Chapter 5 of The Rationality of Regious Belief, ed. W.J.Abraham and S.W.Holtzer, Oxford, 1987, pp.71-84.

Reason Restored


Hume rubbished reason. Kant's critique did little to restore its standing in the eyes of philosophers, and in the subsequent two centuries academics and intellectuals of all sorts have had only a fragile faith in the power of reason to guide them into all truth, and many truths, especially those of religion and morality, have been relegated to the realm of feeling or fiat. Only the natural sciences have been exempt. No failure of noetical nerve has prevented the scientists from speculating, conjecturing, and theorizing about the nature of things, and from advancing the boundaries of human knowledge with no more than a polite nod in the direction of philosophers' fears that they might be outrunning the powers of reason and overreaching the bounds of possible experience. Scientists are sure of the cognitive standing of their subjects, but other thinkers, and especially philosophers of religion, have been unmanned by doubts whether they are engaged in a rational activity at all, or whether they are just expressing their emotional preferences or merely avowing an arbitrary leap of faith.

The consequences for the philosophy of religion have been disastrous. It has been fighting a war on two fronts, and losing it on both. On the philosophical front natural theology has been unable to resist the corrosive acids of Hume's scepticism, and against the claim made by some scientists that science has shown that no theistic world-view is tenable, it has been unable to counter the confident. dogmatism of the atheists by bringing to bear against them the doubts the philosophical sceptics have raised against theology. Yet at least one of these counters must be possible. If science is possible, Hume must be wrong. And if it is reasonable to enquire into the rationality of religion, it must be reasonable also to enquire into the rationality of science, and to conclude that the findings of science are not unquestionably the only ones worthy of credence by a rational man.



Hume attacks reason on many grounds. He attacks inductive reasoning on the grounds of its not being deductive, reasoning to unobserved entities on the grounds that it is neither deductive nor inductive, moral reasoning on the grounds that it transcends moods. Each form of reasoning is faulted for not being something else. It is an expedient often made use of by modern reviewers.

It is pertinent to point out what the sceptical strategy amounts to, and it may lead us to doubt its cogency. Once we recognize that there are many different forms of reasoning, and many different types of cogent argument, we shall turn a less than sympathetic ear to the sceptic who complains that moral, or philosophical, or theological, or metaphysical argument is not some other form of argument. Instead of lamenting that metaphysics is not mathematics, we may be led to reflect on the nature of metaphysical argument and develop criteria for distinguishing good arguments from bad. Basil Mitchell often does this, especially in The Justification of Religious Belief, and points to the parallel between the arguments of the theologians and those of the lawyer or the literary critic. But although a detailed exegesis of theological reasoning is of great value, it is not a conclusive defence and will not convince the sceptic. It is like the philosophy of history. Much insight has been gained by the careful philosophical exposition of the ways in which historians reason and the aims they hope to achieve, but Henry Ford is unimpressed, and still maintains that history is bunk. In the same way, many post-Humean sceptics are not interested in how theologians reason, holding that any argument which fails to conform to their canons of reasoning is simply invalid and unworthy of credence. Against such a claim it is not enough to maintain, as Strawson and Wittgenstein have done, that since we do, as a matter of fact, reason in certain ways, these ways constitute the standards of what should count as good reasons. That would be to make reason immune to rational scrutiny. And while the presumption that any form of reasoning widely practised must be cogent is strong, it is not incontrovertible. After all, astrology is much practised.

The most telling objection against the sceptics' claims is that they cannot be argued for without thereby showing them


false. For arguments are normative. A valid argument indicates what must be acknowledged, if the premisses be granted. If the only derivations are deductions, and we cannot deduce an `ought' from an `is', then clearly no conclusion can be adequately grounded about what sorts of argument we ought to be guided by. If, however, inductive as well as deductive arguments are admitted, then it might seem possible to make an inductive inference that all patterns of reasoning which were actually valid conformed to the canons of deductive or inductive argument. But before drawing such an inference, we should have to examine putatively valid inferences, and discover that only deductive and inductive inferences were actually valid. And this we could not do without some other test for validity. We cannot appeal to an inductive inference to give us a generalization which we shall then use to rule out possible counter-examples as not being inferences at all. If I am drawing merely inductive inferences about patterns of argument, then I must examine all patterns of argument, and I shall find that there are many arguments we use-moral arguments, political arguments, philosophical arguments, and historical arguments-which do not fit Hume's formula. Indeed, they are counter-examples to Hume's thesis. And, therefore, Hume's thesis cannot be established as a valid generalization about patterns of valid arguments by inductive argument alone.

The sceptic's position cannot be coherently argued for, but could conceivably be true. Sextus Empiricus and Wittgenstein likened the sceptical argument to a ladder one could climb up but must then jettison. Although the sceptic himself cannot argue that we ought to be guided only by arguments conforming to his criteria, he may nudge us into adopting that position, and if once we have adopted it, or even reckon that at least it is a tenable position, then we shall be hard put to it to see how, if we were to adopt it, we could be led to abandon it. And, of course, we cannot be forced to do so. By limiting the types of reasoning recognized to be cogent, the sceptic limits also the range of arguments which can be brought against him. In particular, if only deductive arguments are allowed as cogent, no position can be shown to be untenable unless it is actually self-contradictory. The sceptic's position can thus be


made secure-but unappealingly vacuous. If the only cogent arguments are deductive arguments, then very few arguments are available either against or for any philosophical position. Any substantial thesis is one which makes some claim, and which can therefore be denied without self-contradiction. So, in the absence of some self-evident principle which can serve as an indisputable premiss, no substantial philosophical thesis can be refuted or established by argument. Argument, on the sceptic's view, becomes irrelevant to philosophy. The sceptic cannot be argued out of his position; but equally nobody else can. Hume's disciple is impregnable in his unbelief; but so too is Plantinga in his belief. Once he has shown that there is no inconsistency in Christian theism, the believer has done all he need, or can, do. Any position that can be stated without self-contradiction is tenable, and reason, if it is confined to deductive reason, is powerless to decide between differing positions. If the sceptical thesis be true, not only is there no reason why we should adopt it, but there is no reason why we should not adopt any other position that tickles our fancy.

The claim that only deductive arguments are valid has drawn much strength from the example of mathematics. Mathematics has been taken as a paradigm of rigorous reasoning. Only if we argue more geometrico can we be sure that we are reasoning properly. But the absolute clarity of mathematical argument has become cloudy in the course of this century. A divergence has appeared between a formal definition of deduction in terms of axioms and rules of inference, and an incompletely formalizable notion of deduction in terms of models and intended interpretations. We can capture the spirit of the former in what has come to be known as First-order Logic (or to be more precise, First-order Predicate Calculus with Identity). First-order Logic behaves itself. Theorems can be proved, more geometrico, and each theorem is true under every interpretation of the calculus in which the logical constants have their usual sense; moreover, each formula which is true under every such interpretation is a theorem and can be proved. That is to say First-order Logic is not only sound, but complete. It captures all, and only, those inferences that a computer could be programmed to carry out. But it is not adequate for mathematics. For that, we must


either use Higher-order Logic, as Frege did, or adjoin to Firstorder Logic some extra postulates, for example Peano's five postulates for Elementary Number Theory or Zermelo's and Frankel's axioms for Set Theory. In either of the latter cases the resulting system is incomplete. There are some formulae which are true under the intended interpretations but which cannot be proved and are not theorems. A comparable result ensues if we follow Frege, and ground mathematics in Higher-order Logic. In that case we do not have to adjoin extra postulates, and we escape certain other infelicities of First-order Logic, but find that our Higher-order Logic is not completely axiomatizable: we cannot formulate a set of axioms and rules of inference which will be sufficient to prove all and only those formulae that are true under the intended interpretations of the system. Either the axiomatization will not be sound-we shall be able to prove as theorems formulae which are not true under all intended interpretations-or it will not be complete-some formulae which are true cannot be proved as theorems in that axiomatization. It is reasonable to discern in the history of mathematics a succession of principles being recognized as true although not deducible from hitherto established axioms: for example, the principle of mathematical induction, the axiom of choice, the continuum hypothesis, the generalized continuum hypothesis. How exactly we recognize these as true is a matter of great dispute. G6del himself was a Platonist, but few mathematicians are happy with Plato's perceptual metaphor. It is, perhaps, better to say that we establish them by reason, but if so not by a formal proof-sequence. Either we give a formalist account of deductive argument in terms of formal rules of inference finitely formulated and unambiguously applied, in which case mathematics is not entirely deductive, or mathematics is a deductive discipline, but deduction is not finitely axiomatizable. If the sceptic takes the former course, he is not letting himself in for much in allowing deductive inference as a cogent form of argument, but he is obliged to be sceptical about even the widely accepted propositions of mathematics. If the sceptic takes the latter course he can avoid having to profess unconvincing doubts about mathematic truths, but he is no longer able to be confident that he has not landed himself with more than he bargained for.


Few sceptics confine themselves rigorously to deductive argument alone. Most, including Hume in some of his moods, acknowledge inductive inference too. But it is unclear what the bounds of inductive reasoning are. If all the swans I have ever seen or heard about are white, it is plausible to infer that the next swan I see will be white too. This is a paradigm minimal inductive inference, which Hume tried to explain in terms of a conditioned reflex, and many philosophers would allow as valid. But if it is in these circumstances rational to conclude that the next swan I see will be white, it is rational also to conclude that the next one after that will be white, and the next again, and so by similar reasoning that every swan is white. The latter proposition, however, is of a different logical form, and instead of arguing from particular propositions to particular propositions we are arguing from particular to general. Such arguments are commonly accepted as inductive, but they are of a significantly different form. `The next swan is white' is not only a particular proposition, but a tensed one. `Every swan is white', or, equivalently, `All swans are white', is not only general, but senseless; we can infer from `Every swan is white' and `Leda was a swan' the conclusion that `Leda was white'. Such an inference would not be valid if the `is' of the first premiss were a present-tense `is'. It is, rather, an omnitemporal use of the verb `to be' which is put into the present for lack of a better tense to put it into. Such a use of the present tense is sometimes indicated, following a suggestion of J. J. C. Smart, by italics. So we write `Every swan is white' or `All swans are white' to indicate that the grammatically present tense is being used in a logically senseless way. Such a use is entirely unobjectionable. But it heightens the profile of induction. Induction does not merely argue from particular to particular in the ordinary tensed indicative mood to general in a different, senseless mood. The mood is clearly different, not only because it does not conjugate like the ordinary indicative mood, but because it yields counterfactual propositions, such as `If Zoe were a swan, she would be white', which the ordinary indicative mood does not. It then becomes difficult to disallow, as also a species of inductive inference, arguments from actual instances to natural laws and from observed phenomena to unobserved entities. We


argue from the regular whiteness of swans to a rule that they must be white, and from white appearances to a genetic make-up that accounts for them. Such inferences, although rejected by Hume, have commanded themselves to scientists ever since. We seek generality, integration, unification, and explanation in our account of the world, and it seems reasonable so to seek. Although quarks, psi-functions, and wavicles all transcend the bounds of possible experience, we form some sort of concept of them, and succeed in saying things about them which can be significantly affirmed or denied. Nobody makes out that Special Relativity, General Relativity, and Quantum Mechanics are plain sailing. They are difficult, and it is easy to be confused and talk nonsense about them. But it does not follow that rational argument about science is impossible, or that reason must acknowledge that such knowledge is too high for it, and it cannot attain unto it. The arguments Hume put forward for ruling out altogether knowledge of unobserved entities or explanations of the universe as a whole, would, if they were cogent, rule out all sub-atomic physics and cosmology. But, while many thinkers fear-or hope-that they are cogent when deployed against natural theology, few seriously suppose they cast any aspersions on the reputability of modern science.

The transition from minimal inductive inference to more general and generous types of inductive inferences may be resisted. It would be reasonable to reckon that the next lottery ticket I encounter, and indeed any particular lottery ticket I consider, will fail to win a prize, and yet it would be false to conclude that every lottery ticket will. The next raven I meet will be black, and likewise the next after that, and the next, and the next, but no biologist familiar with the phenomenon of albinism would dare claim that all ravens are black; and if there can be albino ravens, it would be prudent to reckon with the possibility of non-albino swans. Hydrogen atoms with atomic number I (i.e. protium atoms) have been observed to be very stable, and it would be foolish to take at all seriously the possibility that the next, or that any particular one will decay spontaneously: but shall we then conclude that none ever will? That would be foolhardy indeed. A general proposition, beginning with the words `All' or `None', extends far, far


further than any particular proposition does, and is therefore exposed to a far greater risk of being falsified, so that a canny man should play cautious, and refuse to move from the relatively safe ground of particular predictions to the much more dangerous terrain of generalization.

But it is difficult to be consistently cautious. The very examples cited depend for their plausibility on the prior acceptance of the calculus of probabilities and the general canons of inductive inference. Granted these, we can construct counter-examples to the generalizing policy, just as Bertrand Russell did with the Michaelmas goose. An inductive inference always can---in the deductive logical sense of `can'---prove mistaken, and once the principle of inductive reasoning is established, we develop much more subtle rules of application: and then it will be possible to devise special cases in which, granted some generalizations already accepted, the rationality of the one inference would not establish the rationality of the other. But we are concerned only with scepticism about principles, and if we can in principle always argue to any particular swan's being white we can in principle argue also to every swan's being white. For no counter-example is possible, granted the validity of minimal inductive inference. If it were not the case that every swan was white, then there would be some swan which was not white. And yet for this swan the minimal inductive inference applies, and shows that it is white. And hence the argument from Any to All holds, and the minimal inductivist is led to allow, as also valid, inductive generalization.

Some residual discomforts remain. They are due in part to an unclarity about the nature of inductive inference and the ways it can be justified, as well as to a special, logician's reluctance to concede the validity of the inference from Any to All. Some justifications of induction have been in terms of Confirmation Theory, and we often say that inductive inferences are `merely probable' to distinguish them from deductive ones. And then, if there is a finite probability of any particular instance of a prepositional function being false, the probability of their all being true is small indeed. But Confirmation Theory is not the only way of justifying induction, and it is in fact dubiously applicable to most inductive inferences, and the



sense in which it is only probable and not absolutely certain that the sun will rise tomorrow is very different from that used in the calculus of probabilities. Moreover, even in the natural sciences, our generalizations are not quite as hard as logicians make out, and can tolerate the occasional anomaly or `sport'. In human affairs we are very ready to say, with Aristotle, that generalizations hold only for the most part, only hos epi to polu, and the sciences are much more exacting than that. But they are not absolutely exact, and the occasional monstrous birth, and even the one-oft spontaneous disintegration of an atom of protium, would not actually falsify a sufficiently well-confirmed generalization.

The sceptic who allows minimal inductive inferences but balks at inductive generalisations is difficult to argue with because we often justify minimal inductive inferences by appeal to some principle of generalization, some law of the uniformity of nature, rather than vice versa. We are inclined to say to him `You cannot justify minimal inductive inferences unless you have already accepted inductive generalization', but although many justifications of minimal inductive inference presuppose the validity of inductive generalization, it is not true that all do. And in any case the sceptic may refuse to justify, and simply say, like Hume, that minimal inductive inference is a habit he has happened to form, and he sees no need either to justify it or to extend it.

Some such line can be held-just-but is, once again, unappealing. The argument from Any to All can be resisted without full-blooded inconsistency. I can, in some systems of formal logic, prove that for each number a property can hold of it, and yet prove also that it does not hold for all. Such systems are not full-bloodedly inconsistent, but, rather, 0)inconsistent. And formal systems can likewise be w-incompletc. But these are defects of particular formal systems, not merits in a serious logician seriously concerned to know the truth. A sceptic who did not mind being convicted of something like w-inconsistency or (o-incompleteness could not be proved to be inconsistent or inadequate in any more straightforward sense. But the onus is on him to show why the bounds of reason should be drawn at just this implausible place, rather than on us to show that they cannot be. After all,


we do naturally and normally accept inductive generalizations. Once it is no longer maintained that no non-deductive argument can be valid and it is allowed that some sort of inductive arguments-minimal inductive inferences-are valid, then some reason is required to justify the claim that these alone among inductive arguments, and no others, are valid. And no such reason is forthcoming.

Once it is recognized that inductive inferences can lead from a tensed `was' to a senseless `is' or `be', it becomes hard to maintain as a matter of logical principle that we cannot derive an `ought' from an `is'. We may not be able to deduce an `ought' from an `is'---any more than we can deduce a `will be' from a `was'---if we take care to define our `ought's and `is's carefully enough. But it is a very evident fact that we do argue about morals, and pass judgement on what we ought to do and ought to have done. To claim that we cannot do, or cannot properly do, what we do do needs arguing for. And, as we have seen, such arguments cannot be available, in as much as they would have to be based on some sort of `is'---facts (perhaps metaphysical facts)---and would lead to some sort of `oughts'---values, norms, precepts (perhaps logical `oughts' or logical `ought nots').

Moral arguments in particular and practical arguments in general differ from deductive and inductive arguments in that they have much weaker canons of relevance. Questions about mathematics and natural science are `academic'. They do not have to be decided. If we cannot produce a cogent deductive or inductive argument, we suspend judgement. We do not have to decide whether Goldbach's conjecture is true, or whether Quantum Mechanics is complete. Much as we may want to know the answers to these questions, if we cannot obtain one according to the relevant criteria, we may simply have to say that we do not know. We can afford to be choosy about what counts as a mathematical or scientific argument because we always have the option of not reaching a conclusion. It is otherwise in practical life. Decisions have to be taken. Not to decide is in effect to take a particular decision. The option of suspending judgement is not open. Our information may be imperfect, our reasoning ill-considered, but we must do the best we can in the time available and in the light


of what we know at the time. Practical reasoning is thus messy, and especially moral reasoning, which has a certain ultimacy about it that precludes complications being ruled out by custom, convention, or fiat. The messiness of practical reason shows up especially in the two-sidedness of the arguments, some being for and others against a particular decision. Two-sidedness is not peculiar to practical reasoning. It is vestigially present in inductive argument-no matter how many white swans I have seen, if I have seen a black one, that constitutes a decisive argument against the claim that all swans are white. It is none the less in practical argument that two-sidedness is dominant. Almost all practical arguments have two sides, and we have to weigh them and strike a balance between them. Our decision will depend not only on the strength of the arguments on one side, but on the weakness of those on the other. Many arguments are cogent in the absence of counter-considerations, and we often state them explicitly with this proviso, `other things being equal', ceteris paribus, `in the absence of special circumstances', `as a general rule', hos epi to polu. The logic of practical reasoning is not one of incontrovertible proof-sequences but of prima-facie arguments and counter-arguments, of rebuttals and objections, of exceptional circumstances and special cases; and the fundamental connective is not `therefore' but `but'.

The two-sidedness of practical reasoning not only imposes a dialectical structure on our deliberations but gives a key to our knowledge of other minds and our understanding of the humanities. Besides making up my mind about what I shall do, I can consider what I should do if circumstances were different; and although in the present circumstances I must override and reject some considerations in accepting and acting on others, I can fully appreciate how I might in other circumstances act on them, and so I can appreciate also how you in your circumstances might act on them. Because I know what I shall do in the actual situation, I can know what I should do in hypothetical situations, and so understand what I might do if I were you. Empathy is possible because I experience in my own deliberation the conflict of argument and feel the force of factors inclining me to act in various ways.


I never have murdered any of my colleagues or pupils: fortunately the sixth commandment has always retained sufficient sanctity in my eyes to restrain me; but I have been tempted, and so can understand the minds of those who have found the temptation irresistible. Equally I can enter into the minds of historical agents or those portrayed in literature, and although sometimes their reasoning and reactions will be entirely opaque to me, often there will be enough resemblance between their situation and my actual or possible deliberations for their response to be one of which I can see the rationality. I do not have to suppose, counterfactually and sometimes implausibly, that I would in the event respond in the same way, but only that I might-only that there would be some reasons for so acting, in the absence of weightier considerations against. And that supposition is one that is much easier to make. I can understand what makes other people tick because of the many-sidedness of what goes on in making up my own mind. The messiness of practical reasoning, and the many decisions it partially leads me to take, gives me a width of understanding I could never otherwise obtain, and a partial entrée into the minds of all sorts and conditions of men far beyond my actual ken.

Theological reasoning, as Mitchell has persuasively argued, has the two-sided structure typical of practical reasoning in the humanities. That is only to be expected. For one thing, it carries moral consequences. If God exists, it matters what we do, and if God is a God of Love, our response should be a response of love too. And, secondly, if theism is true, the fundamental category of the universe is personal, and the fundamental category of reason should therefore be personal reasoning. Although the sciences are useful to the Christian apologist as a shield against Hume's scepticism, they do not provide perfect paradigms of theological reasoning. History and literary criticism offer better parallels. The theologian should not expect to prove his case with the conclusive finality of a chemist or physicist, but having put it forward more tentatively after the manner of a critic offering an interpretation of, say, King Lear, should consider possible objections and how they may be countered, and only then, in the absence of sustainable objections, come down in favour of his interpretation.


It is a matter of sic et non rather than of definitive proof. But although in this way theological reasoning has fewer resources for compelling assent than has mathematical or scientific reasoning, it has a wider range of reasons that may win acceptance. The theologian can press much harder the question `What is the alternative?' Although any decision he takes about the nature of the whole universe is taken under conditions of imperfect information, and so is one that always could conceivably, and sometimes more than conceivably, be wrong, it is a decision he has to take, since the way he is to live his life depends on it, and life cannot be postponed. The Either/Or of practical decision-making extends backwards into the way in which the world is to be viewed, and the theologian is entitled to adduce in favour of his world-view not only direct arguments for but also arguments against the available alternatives. If the only alternative to Christian theism is some form of materialism, and no form of materialism can adequately account for consciousness, conscience, rationality, or the thirst for truth, then the rational unappealingness of materialism is to that extent a consideration in favour of theism. Of course, we must be careful. It is all too easy to pose the alternatives wrongly, and to engage in theological ping-pong, where both sides are right in what they say against each other, but wrong in assuming that theirs are the only alternatives. It is important, but difficult, to identify what the alternative world-views that are seriously available really are. But these are difficulties in practice, not insuperable difficulties in principle. In principle theological reasoning is not ruled out, and is likely to have the two-sided, dialectical character typical of practical argument and reasoning in the humanities, in which we seek out and meet objections, weigh considerations, and are guided by the cumulative weight of the arguments on either side.

Reason is much less circumscribed than Hume or Kant supposed. There are no good arguments for supposing that we cannot reason about religion, or that statements of theology lack cognitive status. Nevertheless, we should be wary of too extreme a rationalism. Although human beings are rational agents, each has a mind of his own which he has to make up for himself and which he is capable of making up differently


from other people. Although we share a common rationality, and can very largely agree on what constitutes reasons for or against some course of action, we often disagree exactly how the balance is to be struck between conflicting reasons. Nor is it evidently the case that there is always only one right decision. Different people may differ in their assessment of the weight of argument on either side without either being definitely wrong. The hard guidelines of the Decalogue and Christian morality are relatively few, and leave much scope for the Christian to do his own thing in his own inimitable, but recognizably Christian, way. It is the same with God. If God is personal, he is rational, but not merely rational. Hence the sense of his hiddenness and inscrutability, from which in turn stems the need for revelation. It is characteristic of persons to be not rationally transparent but to have some privacy of intention and some privacy of thought. I cannot tell what you are going to do until you have made up your mind, and avowed your intention. So too with God. We cannot see through him, but must wait on his choosing to share his thoughts with us, and show us what he has in mind. Reason is not opposed to revelation, but requires it to complete our knowledge of a rational, but personal, God we are led by reason to believe in. Instead of being led, as was supposed, to the conclusion that we must abolish knowledge to make room for faith, we are being shown that the God of the philosophers cannot be just the God of the philosophers but must be also the God of Abraham, Isaac, and Jacob, and the Father of Jesus.