The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
The existence of God, Part 2: The cosmological argument


The existence of God, Part 3: The natural law argument
Last modified on Sun Dec 3 16:37:38 2017


This is the latest post in a series about Bertrand Russell's essay Why I am not a Christian, in which I run through his various arguments and show that they either don't apply to classical theism, or were invalid in the first place. Russell's essay is split into several topics, the first of which (after his introduction) is to discuss some philosophical arguments often used in favour of the existence of God. In the previous essay, I looked at the first of these, his version of the cosmological argument. Now, I turn to the second, the argument from the structure of natural law.

Before I start, I ought to clarify a confusion in Russell's terminology. For the Aristotelian (such as myself), the phrase natural law refers to a theory of ethics. The idea is that there are certain ethical principles which can be derived from a secular understanding of nature. For example, the idea that it is evil to commit murder is a consequence of the inherent tendencies of living organisms. To commit murder is to deliberately frustrate those tendencies, and that is the definition of a moral evil. This is distinguished from divine law, which are those moral requirements which are only known from specific commandments from God, for example the commandment to keep the Sabbath holy.

In this section of his essay, however, Russell uses the phrase to mean something else, namely the laws that govern the motion of matter, namely what I call the laws of physics. Russell was here referring to an idea, popular in the early days of the scientific revolution but not so much today, that the harmony and consistency of the universe as uncovered by the study of physics in itself is evidence for the existence of God. God is seen as a divine lawgiver; one cannot have a lawgiver unless there are laws he has given. Equally, it is argued in the simplest form of this argument, one cannot have laws without a lawgiver. In the case of the laws of physics, that lawgiver cannot Itself be bound by physics. Since physics describes everything within the material universe, that means that the lawgiver must be immaterial. And we are now, it is claimed, well on the way to reaching God.

My presentation in the previous paragraph was somewhat too naive. For example, it relied on an analogy between human laws and physical law, and arguments by analogy are often weak. So, before moving to the objections, I will present a more detailed and mature form of the argument.

In theism, God is not only the creator of the universe, but is active in sustaining it in every detail. This act of sustaining the universe involves keeping objects in existence, controlling their motion and movements, and keeping complex beings bound together. But this is, of course, precisely the area that comes under the purview of physics. Thus, for the theist, physics is no more and no less than a description of God's sustaining of the universe. As such, we can expect that the laws of physics (whatever is meant by that term; and different versions of theism mean different things) should in some way reflect the nature and character of God. The argument from natural law in its weak form states that physical law has the features that we would expect were it a description of God's general concourse. In its strong form it states that only a description of God's general concourse could explain why physics takes the form it does.

There are several directions in which this thought can be taken. The first is occasionalism, which is to state that God can do anything to anything. There is no reason for us to expect regularity in the universe -- there is no reason why a hat should not suddenly turn into a rabbit and hop off our heads. This implies that a study of physics would be limited; since most expressions of physics assume an underlying regularity and homogeneity of nature, and in occasionalism this assumption is invalid; at best only approximate. Laws of physics would just be our own description of observed regular conjunctions, but without a connection to the real world. For those who subscribe to this doctrine, to say that the universe is regular would put a limitation on God's power, which is, to them, clearly absurd.

The second direction is deism, which takes the opposite extreme. This focuses on the rationality of God, and diminishes God's free will entirely. It is first of all argued that since God has perfect knowledge of the future, this can only happen if the future is perfectly predictable. This means that there are distinct laws of nature which can in principle be used to predict how matter in the universe changes in time. These laws stand as something of an intermediary between God and created matter. God is their author, but once formulated they continue to guide matter indefinitely without further intervention from God. They must exist because God Himself uses them to predict the future. Since our intellect is patterned on that of God, we also can understand them, at least partially, and should seek to do so. They inherit from God the properties of universality, rationality and self-consistency, that they are unchanging in time and space, that no matter is outside their purview and they show no favouritism to different corpuscles of matter, and, as already mentioned, they are deterministic in the sense that given complete knowledge of the universe at one moment in time it is possible to predict how it would be at each subsequent moment in time. The study of and attempt to uncover these laws through a combination of careful experimentation and logical or mathematical reasoning is natural philosophy, or (as later came to be known), science.

The middle ground is provided by the theistic forms of Aristotelian philosophy. This states that instead of being a single law of nature, each individual type of being has its own inherent tendencies to act in certain ways. When God acts in the universe, He respects these tendencies. Against the Occasionalist, the Aristotelian theist would argue that this does not limit the power of God, because God established the tendencies in the first place. Unlike in deism, there is not a single tendency for each being. God has the freedom to choose which of these are actualised at any given moment. Thus the universe need not be deterministic (it could be, but need not be). Against the objection of the deist, the Aristotelian would say that God does not know what is to us the future through prediction, but on account of His timeless nature, where He observes each moment in time not in succession (as we do) but together. This allows both free will (both for God and for us), and perfect knowledge of the future (for God, but not for us). Since these tendencies ultimately come from God, they inherit certain properties from God: the tendencies themselves are unchanging in time and space, depending only on the type of being, and the likelihood for each tendency to be actualised at any given moment is also unchanging, depending only on the type of being and the external circumstances. Since this ordering of nature ultimately arises from God's intellect, and our intellect is in the image of God's, we can gain at least a partial knowledge of it, and the attempt to do so through careful experimentation or logical, mathematical and probabilistic reasoning is known as natural philosophy, or more recently, science.

The ancient Greeks proposed that the universe was fundamentally mathematical in nature. This idea was adopted by Plato, and thus remained in the background throughout the Christian era, albeit suppressed by the non-mathematical Aristotelian physics. The problem was that for a long time nobody figured out how to apply mathematics to the physical world in a way that gave useful results. This difficulty was overcome in the fourteenth century, and a succession of scholars, starting with the likes of Bradwardine and Buridan, and culminating in de Soto and Galileo. These scholars showed that physics not only could be understood mathematically, but it should be understood so. (At the same time, a second, experimental approach to modern science was developed; Galileo's genius was chiefly to apply the experimental approach to test the mathematical ideas of the Oxford and Parisian scholars). The main weakness of these early pioneers (and why Renaissance scholars such as Francis Bacon could arrogantly dismiss their efforts) was that they knew insufficient mathematics to fully express the laws of nature. They had at their disposal Greek geometry, Indian number theory, and Indian and Greek algebra as systematised and developed by the Arabs, and that got them a fair distance, but not as far as needed. Gradually, the mathematicians filled in the missing ingredients: Descartes' coordinate geometry, and Newton and Leibniz's calculus were enough for Newton to develop his laws of motion. Since then the achievements of later mathematicians in group theory, non-Euclidean geometry, topology, differential geometry, probability and others have all provided crucial insights which the physicists have built on.

The mechanistic world view, which was developed in the late middle ages and dominated scientific philosophy until the early twentieth century, is the combination of the insights of the mathematical physicists and the deistic idea of the laws of nature. It adds to deism the idea that there are fundamental building blocks of matter, these corpuscles are indestructible, and that everything can be explained in terms of the matter and locomotion of these particles. It is possible to map from the physical world to an abstract, mathematical and geometrical representation of it, perform calculations in the representation, and then map back to the physical world. The true representation is not analogous but based on an explicit mathematical mapping, thus it carries a direct and precise link to the real physical world; what happens in the representation happens in the actual world.

Of course, in addition to the true mathematical representation of the world, we also have our own attempts to reconstruct it. There is clearly a difference between the two, and the difference is this. Firstly, our knowledge of the laws of physics (the mathematical rules that govern the representation) is only approximate. This, however, can be and is gradually improved over time. We know a lot of the features the true laws must have, but some of the details are still a bit fuzzy. But we know (to a large extent) where that fuzziness is, and we know how big it is. Secondly, our knowledge of the location, locomotion and structure of matter is necessarily imprecise due to experimental uncertainty. The true model is precise; our model imprecise. This is not such a serious problem, since the mathematics of probability allows us to treat that uncertainty in a systematic way. Our knowledge remains linked to reality, not by the precise mapping of the true theory, but through a probabilistic mapping. We cannot say that the final answer is precisely this, but we can limit it to within narrow bounds, and state the probability for each possible answer given our initial observations and our uncertainty of the laws of physics.

Thus modern science arose from premises derived in part from deism. Its success seemed to vindicate those premises, and consequently the deistic world view. In particular, deisms rivals, such as polytheism, dualism, classical theism, occasionalism, and even the early forms of atheism could not provide those assumptions; indeed they led to perspectives that were contrary to the developing science. This, then, is (with most of the details omitted) the argument for the existence of God from physical law more or less as it would have been presented in the sixteenth to eighteenth centuries.

Of course, this early form of the argument, which is claimed to lead to deism, assumes that pre-quantum physics is correct. The picture needs modification when it encounters quantum physics, and the argument is, perhaps, weaker because it loses its historical vindication. In particular, deism is inconsistent with the indeterminacy of quantum physics. This doesn't mean that the argument has gone away; there are plenty other philosophies which incorporate a belief in God, not least the classical theism which was original philosophical basis used for Christian theology. A modern form of the argument would attempt to trace back from quantum field theory to, say, an Aristotelian philosophy, which allows and more naturally fits in with quantum indeterminacy.

The argument from natural law is now straight-forward to express. Its theological roots mean that the laws of physics would inherit certain properties from God. If the laws of physics did not come from God, there is no reason why they should inherit those properties, such as being universal in time and space. Indeed, without God there is no reason why there should be universal laws in the first place. Thus theological philosophies such as deism or classical theism make predictions about the nature of those laws, predictions which seem to be realised; the atheist philosophies make no such predictions (and stronger forms of this argument would say that they make predictions which contradict what we observe; however modern atheism takes the existence of regular, rational, laws independent of God as an unsubstantiated premise). This means that the existence of God is a far more reasonable explanation of why the laws of physics are as they are than God's absence. For example, some atheist presuppositions imply Hume's ludicrous views on causality, which directly contradict modern physics; therefore those pre-suppositions are false.

The argument from physical law is thus a compliment to the cosmological argument. Certain forms of the cosmological argument argue from physical law to the principle of causality and from there to God; this argument goes from God via causality to certain properties which any physical law must satisfy, these properties are subsequently tested against reality. The argument from physical law is weaker than the cosmological argument, since the cosmological argument is based on deduction, so if the premises are true then so is the conclusion, while the argument from physical law is based on falsification. There is always the chance that a wholly different set of premises that we haven't yet thought of could lead to the same conclusion. However, falsification has served us well as the basis of much of modern science, so we shouldn't write it off so quickly either.

So that is the argument: how does Russell respond to it?

  1. A great many things we thought of as natural laws are human conventions. Three feet make a yard even in deepest space.
  2. Atoms are a lot less subject to law than you might think, and such laws there are are different to what was supposed, being statistical averages. We do not regard that a roll of a double six comes up one time in thirty six as evidence for design; design would imply that they came up double six every time.
  3. That which represents the momentary state of science today might change tomorrow.
  4. The idea that natural laws imply a law-giver is based on a false analogy with human laws.
  5. One would have to ask Why those laws and not others? Theologians say that it was to create the best possible universe -- you would not believe that by looking at it -- but if there was a reason for God choosing those laws, then that reason is more fundamental than God and God Himself is subject to law, and you have got nowhere by including God in the argument.
  6. The arguments used to show the existence of God change their character as time goes on. They contain definite fallacies, which are exposed.
  1. The first of these responses is a clear straw man. Yes, we use various conventions (such as three feet make a yard, or the speed of light is about three hundred million meters per second) when mapping from physical reality to the mathematical representation. But the final result we get, when we map back to physical reality at the end of the calculation, is independent of these conventions. The expression of Physical law is not tied to one set of conventions; it works for all of them. Physics provides us with the means to map from one set of conventions to another, and allows us to perform calculations regardless of which set of conventions we choose (as long as we are consistent in our choice). Beneath the convention dependent surface, there is a more important convention-blind layer which can be applied to whatever conventions we happen to favour. It is that more fundamental, convention independent, expression of physical law which is the focus of this argument. So pointing out that some aspects of our calculations are convention-dependent is an irrelevance because this is not denied by those who make the argument.
  2. Next Russell turns to quantum mechanics. Now, Russell has a point here, in that the form of this argument that he was thinking of was based on deism, which implied a deterministic universe which is contradicted by quantum indeterminacy. However, deism is a relatively recent novelty in Christian thought (by recent I mean less than a thousand years old). Russell's argument here is thus powerful against the argument from deism. Deism makes certain predictions about the nature of physics; those predictions have turned out to be false, therefore deism is false.

    But instead, we should turn back to theism. Obviously, we can't take theism precisely as it originally stood in early Christianity; we need to combine it with the insights of the mathematical physicists. The early theists denied that physics was mathematical; but that assumption was taken from Aristotle's prejudice rather than theism itself. Replace it with the assumption that physics can be represented mathematically, and keep the theism. See where that takes us. Once we have done so, we can develop a new physical law argument based on those premises, an argument which is, if anything, closer to the spirit of Christianity as originally formulated. This understanding does not require that physics is deterministic, indeed, given God's free will, it works best with an indeterminate physics. So we expect laws of nature that are unchanging in time and space, not coordinate system or convention dependent, rational in that nothing emerges from nothing, and indeterminate in the sense that particles have several distinct decay channels, but we cannot predict which of them will be actualised. The result is in remarkable agreement with modern quantum field theory. I can't go into details in this post, but I do present this argument in full detail in chapter 15 of this book.

    When we roll two die, that they come up double six one time in thirty six is a feature of the design of the dice. The dice has certain symmetries, and a limited and known number of possible results. The indeterminacy arises from our lack of knowledge of the initial conditions. (Quantum indeterminacy is, however, more fundamental). These features allow us -- given various other assumptions -- to compute the probability of each possible outcome. That it is governed by a probabilistic law does not mean that it is not governed by any law. If it were governed by no law, then if we rolled the dice, then we could roll a pair of sevens, or one of them could turn into a rabbit and the other a bunch of flowers. That that does not happen -- cannot happen since it violates the conservation of energy and momentum -- implies that the dice is subject to law. Laws do not need to be deterministic, and given God's freedom a classical theist would not expect physical law to be deterministic.

  3. Next, Russell argues that our knowledge of physical law is incomplete. That is still true, though less so than in his day. But what of it? Science works by falsification. That means that although we cannot be certain that what we have is the final answer (we can be sure that what we have now isn't the final answer), we can be sure that the final answer will not be certain things. As a corollary, we can describe certain features that we know the final answer will have. The basic principles derived from theism are among these. I do not think that we can, from classical theism, show that there are three families of particles or whether or not supersymmetric partners exist and a host of other things, but a lot of the symmetries and structure which sit behind the modern expressions of physical law emerge from classical theism. Those symmetries are firmly established. If they were broken, then that would imply consequences which would have been observed. As we refine our understanding of physical law, that will allow us to refine the precise details of the theism which sits at its base (if the argument from physical law is correct), just as we switch from deism to theism when we move from classical to quantum physics. This is no different than what the scientist does in refining their theories in the light of new evidence. But the basic features of physical law implied by theism (and in the stronger forms of the argument contrary to atheism) are so established that they are not going to be changed. New findings in physics lead to a fine tuning of the theology, not its overthrow.
  4. Some forms of the argument from natural law are based on analogy. Arguments from analogy are invariably weak -- one has to show that the features the example has in common with the real object of study are those very features under consideration; that none of the differences are of importance. However, not every form of this argument arises from analogy; in particular not the detailed form I gave above. Therefore this objection fails to answer all forms of the argument from natural law, and certainly not the one I present.
  5. Not every theologian depends on ideas of this being the best possible world, though some have, perhaps most notably Leibniz. Why this world and not others? To a certain extent, that is answerable, and to a certain extent it is unanswerable. The argument is not that given God, we must get precisely this form of physics; but rather we must get one of a certain subset of possible physical theories. Which of those theories God selects is entirely God's free choice. If we suppose that God had certain purposes in creation (such as that a species of rational animals might emerge), then the constraints that places on the fundamental physical constants becomes very restrictive, but God still has some choice.

    There is thus a middle ground between saying that God must produce this particular physics (which might make God subject to the sort of Law that Russell has in mind) and that we can say nothing about the type of physics that would describe God's sustaining of the universe (which would invalidate the argument from natural law). We say that we can deduce the nature of physics in part but not completely from our knowledge of God. That partial knowledge is enough to establish an argument from natural law; that it is not complete invalidates Russell's objection.

    Furthermore, the laws of physics, which we are interested in, describe the evolution of matter; how God sustains the material universe. Any law describing God would be of a very different nature, since God is not material. Thus Russell's objection relies on a false analogy between the two.

    Finally, the argument from physical law does not say that physics is linked to God by some law which God is bound by. Rather, it states that God is the origin of physical law, which is constrained by the nature of God. We can describe that nature, through either revelation or philosophical reasoning, but such descriptions do not make God bound to a law which consequently needs to be explained. Rather, God and His nature is the terminus of all explanations.

  6. Theistic arguments are tested by time and found wanting? Rather, it is the atheist arguments which have increasingly found to be build on fallacy. But I can only dispense with them one at a time.
I have not in this post shown that the argument from physical law is valid. That takes an entire book, and I have only scratched the surface of a possible modern presentation of the argument in my work. But what I hope to have shown in this post is that the arguments raised by Russell in response to the argument are invalid. It needs a closer look than most contemporary people have given it.

The existence of God, Part 4: The design argument


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