The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
The existence of God, Part 1

The existence of God, Part 2: The cosmological argument
Last modified on Sun Dec 3 16:37:06 2017

This post is one of a series discussing Bertrand Russell's essay Why I am not a Christian. I have reached his discussion of the oldest and most common philosophical arguments for God's existence, the cosmological argument.

The cosmological argument is among the oldest and possibly the best known of the arguments used to support the existence of God. Actually, that is a little bit simplistic, since there is not a single cosmological argument, but rather the name represents a family of related arguments, each taking slightly different premises, and all given the same label. The premises tend to be drawn from observation, or basic ideas induced from observation, and thus it is not an argument a priori such as the ontological argument. The cosmological argument can also serves as providing the definition for God. It ends with an uncreatable creator, which is a classical definition of God.

Before discussing Russell's response to the cosmological argument, I should frame a version of the argument myself. The following is based roughly on Aristotle's version of the argument, though expressed in my own language (and thus not completely identical to Aristotle). In the following, when I write cause, I mean Aristotle's efficient cause (I will discuss what that means in more detail below).

  1. An instrumental series is one where the power of one agent to influence the next member of the series is derived through its relationship with its predecessor (for all but the first member of the series).
  2. In an instrumental series, A → B → C → D, while C is the direct predecessor of D, there is also a sense in which A produces the result D using B and C as tools.
  3. The power to influence subsequent members of the series cannot originate from intermediate members of the series, but only the first member.
  4. Therefore every instrumental series must contain a first member.
  5. Therefore no instrumental series can be infinite.
  6. The first member of the series is qualitatively different from secondary members since it alone can provide the ability to influence others without deriving it from something else.
  7. The sequence of causes, in which things are excited from their ground state and then pass on that energy to something else, is an instrumental series.
  8. It is obvious to our senses that some things are caused.
  9. Everything that is caused by definition has something which causes it.
  10. This sequence of causes must either terminate with something which could have a cause, something which cannot be caused given its nature, or continue indefinitely.
  11. It cannot continue indefinitely, because that would mean an infinite instrumental series, which is impossible.
  12. Therefore, if there are some things with a cause, there must also be some things without a cause.
  13. Those things without a cause cannot be so accidentally, because if it is possible for something to be caused, then given enough time every possibility will happen.
  14. Therefore the sequence must terminate with something which cannot in principle be caused.
  15. If something is capable of change, then there must be at least two states in which it could exist. Change is movement from one state (or potentia) to another. If it is possible for a being to move from state X to state Y and vice versa, then X is a possible cause of Y and Y is a possible cause of X. But the first in the sequence of causes cannot have possible causes. Therefore, it can only exist in one state X. This means that the first cause is incapable of change, including coming into and out of existence.
  16. Thus the first cause has no boundary in time, space or anything else, since each of these would represent a coming into or out of existence in some sense.
  17. The first cause cannot be composed of parts, since the principle binding those parts together would be more fundamental than the cause itself, which is a contradiction. Therefore the first cause is simple.
  18. If there were more than one such first cause, then their combination would not be simple. Therefore there can only be one first cause.
  19. Every material being is composite, a union of form and matter. Therefore the first cause has to be immaterial.
  20. There is therefore one being which is omnipresent, eternal, unchangeable, immaterial, and the cause of everything else while incapable of being caused itself.
  21. This is the standard definition of God.
  22. Therefore God exists.

That is (more or less) Aristotle's version of the cosmological argument. Later Jewish, Islamic and Christian scholars realised that when you combine the argument from efficient causality with arguments from formal and final causality then God also has to have an intellect (indeed an omniscient intellect) and a will (indeed an omnipotent will). Add in ethical considerations, and we see that God will be active in the world to combat evil and its effects. We are not quite at the God of the monotheistic religions, but we are well on the way towards getting there.

Criticisms of this argument tend to focus on two aspects: 1) Can the sequence of causes be infinite? 2) Aristotle's vision of causality, which is essential to this particular form of the argument. There are other arguments against the possibility of an infinite series (as a physicist, I find the one based on the second law of thermodynamics especially appealing); to combat this particular argument, one would have to demonstrate that the sequence of causes is not instrumental, or that an instrumental series can be infinite in extent. I will leave this question to one side for now, since it will take me too far from Russell's essay to discuss it (I discuss it in more detail here). For now, I want to look in a bit more detail at the principle of causality.

There are essentially six main ways in which people have thought about causation. Obviously within each of my categories there are possible variations; this list is a summary not a definitive discussion. Four of these six ways admit to the existence of causes, but have different ideas of what it is; while two deny causes, one altogether and the other says that it only exists in our thoughts.

The main differences between those who agree that causality is a feature of reality, and not just our conception of reality, are related to two questions: 1) Do causes link events or do they link beings? 2) are causes a necessary connection, or can a cause lead to different possible effects?

An event based causality works like this. We have the effect, which is a broken window. The cause of the broken window is an event, namely it being hit by a brick. The cause of the event can be traced back to another event, namely someone throwing it. Thus the sequence goes Object State→Event→ Object State→Event→…. Every state of matter (or Object State) is caused by an event; every event is caused by the coming together of various states of matter (for example in a collision), or, perhaps, another event. A substance based causality skips over the events: Object State→Object State →Object State→…. Every state of matter is preceded by some previous state of matter (and they are in some way connected), but only states of matter can be caused or causes. An event is when a change occurs, but to ask whether an event is caused is meaningless since (in this view) causation simply does not apply to events but only links one object to another.

The second difference is whether causation is a necessary connection. This is not saying that everything that is caused has a cause, but rather that given an event, then a particular outcome is inevitable. Those who deny that causation is a necessary connection say that state of matter W could remain as W or become X or Y or Z, and it is not necessarily possible to predict which one will occur given knowledge of W. However, should X occur in practice, then there is still a causal link between W and X. The number of possible outcomes depends on W and the external circumstances. It could be any positive integer. It could be one; if it is one universally then we would be back with necessary connection causality. But those who hold to the idea of causality as undetermined would deny that in every situation, there has to only be one possible outcome; in some circumstances there could be more than one. Necessary connection causality is related to physical determinism; its opposite implies physical indeterminism.

Thus we have four expressions of causality:

  1. Substance causality and not a necessary connection.
  2. Substance causality and a necessary connection.
  3. Event causality and not a necessary connection.
  4. Event causality and a necessary connection.

The first of these is what Aristotle meant by his efficient cause. This is the form that is used in the cosmological argument used above; if one of the alternatives is correct then the argument is undermined. It is what almost everyone meant when they said cause until the first stirrings of mathematical physics in the fourteenth century. The emergence of mechanism, with its denial that the fundamental material objects could exist in different states, lead to people to seek a different reason why change occurred: they chose events, and thus event causality was born. A little bit later, when physics appeared to be deterministic, people started to define causality as a necessary connection (the first I have encountered to define it in this way was Leibniz; that is not to say that he was the first, but I believe that this view started to dominate around that time). The fourth of these understandings of causality most naturally fits in with the mechanical world view, and dominated philosophy from the sixteenth to early twentieth century.

It wasn't completely dominant, though, as two more views arose during the enlightenment:

  1. Causation is in our understanding; we label A as the cause of B when we see that there is a regular conjunction and B has the tendency to follow A. However, there is no underlying reason why this should be the case (or at least we cannot know of such a reason); we just observe it and ascribe it as a cause. I take Hume to be the leading proponent of this view. The understanding is based on Hume's empiricism, which states that we can only know that which we observe (apart from basic mathematical or logical principles), and which specifically denies that we can have knowledge of metaphysics or, indeed, scientific theory beyond merely connecting up experimental data in a mathematical function. For example, Hooke's law was first derived by performing an experiment and noting that for the measured data points, force was proportional to the extension of the spring and then infers that this is a general rule. This sort of reasoning the empiricist will allow, since it is inferred directly from observation. However, a modern physicist would derive Hooke's law from more fundamental theoretical principles. The empiricist denies this explanation because, since because modern theory isn't something we directly observe, it is not something the empiricist can accept.

    However, causation as traditionally understood (and scientific theory as well for that matter) is primarily concerned with explaining why B is connected to A. While every act of causation implies correlation, not every correlation is a causal connection. In confusing correlation and causation, Hume redefines causality in such a way that it loses its main usefulness. Causality is a construct of theory, not experiment, which is unacceptable for the empiricist. Note that you should not confuse empiricism with empirical science, which states that, while experiment is essential, it is possible to obtain a genuine theoretical knowledge as well; theory is built on both experiment and philosophical and mathematical reasoning (albeit always tested by experiment).

  2. The final expression of causality denies it entirely. After all, scientists hardly ever discuss causes. They discuss forces and energy and locomotion and differential equations or least action principles, but never need to make use of the word cause. Consequently, it is argued, causality is simply not necessary to understand the world, and, if so, an artefact of our imagination that we are better off ignoring.

Before the advent of quantum physics, each of these options were live (at least there were no good scientific reasons to rule any of them out; there are philosophical considerations as well), although the deterministic nature of Newton's laws of motion seemed to favour the idea of causation as a necessary connection, and the early mechanistic assumption that changes in locomotion arose only during collisions implied an event causality. Aristotle's cosmological argument depends on Aristotle's causality. Since it was unclear that Aristotle's understanding of causality was correct, his argument was undermined (although, of course, there are other forms of the argument which assume other formulations of causality). Thus Bertrand Russell could rightly write at the dawn of the quantum age in the 1920s that since many different types of causality had been proposed, the cosmological argument was weakened. This I take to be the strongest argument Russell raised; based on what was known when he was educated it was not unreasonable.

However, physics has moved on. The quantum mechanics of the 1920s is partially indeterminate, with the wavefunction (probability amplitude) evolving deterministically but observations being indeterminate. By the 1950s, quantum mechanics had been replaced by field theory which has no wavefunction and does not rely on differential equations at all; it is wholly indeterminate. This rules out the idea of causality as a necessary connection. Equally, we see that some changes of state are completely spontaneous; for example there is no reason why a radioactive particle decays at that moment. This means that some events are uncaused, which rules out event causality. However, quantum field theory still maintains the conservation of energy and momentum; this ultimately arises from the locality of field theory, which is one of the fundamental principles it is built on. This means that there is always a connection between the particle that decays and the products of that decay. The decay products must get their energy (including their mass) from some other object, and therefore substance causality is maintained. The results of a radioactive decay always emerge from an unstable nucleus; with substance causality the nucleus is the cause of the decay products, and that the event of the decay was unpredictable is an irrelevance because it is not part of the chain of causes. Because it is thus enshrined in our best theory of physics, the perspective that causality is an illusion is also ruled out. The idea that causality is only a matter of our understanding of the world can only be valid if there is a break between our description of physics in terms of the mathematical representation and the actual world. Such a break is, in my view, untenable, since it would not explain why physics does such a good job of predicting the results of experiment. Our mathematical representation of physics is a matter of our best understanding, but it is nonetheless linked to the real world, in such a way that if causality is an essential consequence of the description it must also be present in reality.

This leaves only Aristotle's vision of causality surviving; indeed it not only survives quantum field theory, but is reinforced by our best physics. One cannot argue against the cosmological argument by trying to undermine the conception of causality behind it. That response was tenable a hundred years ago, but not for the past fifty years and certainly not today.

So what of Bertrand Russell's other responses to the Cosmological argument? These are just feeble.

Russell frames the argument in the following way:

  1. Everything we see in this world has a cause.
  2. As you go back in the chain of causality you get to a first cause.
  3. This first cause is God.

As far as I know, the first time that the premise everything has a cause was used was in Hume's straw man presentation of the cosmological argument in his Dialogues concerning natural religion. No defender of the cosmological argument has used this premise, for the simple reason that the argument is trying to demonstrate that not everything has a cause; there must be something which does not have a cause, and from that there must be something which cannot by its nature have a cause. This obviously contradicts Russell's and Hume's first premise, which means that this presentation is not the cosmological argument. The premise of the cosmological argument is that some things have a cause, which is obviously far easier to demonstrate: we just have to find one thing which was caused.

Russell criticises this argument by bringing up an observation from John Stuart Mill: if everything has a cause, then what caused God? The impossibility of answering this conundrum is intended to argue against there being a first cause. This question is obviously powerless against the true cosmological argument; indeed it can be used to prove some of the reasoning to get to God. The cosmological argument goes from something is caused to something must be uncaused. To reach God, we need to argue from this point to there must be something which cannot by nature have a cause. We can ask why the sequence could not stop with something that could in principle have a cause but by some freak of nature didn't. This being wouldn't be God as classically conceived. But then we raise Mill's question, and realise that this termination of the chain is impossible. But the question is meaningless when applied to God: inserting the definition of God gives What caused the being that by definition couldn't have been caused? This question is in itself a contradiction. Thus this staple of modern argumentation against God is actually one way of traversing part of the argument for God.

Russell then goes on to suggest that if there is something without a cause, then it could just as well be the world as God. No. Firstly, because the chain of causality links one being to another; therefore the first cause has to be a single being. But the world is not a single being. Secondly, from the arguments that follow on from the cosmological argument, we know that the first cause has to be simple, eternal, universal and an immaterial mind; the world is none of these things.

There is no reason why the world could not have come into being without a cause, muses Russell. Well, there is. As a material being, the world is subject to the laws of physics including the conservation of energy and momentum, which governs all interactions between one physical being and another (although obviously not necessarily interactions between immaterial beings and physical beings, where different rules are in play). The world could not have come from nowhere. There is a stronger philosophical point here: the world appears to all observation to be rational (and if it wasn't we would have noticed it). Being rational means that conclusion follows premise which follows more fundamental premise until we reach a statement beyond which we can go no further. But only things with certain properties can be a terminus of the chain of explanations; in the case of the chain of causality those properties lead us to the classical conception of God (something shown in numerous places, such as here, here and even here.

Is the world like an elephant standing on a turtle, and then its turtles all the way down? No, because of the nature of the only form of causality which survives modern physics as an instrumental series. The sequence of turtles is a different type of series. Technically the turtles are an accidentally ordered series, while the efficient causes are an essentially ordered series -- what I have been calling instrumental. The distinction is that in an instrumental series the ability to cause the next member of the series is derived from the previous member of the series (and the members of the series in themselves lack the ability to institute that particular change in the next member), while in an accidental series it isn't. This is explained in more detail here and in the places linked to on that page. Since they are different types of series, the analogy between them is false. Russell does not answer any of the main arguments against the infinite series of causes (and those he drew on, such as Hume, only knocked down straw men), but he only ridicules them. Infinity is fundamentally different from anything else; it is easy to say the words an infinite series of causes than think about what that means. Any sequence of N essentially ordered causes has a first cause (from which the causal power originates) and a last cause. You can keep adding one more cause onto the beginning of the sequence, but you will still always have a first cause. You will never reach infinity, and the situation when you will make the first cause redundant. There will always be a first member of the series.

There is no evidence, writes Russell, that the world had a beginning at all. One could, of course, cite the evidence for the big bang (admittedly not available when Russell wrote that), or the second law of thermodynamics (which Russell should have known about), and deflect any hypothesis about bouncing universes and the like (which might answer the big bang, but can't evade the second law), but that misses the point. Most forms of the cosmological argument do not require that the universe has a beginning. They state that there cannot be an infinite series of causes, not that there cannot be an infinite temporal sequence. Since God is seen as being outside time, there is no reason why he could not have started causal sequences at different times (maybe, in a bouncing universe, once for each big bang), or that there could not have been an infinite time span between different events in the chain of causality. Neither of these scenarios undermines the conclusion that the sequence of causes had to have a first member fundamentally different from all the secondary causes.

It is often cited by atheists that the cosmological argument has been dealt with, by Hume, Kant and countless others. However, once we go into the details of what these philosophers wrote, and compare them against the most able proponents of cosmological arguments, we find that to a man (and woman) the atheist and deist philosophers invariably miss the point. Their "refutations" are nowhere near as strong as they would like us to believe, and Russell's empty platitudes in his essay are probably the weakest of them all. That doesn't mean, of course, that there isn't a knock-out blow which dismisses all forms of the cosmological argument, but if there is, I am yet to encounter it.

The existence of God, Part 3: The natural law argument

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