The argument I am about to deploy is based on an analysis of the nature and implications of ‘the contradictory’; for it is with myself a conviction of long standing that save through such analysis there is no gateway to sound metaphysical construction. The full grounds for this conviction cannot of course be made apparent in advance of the analysis itself but this much may be said at once. Whatever more specific criteria the intellect may from time to time accept in its endeavours to know the real there is one general and over-riding criterion from which its allegiance can at no point be withheld viz. ‘non-contradiction’. An ‘object’ that is self-contradictory in the sense that the characters we ascribe to it in our conception of it contradict one another cannot as so conceived be accepted by thought as the reality it is seeking to know. It goes without saying that pending analysis of the nature of contradiction the mere knowledge that what is real has the formal character of non-contradiction is of very little account. But I shall try to persuade you that when the nature of the contradictory is correctly elucidated certain conclusions of the utmost importance follow about the nature of a reality which whatever else it may be must be assumed to be at least such that it does not contradict itself.

2. I want to begin however with some discussion (though I shall keep it within the briefest possible limits) of the status of what is traditionally known as ‘the Law of Contradiction’ (or the ‘Law of Non-contradiction’—which expression is used is merely a matter of point of view). Is it really a ‘law’ and if so what kind of a law? Wherein resides its authority as law? And if a law is it a law of thought only or also a law of things? The present state in philosophy makes it imperative that I should define at the outset as clearly as I can and offer some justification of my position in these matters.

Now in actual practice (whatever a man may be driven to say in defending a theory) everyone agrees in rejecting as false a proposition which he believes to involve self-contradiction. The ‘Law’ of contradiction is one whose authority is accepted in all thinking and in that sense is an ultimate for human thought. But just because it is ‘ultimate’ for thought thought cannot ‘prove’ its validity if by ‘proof’ we mean deductive demonstration from some principle more ultimate than itself. Manifestly any reasoning directed to its proof must presuppose the very principle it is purporting to prove. And there are some who would have us suppose that the validity of the principle is rendered doubtful by its not being amenable to this formal kind of proof.

It would surely be foolish however to limit the term ‘proof’ to deductive demonstration. If complete and final theoretic satisfaction that a principle is true can be gained in other ways it is a little pedantic to refuse to call that ‘proof’. And such complete and final theoretic satisfaction about the validity of the principle of contradiction as a law of thought does seem to me to be easily gained. If we make the appropriate ideal experiment we shall find that to ‘think’ a contradiction is strictly and literally not even possible. This anyone may verify for himself if he takes the principle in one of its better formulations—say ‘S cannot both be P and not be P’ and tries to think in defiance of this principle S as both being P and not being P. Attempt this and what do you find? You find do you not that you just have no determinate thought about S at all. The expression ‘Laws of Thought’ I am well aware is one which (like some other useful expressions) is taboo in certain quarters today. But it is surely hard to see how more fittingly—indeed how otherwise—to designate a principle which all thinking accepts as authoritative upon it and which in fact it cannot disobey without ceasing to be thinking.

These last words however introduce us to something of an aporia. We are saying apparently that there is no such thing as self-contradictory thinking. But in that case the Law of Contradiction must be merely a positive law descriptive of human thinking not a normative law formulating an ideal. There could be no sense in exhorting anyone to try to avoid contradiction in his thinking if in fact he cannot contrive to think a contradiction at all. Yet it is obvious that we do constantly condemn thinking in ourselves and in others that is as we say ‘self-contradictory’; and this practice is surely not without solid foundation. How is the paradox to be resolved? What justification can be offered for calling any thinking self-contradictory if there cannot in fact be a thinking of S as both being P and not being P?

I think two main types of case can be distinguished in which we can quite properly call the thinking involved self-contradictory even though it is not strictly a thinking of S as both being and not being P. The simplest type of case is where in the course of a longish argument (which may of course be conducted entirely within one's own mind) one forgets that one has previously recognised S to be P and now asserts that S is not P. But manifestly what we have here is not an act of thought that contradicts itself but two acts of thought an earlier and a later that contradict one another. It is natural however to call this ‘self-contradiction’ since we assume it to be one and the same self who thought the past thought and who thinks the present thought that contradicts it.

A less simple but correspondingly more insidious and certainly much commoner way of contradicting ourselves is as follows. We assert that S is P and that it is also Q failing to notice that at another point in our argument we have already agreed that Q directly or indirectly entails the exclusion of P. Our opponent will then be in a position to point out that in asserting S to be P and also to be Q we are really involved in asserting S both to be P and not to be P—a self-contradiction. Against this type of self-contradiction we are all of us aware that we have constantly to be on our guard. But here again it is evident that our thinking though legitimately enough called self-contradictory involves no act of thought in which we accept S as both being P and not being P. On the contrary as soon as we are reminded that Q entails the exclusion of P and that to assert that S is P and that S is also Q involves us in asserting that S both is and is not P we straightway either abandon our original assertion or reconsider the entailments we had already perhaps too hurriedly admitted.

Enough has been said I hope to show that there is only a seeming not a real incompatibility between saying that men frequently fall into self-contradiction in their thoughts and saying that the Law of Contradiction is a law which thinking cannot disobey without ceasing to be thinking at all. We may now observe that if the Law must be so understood this disposes completely of what seems to me one of the least defensible among recent philosophical innovations—the doctrine that all logical laws including the law of contradiction are mere ‘conventions’. According to our argument above a man cannot not accept the principle of contradiction if he is to think at all. But where we have a principle which we have literally no choice but to accept to talk of that principle as a ‘convention’ is nonsense. Acceptance of it is a matter of necessity not convention. As Aristotle pointed out a long time ago ‘a principle which everyone must have who understands anything that is is not a hypothesis.’¹

Just as obviously untenable it seems to me is the view still advanced on occasion that though the Law of Contradiction may be a law of thought we are not entitled to assume that it is also a law of things holding good of ‘reality’. This view if sound would of course be fatal to the ultimate objective of the present lecture. But it is surely open to decisive rebuttal. If once we admit that we cannot think S both to be and not to be P i.e. that Contradiction is a law of thought must it not be mere verbiage to say that nevertheless S might in reality both be and not be P—i.e. that Contradiction may not be a law of things? For by our own admission the ‘hypothesis’ we are putting forward that in reality S both is and is not P is one which we cannot think. Its formulation can only be (at its crucial point) a matter of words. It seems to me clear therefore that this logical law and other logical laws (if such there be) of like status are unavoidably metaphysical as well as logical in their import.

I conclude that the Law of Contradiction is a genuine ‘law’ an ultimate law and a law both of thought and reality. And let me add that if I have not debated these matters extensively this is less for lack of space than because the traditional arguments for the conclusions I accept have nowhere to my knowledge been met but would appear rather to have been simply forgotten by those contemporary philosophers who explicitly or by implication accept contrary views. It is not easy to know what sort of supplementation of them would be useful until their defects as ordinarily presented are clearly exposed. Here—as I am afraid rather often elsewhere in these lectures—I find myself embarrassed by what one can only describe as the virtual obliteration from the contemporary philosophical mind of a whole philosophical tradition. I may very well be mistaken in my belief that many elements of value can still be recaptured from that tradition. I do not think I am mistaken in my belief that secure advances in philosophy are unlikely to be made if one simply averts one's gaze from a movement of philosophic thought which for several decades in a by no means remote past commanded the allegiance of almost all the leading philosophers in the English-speaking world.

3. It is one thing however to see that the Law of Contradiction is a genuine ‘law’ is an ultimate law and is a law both of thought and of things. It is quite another thing to see what precisely it is that constitutes contradiction. This latter task to which we must now address ourselves is in fact about as difficult as the former task was easy. As was pointed out by F. H. Bradley (whose account in Note A of the Appendix to Appearance and Reality I shall be following very closely in the early part of this lecture) it is surprisingly hard to avoid a petitio principii when one attempts to define contradiction. Everyone agrees that contradictory propositions cannot both be true. But when one asks what it is that makes propositions contradictory what is the essential nature of contradiction itself almost all the stock answers seem covertly to presuppose the very thing that is to be defined.

Consider for example the common suggestion (which has many variants of detail) that contradiction can be defined as the uniting of ‘opposite’ predicates in the same subject. Immediately the question forces itself upon us what is to be meant here by ‘opposites’? And on reflection it is difficult to give any answer save that opposite predicates are predicates whose union in the same subject we find that thought rejects. But then is this not just another way of saying ‘predicates whose union in the same subject thought finds to be contradictory’? Are we not in effect defining the concept of opposition in terms of the contradictory and then using the concept of opposition in order to define the contradictory—a circular procedure which gets us nowhere? If we are to define contradiction without circularity clearly we must seek an answer to the prior question what sort of union of predicates in the same subject does thought find itself obliged to reject?

The trouble is however that if we may not use ‘opposition’ or any equivalent term in order to designate the kind of predicates whose union in the same subject thought rejects it is not at all easy to see what terms we can use to designate it. It certainly does not look as though it would do simply to replace the term ‘opposition’ by the term ‘difference’ and to say that thought rejects the union of differences in the same subject. For thought is uniting differences constantly; indeed where it does not do so it appears to be reduced to sheer tautologising which is not thinking at all.

Now it is just at this point that Bradley makes his distinctive and (as I think) decisive contribution to the problem of what constitutes contradiction. Beyond a doubt he agrees thought requires the uniting of differences for its very life. But it does not follow that thought is prepared to accept a union of differents irrespective of the manner of their union. ‘Thought demands’ Bradley reminds us ‘to go proprio motu or what is the same thing with a ground or reason.’² A merely external union of differences (such as we get in sense perception where the togetherness of certain differents seems given to us from without) is not in the end acceptable to thought. It is of the very essence of thought to seek some ground for their union; and so long as no adequate ground is discoverable intellectual dissatisfaction persists. A bare conjunction of differents unmediated by any ground thought rejects as alien to its nature as ‘irrational’. Here then Bradley argues is the sort of union in the same subject that thought rejects and here by the same token we find our answer to the question of what constitutes contradiction. Contradiction consists in uniting differences simply in and as a bare conjunction. What the concrete nature of the differences happens to be is not of the essence of the matter. The crucial point is that thought cannot qua thought accept their union unless it conceives some actual or possible ground for their union.

One can hardly exaggerate the extent to which the course of Bradley's thought throughout all its well-known sceptical ramifications is determined by the analysis of contradiction here briefly sketched. It is profoundly unfortunate therefore that this analysis should have been almost consistently ignored by Bradley's critics. Time and again criticisms are launched against Bradleian doctrines which betray failure to grasp that underlying the positions criticised is Bradley's theory of what constitutes a contradiction. It may be instructive to consider briefly an outstanding example both for its own sake and because it may help to throw into relief what is central in Bradley's analysis of contradiction.³

I refer to the common but surely mistaken charge that the difficulties Bradley notoriously finds in the judgment-form are due to his confusing the ‘is’ of predication with the ‘is’ of identity. It is merely this confusion the critics allege that leads him to impute self-contradiction to the judgment-form ‘S is P’. If one chooses to commit Bradley's mistake of interpreting the ‘is’ of predication as though it were the ‘is’ of identity then of course we are told one will find contradiction in the judgment-form; for no one denies that it is contradictory to identify S with P—or with any other not-S. But one has only to refrain from falling into this elementary logical blunder (so it is said) for the alleged contradiction to vanish utterly.

Now it would be extremely odd if a great logician had really gone blindly on repeating the same elementary logical blunder for a full forty years of active philosophising; and all the more odd where that logician's critics have been so good as to indicate to him the error of his ways not once but many times. The real oddity in the situation however is I suggest the unanimity with which Bradley's critics have missed his point. It will presumably be agreed that on any theory the ‘is’ of predication implies that the differences S and P are at least being united or combined in thought. The distinctive point that Bradley is concerned to make when he imputes contradiction to the judgment-form as ordinarily represented is that to unite differences without any conceived or implied ground for their union—to unite bare S with P as the formula S is P suggests—is unacceptable to reflective thought and is therefore (on his view of what constitutes contradiction) a contradiction. In other words he does not assume that the ‘is’ of predication means identity. He assumes like everyone else that it means at least union; and he insists that thought can no more accept a bare union of differents than it can accept their identity. Indeed the bare union of differents turns out when we reflect upon it to be tantamount to their identification. ‘It is idle’ Bradley tells us ‘from the outside to say to thought “Well unite but do not identify.” How can thought unite except so far as in itself it has a mode of union? To unite without an internal ground of connection and distinction is to strive to bring together barely in the same point and that is self-contradiction.’⁴

Some further clarification of this doctrine of the contradictory—and also I think important justification—may be gained if we comment now upon an objection from the side of ‘Common Sense’ (to which of course most philosophers appeal eagerly when it seems to support them). ‘You speak very freely’ it may be said ‘of thought rejecting a bare conjunction and thought being dissatisfied with any union of differences that rests on no “ground”. But what is this thought of which you speak? It can hardly be thinking in general for does not ordinary thinking constantly accept without a qualm bare conjunctions of differents?—e.g. in the realm of sense-perception to which you have yourself alluded. Your analysis of contradiction seems to rest entirely on the dogmatic assertion that “thought” rejects what common-sense observation shows us “thought” has often no compunction whatever in accepting.’

But I think there is no real difficulty of principle here. Everyone will agree I take it that much of our ordinary thinking is carried on with no pretence at self-criticism by strict intellectual standards; and will agree also that this uncritical thinking often fails to notice contradictions that are apparent enough to critical thinking. In other words critical thinking often finds itself obliged to reject what uncritical thinking accepts ‘without a qualm’. Now when we spoke above of thought rejecting ‘bare conjunctions of differents’ it was of course (as was surely legitimate) critical thought we had in mind thought that is going about its proper business of seeking theoretical satisfaction. Undoubtedly the demands that are intrinsic to the intellect are much obscured from us in ordinary experience since there our thinking is guided primarily not by the motive of theoretic satisfaction but rather by the needs of practical living; and we are normally content to stop at the point where these needs seem adequately met. But thought's intrinsic demand for a ‘ground’ is surely plain enough in those activities of thought such as science and philosophy in which the theoretic interest dominates; in which truth not practical convenience is our goal and in which therefore if anywhere we might expect to discover the authentic nature of the intellect's demands. In science and philosophy ‘brute facts’ ‘bare conjunctions of differents’ are not just ‘accepted’. On the contrary intellectual unrest persists so long as we see no way to deliver them from so ‘irrational’ a status. ‘Brute facts’ are for science and philosophy problems: problems not solved to our satisfaction until we have mediated the ‘bare conjunction’ through what appears to us an adequate ‘ground’. Just as ‘Nature abhors a vacuum’ so ‘the intellect abhors a bare conjunction’.

Before proceeding to the next phase of the argument from the nature of the contradictory it may be well to pause for a moment to observe the implications for metaphysics of the argument at its present stage.

Metaphysics we assume seeks conceptual knowledge of the ultimate nature of the real; and conceptions of this real we may further assume cannot be knowledge (since they cannot be true) if they are self-contradictory. Now self-contradiction we argued (following Bradley) consists in uniting differences without a ground for their union. If then any object before the mind is such that as conceived it involves the uniting of differences without a ground for their union that object as conceived is not a reality. The form in which we conceive it may serve well enough for all the practical purposes of ordinary life. But metaphysics is concerned with ultimate truth not with mere pragmatic validity. From the standpoint of metaphysics accordingly objects as so conceived stand condemned. They are ways in which the real appears to us; but as it so appears it appears falsely; the appearances are in that sense ‘mere’ appearances.

4. But can thought ever get its objects into a satisfactory form a form in which the differences are intelligibly united? This brings us to the second main phase of the argument. There is no great difficulty in seeing how in general thought proceeds in its endeavour to secure grounds which will make the union of differents intelligible. If we take our clue from the way in which those disciplines in which the theoretical interest predominates viz. philosophy and the sciences pursue their objective the key-word it seems clear is ‘system’. Reflective thought aims at exhibiting the differences A and B whose apparent connection sets the problem as no longer separate ‘units’ but as distinguishable members of the same system X the structural principles of which are such that given A we necessarily have B and given B we necessarily have A. The ground of the connection or union lies in the system to which the differences belong; and the ground is adequate one which really does ‘explain’ or render intelligible the connection if the system can be seen to be one in which A and B really are mutually implicatory members. But the question arises is a ground that is adequate capable of attainment even in principle by the human intellect? Bradley is convinced that it is not: and I believe him to be right.

The argument which (in this context) Bradley advances for his sceptical conclusion is simple enough in form. In the nature of the case any ‘ground’ to which the intellect can appeal must be something beyond and thus at least partly external to the complex of differences it is to explain. For if it lay within the complex before us the complex would be self-explanatory and would set us no problem. But if the ground is in any way external to the complex then it ‘becomes for the intellect a fresh element and it itself calls for synthesis in a fresh point of unity. But hereon because in the intellect no intrinsic connections were found ensues the infinite process.’⁵ There can be for the intellect no final halting-place. Every achievement of a ground is in the nature of the case the basis of a further problem.

An example even if a rather rough and ready one will I think be helpful to elucidate this ascription of radical and inherent defect to the ‘grounds’ by which the intellect seeks to make unions of differents intelligible. Suppose we find the sliding roof of our car jamming in hot weather. We want to understand to explain to ourselves the S-P connection in the proposition that is here implied. Our first ‘solution’ will doubtless be that since the roof and the car body are of metal and since metals expand under the influence of heat the adjacent sections of roof and body will necessarily when the weather is hot tend to approach one another and at a certain degree of heat to jam. And with this answer our intellect undoubtedly achieves a partial satisfaction. But only partial. The core of the explanation the ‘ground’ is the expansion of metals under the influence of heat. But this introduces ‘a fresh element’ calling for ‘synthesis in a fresh point of unity’. The proposition ‘all metals expand under the influence of heat’ is one in which the union of differents S and P is no more self-explanatory than the union of differents in the proposition ‘The sliding roof of our car jams in hot weather’. The intellect is obliged therefore to ask why to look for some ground for this new connection; and obviously it has not secured a satisfactory ground for the first connection to be explained if it has not secured a satisfactory ground for this second connection in terms of which it sought to explain the first. Our problem has now become why do metals expand when heated? And at this stage a ground in terms of traditional physical science is still easily enough available. Heat is a form of energy we may remind ourselves and in proportion as a body becomes ‘hotter’ the motions of the constituent molecules increase in violence and tend by their jostling of one another to disturb the existing cohesion and to create a ‘bulging’ beyond the normal boundaries—i.e. the body expands. With this answer again the intellect attains a partial but only a partial satisfaction. However well-accredited there is nothing self-evident about the propositions implied in our new ground. Why e.g. should one moving body (say a molecule) impinging upon another moving body (another molecule) affect the motion of the second body in this way—or indeed in any way? A vast multitude of observed facts can be pointed to in support of such generalisations but it is a philosophical commonplace that they do not and cannot make the connections intrinsically intelligible. It remains entirely conceivable that a case should arise in which the connection in question does not hold. Hence the intellect is forced once more to ask why to search for a ‘ground’ for this new union of differents. By this stage we are coming within the region of basic laws of the traditional physics and there is perhaps little to be gained by carrying the illustration further. The result will be the same however far we take it. Neither the primary laws of motion nor any ‘paramechanical’ laws to which more recent scientific achievements may allow us to appeal have the status of self-evident truths propositions in which subject and predicate are united in a way that satisfies the intellect. In the course of our search after grounds we acquire a deeper intellectual satisfaction by seeing the coherence of our original connection with a progressively wider range of connections in the total field of experience. But at every stage the new ground merely sets us at a higher level the same problem that confronted the intellect at the beginning.

Now if this account of the matter be substantially correct as I believe it to be; if every ground for the union of differents achieved by the intellect merely presents us at a higher level with differents united without a ground; then Bradley would seem to be justified in his contention that the human mind is incompetent in principle to know the reality it seeks to know. Any ideal complex by which it seeks to characterise reality no matter how high its degree of systematic coherence will still be a union of differents that requires a ground beyond itself for its intelligibility. Asserted as it stands it contradicts itself: whereas an ideal complex that truly characterises reality must be non-contradictory. There would seem to be one way only in which the intellect can avoid falling into self-contradiction; and it is a way that does not yield truth. The intellect can assert the complex before it not as absolute but as conditioned by unknown factors in the as yet unfathomed ‘background’ of reality; frankly accepting the implication that in the complex as it stands we have not got the real but only an appearance of it ‘less or more false in proportion as the unknown conditions if filled in less or more would swamp and transform it.’⁶

The position then would seem to be as follows. Qua thinking beings we have no alternative but to accept thought's criterion of truth and reality viz. non-contradiction. In the real differences are united and they must be united intelligibly in a way that would satisfy thought. But this ‘way’ cannot be the way of systems of terms in relation the only way the intellect has of setting about its task of uniting differences intelligibly. For any such system we have seen points beyond itself requires a ground partly external to it for its own justification. It follows that we are forced to recognise a radical discrepancy between on the one hand the kind of unity at which the intellect ideally aims and which it can alone accept as giving us reality—viz. a unity in difference in which the ground of the union is in no way external to the differences—and on the other hand the kind of unity which the intellect can alone achieve; a radical discrepancy therefore between reality ‘as it is’ and reality in any form in which the intellect however far it advances proprio motu is able to conceive it. In other words Reality must be held to be supra-rational.

5. We cannot properly proceed however to ask what further conclusions the argument from the nature of the contradictory warrants about the nature of ultimate reality and how these conclusions bear upon the religious view of ultimate reality until we have come to grips with an objection of far greater force and of far greater consequence than any we have so far encountered. The importance of this new objection lies not merely in the threat it carries to the conclusion already reached—that reality is supra-rational. It lies also in the fact that when due account is taken of it it suggests an envisagement of the relationship between finite minds and ultimate reality which has I think very great significance for religion. This objection I shall now formulate and thereafter discuss.

The intellect's demand for a ‘ground’ beyond any given union of differents with the ensuing infinite process arises from the apparent inability of the intellect to find satisfaction in any such union merely as it stands. If in such a union ‘no internal connection of diversity natural to the intellect can be found’ Bradley declares ‘we are left with a diversity belonging to and conjoined in one undistinguished point. And this is contradiction and contradiction in the end we found was this and nothing but this.’⁷ The trouble as Bradley sees it is that the required ‘internal connection’ is nowhere to be discerned—or at any rate that he is himself not able to discern it. ‘I cannot say that to me any principle or principles of diversity in unity are self-evident.’⁸ Hence the intellect's demand for a ground ‘beyond’ any given union remains insatiable. Any union of differents is for the intellect as it stands self-contradictory and thus inadequate to portray the real.

Now though Bradley is unhappily very sparing of examples one gets the impression that it is thinking in the empirical sciences that he has had chiefly in mind. There undoubtedly his case is a very strong one. No one I take it now claims that the unions of differents formulated in science's basic ‘laws’—and a fortiori in its special laws—‘satisfy the intellect’ and provoke no further question. But there are other fields of knowledge in which it is much more difficult to be persuaded that there are not connections which the intellect finds satisfactory as they stand. If it should turn out that there are any such intellectually satisfactory connections then here at any rate the criterion of non-contradiction is fully honoured truth is achieved by the intellect and the doctrine that the real is supra-rational must call for drastic revision.

As an example of the kind of connection that raises difficulties for Bradley's view let us take the judgment made with reference to the space in which objects are perceived that ‘any given space is part of a larger space’. We have here as in all judgments an S and a P that are different from one another and the assertion in thought of their union. Now is there really anything in this union of differents that the intellect finds unsatisfactory and that impels it to seek justification in some ground beyond the complex itself? Do we not have here a union of differents that is intrinsically self-evident to the intellect? If we accept as our test of intrinsic self-evidence that the contradictory of the proposition is inconceivable there are I think strong reasons for answering in the affirmative. For it seems true that we just cannot attach meaning in terms of perception to the suggestion that some given space might not be continuous with space beyond it and thus might not be part of a larger space. Of this ‘continuous’ character of the space of perception we can only say that such is the way we apprehend space and cannot help apprehending it when we are perceiving physical objects. The case here is altogether different in respect of intellectual necessity from that of even the best-accredited physical ‘law’. In the latter it is always possible in principle to suppose the union or connection of differents false. The ‘law’ gets its evidence from a multitude of observations and is subject to revision or even abandonment from further observations. But in the case of the proposition that the space of perception is continuous or that any given space is part of a larger space ‘further observation’ seems irrelevant. The only ‘observations’ to which we seem able to attach meaning are observations conducted within the framework of a space which is continuous in character and thus themselves presuppose the truth of the proposition that is in dispute.

Or again take a proposition from the cognate field of ‘time’. ‘Different times within the time-order in which events are perceived are not simultaneous but successive’ (substantially one of Kant's ‘axioms of time in general’). Is it not the case that here too we see on reflection and for similar reasons that the search for a ‘ground’ for the connection affirmed is completely pointless? To the contradictory of the proposition we can attach no intelligible meaning. The connection is one that is directly implied in the nature of time as we apprehend it and cannot help apprehending it when we perceive events as ‘in time’.

In the face of these apparent instances to the contrary can Bradley really be justified in his contention that every union of differents is as it stands (i.e. as a bare conjunction) intellectually unsatisfactory and therefore if affirmed as it stands a self-contradiction?

Now I am certainly not going to suggest that Bradley would have no answer to give to criticism of his doctrine along such lines. On the contrary I think it is fairly easy to see how if challenged on the matter he would seek to show that even these unions of differents are intellectually unsatisfactory and point beyond themselves for their explanation. I do wish to suggest however that if he had considered such cases explicitly in the context of his discussion of contradiction he would have been forced to recognise an important difference of principle between the ‘intellectual unsatisfactoriness’ of connections of the kind we have just been noticing and the ‘intellectual unsatisfactoriness’ of connections of the kind enunciated in the empirical sciences. With a view to bringing out the precise nature of this difference let us then ask how Bradley might be expected to defend his doctrine against the sort of objection we have been raising.

Bradley would point out I think that we ought to distinguish carefully between what is intellectually incorrigible and what is intellectually satisfactory. It may be granted that such a proposition as ‘The space in which objects are perceived is continuous’ is intellectually incorrigible in that the intellect cannot even conceive the space of perception as otherwise constituted. But that is by no means to say that the proposition is intellectually satisfactory. The proposition is after all (like on the last analysis all propositions)⁹ about reality. It is in a fuller formulation the proposition ‘reality is such that the space in which objects are perceived is continuous’. Now if the words ‘such that’ stand here as they apparently do merely for an unknown x how can we reasonably claim that the union of differents in the proposition is an intellectually satisfactory union? The proposition would be intellectually satisfactory in any final sense only if we could see how reality is such that space has this character. And if it be said ‘Well at any rate even if we don't know how we do know that space is thus’ Bradley's reply would be I think that we do not even know that space is thus. There is no certainty at all that if the reality within which space is but one feature became (per impossibile) fully intelligible to us so that space was apprehended as integrated within a system that is a genuine unity in difference space would then be apprehended to be just as it now appears to us. The presumption is rather the other way. It is more than doubtful whether any member of a truly coherent whole could be the same when apprehended in isolation from that whole as it would be when apprehended in integral relation to it.

6. Is this way of defending the doctrine that there are no connections of differents intrinsically satisfactory to the intellect one that we can accept? Up to a point I think that it is. I think we must admit that a connection is never fully satisfactory to the intellect if it remains at the level of brute fact even if the brute fact be of such a kind that we can see the impossibility of our ever transcending it. It is a perfectly intelligible question and one to which the intellect would like to know the answer (one indeed to which some philosophers as I think mistakenly have sought to give an answer) how space and time stand to the reality within which they fall. We should like to be able to clear up the mystery of the ‘such that’ in propositions of the type ‘Reality is such that space and time are continuous’. But the point I want now to emphasise is as follows. Even if we grant all this to Bradley surely we must go on to recognise that there is nevertheless a profound difference in epistemological status between the ‘intellectual unsatisfactoriness’ of connections which it is in principle possible for the intellect to correct and the ‘intellectual unsatisfactoriness’ of connections like those we have just been discussing where this is not possible in virtue of the fact that all finite thinking presupposes their acceptance? The former are faulty even by the standard of theoretical satisfaction which is concretely attainable by finite thinking. The latter are faulty only by a standard of theoretical satisfaction which finite thinking is in principle incapable of attaining. So strong indeed is the element of intellectual satisfactoriness in propositions of the latter sort propositions which admit of no correction without transcending the very conditions of finite thinking that it would be seriously misleading simply to dub them ‘false’. We require a name for them which will indicate their aspect of intellectual satisfactoriness no less than their aspect of intellectual unsatisfactoriness. We might perhaps best bring out their ambivalent character by calling them ‘phenomenal truths’; or to anticipate the possibility that phenomenal truth admits of degrees ‘final phenomenal truths’.¹⁰

Now to speak of a ‘truth’ that is merely ‘phenomenal’ has I am aware a somewhat paradoxical ring. I am persuaded nevertheless that the human situation is such that we are obliged to recognise two distinct—though of course closely related-kinds of truth noumenal truth and phenomenal truth. ‘Noumenal’ truth pertains to that which would fully and finally satisfy the aspirations of the intellect a union of differences in which the unity and the differences are in no way external to one another. Only differences so united can the intellect accept as giving truth or reality simpliciter. But this ‘noumenal’ truth must remain for the intellect only an ideal though it operates negatively upon the intellect in forcing the relegation of all that falls short of it to the realm of ‘appearance’. ‘Phenomenal’ truth pertains to unions of differents that reach as far as can be reached in the direction of theoretical satisfaction without transcending the conditions of finite thinking as we know it. In some few cases this ‘phenomenal’ truth can be final; in those cases namely where propositions affirm unions of differents that are presupposed in all significant experience and which can thus be said to constitute the basic framework of our human situation. Within that framework however the possibilities of advance in phenomenal truth are limitless. There is as we have seen no end to the process illustrated best by the physical sciences of seeking adequate grounding for connections through more and more comprehensive and coherent systems of terms in relation.

The affinity between noumenal and phenomenal truth—that which justifies us in using the same term ‘truth’ with due qualifications of both of them—lies in their analogous relationship to the intellect's quest for satisfaction. Noumenal truth would yield intellectual satisfaction absolute. Phenomenal truth yields intellectual satisfaction in so far forth as that is positively attainable under the conditions of finite experience.

This affinity so far as I can see is not something which it is open to a man to believe in or to disbelieve in as he thinks fit. It would seem rather to be an affinity which man must believe in if he is to function intellectually at all. For it is surely by something we can only call ‘an inward necessity of the mind’ that our aspiration after intellectual satisfaction after that non-contradictory union of differents in which noumenal truth and reality consist seeks its fulfilment in these progressively more coherent and comprehensive systems of terms in relation in which in its degree phenomenal truth consists? Our finite minds being constituted as they are the ideal of noumenal truth impels us to take the path that leads to phenomenal truth. The affinity in short seems grounded in the very nature of our human condition. It is in a not seriously misleading sense of that term an a priori affinity.

7. Now if this in principle be indeed the nature of the affinity between noumenal and phenomenal truth we can see what promises to be a most interesting parallel beginning to emerge between on the one hand the cognitive attitude towards God which we earlier judged to be appropriate to the religious consciousness and on the other hand the cognitive attitude towards ultimate reality which we now discern to be appropriate to the intellectual consciousness. For the religious consciousness the object of its worship transcends human conception; but by reason of the recognised affinity between the emotions which that object evokes and the ‘natural’ emotions felt towards the highest conceivable exemplifications of ‘power’ and ‘value’ the religious mind is impelled to interpret its object symbolically in terms of the highest conceivable power and value; and because this affinity has nothing subjective or arbitrary about it but is based on ‘an inward necessity of the mind’ this symbolism we argued has objective validity as symbolism. We can even speak significantly it seemed to us of a symbolic ‘knowledge’ of God. For the intellectual consciousness as sanctioned by metaphysics the ultimate reality transcends human conception likewise—is ‘supra-rational’; and because of the recognised affinity between noumenal and phenomenal truth based on ‘an inward necessity of the mind’ there is a like objectively justified impulsion to interpret the perfect union of differences that characterises noumenal truth symbolically in terms of the highest unions of differences attainable along the path to phenomenal truth. Here I suggest we have something more than the bare elements of a rapprochement between metaphysics and religion something that promises a genuine if partial metaphysical corroboration of the objective validity of the religious consciousness. In my next and final lecture I propose to follow up this suggestion; and then gathering together the several strands of the argument of this course I shall try to summarise as clearly as possible the general conclusions which the argument seems to me to warrant concerning ‘the truth of religion’.