Encyclopedia of Philosophy‘s entry on correspondence theories of truth, Marian David writes:

The metaphysical version presented by Thomas Aquinas is the best known: “Veritas est adaequatio rei et intellectus” (Truth is the equation of thing and intellect), which he restates as: “A judgment is said to be true when it conforms to the external reality”—he tends to use “conformitas” and “adaequatio”, but also uses “correspondentia”, giving the latter a more generic sense (De Veritate, Q.1, A.1-3; cf. Summa Theologiae, Q.16)…

Aquinas’ balanced formula “equation of thing and intellect” is intended to leave room for the idea that “true” can be applied not only to thoughts and judgments but also to things or persons (e.g., a true friend). Aquinas explains that a thought is said to be true because it conforms to reality, whereas a thing or person is said to be true because it conforms to a thought (a friend is true insofar as, and because, he conforms to our, or God’s, conception of what a friend ought to be). Medieval theologians regarded both, judgment-truth as well as thing/person-truth, as somehow flowing from, or grounded in, the deepest truth which, according to the Bible, is God: “I am the way and the truth and the life” (John 14, 6). Their attempts to integrate this Biblical passage with more ordinary thinking involving truth gave rise to deep metaphysico-theological reflection. The notion of thing/person-truth, which thus played a very important role in ancient and medieval thinking, is disregarded by modern and contemporary analytic philosophers but survives to some extent in existentialist and continental philosophy.

I am, in general, antipathetic to continental philosophy. However, as incomprehensible as I find most of his writing, I still retain a deep respect for Heidegger. It appears I am not the only one with analytical tendencies who nevertheless cannot help admiring him; in Atheism and Theism (Wiley-Blackwell, 2003, p. 32), J.J.C. Smart writes:

Despite the fact that I am repelled by Heidegger’s style of philosophical writing, there is nevertheless one respect in which I have a sneaking fellow feeling with him. This is his propensity to ask why there is anything at all.

Although I find his answers baffling, I share with Smart a respect for Heidegger’s propensity to ask important questions. Smart refers to the key question which underlies all of Heidegger’s philosophy but there are two subsidiary aspects of that enquiry that appeal to me strongly. One is his view of death, which I have mentioned before. The other is his view of truth.

Heidegger distinguishes between two different understandings of “truth”. The first, which Bernd Magnus has called the epistemological concept of truth, is the correspondence theory of truth that Heidegger associates with Western metaphysics from Plato onwards. The second, which Magnus has called the ontological concept of truth and which Heidegger claims is an earlier, pre-Socratic understanding, is the concept of alétheia. This is an Ancient Greek word that Heidegger interprets as “un-hiding”, “un-forgetting” or in more natural English: “disclosure”.

Heidegger contrasts the epistemological notion of truth as correspondence with his ontological notion of truth as disclosure. Another friend of mine, rather different in attitude from the friend mentioned above, once told me that the truths of fiction are “more true because they are fiction.” I think that’s a somewhat over-the-top way of making the point but I believe I understand what he is trying to say. In a similar manner to Heidegger, he has rejected the correspondence theory of truth, according to which we divide literature into fact and fiction, in favour of a notion of truth that can better be described as revealing or disclosing the intrinsic nature of the world. Rather than a relationship between propositions and facts about reality, alétheia is the disclosure of reality itself.

Of course, this veering off into continental philosophy would be rejected by those of an unsympathetic scientific bent. Indeed, Heidegger is a figure of hatred and ridicule for many analytical philosophers. This is only slightly unfair: he deserves much of the vituperation sent his way for his writing is so unbelievably obtuse. I get his point that the deep truths of reality elude logical expression, or even expression in everyday language, but is that really a justification for writing enormous tomes in his own convoluted language? Not only does he make up unnecessarily confusing terminology but he also perverts the usual rules of grammar to such an extent that it is pretty much impossible to be sure of what he was trying to say. I blame Heidegger, along with Hegel and Husserl, for encouraging the pretentious nonsense that calls itself postmodern philosophy today. But it may be noteworthy that Heidegger himself had no truck with existentialism and regarded Sartre as having completely misunderstood his work.

Nevertheless, despite his faults of expression, I find much to be admired in Heidegger’s critique of modern Western philosophy. Perhaps Heidegger’s work functions better as a guidebook than a textbook — most of my understanding of Heidegger comes from the commentary of others rather than primary texts, which I have tried but failed to comprehend — but that is no reason to dismiss it out of hand.

In summary, I consider some of the truths about the world — which are not necessarily “higher” or “deeper” than scientific truths, whatever that might mean, but merely of a different order — to be fundamentally unanswerable by empirical observation. I do not think it is reasonable or rational to define either reality or meaningfulness in terms of that which is amenable to the scientific method. Thus any attempt to use such definitions to argue for the non-existence or meaninglessness of morality is doomed to failure before it even begins.

I do not know how seriously I should take Heidegger’s view of truth, although I do find it aesthetically appealing, but I mentioned it here mostly to demonstrate that a correspondence theory of truth is not the only way to save truth from relativism. One advantage of Heidegger’s alétheia, as I see it, is that it provides a possible foundation for truths, especially moral truths, without the need to somehow deduce them from physical fact. It appeals to me especially as a description of the sense in which myths are true: that myths are neither allegory nor history but rather tales that disclose truth makes perfect sense to me.

Finally, just to annoy the Heidegger-haters out there, I quote with admiration a description of Heidegger’s take on Germany in the 1930s:

Heidegger believed in German culture, tradition and a third way between communism and capitalism. He said: “Everything essential and great has only emerged when human beings had a home and were rooted in a tradition.” He was a critic of modern science and what he thought was humanity’s subjugation to technology. He wrote with a sense of impending crisis or catastrophe and spoke of a “darkening of the world” and an “enfeeblement of the spirit.” He referred to Germany caught between the world of Anglo-American democracy to the west and Soviet communism to the east. Germany, he believed, was thereby under pressure and “most endangered.”

Published in: on July 6, 2009 at 2:20 am  Leave a Comment