Swinburne: The problem of evil

This chapter is completely misnamed, because Swinburne doesn't seem to find evil any kind of problem at all.

His first line of argument is that some evils can serve greater good. Parents rightly allow a dentist to cause pain to their children for the greater good of healthy adult teeth. And God (if he exists) can cause or allow what appear to be evils in the service of a greater good which we cannot necessarily yet perceive. He states that one important greater good is that without evils and suffering, our ability to have and show concern for others is impaired. We cannot be concerned for somebody's welfare and take action to assure it unless that person's welfare is somehow at risk, and if there is no suffering there is no possibility of that happening.

His next line of argument is the "Argument from the Need for Knowledge", that we are endowed with free choices, and without natural evils our ability to make choices would be impaired in that the choices would have no effect. Also, without the chance to observe evil outcomes, we have no knowledge as to the likely good or bad effects of a choice, and no means ever of obtaining such knowledge. Since knowledge is a good thing, this is a greater good that is served by the presence of evil.

He then argues God's right to inflict harm, that parents have a right to do some degree of harm to their children for their own long-term good, and that God, being so much more than parents to us all, similarly has a right to inflict harm for the good of our souls.

He then goes on to address the quantity of evil in the world, the idea that, even given all these arguments, with things such as Hiroshima, the Holocaust, ther Lisbon Earthquake and the Black Death, God might have overdone it a bit. This is his response.

Suppose that one less person had been burnt by the Hiroshima atomic bomb. Then there would have been less opportunity for courage and sympathy; one less piece of information about the effects of atomic radiation, less people (relatives of the person burnt) who would have had a strong desire to campaign for nuclear disarmament and against imperialist expansion. Ando so on. Of course, removal of one bad state or the possibility of one bad state will not remove much good, any more than the removal of one grain of sand will make much difference to the fact that you still have a heap of sand. But the removal of one grain of sand will make a bit of a difference, and so will the removal of one bad state.

What he seems to be arguing is that evil is in fact good, in that the more evil there is, the more opportunity there is for people to do good in response. This is a torturer's charter. "I'm only doing this to you for the good of your family, so they can show sympathy to you in your injured state once I have finished with you." It excuses all kinds of evil. It is easy enough for people to do evil believing they are doing good without cover from this kind of fatuous philosophy. If the Hiroshima bomb had never been built, nobody would have been burned by it, and if nuclear weapons had never been developed, there would have been no need for people to campaign for nuclear disamament, and could perhaps have turned to other more substantive forms of good work.

It also suggests that there is ultimately nothing that can be done to reduce the total amount of evil in the world - that God decides how much evil there should be, and that everything is always for the best in this the best of all possible worlds.

There are two issues here. The first is how nauseatingly grotesque this philosophy is, and how easily it can be turned to the service of evil actions. The second is how completely without evidence all this hypothesising is. It depends on us making the assumption without specific evidence that there is a God, that he is good, that he allows evil for the the benefit of our immortal souls, that the amount of evil is at its optimum value for God's perfectly good purposes, and that the removal of even one small amount of human or natural evil will remove as much or more opportunity for humans to be good in response. Phooey.

But it gets worse. Swinburne's next argument is the "Argument from Hiddenness", the idea that keeping himself largely hidden from human sight is just the sort of thing a perfect God would do, since too obvious a Godly presence inhibits the ability of humans to make a free choice whether or not to worship God, and that allowing evil into the world is a part of the process of keeping God hidden from view. If you take this argument, then God ceases to be any kind of scientific proposition at all, he becomes a mechanism by which any possible phenomenon can be interpreted as being consistent with God's existence. If there is no possible phenomenon that can be shown, even in principle, to be incompatible with God's existence, then you now have an unfalsifiable proposition, and therefore all Swinburne's ideas of probability, flawed though they were from the outset, go out of the window, because probability has no meaning at all in the context of unfalsifiable propositions, and no evidence one way or the other can affect one's thinking on the matter.

But for all that, he grandly concludes that the existence of evil in the world does not form a C-inductive argument against God, and the probability of God's existence is unimpaired. There is no explaining going on here, merely explaining-away.

Swinburne: Arguments from Consciousness, Morality and Providence

Time to skip though a bit faster, so I'm taking the next two chapters together: Arguments from Consciousness and Morality, and The Argument from Providence. The form of the argument will by now be fairly familiar, so I don't need to rehearse it in such detail, even though the subject matter is different.

In Arguments from Consciousness and Morality, Swinburne makes the same general point, that he finds it hard to conceive of a way in which consciousness could have come about through natural processes. He accepts evolution as a means by which animals have come about, but finds it hard to understand why thought should have evolved. The only quotation he provides in the whole of the two chapters is from the 17th century philosopher John Locke

Divide matter into as many parts as you will ... vary the figure and motion of it, as much as you please ... and you may as rationally expect to produce sense, thought, and knowledge by putting together in a certain figure and motion, gross particles of matter, as by those that are the very minutest, that do anywhere exist. They knock, impel, and resist each other just as the greater do, and that is all they can do.

On the other hand, Swinburne thinks that human beings who think are just the sort of thing that God would make if he exists, and so he regards this as a good C-inductive argument for God.

He takes a similar line with The Argument from Moral Truth, which he comes to later in the chapter, that there is no reason for an awareness of moral truth to come to use by natural means, but implanting an awareness of them in us is just what God would do.

In essence, this is what Dawkins calls the Argument from Personal Incredulity. Just because Swinburne finds it hard to think of a way that these phenomena could have occurred naturally, he therefore assumes them to be extremely unlikely to be natural phenomena. This simply highlights the subjective nature of his assessments, since scientists with more knowledge of the subject are apt to regard the natural explanation as perfectly plausible and likely.

In The Argument from Providence, Swinburne regards it as wonderfully helpful of God to have created a world in which mankind can look after himself (feed himself, clothe himself) without apparent divine intervention every day. That the universe should have configured itself that way naturally he thinks to be unlikely, and so again it is regarded as a C-inductive argument for God.

Similarly, he is most impressed by the fact that the world offers us opportunities to help each other. he goes through various kinds of worlds that God might want to create, and settles on what he calls world-IV as being the most likely, in which there is exist humanly free agents who are born and die. In other words, he regards this is the best of all possible worlds, and therefore the one that God would most want to create. He argues

Given that ... we may expect God to create humanly free agents with a large degree of free choice and responsibility, subject to a limit of harm (that is, positive evil) they can do to each other, it is moderately probable that God will make a World-IV, including natural death for all and free agents having the power to cause death.

It seems to me that there is a glaring hole here (quite in addition to all the holes I've already identified in this general form of argument) and that is that we are not in a World-IV by Swinburne's description. We live in a universe where humans in fact have unlimited power to do evil to each other, to the extent of being able to use atomic weapons in such a way as to extinguish all life from the planet. So far we have chosen not to. But that doesn't change the fact that the power exists for us to do unlimited harm.

Swinburne: Teleological Arguments

Swinburne goes on next to look at teleological arguments, the arguments from design. He goes through several of them: the Argument from Temporal Order, the Argument from Spatial Order, the Fine Tuning Argument, and slightly curiously the Argument from Beauty is tacked on the end.

The Argument from Temporal Order looks as the fact that there are regularities in time - i.e. that one event causes another in a regular way, such that we are able to predict the future.

The argument from Spatial Order looks at the fact that atoms arrange themselves in regular patterns spatially to form a variety of substances. Although he makes a generally approving reference to Michael Behe’s “Irreducible Complexity” and describes the idea at more length in an appendix, Swinburne is careful to say that the argument from Spatial Order as he describes it does not depend on Behe’s ideas, and is fully compatible with Darwinian evolution. Swinburne’s version of the argument concerns inorganic materials of the right sorts to form themselves into organic compounds, and later into life and eventually into us humans. According to Swinburne, it is amazing that inorganic materials of the right sort, particularly carbon with its very special abilities at being organised into long chains in large molecules, should exist in the first place so that Darwinian evolution can get started.

The Fine Tuning Argument is about how amazing it is that natural laws are adjusted in such a way that multiple elements are created so that chemistry can happen.

The Argument from Beauty is that it would make no sense for God to make a universe that wasn’t sufficiently beautiful for us to appreciate it.

All these argument are made in much the same form. All these varieties of order are the sorts of things a God would create if he wanted to create beings like humans, and therefore the conditional probability of each of these is high given God, and the probability that these would arise in a Godless universe is accordingly much lower. Therefore each provides what Swinburne calls a C-inductive argument in favour of God. Remember from the previous chapter that this isn’t what most people think of as a C-inductive argument but instead it is a line of argument that suggests that the conditional probabilities, when fed through Bayes’ Theorem, will result in a higher than previous overall probability.

If you define a sort of God who you think would do these sorts of things, then of course you will assess as quite high the probability that God has done it. But for this to have much effect on the outcome of Bayes’ theorem (even if you accept this use of it, which I don’t) you would have to assess the prior probability as significantly greater than zero. Time for another down-to-earth example, this time taken from Ben Goldacre’s Bad Science, for no better reason than I’m a fan of his book and blog. I’m going to use his particular example of datamining to identify terrorist suspects.

In this example, Ben Goldacre is looking at the use of data about individuals to assess whether they should be considered to be terrorist suspects.

Let’s imagine you have an amazingly accurate test, and each time you use it on a true suspect, it will correctly identify them as such 8 times out of 10 (but miss them 2 times out of 10); and each time you use it on an innocent person, it will correctly identify them as innocent 9 times out of 10, but incorrectly identify them as a suspect 1 time out of 10.

On the face of it, that sounds quite promising. But let’s go on.

These numbers tell you about the chances of a test result being accurate, given the status of the individual, which you already know (and the numbers are a stable property of the test). But you stand at the other end of the telescope: you have the result of a test, and you want to use that to work out the status of the individual. That depends entirely on how many suspects there are in the population being tested.

If you have 10 people, and you know that 1 is a suspect, and you assess them all with this test, then you will correctly get your one true positive and – on average – 1 false positive. If you have 100 people, and you know that 1 is a suspect, you will get your one true positive and, on average, 10 false positives. If you’re looking for one suspect among 1000 people, you will get your suspect, and 100 false positives. Once your false positives begin to dwarf your true positives, a positive result from the test becomes pretty unhelpful.

I agree. A test that gives you the wrong result 10 times out of 11 is getting to be less than entirely useful. But it gets worse.

Remember this is a screening tool, for assessing dodgy behaviour, spotting dodgy patterns, in a general population. We are invited to accept that everybody’s data will be surveyed and processed, because MI5 have clever algorithms to identify people who were never previously suspected. There are 60 million people in the UK, with, let’s say, 10,000 true suspects. Using your unrealistically accurate imaginary screening test, you get 6 million false positives. At the same time, of your 10,000 true suspects, you miss 2,000.

So, using Swinburne’s notation, this means that that even if P(e|h & k) is very much higher than P(e|~h & k), if P(h|k) is very low, it doesn’t help you very much. In the terrorist example above, P(h|k) is 10,000 in 60 million, or 0.017%. Even though P(e|h & k) is greater P(e|~h & k) by a factor of 8, the false positives still swamp your numbers. The overall probability is still dominated by the prior probability, so processing the numbers through Bayes means that the probability that a person testing positive actually is a valid terrorist suspect has only been raised from 0.017% to 0.13%. That isn’t all that useful.

Swinburne, as part of his version of the Argument from Spatial Order, regards it is very unlikely that a godless universe would come into being sufficiently fine-tuned that would allow “humanly free agents” to appear, even through the process of Darwinian evolution. He helpfully defines what he regards as the necessary characteristics of humanly free agents as follows.

1. Sense organs with an enormous variety of possible states varying with an enormous variety of possible inputs caused by different world states

2. An information processor that can turn the states of sense organs into brain states that give rise to beliefs of prudential or moral importance

3. A memory bank, to file states correlated with past experiences (we could not consciously reason about anything unless we could recall our past experiences and what others have told us)

4. Brain states that give rise to desires, good and evil (desires to eat and drink, to care for others or to hurt them, and to discover whether or not there is a God)

5. Brain states caused by the many different purposes we have

6. A processor to turn these states into limb and other voluntary movements (to turn, for example, my purpose of telling you that it is Friday into those twists of lip and tongue that will produce an English sentence with that meaning)

7. Brain states that are not fully determined by other physical states

Clifford Longley quoted Professor David Deutsch out of context to support the fine-tuning argument in favour of God when Longley complained to the Advertising Standards Authority against the Atheist Bus Campaign. I took the trouble to contact Professor Deutsch at the time to find out his true views on the subject. He responded as follows.

I do not believe that the 'fine-tuning' of physical constants provides any sort of argument for the existence of God or anything else supernatural. That is because if the constants had been set intentionally by supernatural entities, then the intentions of those entities must themselves have been at least as 'fine-tuned' when they set the constants, and that fine-tuning would remain unexplained. Hence that supernatural hypothesis does not even address the fine-tuning problem, let alone solve it.

Think about that for a moment. Something as complex as a human needs quite a lot of explaining, and a universe with natural laws that permit Darwinian evolution to get going also needs much explaining. But God, as Swinburne describes it, has all of the characteristics of “humanly free agents”, on a far greater scale and with infinitely more complexity and capability than is possessed by mere humans. Humans have sense organs that can detect light, sound and smell passing through a very small corner of the universe. According to Swinburne, God has sense organs that can directly detect anything happening going on anywhere in the whole universe. Humans have a processor that can turn brain states into limb movements. But God has a processor that can by means of “basic actions” (i.e. unmediated direct actions) affect any atom in the entire universe. If the probability of a Godless universe capable of supporting humans is regarded by Swinburne as being very small because of the complexity involved, then Swinburne’s own argument against uncaused complexity applies equally and with even more force to the prior probability of God’s existence, or the intrinsic probability of theism as Swinburne describes it.

Swinburne earlier airily described God as being immaterial (i.e. not made of matter) and as being all of one substance (presumably an immaterial substance, whatever that might be) and therefore simple. But whatever substance God consists of, to be God he still needs all the capabilities Swinburne describes as being necessary for humans, but with a scale and capability vastly increased. Moreover, since God is omnipresent, omnipotent and eternal, by Swinburne’s definition there is not even any means analogous to Darwinian evolution by which God could have come into existence. It would all have to have been there in full from the very beginning. If it is improbable for a universe to exist uncaused with sufficient order and complexity to support a Darwinian process resulting in us, then a God with even greater capabilities coming about uncaused directly is even more improbable, by many, many orders of magnitude.

Swinburne of course says nothing about the effect of teleological arguments on the prior probability of God. He has already addressed in a previous chapter the intrinsic probability of theism, being the probability of God on no evidence at all, and has no intention of revising his estimates of it. He has declared God to be simple and that is that. Instead, he concentrates solely on the conditional probabilities of the universe given God’s existence or nonexistence.

But this hides the fact that the line of reasoning he follows renders the prior probability of theism so low that even deciding that the conditional probability of the universe being as it is, given God, is quite high, it isn't going to shift the Bayesian calculus very far in the right direction, even if Swinburne were to go the whole hog and say that the probability of God creating such a universe is 1.

So he’s continuing to make up numbers, but now he’s not even being consistent about how he applies his own rules concerning how he makes up his numbers.

Swinburne: Cosmological arguments

In Chapter 7, Swinburne finally gets round to looking at the evidence for or against God. He starts with the Cosmological argument, in essence looking for answers to the question “Why is there anything rather than nothing?”

It is of course a very good question, and one we don’t know the answer to. We know that the universe does exist if only because we are part of it and observing it. At this point, Swinburne is concerning himself solely with the existence of the universe, not with any of its properties.

Swinburne is very keen on quoting 18^th-century philosophers. He frequently quotes Hume (whom he doesn’t like) and Liebnitz (whom he does like), but broadly speaking he doesn’t draw on anybody more recent except in as far as they comment on Hume and Liebnitz, or on Aquinas. There is one exception to this. He likes to quote himself, extensively.

But this gives his arguments are rather mechanistic feel to them, as if his understanding of atoms is that they are Newtonian billiard balls. He is aware of the Big Bang theory but if he knows anything more about it than the name of the theory and the approximate age of the universe (which he puts at 15 billion years) then he doesn’t let on.

Swinburne discusses the regression to the first cause. He spends about 10 pages on this, but after all the quotations and arguments, it boils down a fairly simple point. Either the universe is infinitely old or it isn’t. If it is infinitely old, then it is ultimately uncaused. If it isn’t then it had a first cause, which either comes from God, or is ultimately uncaused. So we ultimately have a choice of explanation, either the universe exists uncaused, or the universe was created by God, who exists uncaused.

And not surprisingly, he prefers the latter explanation. He conveniently summarises his reasons in the last paragraph of the chapter.

There is quite a chance that, if there is a God, he will make something of the finitude and complexity of the universe. It is very unlikely that a universe would exist uncaused, but rather more likely that God would exist uncaused. Hence the argument from the existence of the universe to the existence of God is a good C-inductive argument.

His assertion that the universe existing uncaused is less likely than God existing uncaused is based on his belief that God is simpler than the universe, and that simpler things are more probable than complex ones. At the end of Chapter 5, Swinburne said that the intrinsic probability of theism was low, but because he regarded theism as a simple concept, it was more probable than any one of many other individual hypotheses for the existence of things. He reached that conclusion without examining or even naming any alternative hypothesis, so if we are to agree with him, we have to take his assertion on trust, without evidence.

But now, in Chapter 7, this has suddenly transformed itself into a 2-way choice between the universe existing uncaused and the universe being caused by God, with the latter being judged more probable. It is almost as it he expects us not to have read (or at least not to have remembered) what he wrote in the previous chapters.

Note that he characterises this as a C-inductive argument. Remember that back in chapter 1 he gave an example of a C-inductive argument, where the premise that 100 ravens have all been observed to be black is a C-inductive argument towards the conclusion that all ravens are black.

A C-inductive argument is characterised by the existence of a hypothesis where all the relevant evidence confirms the hypothesis and none of it disproves it, but where the possibility remains that some evidence at present unknown might someday disprove the hypothesis. Irrelevant matters do not contribute to the C-inductive argument, so for instance the colour of seagulls is not relevant to the hypothesis that all ravens are black. Seagulls of any colour are equally consistent both with the hypothesis that all ravens are black and with its converse, that there exists at least one non-black raven.

At the moment, we don’t know enough about the universe to know its first cause. Therefore, so far as we can tell, the existence of the universe is consistent both with God’s existence and with God’s nonexistence. It is therefore a piece of irrelevant evidence just like the colour of seagulls. To call the existence of the universe a C-inductive argument for God is incorrect.

However, Swinburne’s definition of a C-inductive argument has morphed a bit. It now isn’t anything to do with the example he gave. In terms of how he is actually using the phrase, a good C-inductive argument is one which results in a conditional probability greater than the prior probability you had before you evaluated the new evidence. In other words, a C-inductive argument is one where you feed the numbers into Bayes’ theorem and come out with a probability greater than you started with.

In this, he is demonstrating again this fundamental misunderstanding of what Bayes’ theorem does. As I described in the previous chapter, Bayes allows us to refine our understanding of the population of a certain class of entity, by allowing us to eliminate on the basis of evidence certain proportions of a larger population whose characteristics we are aware of. In the example I gave in the previous article, we were able to refine probabilities by eliminating from consideration skirt-wearers and children with short hair from an overall population of schoolchildren, in order to assess how many long-haired trouser-wearers were girls.

We don’t have a population here. We don’t have a bunch of universes, some of which exist uncaused and some of which are made by God. We don’t have a way of distinguishing caused universes from uncaused. All we have is Swinburne making numbers up again.

Swinburne Chapter 6: The Explanatory Power of Theism

Swinburne pauses for breath here, and goes over Bayes’ Theorem once again. He repeats the original formulation

P(h|e & k) = [P(h|k)P(e|h & k)] / P(e|k)

Where

P(h|e & k) is the probability of the existence of God, given all the various bits of evidence we will come to,

P(h|k) is what he calls the intrinsic probability of God (i.e. the probability before we consider the evidence),

P(e|h & k) is the probability that the evidence would be as it is, given that God exists,

P(e|k) is the intrinsic probability of the evidence.

He expands this last term (correctly) as follows

P(e|k) = P(e|h & k)P(h|k) + P(e|~h & k)P(~h|k)

The first term is the same as the top line of the equation. The second is the converse, i.e. the probability that the evidence would be as it is, given that God does not exist, multiplied by the intrinsic probability of God’s nonexistence.

So overall we get the following equation

P(h|e & k) = [P(h|k)P(e|h & k)] / [P(e|h & k)P(h|k) + P(e|~h & k)P(~h|k)]

Now, if it is a while since you last did any maths & algebra at school, all these letters and symbols might look a bit intimidating. Of course, they are intended to look that way. So let me show you how the theorem actually works on a more down-to-earth example.

Suppose that at a particular a school, 60% of the pupils are boys, and 40% are girls. There is a school uniform, and all the boys must wear trousers, but the girls have a choice between trousers and skirt. A quarter of all the girls choose to wear trousers. You see a child in the distance wearing the school uniform, and can see that the child is wearing trousers. What is that probability that the child is a girl?

We use precisely the same equation.

P(h|e & k) is the probability that the child is a girl, given the evidence of wearing trousers. This is what we are trying to calculate.

P(h|k) is the prior probability that the child is a girl. We know that number, it is the proportion of girls in the school, i.e. 40% or 0.4.

P(e|h & k) is the probability that any particular girl wears trousers. We know this is 0.25.

P(e|~h & k) is the probability that a boy wears trousers. This is 1, since all boys must wear trousers.

P(~h|k) is the prior probability that the child is not a girl. We know this is 0.6, because we know that 60% of the children in the school are boys.

So we have all the numbers we need, and can plug them into Bayes’ equation.

P(h|e & k) = ( 0.4 x 0.25 ) / [ ( 0.4 x 0.25 ) + (1 x 0.6 ) ]

Get the pocket calculator out (or multiply it out in your head), and it comes out at 1/7, or about 14%.

You can check this out by another method. Out of every 100 children, 60 will be boys, and 40 will be girls. Of the girls, 10 wear trousers, and 30 wear skirts. We aren’t interested in the skirt-wearing children – we can see that the child has trousers. Of the trouser-wearing children, 60 are boys, and 10 are girls. So 10 out of every 70 trouser-wearing children are girls, or 1/7.

You can extend this to cover multiple pieces of evidence. For instance, taking the above example, suppose that 80% of the girls in the school have long hair and only 10% of the boys, and you can see that the child in the distance has long hair and is wearing trousers, you can make the calculation simply by plugging the new numbers into Bayes’ theorem. First, you calculate for the trouser-wearing (as shown above). That gives you a new set of prior probabilities, for the probability that a trouser-wearer is a boy or a girl. Our new evidence is the long hair. Modify the definitions above, replacing trousers with long hair, and plug the numbers into the equation. We now get this

P(h|e & k) = ( 0.14 x 0.8 ) / [ ( 0.14 x 0.8 ) + ( 0.1 x 0.86 ) ]

0.14 is the proportion of girls among trouser-wearers, and similarly 0.86 is the proportion of boys (i.e. 1 – 0.14). 0.8 is the proportion of girls with long hair, 0.1 is the proportion of boys with long hair.

Calculate this out, and it turns out that the chance of a long-haired child wearing trousers being a girl is about 0.57, or 57%.

How can that be? The chance of any trouser-wearer being a girl was only 14%! Well, by being aware of this new piece of evidence, we can now eliminate from consideration a much larger proportion of the children i.e. all the short-haired ones.

We can check it out using the other method as well. We previously worked out that for every 100 children in the school, there were 70 trouser-wearers, of whom 10 were girls. 8 out of 10 girls have long hair, but only 6 out of the 60 boys have long hair. So among the long-haired trouser-wearers, 8 out of every 14 are girls, i.e. 57%.

And that in essence is what Bayes’ theorem is all about. There is a whole load of algebra which I shan't bother to go into here which shows why Bayes' theorem works. If you're interested in probability and statistics you shouldn't just take my word for it, I recommend that you look up the maths and understand it for yourself. But the fact is, Bayes' theorem does work.

What Swinburne hopes to do is to make estimates of the various probabilities regarding God, feed them into Bayes’ theorem, crank the handle and produce an overall probability for God’s existence.

In the previous chapter, Swinburne was trying to make an assessment of the prior probability of God’s existence, which he called the intrinsic probability of theism. In the example of the schoolchildren described above, we know the prior probability that any particular child is a girl. We know that because we know how many girls and how many boys are at the school, we can simply count them. Even when we can’t count an entire population, we can sample it – that is what opinion polls are all about. And with that sample we can get a fairly accurate estimate of probabilities which can be fed into Bayes’ theorem.

But we don’t have a population of gods, nor do we have a population of universes, some of which have been made by God and some of which haven’t. We have a hypothesis regarding the existence of just a single God, and evidence in the form of just one universe whose existence we know of. And yet, Swinburne wants to make use of Bayes’ theorem in order to assess the “balance of probability” of God’s existence. In order to do that, he will have to put a number on each of the following concepts.

1. The prior probability of God’s existence
2. The probability of God’s existence given each of the various “pieces of evidence” that he puts forward (the cosmological argument, the teleological argument etc)

In the previous chapter, Swinburne was working his way towards suggesting a figure for P(h|k), the prior probability of God’s existence. Even to describe it in those terms is to show the futility of the effort. Either God (by Swinburne’s definition) exists or he doesn’t, and scientific investigation should in principle be able to uncover evidence one way or the other. For instance, if God performs miracles, we might reasonably hope that one or two of them would happen while scientists have their instruments pointed in the right direction. Because Swinburne’s hypothesis is not looking for what proportion of all gods have a particular set of characteristics, there isn’t any way of expressing it as a numerical probability.

The same applies to the various conditional probabilities he is looking to assign numbers to. We know what proportion of girls at the school wear trousers, we can count them. In a larger population, we could sample. Either way, we would have a statistical method by which we could come up with a number. But how can we estimate the probability of whether God would make the universe the way it is, if he exists? There is only one way available, and that is quite simply to make the numbers up.

And that is what Swinburne does, though he disguises the fact under a huge torrent of words. By the end of this chapter, we have been through 132 pages of argument which describe Swinburne’s reasons for saying that it is justified to make up the numbers, and on what basis he will choose one number over another. In the latest chapter he describes various reasons for thinking it probable that God would want or need to create a universe containing humans. I’ll paraphrase it rather than directly quoting. He thinks that it is a good thing that humans exist, and since God is perfectly good by definition, creating humans is the sort of thing that we might reasonably expect God to do. God might also want to create animals as well, but there isn’t such a good reason for him to want to do that, so animals don’t tip the matter much one way or the other. Swinburne then for the first time in the book goes on to actually assign a number which will get plugged into Bayes’ equation. This really is worthy of direct quotation.

I have argued in this chapter that there is a modest probability intermediate between 1 and 0, to which I will give the artificially precise value of 1/2, that a God will create humanly free agents located in a beautiful physical universe, perhaps also containing animals.

If you understand probability and statistics it is possible to decode this. It means that by his own admission none of his arguments are sufficient to make any kind of estimate of probability in the matter (it's impossible by definition to have a probability outside the range 0 to 1, so he is in fact ruling nothing out at all), but because he needs a number in order to proceed to the next chapter, he's going completely arbitrarily to decide to use 1/2.

Yes, that really is how he proceeds.

Swinburne: The Intrinsic Probability of Theism

In Chapter 5, The Intrinsic Probability of Theism, Swinburne looks again at the definition of the theistic God and adds more detail to it, and then makes his assessment of its prior probability in terms of how simple he finds the conception of God to be.

Whether you agree or not with Swinburne’s idea that a simple concept has a higher prior probability than a complex one (I don’t, because the concept of prior probability is meaningless in this context), it is worth examining this concept of simplicity. All the evidence of the universe available to us is that complex things develop slowly through natural processes from simpler ones. This applies not only to life through evolution, but apparently also to the relatively complex present structure of the universe from simpler beginnings. So even though I find Swinburne’s talk of prior probability entirely misguided, there is still the point that the start of the universe apparently needs to be something simple.

Let’s take a look at what Swinburne thinks of this, starting with Swinburne’s understanding of God

There exists now, and always has existed and will exist, God, a spirit, that is, a non-embodied person who is omnipresent. … In essence, to say that God is disembodied is to deny that there is any volume of matter such that by his basic actions he can control only it and such that he knows of goings-on elsewhere only by their effects on it. By contrast, to say that God is an omnipresent spirit is to say that he knows about goings-on everywhere without being dependent for that knowledge on anything, and can control by basic actions all states of affairs everywhere (in this or any other universe) without being dependent for that power on anything. God is creator of all things in that for all logically contingent things that exist (apart from himself) he himself brings about, or makes or permits other beings to bring about, their existence. He is, that is, the source of the being and power of all other substances.

Clear enough. According to his hypothesis, God created everything, is everywhere, and can do anything not logically contradictory. He then goes on to justify this in terms of simplicity, in order to claim that the hypothesis that there is such a being has a high prior probability.

To start with, theism postulates a God who is just one person, not many. To postulate one substance is to make a very simple postulation.

Quite why one is simpler than zero is not stated. But never mind. Let us continue.

He is infinitely powerful, omnipotent. This is a simpler hypothesis than the hypothesis that there is a God who has such-and-such limited power (for example, the power to re-arrange matter but not to create it). It is simpler in just the same way that the hypothesis that some particle has zero mass, or infinite velocity is simpler than the hypothesis that it has a mass of 0.34127 of some unit, or a velocity of 301,000 km/sec. I finite limitation calls out for explanation of why there is just that particular limit, in a way that limitlessness does not.

I must say that Swinburne is being very selective here. He claims that there must be a limit to human understanding of the universe, and that the existence of this limit doesn’t need explanation, but that there is no limit to the powers of God, and this lack of a limit also requires no explanation. In fact, anything that he chooses to posit appears to require, by definition, no explanation.

As I noted in chapter 3, scientists have always preferred hypotheses of infinite velocity to hypotheses of very large finite velocity, when both were equally compatible with the data. There is a neatness about zero and infinity that particular finite numbers lack.

This is simply ignorant. Swinburne is trying to claim scientific justification for his hypotheses without having taken the trouble to find out how scientists actually think. Scientists haven’t always preferred infinities and zeros and they don’t today. Since Swinburne is keen on talking about Newton and gravity, let us note that Newton himself was extremely bothered by the fact that the action of gravity by his equations appeared to operate at infinite speed – and yet the equations didn’t work for a finite speed for gravity. Newton wrote the following to a colleague in 1692.

“That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.”

Newton was careful to say that he didn’t know why gravity works and what causes it, merely that it does work according to the equations. In the second edition of Principia he wrote.

“I have not yet been able to discover the cause of these properties of gravity from phenomena and I feign no hypotheses... It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies.”

By the way, this also refutes the idea suggested in a previous chapter that scientists were satisfied at the time that Newton’s laws represented a terminus in scientific understanding.

Anyway, on with Swinburne’s simplicity of theism.

Yet a person with zero powers would not be a person at all. So in postulating a person with infinite power, the theist is postulating a person with the simplest kind of power possible.

By accident, Swinburne lets slip a fundamental weakness of his case, even stated in its own terms. A lack of a person, and therefore no associated powers, is simpler – it is zero in both cases, whereas a single person with infinite powers is a single person, and therefore more complex. But onward…

God’s beliefs have a similar infinite quality. Human persons have some few finite beliefs, some true, some fasle, some justified, some not. In so far as they are true and justified (or at any rate justified in a certain way), beliefs amount to knowledge. It would seem most consonant with his omnipotence that an omnipotent being have beliefs that amount to knowledge. For, without true beliefs about the consequences of your actions, you may fail to realize your intentions.

This isn’t making any kind of argument about simplicity. This is merely taking a premise (that God is omnipotent) and following a line of argument that leads to a conclusion that God is also omniscient. The value of the conclusion is only as good as its premise, and so this line of reasoning doesn’t seem to add anything to his claims of prior probability at all.

For a person to act, he has to have intentions. A person could be omnipotent in the sense that whatever (logically possible) action he formed the intention to do, he would succeed in doing, and also omniscient so that he knew what were all the (logically possible) actions available to an omnipotent being in his situation, and yet be predetermined to form certain intentions. His intentions might be determined by causal factors outside his control, or at any rate, as are those of humans, greatly influenced by them. But, if a person is predetermined (or has an inbuilt probabilistic tendency) to act in certain specific ways, this means that a tendency to act in certain ways is built into him. But a person with an inbuilt detailed specification of how to act is a much more complex person than one whose actions are determined only by his uncaused choice at the moment of choice. Such a being I call a perfectly free being. Theism in postulating that God is perfectly free makes the simplest supposition about his choice of intentions.

This tells us nothing about whether such a being is possible. It seems to me that the greater the capabilities, the greater the complexity needed in order to achieve them, and if there is perfect freedom in terms of intentions, then I suggest that involves quite a lot of capability.

A substance who is essentially omnipotent, omniscient, and perfectly free is necessarily a terminus of complete explanation. For if some state of affairs E is explained as brought about by God in virtue of his powers and beliefs and intentions, to bring about E, how can the action be further explained?

Well, it would help if there were an explanation of how God came to be in the first place. Swinburne argues as follows

God’s being omnipotent, omniscient, and perfectly free is involved in his existing, given that, as we have supposed, these qualities belong to the divine essence. But his existing cannot be due to any contemporaneous factor that makes him exist or allows him to exist. For, if his existence depended on some factor apart from himself, that factor could not depend for its existence on himself (for one cannot have causation in a circle). But if this factor did not depend on God, then God would not have been able to make it exist or not exist, and so would not be omnipotent.

It seems to me that Swinburne has rather painted himself into a corner here. There is no means of explaining the existence of an omnipotent God, since any factor causing God to come into being is by definition not under God’s control, and this would render God not omnipotent. But if he isn’t omnipotent but has circumscribed powers, then the limit of those powers is something which in turn needs to be explained.

Therefore, we simply have to accept the prior probability of a God whose existence (in the form defined by Swinburne) is fundamentally inexplicable without engaging in logical contradictions.

But despite all this, Swinburne grandly concludes.

The intrinsic probability of theism is, relative to other hypotheses about what there is, very high, because of the great simplicity of the hypothesis of theism.

I notice he manages to reach the end of the chapter and conclude that theism is intrinsically more probable than any other hypothesis without considering in detail or even naming any other hypotheses. Moreover he has incorrectly stated the necessary comparison. The correct comparison is the hypothesis of theism against the sum of all hypotheses which do not posit the existence of the theistic God.

Swinburne: "Complete" explanations

In chapter 4, Swinburne looks at what makes a Complete Explanation. He starts out by looking at what he regards as possible limits to scientific explanations.

Phenomena of two kinds can be shown not to be explicable scientifically. First there are the phenomena which are too odd to be fitted into the established pattern of scientific explanation, and, secondly, there are phenomena that are too big to be fitted into any pattern of scientific explanation.

This seems to be a variety of the Argument from Personal Incredulity. If Swinburne thinks some phenomenon is too strange or big to have occurred naturally, then God possibly/probably did it. (The phenomena he is thinking of are both too strange and too big to fit into the category of personal explanations in the form of intentional actions by humans.)

The most obvious problem with this approach can be easily shown by a brief look at the history of science, which shows a progressive widening of the scope of things which were previously thought to be the work of God but which have since been shown to be the result of the operation of unchanging natural laws. It seems that our perception of what is too odd to have a natural explanation is constantly changing, a fact which Swinburne seems not to take into account.

Swinburne goes on further about odd phenomena:

To show phenomena too odd to be explicable scientifically, the theist needs to show that there is good evidence for a scientific system h covering a certain range of phenomena, but that it is not a consequence of h (within the general range of h) occur, and that any attempt to amend or expand h that would allow it to predict e would make h so complex that it would be very improbable that it is true.

This is again a gross misuse of the term “improbable”.

Swinburne describes two categories of odd phenomena. One is miracles, and the other is general classes of phenomena for which a scientific explanation is too complex to be plausible.

If a phenomenon can be accurately explained and predicted by means of a theory, I see no reason to be concerned with how complex the equations are. I’m sure I would rapidly get lost in the mathematics of quantum electrodynamics for which Richard Feynmann received his Nobel Prize. Is the fact that the equations for explaining something supposedly very simple (i.e. the behaviour of subatomic particles such as electrons) are very complex a reason for thinking the theory isn’t true? Do we have instead to assume that Feymann’s quantum electrodynamics is wrong (even though its predictions are very accurate) and that it is really God making all those electrons behave in that particular way? Swinburne (at this stage) offers no criteria for deciding whether a scientific explanation for a phenomenon is too complex to be plausible.

Swinburne also makes a description of big phenomena

The other phenomena that cannot be explained scientifically are phenomena that are too big for science, and too big not merely for some particular well-established scientific system, but for any scientific system. … But what, as I shall show more precisely in chapter 7, science cannot explain is why there are any states of affairs at all; it can only explain why, given that there are such states, this state is followed by that state. Nor could it explain, as I shall show more precisely in chapter 8, why the most fundamental natural laws of all hold. Either these are brute facts about the world, or they have an explanation of a different kind.

Quite clearly, we don’t have those scientific explanations yet. But Swinburne’s assertion is that it is fundamentally impossible for science to elucidate these matters at any point in the future.

When making such statements regarding ultimate limits to knowledge (as opposed to the limits of what we have learned so far), it is wise to couch them in something more than a statement to the effect “I don’t see how this could ever be found out”.

Let’s give Swinburne the benefit of the doubt here - all he is so far saying is that he thinks there are ultimate limits - he isn’t (yet) saying where they are or why. We can wait for those later chapters to see him expand on this theme.

Next Swinburne goes on to make several definitions of varieties of complete explanation. I suspect these will get used extensively further on in the book, so we had better be familiar with them.

A full explanation of a phenomenon exists if it includes a cause and a reason, which together necessitate its occurrence. (The cause is the initial condition and the reason is the operation of some law of behaviour.) If a phenomenon has a full explanation, nothing more needs to be described about how the initial condition resulted in the final state.

A partial explanation is where the suggested cause and reason, while necessary to the understanding of the final state, leave unexplained or unstated the operation of some underlying law. (In Dennett’s nomenclature as described previously, the use of the design stance would be a partial explanation of exactly this kind.)

A complete explanation is a full explanation where the details of the causes - the initial conditions, and the manner of operation of the reasons is itself explained.

Quite why this deserves a separate definition is not clear, but there it is. It seems to me that there are varying degrees of partial explanation which are described at varying levels of abstraction, and the varying levels don’t really need separate definitions - you merely need to know what level of abstraction you are working with and therefore what assumptions are being made about the underlying physical laws whose operation has been abstracted. For instance, laws of chemistry assume that the laws of physics are in operation, laws of cell biology in turn assume the operation of the laws of chemistry, and the laws of botany or zoology assume that the laws of cell biology are working. When explaining something, you choose the level of abstraction that is appropriate to the situation. Of course, there is a need to ensure that your abstractions are correct, and that nothing that you postulate within your chemical theories actually violates any known laws of physics.

Then an ultimate explanation is a complete explanation which traces itself back to original causes - ultimate brute facts for which there is no further explanation.

Finally there is an absolute explanation which is an ultimate explanation in which all the factors cited are either self-explanatory or logically necessary.

We don’t yet have ultimate or absolute explanations for the universe, and might never discover them. Nevertheless, Swinburne is confident that it is possible to decide on the basis of balance of probability whether the ultimate explanation for the universe is God. He shies away from claiming that God is an absolute explanation, since he considers it impossible for anything to explain itself.

Swinburne then describes how Newton’s laws of motion were so delightfully simple and so powerful in their explanatory scope that the scientists of the day genuinely believed that science had reached a terminus in Newton’s laws. We aren’t in that position today, but Swinburne suggests that if and when a theory of that explanatory power is devised that explains all the phenomena we know of today, then we will have good reason to believe we are at a terminus. Quite why a mistaken past belief of the existence of a terminus in explanation should be regarded as a model for defining criteria for a future belief that a terminus has been found is left unexplained. It seems to me that something more than simplicity and explanatory power is going to be needed if we are to be sure we haven’t fooled ourselves into thinking that there are no new unexplained phenomena to be discovered.

Although simplicity is regarded by Swinburne as an indicator of “prior probability” (a term I dislike for reasons stated before) he gives no indication as to what level of complexity in his view rules out a natural law as being a plausible explanation. Trying to work out what he means in all this is a bit like trying to wrestle with fog. One always harbours the suspicion that these criteria will get refined at a later stage so that God just so happens to turn out to be really quite probable.

Swinburne now turns again to personal explanations. Time for another quote.

Scientific and personal explanations are on a level—that is, are rivals for the explanation of phenomena—it would seem to follow that a scientific explanation could explain a personal one, and conversely; and that the criteria that it does so are any gain of prior probability and explanatory power that would result from supposing that it does. By a scientific explanation explaining a personal explanation, I do not mean the one being analysed in terms of the other—we saw in Chapter 2 that a personal explanation cannot be explained in terms of a scientific explanation, and it is surely equally plausible to suppose that a scientific explanation cannot be analysed in terms of a personal explanation. What, rather, I do mean by a scientific explanation explaining a personal explanation is the existence and operation of the factors being involved in a personal explanation being explained by the existence of factors involved in a scientific explanation. A scientific explanation might be given of how people come to exist, and to have the intentions, beliefs and basic powers that they have.

Hang on! Back in chapter 2 he was saying that personal explanations aren’t scientifically analysable, and now he is saying that they are. Or perhaps he is saying that they both are and aren’t. If intentions are analysable in the terms he has just described (and which by the way agrees quite nicely with Dennett’s approach), then there is no need to posit the inescapable dualism he brought up in Chapter 2. It seems that this argument is in danger of disappearing up its own fundament.

But let us go on and see what more he has to say on this.

It is the programme of physicalism to effect a reduction of just this kind. The theist who tries to explain why the world is and works as it does is attempting the reverse programme—to give a personal explanation in terms of God, of the existence and operation of the factors involved in scientific explanation.

In what sense would such an explanation be an ultimate or absolute explanation which Swinburne is seeking? By his own definitions, complete explanations work by taking full explanations pitched at a high level of abstraction, and explaining them by means of the operation of physical laws at a lower level of abstraction. By all appearances, explanations expressed in terms of intentions are an extremely high level of abstraction, depending in turn on the laws of biology, of chemistry and physics for progressively more detailed levels of explanation.

So if we are looking for an ultimate explanation expressed in terms of theism, we would need to explain how God’s intentions (unlike human ones) operate at the lowest level of abstraction – below that of physics, instead of at a very high level of abstraction – above that of biology. Let’s see what Swinburne makes of that in future chapters.

Swinburne chapter 3, The Justification of Explanation

In chapter 3, The Justification of Explanation, Swinburne looks at the grounds for deciding whether a particular explanation of some phenomenon is a good one.

Swinburne is more interested in his scientifically unanalysable personal explanations, but starts out with scientific explanations. And he seems to have some very odd ideas about how scientific theories are developed.

He starts out by defining a term he uses a great deal from here on: prior probability. According to Swinburne:

The prior probability of a theory is its probability before we consider the detailed evidence cited in its support. The prior probability of a theory depends on its degree of fit with background knowledge (an a posteriori matter), and on its simplicity.

This is so wrong and backwards that it is hard even to start explaining how terribly bad this line of reasoning really is.

Firstly, the fact is quite simply that scientific theories aren’t devised this way. As a scientist, you don’t start with a theory and then go looking round for detailed evidence which might or might not end up fitting it. You start with the detailed evidence which is so far unexplained by existing theories, and see if you can work out a theory which explains it. Starting with a theory and then looking around for evidence for it is what many religious people imagine scientists do (as I have mentioned before), but I hadn’t expected somebody of Swinburne’s academic achievements to fall into this particular trap.

Next we have this dread word probability again. We aren’t dealing with statistical data, nor are we dealing with known causes. When we develop a new scientific theory, we are trying to elucidate previously unknown causes. The techniques of probability mathematics are entirely inappropriate here. When your causes are unknown, even if you think that you are developing a probabilistic theory, such as used in quantum mechanics, you do not and cannot evaluate the prior probability of a theory in this way.

And even in those cases where you do use probability and statistics a lot, such as in the analysis of clinical trial data to assess the effectiveness of some new drug, you can’t go back into your data and revise your hypothesis so that the data is now being used to answer a different question from the one you were asking before you collected the statistics, so that you get some kind of positive answer. Games like that make the mathematics go all wonky, even when the use of statistical techniques is appropriate.

Lastly, the scientific understanding of simplicity is quite different from Swinburne’s. A scientific theory is regarded as appropriately simple if it includes no more than is necessary to explain the phenomena in question and make predictions concerning the future behaviour of them and possibly also of other phenomena so far unobserved. So Newton’s theory of gravity is appropriately simple because it talks of a gravitational force, and describes its strength. It doesn’t make the claim that the sun exerts its force on the planets by sending out teams of invisible horses to drag the planets along their orbits. Such a claim (whether or not it happened to be true) offers no predictive power and no additional explanatory power relative to the phenomena addressed by the theory.

It is utterly meaningless to say that the theory would have been “simpler” had the gravitational force been inversely proportional to the distance between bodies rather than to the square of the distance. That greater supposed simplicity has no effect on whether the theory has a higher “prior probability” of being right before you look at the detailed evidence, because you already know that the detailed evidence doesn’t fit the simpler theory, and so you know (without any kind of evaluation of probability) that the simpler theory is simply wrong. In any scientific theory, you make our explanation as complex as is necessary to provide a generalisation which allows you to explain existing phenomena and predict future phenomena.

Swinburne then goes on to look at personal explanations and the use of prior probability. Leaving aside his dubious claim that personal explanations cannot be analysed scientifically, he is on somewhat firmer ground here, because there are lots of people in the world, and you can make statistical analyses of the sorts of things they do, and “prior probability” can return to its traditional meaning within the realms of statistical mathematics, particularly of Bayes’ Theorem. In other words, when making theories about humans behave, it is perfectly possible to create those theories in the form of P-inductive arguments.

But this doesn't help much, since Swinburne isn’t much interested (at least not in this book) in the prior probability of events caused by humans. He is interested in the “prior probability” of events of unknown ultimate cause and which he thinks might have been caused by God. At this point he is back into the realms of serious abuse of mathematics and statistics. All the equations he quotes are all perfectly good equations – when used within their appropriate context. As far as I can tell, he hasn’t made any obvious mathematical howlers, though quite frankly I haven’t looked all that hard because it really doesn’t matter whether he has the algebra right or not. The use of Bayes’ equations in this context is totally inappropriate and any conclusions based on them are completely worthless.

Swinburne on Inductive Arguments

(I haven't finished with Spong yet, but have decided that I will run the remaining chapters of Spong in parallel with some comments on Richard Swinburne's The Existence of God. Here are some comments on the first chapter of the latter.)

Richard Swinburne is one of Britain’s leading academic theologians. He is a Fellow of the British Academy. From 1985 to 2002 he was Nolloth Professor of the Philosophy of the Christian Religion at the University of Oxford.

Swinburne says in the Preface to the second edition of The Existence of God:

The Existence of God is the central book of all that I have written on the philosophy of religion. It was originally published in 1979. A ‘revised edition’ was published in 1991, but the revision consisted merely in the addition of two appendices; the main text remained intact. The present revision is a far more substantial one.

He goes on to describe the various chapters that have been changed, and the nature of those changes. The book has received good reviews, and it contains material originally published in various academic journals, including Philosophy, Religious Studies, Reason and Religion, American Philosophical Quarterly, Physical Cosmology and Philosophy, Comparative Theology, and Faith and Philosophy. The book is used as a textbook in undergraduate courses on theology and the philosophy of religion.

So this is not some ignorant backwoods preacher who wouldn’t know a philosophical argument if it hit him over the head. This is a serious theologian who sits at or near the top of his academic discipline, and The Existence of God is the book which in his own words is central to his understanding of the philosophy of religion, and which is the result of more than 30 years accumulated thought and wisdom on the subject. If Swinburne had turned up on my blog in response to my invitation to believers to produce an argument in favour of God’s existence, I could hardly have found somebody more qualified to put the case. I’m going to take this book as a kind of response to that invitation.

A bit first on the structure of the book. This is a serious academic work, the language is densely packed - it is not really intended for a popular audience. I don’t mind that - I’m prepared to put in the hard work of reading and understanding it, and explaining to you what it means to the best of my understanding.

If you are looking for simplistic arguments such as arguments from scripture, you will be disappointed. There is little or no biblical quotation, and nothing in the way of argument that “the Bible says X, therefore it must be true”. I’m sure that Swinburne is perfectly well aware that circular arguments (using your assertions as evidence of their own truth) do nothing more than go in circles. Swinburne also makes a deliberate decision to leave aside ontological arguments in this book. All his arguments have as a starting point at least one known and largely undisputed physical fact, such as the existence of the universe.

But it is quite a way into the book before he gets on to any of these arguments. He starts out in the early chapters by describing what he thinks of as being a good structure to an argument. The first six chapters have the following titles:

1. Inductive Arguments
2. The Nature of Explanation
3. The Justification of Explanation
4. Complete Explanation
5. The Intrinsic Probability of Theism
6. The Explanatory Power of Theism: General Considerations

It is only in chapter 7 (after 132 pages of introduction) that he starts on the first of his arguments in favour of God “The Cosmological Argument” using the principles he establishes in the first 6 chapters. He then goes on in subsequent chapters through Teleological Arguments (i.e. arguments from design), Arguments from Consciousness and Morality, The Argument from Providence, The Problem of Evil, Arguments from History and Miracles, and The Argument from Religious Experience. He rounds it all off with a short chapter “The Balance of Probability”.

It would be tempting to skip the first 6 chapters and go straight to the actual arguments. But unless we look first at what Swinburne thinks characterises a good argument, and whether he is right, it is not going to be possible to work out what he is talking about when dealing with the actual arguments.

So it is going to be necessary to look at these early chapters even through they don’t directly address the question of God.

The first chapter is called “Inductive Arguments”. Swinburne starts out by offering three examples of differing kind of arguments. He offers the following as an example of a valid deductive argument, where the premises (provided they are true) make the conclusion certain.

P₁: No material bodies travel faster than light.
P₂: My car is a material body.
C: My car does not travel faster than light.

The next example he gives is what he calls a P-inductive argument, where the premises, while not making the conclusion certain, render it probably true. How good the P-inductive argument is depends on how probable the premises render the conclusion.

P₁: 70% of the inhabitants of the Bogside are Catholic.
P₂: Doherty is an inhabitant of the Bogside.
C: Doherty is Catholic.

The third kind of argument Swinburne describes is what he calls a C-inductive argument.

P: All of 100 ravens observed in different parts of the world are black
C: All ravens are black.

That you have seen 100 black ravens does not by itself render the probability very great that all ravens everywhere (past present and future) all have been, are and will be black. But according to Swinburne each additional black raven you come across increases the probability that the conclusion is correct.

Swinburne states

Most of the arguments of scientists from their observational evidence to conclusions about what are the true laws of nature or to the predictions about the results of future experiments or observations are not deductively valid, but are, it would be generally agreed, inductive arguments of one of the above two kinds.

This is true, but before we see how Swinburne proceeds from here, there are a few things that need to be said about that statement.

First, a P-inductive argument can only be built if you have statistical data to work from, in the form of a population of some entities whose characteristics vary, and about which one can draw conclusions based on statistical mathematics. The mathematics of statistics has been well developed over the past 100 years or so, to the extent that a decent understanding of statistics is a necessary part of the syllabus in most scientific subjects at degree level. This is not merely the physical and biological sciences, but also all the engineering disciplines, computer science, and social sciences including sociology, geography and history.

If you want to be a mathematician in this field, it is necessary to know precisely how the mathematics works in order to make new discoveries (otherwise you can end up re-inventing old discoveries). If you merely want to make use of statistical techniques, in order to draw justified conclusions in other fields, then the vital knowledge needed is whether and under what circumstances it is valid to use a particular technique. If you use a statistical technique in circumstances it is not valid for, then your conclusions are worthless - though anybody who doesn’t understand statistics would be unaware of the fact.

Secondly, a C-inductive argument is only valid if you have not come across any contrary observations. In the example given, the observation of a 100 or any larger number of black ravens doesn’t contribute at all to the probability that all ravens are black if you are already aware of the existence of an albino raven. Therefore, conclusions that you draw on the basis of C-inductive arguments are always provisional, until they are overthrown by a contrary observation (i.e. a raven of another colour), or are explained by the discovery of some underlying natural law which explains why all ravens must be black and that it is not possible for ravens to be any other colour. If scientists have a natural law which has been established by means of a C-inductive argument, they always continue to look for that underlying explanation.

Thirdly, to use the term “probability” in the context of C-inductive arguments is misleading, because it suggests you are dealing with statistical mathematics when in fact you aren’t.

This is all very important. Swinburne in the first chapter states that he believes there to be no valid deductive arguments either for or against the existence of God which are based on premises universally accepted to be true. Therefore, the entire book consists of an estimate of the balance of probability of God’s existence, based on the strength of the various P-inductive and C-inductive arguments he works his way through.

The main tool that Swinburne uses is Bayes’ Theorem. In brief summary, Bayes’ Theorem is a mathematical tool that allows you to work backwards when calculating conditional probabilities. Even without Bayes' Theorem, it is easy to work out the probability of some overall outcome consisting of some combination of individual events by multiplying the probabilities of individual events.

Bayes’ Theorem allows you to work in the opposite direction. If that you know that various combinations of events of different probabilities that can lead to a particular outcome, Bayes’ Theorem allows you to calculate the relative probability of the various possible routes to that outcome, given that it has actually happened.

Swinburne doesn’t mention Bayes’ Theorem by name until Chapter 3 and page 66, but he starts using concepts and terms from it right in the first chapter. This is clear from the fact that the index contains the term “confirmation theory” giving page ranges in the first chapter, and then also says under the term “see also Bayes’s Theorem”. Let’s let Swinburne take up the narrative in his own words.

My strategy will be as follows. Let h be our hypothesis - ‘God exists’. Let e₁, e₂, e₃, and so on be the various propositions that people bring forward as evidence for or against his existence, the conjunction of which form e. Let e₁ be ‘there is a physical universe’. Then we have the argument from e₁ to h - a cosmological argument. In considering this argument I shall assume that we have no other relevant evidence, and so k will be mere tautological evidence [i.e. all other irrelevant knowledge]. Then P(h|e₁ & k) represents the probability that God exists given that there is a physical universe - and also given mere tautological evidence, which latter can be ignored. If P(h|e₁ & k) > 1/2 then the argument from e₁ to h is a good P-inductive argument. If P(h|e₁ & k) > P(h|k), then the argument is a good C-inductive argument. But when considering the second argument, from e₂ (which will be the conformity of the universe to temporal order), I shall use k to represent the premiss of the first argument e₁; and so P(h|e₂ & k) will represent the probability that God exists, given that there is a physical universe and that it is subject to temporal order.

You should be able immediately to spot the problem. Since we aren’t dealing with statistical propositions, Swinburne has no statistical data to work from, and so has no numbers to plug into Bayes’ equations.

Moreover, Bayes’ Theorem works only on known causes with known probabilities, (known at least to some degree of precision). Swinburne’s situation is that we don’t know the causes of the universe. Because we don’t know, we have no means of allocating probabilities to this or that hypothesis. All we can do is keep looking for more evidence that enables us to form a hypothesis that goes further than our present knowledge. And when we do so, we still won’t be able to assign a probability to it, since we don’t have a population of universes of differing characteristics from which we can draw statistical conclusions. Any attempt to put a number on it is entirely arbitary, nothing more than saying "I think this is 60% probable because I think that number sounds about right."

This to me seems to be a misuse of statistical techniques so basic that it ought to go into statistics textbooks as a classic example of how not to do it.

I find it hard to account for this remarkable state of apparent ignorance on Swinburne’s part. It seems that he really doesn’t understand the limits of Bayes’ Theorem and the purposes to which it can be put. This would require that in the 17 years in which he was Nolloth Professor at Oxford, surrounded by some of the world’s leading academic experts on almost every topic under the sun, no academic with any knowledge of statistics was invited to read the first chapter of his book (for instance when he was preparing the Revised Edition while at Oxford) and advise whether the use of Bayes’ Theorem in this context was appropriate, and that Swinburne, though surrounded by all these experts, never consulted any of them in order to ensure that he had a correct understanding of Bayes’ Theorem.

Furthermore it would appear that none of the journals which published material subsequently incorporated into this book noticed anything amiss, and likewise none of those who conducted peer review of any of his papers noticed any problem.

If this is the case, then this doesn’t merely reflect extremely poorly on Swinburne himself, but on the whole academic study of theology, and the extent to which it has walled itself off from any other field of knowledge.

There is another possibility: that I’m mistaken in my own understanding of Bayes’ Theorem, and that Swinburne’s use of it is in fact justified. I’ve given my reasons for thinking I’m right. Bayes’ Theorem is well enough documented. You can look it up and judge for yourself.

Richard Swinburne "The Existence of God"

I got this book out of the library last weekend - the second edition published in 2004. In it, Richard Swinburne spends about 350 pages going through the various arguments for God, and finds them persuasive.

Interestingly, Swinburne's definition of God is somewhat narrower than that provided by Dawkins in The God Delusion, and also narrower than Spong's definition of the Theistic God in A New Christianity for a New Age. I think it is worth making a direct comparison between them.

Here is the Dawkins version:

There exists a superhuman supernatural intelligence who deliberately designed the universe and everything in it, including us.

Here is Spong's understanding of a theistic God:

A being, supernatural in power, dwelling outside this world and invading the world periodically to accomplish the divine will.

Note that there is some difference here. Dawkins' definition encompasses the non-interfering God of deism as well as the activist God of theism, while Spong is specifically describing a theistic God. Spong isn't making explicit Dawkins' claim that God created the universe, but that doesn't matter a great deal. If God is outside the universe, then whether or not God created the universe, he must have come into existence separately from it, and therefore Dawkins' arguments against God apply with just the same force to Spong's definition as to his own.

Swinburne's version of the God proposition is this:

There exists necessarily a person without a body (i.e. a spirit) who necessarily is eternal, perfectly free, omnipotent, omniscient , perfectly good, and the creator of all things.

This seems to me to be a narrower definition than either Spong's or Dawkins'. Although Swinburne doesn't actually use the word "supernatural" in his definition, this can be inferred, since omniscience and omnipotence are both generally regarded as being supernatural properties. Swinburne and Dawkins agree in their definition being one of a God who is the creator of all things, but Swinburne adds "without a body", "perfectly free" and "perfectly good" to his definition, and makes the existence and properties of such a God both "necessary". What this means is that Swinburne's definition is a subset of Dawkins' definition - Swinburne's God meets all the critera of Dawkins' definition, and so all Dawkins' arguments are applicable to Swinburne's God. Since they reach opposite conclusions, one or other of them must be wrong.

Swinburne's definition is also a subset of Spong's. Spong makes no statement concerning the characteristics of "the divine will" but Swinburne talks of it being "perfectly good".

Interestingly, in the first chapter Swinburne accepts that there are no conclusive deductive arguments for or against God's existence that start from generally-accepted premisses. So he accepts that one can neither prove nor disprove the existence of God. So he starts out by stating that he proposes to use inductive arguments, and explains at considerable length what he means by this and how he proposes to use them. By means of these inductive arguments (whose subject matter cover the usual range of topics I've written about before), he finds that the balance of probability greatly favours the existence of God.

I think there are some fundamental errors in Swinburne's approach, which result in his conclusions being invalid. It will take a good deal of detail to explain what those errors are, so I'm not going to go into them now. Instead, I intend to go though the book in the same level of detail as I'm covering Spong, but only after I have finished the Spong blog.