Modes of Thought
Lecture Three: Understanding
Alfred North Whitehead
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IN THE TWO FOREGOING LECTURES, Importance and Expression have been discussed. The notion of Understanding is the third of the trilogy, upon which we base our endeavour to analyse the intelligence of mankind. Our quest is to understand Understanding.
I submit to you that in its full extent this is a hopeless task. We can enlighten fragmentary aspects of intelligence. But there is always an understanding beyond our area of comprehension. The reason is that the notion of intelligence in pure abstraction from things understood is a myth. Thus a complete understanding is a perfect grasp of the Universe in its totality. We are finite beings; and such a grasp is denied to us.
This is not to say that there are finite aspects of things which are intrinsically incapable of entering into human knowledge. Whatever exists, is capable of knowledge in respect to the finitude of its connections with the rest of things. In
( 59) other words, we can know anything in some of its perspectives. But the totality of perspectives involves an infinitude beyond finite knowledge. For example, we know about the colour 'green' in some of its perspectives. But what green is capable of in other epochs of the universe, when other laws of nature are reigning, is beyond our present imaginations. And yet there is nothing intrinsically impossible . in the notion that, as years pass, mankind may gain an imaginative insight into some alternative possibility of nature, and may therefore gain understanding of the possibilities of green in other imagined epochs.
There is a rhyme which fits onto the tradition respecting Dr. Whewell, who was Master of Trinity College, Cambridge, about eighty years ago. The rhyme is well-known, and runs thus:
I am Master of this College;
And what I know not, Is not knowledge.
This attitude is always prevalent in the learned world. It sterilizes imaginative thought, and thereby blocks progress.
In our discussion of Understanding, this is the first heresy that I wish to combat. I am not attributing this heresy to Dr. Whewell, although he is said to have exhibited an arrogance, perhaps justified by his very extensive learning. My point
( 60) is that understanding is never a completed static state of mind. It always bears the character of a process of penetration, incomplete and partial. I fully admit that both aspects of understanding enter into our modes of thought. My thesis is that when we realize ourselves as engaged in a process of penetration, we have a fuller self-knowledge than when we feel a completion of the job of intelligence.
Of course in a sense, there is a completion. But it is a completion presupposing relation to some given undefined environment, imposing a perspective and awaiting exploration. Thus we have a large knowledge of the colour 'green'. But this knowledge is limited by the perspective of the present epoch of the Universe. It is relevant to a definite unexplored immensity; and this immensity is only itself to be understood by its relevance to alternative immensities.
Shelley, in a chorus of his dramatic poem 'Hellas', writes
Worlds on worlds are rolling ever
From creation to decay,
Like the bubbles on a river,
Sparkling, bursting, borne away.
Amidst this passage of Creation, Understanding is limited by its finitude. Yet amidst the infinity of things finite, there is nothing finite which is
( 61) intrinsically denied to it. Such ignorance is accidental; and such possibility of knowledge discloses its relevance to unexplored aspects of things known. Any knowledge of the finite always involves a reference to infinitude.
The specialization which is necessary for the development of civilized thought had in the last century a most unfortunate effect on the philosophic outlook of learned people, and thence on the development of institutions for the promotion of learning. The various departments of Universities emphasized their independence of each other. Also a University gained reputation in proportion to its expansion in terms of such subdivision.
As science grew, minds shrank in width of comprehension. The nineteenth century was a period of great achievement, suggestive of an ant-hill. It failed to produce men of learning with a sensitive appreciation of varieties of interest, of varieties of potentiality. It criticized and exploded, where it should have striven to understand. The detailed setting of its interest is, in every age, a crude mixture of depth of understanding and of triviality of setting, when looked at from beyond that age. And yet to understand the nature of existence, we must grasp the essential character of that depth which, beyond all mistaken details, is the mainspring of the as-
( 62) -cent of life discernable in its own age. And here another qualification must be added, namely—If ascent there be.
The very Renaissance itself, of which the last century was the final phase in the agonies of begetting its successor, carried in itself limitations which obstructed the proper expansion of intellectual interest. It was rooted in Greek learning, conceived as the only begetter of civilization. Undoubtedly, the debt of Europe to Greece is beyond words to express. But, after all, Grecian thought, even when expanded into Greek—Hebrew—Egyptian thought, only presents one finite aspect of the many-sided modes of importance which are pressing upon the out-skirts of human consciousness.
We must enlarge our effort at understanding. In the nineteenth century, the Greek scholars were somewhat narrower than the best of the Greeks, the Christian scholars were somewhat narrower than the best of the early Popes, and the men of science were somewhat narrower than the founders of the study of mathematics and of physical science. The nineteenth century in the aggregate knew immeasurably more than the Greeks, and the Popes, and the Founders of science, all put together. But the moderns had lost the sense of vast alternatives, magnificent or hateful, lurking in the background, and awaiting
( 63) to overwhelm our safe little traditions. If civilization is to survive, the expansion of understanding is a prime necessity.
z. What is understanding? How can we characterize it? In the first place, understanding always involves the notion of composition. This notion can enter in one of two ways. If the thing understood be composite, the understanding of it can be in reference to its factors, and to their ways of interweaving so as to form that total thing. This mode of comprehension makes evident why the thing is what it is.
The second mode of understanding is to treat the thing as a unity, whether or no it be capable of analysis, and to obtain evidence as to its capacity for affecting its environment. The first mode may be called the internal understanding, and the second mode is the external understanding.
But this phraseology tells only part of the tale. The two modes are reciprocal: either presupposes the other. The first mode conceives the thing as an outcome, the second mode conceives it as a causal factor. In this latter way of stating our meaning, we have drifted into the notion of understanding the process of the universe. Indeed the presupposition of process seems even to enter into our previous analysis. We can take these ways of explanation of meaning as applying to
( 64) the understanding of the passage of nature.
It is true that nothing is finally understood until its reference to process has been made evident. And yet, there is the understanding of ideal relationships in abstraction from reference to the passage of brute fact. In the notion of such relationships there is no transition.
For example, throughout mathematics, in one sense, transition does not enter. The interconnections are displayed in their timeless eternity. It is true that the notions of time, and of approach, and of approximation, occur in mathematical discourse. But as used in the science, the timefulness of time and the motion of approach are abstracted from. In mathematics, as understood, the ideal fact stands out self-evident.
There is very little large-scale understanding, even among mathematicians. There are snippets of understanding, and there are snippets of connections between these snippets. These details of connection are also understood. But these fragments of intelligence succeed each other. They do not stand together as one large self-evident coördination. At the best, there is a vague memory of details which have recently been attended to.
This succession of details of self-evidence is termed 'proof'. But the large self-evidence of mathematical science is denied to humans.
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To give an example, the snippet of knowledge that the addition of 1 and 4 produces the same multiplicity as the addition of 1 and 3, seems to me self-evident. It is a humble bit of knowledge; but, unless I deceive myself, it stands before me with a clarity of insight. I hesitate to claim any, such self-evidence when larger numbers are involved. I have recourse to the indignity of proof. Other people have wider powers.
For example, consider Ramanujan, the great Indian mathematician, whose early death was a loss to science analogous to that of Galois. It was said of him that each of the first hundred integers was his personal friend. In other words, his insights of self-evidence, and his delight in such insights, were of the same character as most of us feel for the integers up to the number 5. Personally, I cannot claim intimate friendship beyond that group. Also the restriction of the group somewhat, in my own case, hinders the growth of that feeling of delight which Ramanujan enjoyed.
I confess to a larger pleasure in patterns of relationship in which numerical and quantitative relationships are wholly subordinate. I mention these personal details in order to emphasize the great variety of characters that self-evidence can assume, both as to extent and as to the character of the compositions which are self-evident. The
( 66) sense of 'completion', which has already been mentioned, arises from the self-evidence in our understanding. In fact, self-evidence is understanding.
The sense of penetration, which also clings to our experience of intelligibility, has to do with,the growth of understanding. To feel the completion apart from any sense of growth, is in fact to fail in understanding. For it is a failure to sense dimly the unexplored relationships with things beyond. To feel the penetration without any sense of completion, is also to fail in understanding. The penetration itself is then deficient in meaning. It lacks achievement.
3. We now come to the notion of 'proof'. The thesis that I am developing conceives 'proof', in the strict sense of that term, as a feeble second-rate procedure. When the word 'proof' has been uttered, the next notion to enter the mind is 'half-heartedness'. Unless proof has produced self-evidence and thereby rendered itself unnecessary, it has issued in a second-rate state of mind, producing action devoid of understanding. Self-evidence is the basic fact on which all greatness supports itself. But 'proof' is one of the routes by which self-evidence is often obtained.
As an example of this doctrine, in philosophical writings proof should be at a minimum. The whole effort should be to display the self-evidence
( 67) of basic truths, concerning the nature of things and their connection. It should be noticed that logical proof starts from premises, and that premises are based upon evidence. Thus evidence is presupposed by logic; at least, it is presupposed by the assumption that logic has any importance.
Philosophy is the attempt to make manifest the fundamental evidence as to the nature of things. Upon the presupposition of this evidence, all understanding rests. A correctly verbalized philosophy mobilizes this basic experience which all premises presuppose. It makes the content of the human mind manageable; it adds meaning to fragmentary details; it discloses disjunctions and conjunctions, consistencies and inconsistencies. Philosophy is the criticism of abstractions which govern special modes of thought.
It follows that philosophy, in any proper sense of the term, cannot be proved. For proof is based upon abstraction. Philosophy is either self-evident, or it is not philosophy. The attempt of any philosophic discourse should be to produce self-evidence. Of course it is impossible to achieve any such aim. But, none the less, all inference in philosophy is a sign of that imperfection which clings to all human endeavour. The aim of philosophy is sheer disclosure.
The great difficulty of philosophy is the failure of language. The ordinary intercourse of mankind
( 68) is concerned with shifting circumstance. It is unnecessary to mention self-evident facts. Thus hunting scenes had been depicted on the walls of caves for thousands of years before the more permanent spacial relations had become a topic for conscious analysis. When the Greeks required terms for the ultimate characters of the actualities of nature, they had to use terms such as water, air, fire, wood.
When the religious thought of the ancient world from Mesopotamia to Palestine, and from Palestine to Egypt, required terms to express that ultimate unity of direction in the Universe, upon which all order depends, and which gives its meaning to importance; they could find no way better to express themselves than by borrowing the characteristics of the touchy, vain, imperious tyrants who ruled the empires of the World. In the origin of civilized religion, Gods are like Dictators. Our modern rituals still retain this taint. The most emphatic repudiations of this archaic notion are to be found scattered in the doctrines of Buddhism and in the Christian Gospels.
Language halts behind intuition. The difficulty of philosophy is the expression of what is self-evident. Our understanding outruns the ordinary usages of words. Philosophy is akin to poetry. Philosophy is the endeavour to find a conven-
( 69) -tional phraseology for the vivid suggestiveness of the poet. It is the endeavour to reduce Milton's 'Lycidas' to prose; and thereby to produce a verbal symbolism manageable for use in other connections of thought.
This reference to philosophy illustrates the fact that understanding is not primarily based on inference. Understanding is self-evidence. But our clarity of intuition is limited, and it flickers. Thus inference enters as means for the attainment of such understanding as we can achieve. Proofs are the tools for the extension of our imperfect self-evidence. They presuppose some clarity; and they also presuppose that this clarity represents an imperfect penetration into our dim recognition of the world around—the world of fact, the world of possibility, the world as valued, the world as purposed.
4. At this point of our discussion another aspect of things claims explicit recognition. It is a general character, whose special forms are termed variously 'disorder', 'evil', 'error'. In some sense or other, things go wrong; and the notion of correction from worse to better, or the notion of decay from better to worse, enters into our understanding of the nature of things.
It is a temptation for philosophers that they should weave a fairy-tale of the adjustment of factors; and then as an appendix introduce the
( 70) notion of frustration, as a secondary aspect. I suggest to you that this is the criticism to be made on the monistic idealisms of the nineteenth century, and even of the great Spinoza. It is quite incredible that the Absolute, as conceived in monistic philosophy, should evolve confusion about its own details.
There is no reason to hold that confusion is less fundamental than is order. Our task is to evolve a general concept which allows room for both; and which also suggests the path for the enlargement of our penetration. My suggestion is that we start from the notion of two aspects of the Universe. It includes a factor of unity, involving in its essence the connexity of things, unity of purpose, and unity of enjoyment. The whole notion of importance is referent to this ultimate unity. There is also equally fundamental in the Universe, a factor of multiplicity. There are many actualities, each with its own experience, enjoying individually, and yet requiring each other.
Any description of the unity will require the many actualities; and any description of the many will require the notion of the unity from which importance and purpose is derived. By reason of the essential individuality of the many things, there are conflicts of finite realizations. Thus the summation of the many into the one,
( 71) and the derivation of importance from the one into the many, involves the notion of disorder, of conflict, of frustration.
These are the primary aspects of the universe which common sense brooding over the aspects of existence hands over to philosophy for elucidation into some coherence of understanding. Philosophy shirks its task when it summarily dismisses one side of the dilemma. We can never fully understand. But we can increase our penetration.
When there is a full understanding, any particular item belongs to what is already clear. Thus it is merely a repetition of the known. In that sense, there is tautology. Thus tautology is the intellectual amusement of the Infinite.
Also in the same sense, the selection of the particular item for emphasis is equally arbitrary. It is the convention by means of which the Infinite governs its concentration of attention.
For the finite individual there is penetration to novelty in its own experience; and the selection of detail is subject to the causation from which that individual originates. Philosophy tends to oscillate between the points of view belonging to the infinite and to the finite. Thus understanding, however imperfect, is the self-evidence of pattern, so far as it has been discriminated. Also for the finite experience, inference is the achieve-
( 72) -ment of further penetration into such self-evidence.
A partially understood pattern is more definite as to what it excludes than as to what its completion would include. As to inclusion there are an infinitude of alternative modes of completion. But so far as there is any definiteness attaching to the incomplete disclosure, certain factors are definitely excluded. The foundation of Logic upon the notion of inconsistency was first discovered and developed by Professor Henry Sheffer of Harvard, about twenty years ago. Professor Sheffer also emphasized the notion of pattern, as fundamental to Logic. In this way, one of the great advances in mathematical Logic was accomplished.
In the first place, by basing Logic upon the concept of inconsistency, the notion of the finite is definitely introduced. For as Spinoza pointed out, the finite is that which excludes other things comparable to itself. Thus inconsistency bases Logic upon Spinoza's concept of finitude.
In the second place, as Sheffer pointed out, the notions of negation and of inference can be derived from that of inconsistency. Thus the whole movement of Logic is provided for. We may notice that this basis for Logic suggests that the notion of frustration is more akin to finite
( 73) mentality; while the notion of harmonious conjunction is derived from the concept of a monistic universe. It is for philosophy to coördinate the two aspects which the world presents.
In the third place, this basis for Logic enlightens our understanding of process, which is a fundamental fact in our experience. We are in the present; the present is always shifting; it is derived from the past; it is shaping the future; it is passing into the future. This is process, and in the universe it is an inexorable fact.
5. But if all things can be together, Why should there be process? One answer to this question embodies a denial of process. According to this answer process is mere appearance, devoid of significance for ultimate reality. This solution seems to me to be very inadequate. How can the unchanging unity of fact generate the delusion of change? Surely, the satisfactory answer must embody an understanding of the interweaving of change and permanence, each required by the other. This interweaving is a primary fact of experience. It is at the base of our concepts of personal identity, of social identity, and of all sociological functionings.
Meanwhile, another aspect of the relationship between inconsistency and process must now occupy us. Inconsistency is the fact that the two states of things which constitute the respective
( 74) meanings of a pair of propositions cannot exist together. It denies a possible conjunction between these meanings. But these meanings have been brought together in the very judgment of inconsistency. This is the sort of perplexity that Plato alluded to, when he makes one of his characters say, 'Not-being is a sort of being'.
The conclusion that I draw is that the word 'together', and indeed all words expressive of conjunction in general, without definite specification, are very ambiguous. For example, the little word 'and' is a nest of ambiguity. It is very astounding how slight has been the analysis of the ambiguities of words expressive of conjunctions. Such words are the death-traps for accuracy of reasoning. Unfortunately, they occur abundantly in sentences, expressed in the most perfect literary form. Thus an admirable literary style is no security for logical consistency.
In reading philosophic literature every word expressive of conjunction must be deeply pondered over. If it be used twice in the same sentence, or in neighbouring sentences, Can we be sure that the two usages embody the same meaning, at least sufficiently for the purposes of the argument?
I suggest to you that the contradictions, famous in ancient and in modern logic, arise from such ambiguities. Many words which are not
( 75) formally 'conjunctions', are expressive of a conjunctive meaning. For example, the word 'class' has all the manifold ambiguity of the word 'and'. The understanding of pattern, and of the conjunctions involved in various patterns, depends upon the study of such ambiguities. On this topic philosophic literature is very simple-minded. So many vigorous and cogent arguments fall into this trap.
We must now return to the topic of 'inconsistency and process'. The concept that two propositions, which we will name p and q, are inconsistent, must mean that in the modes of togetherness illustrated in some presupposed environment the meanings of the propositions p and q cannot both occur. Neither meaning may occur or either may occur, but not both. Now process is the way by which the universe escapes from the exclusions of inconsistency.
Such exclusions belong to the finitude of circumstance. By means of process, the universe escapes from the limitations of the finite. Process is the immanence of the infinite in the finite; whereby all bounds are burst, and all inconsistencies dissolved.
No specific finitude is an ultimate shackle upon the universe. In process the finite possibilities of the universe travel towards their infinitude of realization.
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In the nature of things there are no ultimate exclusions, expressive in logical terms. For if we extend the stretch of our attention throughout the passage of time, two entities which are inconsistent for occurrence on this planet during a certain day in the long past and are inconsistent during another day in more recent past—these two entities may be consistent when we embrace the whole period involved, one entity occurring during the earlier day, and the other during the later day. Thus inconsistency is relative to the abstraction involved.
An easy intellectual consistency can be attained, provided that we rest content with high abstraction. Pure mathematics is the chief example of success by adherence to such rigid abstraction. Again, the importance of mathematics, as finally disclosed in the sixteenth and seventeenth centuries, illustrates the doctrine that the advance of the finite human understanding requires the adherence to some judicious abstraction, and the development of thought within that abstraction. The disclosure of this method has issued in the progressive science of modern civilization, within the last three thousand years.
6. But the discovery has been gradual, and the method is even now imperfectly understood. Learned people have handled the specialization
( 77) of thought with an incredible lack of precaution. It is almost universally assumed that the growth of a specialism leaves unaffected the presuppositions as to the perspective of the environment which were sufficient for the initial stages. It cannot be too clearly understood that the expansion of any special topic changes its whole meaning from top to bottom. As the subject-matter of a science expands, its relevance to the universe contracts. For it presupposes a more strictly defined environment.
The definition of the environment is exactly what is omitted from special abstraction. Such definition is an irrelevance. It is irrelevant because it requires an understanding of the infinitude of things. It is therefore impossible. All that we can do is to make an abstraction, to presuppose that it is relevant, and to push ahead within that presupposition.
This sharp division between the clarity of finite science and the dark universe beyond is itself an abstraction from concrete fact. For example, we can explore our presuppositions. Take the special case of natural science, we presuppose geometry. But what sort of geometry? There are many kinds. In fact, there are an indefinite number of alternative geometries. 'Which one are we to choose?
We all know that this is a topic which has bothered, or elated, physical science during the
( 78) last thirty years. At last the great scientists are coming to conclusions which we will all accept. And yet a sceptical doubt intrudes. How do we know that only one geometry is relevant to the complex happenings of nature? Perhaps a three-dimensional geometry is relevant to one sort of occurrences; and a fifteen-dimensional geometry is required for another sort.
Of course our more obvious sense-perceptions seem to clamour for three-dimensions, especially sight. On the other hand sound, though voluminous, is very vague as to the dimensions of its volumes, as between three or fifteen, for instance. Also any change in scale, to the very small or to the very large, makes surprising changes in the characters of the happenings disclosed so far as we can observe.
We have developed very special types of sensory observation; and in consequence we are wedded to a correspondingly special set of results, true enough if we introduce the proper limitations. But as our science expands the area of relationship to other aspects of nature becomes increasingly important.
Perhaps our knowledge is distorted unless we can comprehend its essential connection with happenings which involve spatial relationships of fifteen dimensions. The dogmatic assumption of the trinity of nature as its sole important dimen-
( 79) -sional aspect has been useful in the past. It is becoming dangerous in the present. In the future it may be a fatal barrier to the advance of knowledge.
Also, this planet, or this nebula in which our sun is placed, may be gradually advancing towardsa change in the general character of its spatial relations. Perhaps in the dim future mankind, if it then exists, will look back to the queer, contracted three-dimensional universe from which the nobler, wider existence has emerged.
These speculations are, at present, neither proved or disproved. They have however a mythical value. They do represent how concentration on coherent verbalizations of certain aspects of human experience may block the advance of understanding. Too many apples from the tree of systematized knowledge lead to the fall of progress.
The sense of advance, of penetration, is essential to sustain interest. Also there are two types of advance. One is the advance in the use of assigned patterns for the coördination of an increased variety of detail.
But the assignment of the type of pattern restricts the choice of details. In this way the infinitude of the universe is dismissed as irrelevant. The advance which has started with the freshness of sunrise degenerates into a dull accumula-
( 80) -tion of minor feats of coördination. The history of thought and the history of art illustrate this doctrine. We cannot prescribe the pattern of progress.
It is true that advance is partly the gathering of details into assigned patterns. This is the safe advance of dogmatic spirits, fearful of folly. But history discloses another type of progress, namelythe introduction of novelty of pattern into conceptual experience. In this way, details hitherto undiscriminated or dismissed as casual' irrelevances are lifted into coördinated experience. There is a new vision of the great Beyond.
7. Thus understanding has two modes of advance, the gathering of detail within assigned pattern, and the discovery of novel pattern with its emphasis on novel detail. The intelligence of mankind has been halted by dogmatism as to patterns of connexion. Religious thought, aesthetic thought, the understanding of social structures, the scientific analysis of observation, have alike been dwarfed by this fatal virus.
It entered European thought at the very beginning of its brilliant foundation. Epicurus, Plato, Aristotle, were alike convinced of the certainty of various elements in their experience, in the exact forms in which they understood them. They were unaware of the perils of abstraction. Later on, in his Critique of Pure Reason, Kant
( 81) gave a masterly exposition of the reasons why we should be so certain. There was a concurrence of genius as to this certainty.
It is a tragedy of history, that in the sense in which these great men held these beliefs, not one of their doctrines has survived the wider knowledge of the last two centuries. Mathematics is not true in the sense in which Plato conceived it. Sense-data are not clear, distinct, and primary, in the sense in which Epicurus believed.
The history of thought is a tragic mixture of vibrant disclosure and of deadening closure. The sense of penetration is lost in the certainty of completed knowledge. This dogmatism is the anti-Christ of learning.
In the full concrete connection of things, the characters of the things connected enter into the character of the connectivity which joins them.
Every example of friendship exhibits the particular characters of the two friends. Two other people are inconsistent in respect to that completely defined friendship. Again the colours in a picture form a composition, which is partly geometrical. If we merely consider the abstract geometrical relationship, a patch of red can be substituted for a patch of blue. In this geometrical abstraction the red is just as consistent with the remaining patches of colours as was the blue. But if we consider the picture more concretely,
( 82) perhaps a masterpiece has been ruined. The red is inconsistent with the concrete effect on the composition produced by the blue.
Thus in proportion as we penetrate towards concrete apprehension, inconsistency rules. Namely, all entities, except one, are inconsistent with the production of the particular effect which the one entity would produce. In proportion to our relapse towards abstraction, many entities will alternatively produce the same abstract effect. Thus consistency grows with abstraction from the concrete.
There is thus an ambiguity in the notion of inconsistency. There is the sheer difference produced by the distinction between entities. If the patch be scarlet, it cannot also be pale blue. The two notions are inconsistent by reason of the sheer distinction between red and blue, in that they are distinct colours. There is also the distinction in aesthetic enjoyment. The blue may be a factor in a picture which is a masterpiece, while the substitution of red in the same geometrical position destroys the whole aesthetic value. On the other hand, if interest be wholly directed to the geometrical relationships, red or blue may do equally well to mark out that area.
We should now understand that there are two types of inconsistency. These may be termed respectively, the logical type, and the aesthetic
( 83) type. The logical type is based on the difference between different things, conceived as alternative factors in a composition. It cannot be indifferent to the totality of a composition, as to which of two distinct things fill an assigned rôle in the pattern of that composite entity. The difference in the factors will produce different compositions. Also the addition of factors disrupts the underlying presuppositions.
We can never understand a composition in its full concrete effectiveness for all possibilities of environment. We are aware only of an abstraction. For this abstraction the change or addition of factors may be indifferent. There is always a nemesis hanging over the equivalence, or consistency, of different things. As we enlarge self-evidence the abstraction shrinks, and our understanding penetrates towards the concrete fact. Thus, sooner or later, growth in knowledge leads to the evidence of antagonism involved in difference.
8. The doctrine of understanding, as developed in this lecture, applies beyond Logic. The aesthetic experience is another mode of the enjoyment of self-evidence. This conclusion is as old as European thought. The relation of the mathematical doctrine of proportion in its application to music and to architecture excited interest in the Pythagorean and Platonic schools.
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Also the feeling, widespread among mathematicians, that some proofs are more beautiful than others, should excite the attention of philosophers.
I suggest to you that the analogy between aesthetics and logic is one of the undeveloped topics of philosophy.
In the first place, they are both concerned with the enjoyment of a composition, as derived from the interconnections of its factors. There is one whole, arising from the interplay of many details. The importance arises from the vivid grasp of the interdependence of the one and the many. If either side of this antithesis sinks into the background, there is trivialization of experience, logical and aesthetic.
The distinction between logic and aesthetics consists in the degree of abstraction involved. Logic concentrates attention upon high abstraction, and aesthetics keeps as close to the concrete as the necessities of finite understanding permit. Thus logic and aesthetics are at the two extremes of the dilemma of the finite mentality in its partial penetration of the infinite.
Either of these topics can be considered from two points of view. There is the discovery of a logical complex, and the enjoyment of that complex when discovered. Also there is the construction of an aesthetic composition, and the enjoy-
( 85) -ment of that composition when composed. This distinction between creation and enjoyment must not be overstressed. But it is there; and the close of this lecture is concerned with the enjoyment and not with creation.
The characteristic attitude of logical understanding is to start with the details, and to pass to the construction achieved. Logical enjoyment passes from the many to the one. The characters of the many are understood as permitting that unity of construction.
Logic employs symbols; but only as symbols. For example, the difference in the spacing of the lines, in the width of the margin, in the size of the page—octavo, or quarto, or duodecimo, has not as yet entered into the symbolism.
The understanding of Logic is the enjoyment of the abstracted details as permitting that abstract unity. As the enjoyment develops, the revelation is the unity of the construct. We are facing a possibility for the universe, namely how the abstract in its own nature harbours that approach to concretion. Logic starts with primitive ideas, and puts them together.
The movement of aesthetic enjoyment is in the opposite direction. We are overwhelmed by the beauty of the building, by the delight of the picture, by the exquisite balance of the sentence. The whole precedes the details.
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We then pass to discrimination. As in a moment, the details force themselves upon us as the reasons for the totality of the effect. In aesthetics, there is a totality disclosing its component parts.
In the history of European thought, the discussion of aesthetics has been almost ruined by the emphasis upon the harmony of the details. The enjoyment of Greek art is always haunted by a longing for the details to exhibit some rugged independence apart from the oppressive harmony.
In the greatest examples of any form of art, a miraculous balance is achieved. The whole displays its component parts, each with its own value enhanced; and the parts lead up to a whole, which is beyond themselves, and yet not destructive of themselves. It is however remarkable how often the preliminary studies of the details—if preserved—are more interesting than the final details as they appear in the complete work. Even the greatest works of art fall short of perfection.
By reason of the greater concreteness of the aesthetic experience, it is a wider topic than that of the logical experience. Indeed, when the topic of aesthetics has been sufficiently explored, it is doubtful whether there will be anything left over for discussion. But this doubt is unjustified.
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For the essence of great experience is penetration into the unknown, the unexperienced.
Both logic and aesthetics concentrate on the closed fact. Our lives are passed in the experience of disclosure. As we lose this sense of disclosure, we are shedding that mode of functioning which is the soul. We are descending to mere conformity with the average of the past. Complete conformity means the loss of life. There remains the barren existence of inorganic nature.
In the three lectures now concluded, the assemblage of these ideas, most fundamental for philosophic thought, has been attempted. The systematization has been of the slightest; and under the guise of three headings a variety of notions has been introduced.
There is one moral to be drawn. Apart from detail, and apart from system, a philosophic outlook is the very foundation of thought and of life. The sort of ideas we attend to, and the sort of ideas which we push into the negligible background, govern our hopes, our fears, our control of behaviour. As we think, we live. This is why the assemblage of philosophic ideas is more than a specialist study. It moulds our type of civilization.
