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.
