Thanks to Michael Bradley for the very detailed attention which he has paid to sentence upon sentence of my writings, and for his apparently powerful critique of my substantial claims. While I acknowledge that I did not make one argument of mine very clear and for this reason can fully understand why Bradley makes the objection that he does, I argue that none of his objections to my substantial claims in his ‘Hume's chief objection to natural theology’ have any force.

My programme in the Existence of God,Footnote ¹ as Bradley recognizes (254), is to consider in turn the main traditional arguments for and against the existence of God, and to show that in most cases the evidence which each argument adduces in its premisses (e) raises the probability of theism (h) above that resulting from the background evidence (k) alone, that is the conjunction of all the evidence used in the previous arguments. In one case the evidence (of evil) slightly lowers the probability of theism; and in two cases (the existence of morality and ‘divine hiddenness’), the evidence makes no difference to that probability. Bradley, however, accuses me of often representing positive arguments, and especially the design argument (from laws of nature), as (independently of other arguments) good P-inductive arguments (that is ones which render their conclusion more probable than not). I don't think that any of the citations which he gives from my writings bears that interpretation; but if I have seemed to claim this, I assure readers that (at least from 1979 onwards) that was never my intention.

In the popular exposition of my natural theology I certainly wrote that the operation of simple laws of nature provides ‘strong grounds’ for believing in God.Footnote ² But since this popular exposition tried to avoid technical terms as much as possible it is unfair to read that sentence as expressing a claim that the grounds provide a good P-inductive argument. But if anyone wants a more precise account of how this claim is to be read, let me say that what I meant by it was merely that the grounds raise the probability of the existence of God by a lot and to a substantial value.

I hold of course (as per 260) that a person's rational belief about a hypothesis is the belief rendered probable by his or her total available evidence; and I was assessing in The Existence of God which belief is rendered probable by the total publicly available evidence. I claim that by the end of the book I have taken account of all the public evidence which has generally been thought to be relevant (apart from detailed historical evidence, especially that connected with Jesus). I argued in the final chapter that all that evidence taken together made the hypothesis of theism more probable than not. (It follows from my arguments elsewhereFootnote ³ that when detailed historical evidence is taken into account the probability of theism is significantly greater.) In discussing the design argument (in the form of the argument from the operation of simple laws of nature) I bring out why I think that it is a ‘strong’ argument in the above sense (my 166, 341).

For each argument from evidence (e), the probability of theism on that evidence together with the evidence considered in previous arguments in the chain of arguments (k) is P(h/e & k)=P(h/k) P(e/h & k)/P(e/k). P(h/e & k) is the posterior probability of h; P(h/k) is its prior probability, and P(e/h & k)/P(e/k) is its explanatory power with respect to e. So for the design argument which is the second argument in the chain, the value of P(h/k) is the value of P(h/e&k) in the cosmological argument which itself is a function of the prior probability of theism on no contingent evidence, that is its intrinsic probability, and the explanatory power of h in explaining the existence of a physical universe.

However, Bradley claims (261) that my ‘own k in the design argument … goes far beyond the mere assumption of a physical world’. That is not so. The paragraph which Bradley goes on to cite appeals to no contingent features of the universe. Its truth does not depend on the existence of coins or paintings. It merely claims that if certain phenomena did occur, a certain kind of explanation of them would be probably true. It is a common procedure in moral philosophy to elucidate the a priori truths of morality by considering thought-experiments, for example, where someone has a choice between, on the one hand, killing one person and saving the lives of five others, and on the other hand, doing nothing and allowing six people to die. We try to elucidate the principles of morality by trying to see principles which underlie the judgments we are inclined to make about such cases; whether or not the cases are actual is irrelevant. And it is equally common to elucidate the principles of scientific inference by considering thought-experiments rather than actual experiments. All I am doing in the cited paragraph is to elucidate the a priori principles of probabilistic inference (implicit in science and elsewhere) underlying the judgments we think it right to make about particular cases; whether or not they are actual cases is irrelevant.

The intrinsic probability of any hypothesis is a function directly of its simplicity and inversely of its scope. I claimed that simplicity is much more important than scope in determining intrinsic probability. The simplicity of a hypothesis consists in its postulating few ‘entities, few properties of entities, few kinds of entities, few kind of properties, properties more readily observable, few separate laws with few terms relating few variables, the simplest formulation of each law being mathematically simple’ (my 53). I illustrate the application of the latter features to personal explanation in terms of ‘constant predictable ways in which persons acquire beliefs from their surroundings’ (my 65). Bradley draws attention (259) to cases where in his view I assume that ‘a theory T is simpler than a theory T₁ if T₁ raises further questions not raised by T or requires some further piece of explanation not required by T’. But he then uses this understanding of simplicity to suggest that a theory (his ‘Epicurean’ theory) is simpler than another theory (my traditional theism) in virtue of being able to explain data unexplained by the other theory. But that was not at all the issue in the cases which he cites.

Cases (i) and (ii) are cases where I defend the postulation of infinite degrees of a property on the grounds of the puzzling character of a particular finite degree of that property. The less puzzling character of the infinite arises, I claim, for the reason with I give on my 54–55 – the relative simplicity of the infinite as such; this is an aspect of mathematical simplicity. Case (iii) is a case where an alternative theory has to invoke an additional divine property (not an essential property, but a property of having done a certain action, such as God choosing to retain his omnipotence), not required by the theory I was defending; the simplicity of the preferred theory arises from it postulating fewer properties. In all of these cases, there is certainly something more in need of explanation on one hypothesis than on another. But what needs explaining is what is postulated by the hypothesis, not observed data which one of the hypotheses cannot explain. The puzzling character is therefore due to features internal to the theory. In none of these cases was I judging the simplicity of a theory by its ability to explain data unexplained by a rival theory. The simplicity of a hypothesis, as I frequently repeat, beginning on my 53, is an intrinsic feature of a hypothesis, to which its ability to explain the data is irrelevant. Its ability to explain the data determines the ‘explanatory power’ and not the simplicity of a hypothesis.

My theistic hypothesis (that there is a God, essentially eternal omnipotent omniscient and perfectly free; from which – I claim – it follows that He is perfectly good) has the same scope as Bradley's ‘Epicurean hypothesis’; each hypothesis purports to explain the most general observable features of the universe. So which has the greater intrinsic probability depends on which is simpler. I claim that my hypothesis is simpler than Bradley's. Whether I am right about this depends in part on whether perfect goodness is entailed by the other divine properties, and Bradley claims (261–265) that my argument purporting to show this is unsound. He sets out what he believes to be my argument for this in eight stages. I do indeed endorse (1), that ‘any agent, human or divine, must have a reason for any action, and this involves seeing the action as a good thing’. But the gloss on it in the text is misleading. Yes, a desire, or rather – to put it more carefully – having a desire, is a reason for an action. (Desires are not themselves reasons; they are causal influences.) And anyone who has a reason for doing some action will have some minimal desire to do it. But there are many and very often better reasons for doing actions than desiring to do them.

It is good for me to give money to Oxfam to feed the starving, because it is good that the starving be fed. If I recognize this good I will also desire that the starving be fed, although the desire may not be very strong; and to satisfy my desire may be not my main reason for giving. Nevertheless the satisfaction of one's own desire (‘the least whim’ – 263) is a reason for acting, and sometimes it may be the only reason for acting – as when I eat a piece of chocolate. Where one has available to one a range of incompatible actions the best action is the one dictated by the balance of reasons, what one has best or most reason overall to do.Footnote ⁴ Now if the fact that one had a desire to do some action A (maybe together with some other reasons) provided a perceived balance of reason in favour of doing the action rather than refraining or doing an incompatible action (and one had no other relevant desires) one would inevitably do A – which is what Bradley's (6) says. Given my understanding of the moral, captured in Bradley's (5) which he does not seek to challenge, the moral good is that which there is some reason to do and the morally best action is that which there is overriding (or most) reason to do. So what one believes to be the morally best is what one believes that there is overidding reason to do. And that (given God's omniscience and the objectivity of the moral) leads directly to (8).

Bradley claims that my (6) is inconsistent with (1). In virtue of my articulation of (1) above, I deny this. Yes, (264) you ‘must have a reason if you perform an action’, but there are plenty of reasons for action, other than having the desire to do it. And ‘desires and inclinations’ are often ‘less reasons’ in the sense ‘not as good reasons’ as ‘the weightiest excogitation’ (264). We are all influenced by reasons; we all desire to do what there is reason to do. Moral conflict arises where persons recognize most reason for doing some action A rather than refraining or doing an incompatible action, but where among the reasons for the latter are that they have a desire to refrain or do an incompatible action, the causal influence of which is out of proportion to its perceived worth. In other words they feel strongly inclined not to do A, even though they recognize that their contrary desire only provides inadequate reason for not doing A; the desire is causally strong but the fact that they have it provides (in their view) only a rationally insubstantial reason for not doing A. In this situation a person may conform to the good, or yield to desire (and thus show akrasia). God however, being ‘perfectly free’, is ‘an agent subject to no ‘non-rational influences’ (my 104); His desires to do an action are proportional to the believed goodness of the reasons for doing the action, and so since (being omniscient) He has true beliefs about the actual goodness of those reasons, He will do whatever is best to do. In articulating this argument, I realise that the text of The Existence of God did not make these points clearly, and for that I apologize.Footnote ⁵

Bradley, however, has his own objection to my understanding of moral goodness. He points out (263) that one may recognize what rules of etiquette prescribe and simply ‘choose for some reason to ignore etiquette and act otherwise’; and he then suggests that ‘the case [of morality] seems no difficult from that of etiquette’. But this is confused. One may choose to ignore etiquette not merely ‘for some reason’, but for some reason which one believes to be overriding. Yet in virtue of the definition of the moral with which we are operating, we cannot choose to ignore the claims of the (believed) morally best action for (believed) adequate reason – for the morally best action just is that which there is overriding reason to do. One may still ‘choose for some reason to act otherwise’ (263), but that is a case of akrasia to which God is not subject.

Bradley's ‘Epicurean’ hypothesis ‘differs from theism only in replacing moral perfection by indifference’ to good and evil (256). But, given the argument which I have just defended that omnipotence, omniscience, and perfect freedom entail moral perfection, that hypothesis is self-contradictory. Indeed, if my argument is correct, no intentional agent could be literally indifferent to good and evil, for the believed good motivates. Rather we would have to suppose that the Epicurean god is weak-willed or sensitive only to certain kinds of good. He could be a lot less free than the traditional God (alas, he cannot easily resist many temptations) or a lot less knowledgeable (alas, he has a very poor understanding of the difference between good and evil.) And each of these Epicurean gods would be, by my criterion that hypotheses postulating large finite values of a property are much less simple than ones which postulate infinite values of that quantity, much less simple than the God of traditional theism. Hence the probability of the disjunctionFootnote ⁶ that there is an Epicurean god of one or other kind will have a lower prior probability than the prior probability of the existence of the God of traditional theism.

But, of course, if the evidence of what Bradley calls ‘the mixed phenomena’ of good and evil were far more probable on the Epicurean hypothesis than on the traditional theistic hypothesis, and so the former had far greater explanatory power, then the posterior probability of the former could exceed that of the latter. And I acknowledged (my 265–266) that we need to add to theism one or perhaps two further hypotheses – God providing life after death for humans, and God becoming incarnate to share their suffering – in order to avoid evil providing a C-inductive argument against the existence of God. And that complicates theism, but not by very much because – I argued – these are acts which it is quite probable that a traditional God would do in virtue of his perfect goodness. So, if we don't add these extra hypotheses, we get a weak C-argument from evil against the existence of God. But then how probable does the Epicurean hypothesis make the mixed phenomena? The answer is not nearly as probable as Bradley claims.

For, first, all my positive arguments for the existence of God are arguments from phenomena which a good God has reason to bring about. Bradley doubts (257) whether a solitary deity would have any reason to create anything. But there is reason for God to create any possible good thing; and there are just so many of them – planets and trees, other rational beings with whom to interact, such beings being endowed with abilities to paint pictures, play instruments, and write books. And so on. There are innumerable possible good things, that is things such that it would be good if they existed (when God existed), and so things which God has reason to create. Of course some of these things may not fit well with others of them, and so there may be reason for God not to create some if He creates others. But to deny that God has any reason to create anything is to deny that a world containing God would be even better for containing other things as well. And surely Bradley wouldn't want to claim that!

And, to repeat, the things which a traditional God has good reason to bring about include all those things which I listed as premises in my positive arguments for the existence of God. Among these good things is the invariable operation of simple laws of nature throughout all known regions of an enormous space and very long time which humans can come to understand, admire, and manipulate. They therefore provide a substantial positive argument for the existence of a God of the traditional kind, but no argument at all for an Epicurean God – for there is no reason to suppose that he would recognize the good reason to produce that sort of universe, and overcome any counter-inclination to doing so. And so on for the other arguments. Phenomena can only be evidence of a designer, given some supposition about the kind of thing that designer would be likely to bring about; and the Epicurean hypothesis does not give us much of a clue about that.

And secondly, even if the Epicurean hypothesis did lead us to suppose that the creator would create an orderly universe and mix some evil in with it, it does not make it in the least probable that the evil would be limited evil of a kind necessary for greater goods (which it is on the hypothesis of traditional theism, if the theodicy which I have developed is correct). The evil in our world has detectable causes and predictable effects, which means that we can learn how to produce or avoid it, and choose freely whether or not to do so; an Epicurean god might create lots of random evil. And the evil in our world is limited – no human suffers for longer than the length of a human life, a short period; an Epicurean god might make some creatures suffer (not as result of their own choice) for ever.

I conclude that the Epicurean hypothesis has both a lower prior probability and a lower explanatory power, and hence a considerably lower posterior probability, than traditional theism.