Chapter II: Part 2

Now Knowledge is the affirmation or judgment which identifies the constructive interpretation of our present perception with the reality which present perception forces upon us. This is clear enough to begin with, but will have to be modified below to suit the more circuitous or mediate types of Judgment.

I take two examples, one from sight and one from sound.

Here is a table. In common language we should all say, “We see that is a table.” The expression is quite correct, because human seeing is a judgment. But yet, if you were asked to reduce your perception to terms of sight pure and simple--I mean of visual sensation--why, unless you were an analytic psychologist or a very skilful artist, you would not be able to do it. To speak of one point only, you would have to eliminate the attribute of depth and distance. That is all, so far as mere vision is concerned, your theory and your interpretation. The problem for an artist is to get back, at his high plane of perceptive power, to what in theory would be the lower plane. He has to re-translate his perception of a thing in space into a flat coloured surface. The difference between his flat picture and a real object in space is a rough measure of the difference made by interpretation or implication in the datum of sense-perception when we say, judging by sight only, “That is a table.” All the experiences of touch and motion, from which we have learned to perceive the solidity of the object, are, theoretically speaking, put into the judgment by us. They are not given by the eye alone, although we cannot now {30} separate them from that which is given by the eye alone. For the artist’s flat picture, which I used as an illustration, is not a stage in our visual education. Our visual education has proceeded _pari passu_ with our education by touch and motion; and we saw objects in space as solids, long before we reflected that for the eye alone a coloured surface would naturally appear as flat. [1]

[1] The view that depth is a visual datum in the same sense as breadth seems to me in flagrant contradiction with experience. But for our present purpose the question is only one of degree, as no one maintains, that either depth or breadth are seen without education as an adult sees them.

But this impossibility of getting at an original datum only shows how entirely we are right in saying that our world is constructed by judgment. For the process of interpretative amplification passes quite continuously from the unconscious to the conscious; and every definitely expressed judgment, though perfectly homogeneous with the processes which have qualified its datum, and though it may fall wholly within the maximum of what in ordinary parlance we should call a simple given perception, contains an identification of some ideal element, enlargement, or interpretation, with that relatively given element which reveals itself through a peculiar quality of presentness pervading the “given” perception.

In the example “That is a table,” the unity of judgment is so well shown that the identification becomes almost unreal. In fact, we never judge except to satisfy an interest and so simple a judgment used as an example, apart from any context which could explain the need for it, has an air of unreality. You may hear a child make such a judgment {31} constantly in the sheer pleasure of recognition. An adult would never make it explicitly unless in some particular context; but it is made, as I shall maintain below, by the mere glance of his eye which takes in the table as a real object in a real world of space. Its appearance to the eye is in this case the datum, while the interpretation consists in construing this appearance as a solid individual existence in space.

We will look at an example in which the discrimination of elements is easier. Take the affirmation, “That is a cab,” assuming it to be made from merely hearing a sound. In this we can much more nearly separate the datum or minimum of sense from our enlargement or interpretation of it, and we know that our interpretation is liable to be wrong; that is to say, the reality into which we ought to construe the sound may be some other kind of vehicle, and not a cab. Now compare this with the affirmation, “That (which I see) is a cab.” This judgment of sight-perception, though its terms are more inextricably interwoven, has just the same elements in it as the judgment of sound-perception, “That (which I hear) is a cab.” In the sound-perception the structure is quite plain. A particular complex quality in the sound suggests as its objective explanation, what is perfectly distinguishable from it in thought, the movement of a cab on a particular kind of pavement. The quality of the sound, its roughness, loudness, increase and decrease, all form points of connection with the sound of a cab as we know it, and with the speed, weight, etc. of such a vehicle. But it is quite easy to consider the sound in itself apart from its interpretation, and we sometimes feel the {32} interpretation to be more immediate, and sometimes more inferential. We sometimes say, “I hear a cab,” just as we say, “I see one,” but in case of sound we more often perhaps say, “That sounds like--” such and such a thing, which indicates a doubt, and the beginning of conscious inference.

Thus we see how continuous is the mental construction of reality. From our unreflective education in seeing, hearing, and touching, to the explicit judgment of the trained observer, which in its turn passes readily into inference, there is no definite break. Once the idea of reality, or of a world, is applied in practice (I do not say reflectively grasped), there is no further difficulty in principle throughout the whole process of its construction.

We may then sum up so far: our knowledge, or our world in knowledge, exists for us as a judgment, that is, as an affirmation in which our present perception is amplified by an ideal interpretation which is identified with it. This interpretation or enlargement claims necessity or universality, and is therefore objective as our world, _i.e._ is what we are _obliged_ to think, and what we are _all_ obliged to think. The whole system in process of construction, viz. our present perception as extended by interpretation, is what we mean by reality, only with a reservation in favour of forms of experience which are not intellectual at all. Every judgment then affirms something to be real, and therefore affirms reality to be defined, in part, by that something. Knowledge exists in the form of affirmations about reality. And our world as existing for us in the medium of knowledge consists, for us, of a standing affirmation about reality.

{33} _Continuous affirmation of waking consciousness_

4. This standing affirmation about reality may be described in other words as “the continuous affirmative judgment of the waking consciousness.” In the common logic-books you will find judgment treated only as the “proposition,” that is, as an assertion made in language. That is a very convenient way of treating the judgment, and is not false, if you remember that the proposition, that is, the assertory sentence, is rather a translation of the judgment than the judgment itself. But the judgment expressed in a proposition is always some one definite assertion, with a limited subject and predicate. We shall speak of the judgment in this sense--the usual sense--later. But to-day I want to describe the judgment in a more extended sense, that is, as co-extensive with the waking human consciousness, so far as aware of a world.

If Judgment consists in the extension of our perceptions by an interpretation considered as equally real with their content, it clearly is not confined to the particular facts and truths which from time to time we utter in language. And more than this, everything that we do definitely utter, implies a great deal which is not definitely uttered. If I say, “I have to catch the train at Sloane Square to go down to Essex Hall,” I only mention the reality of one train, one square, and one building. But my assertion shades off into innumerable facts, the equal reality of which as elements in my world is necessary to make this judgment intelligible and true. It implies the real existence of the underground railway, which implies that of London, and therefore that of the surface of our globe in a certain definite order, and of the civilised world. It implies the reality of this building and of the meetings which we hold in it, of the University {34} Extension system, and of my own life and habits as enabling me to take part in the work of that system. Only a part of this is in the focus of my attention as I judge; but the whole is a continuous context, the parts of which are inseparable; and although I do not affirm the whole of it in so many words, when I say that I am coming down here by train this evening, yet if any part of it was not affirmed the rest would, so to speak, fall to pieces, _i.e._ would lose relations in the absence of which its meaning would be destroyed. Other detached parts of one’s life and knowledge may seem to be separable from the content of such a judgment; but on looking closely we see that this is not the case. So long as we are awake, our whole world is conceived as real, and forms for us a single immense affirmation, which hangs from present perception, and shares its constraining power. My present perception is the illuminated spot, and shades off gradually into the rest which forms the background, receiving from this background its organised systematic individuality, while impressing upon it a relation to its own sensuous presentness. We have only to reflect, in order to illustrate this connection, on the way in which the idea of London forms a determining background for the present perception of this room, while on the other hand it is perceived by us as real in our presentation of this room.

And indeed the simplest example of what I am pointing out is the arrangement of objects and places in space. The visual picture which each of us forms of this room is certainly an affirmative judgment. It is a judgment because it consists of ideas affirmed as true of reality. As we look round, all the distances of the objects and the walls from {35} each other, and their shapes and position, seem to be imprinted on our minds without an effort. But really they are conclusions from long education in the art of seeing and from the experience of the other senses. They are an enlargement or interpretation of sense-perception, taken as real, _i.e._ as forming a system which is one with the content of sense-perception, and touches us through sense-perception, and therefore they exist for us in the form of Judgment. And, as I described before, our whole world, both of things in space and of our own history and circumstances, is also affirmed as the background implied in this picture. That is to say, it is all connected together, it is all taken as equally real, and it is all vouched for by its connection with what is given to us in perception. What do we mean by saying that the Antipodes are real, and implied in my perception of this room? We mean that they are an element, necessary to educated thought, in the same system with which I am in contact at this moment by sight, touch, and hearing, the system of reality. And though I may not have explicitly thoughts of them since entering the room till now, yet, if they were no part of my affirmed system of ideas, my perception of anything in space would be quite different from what it is.

This sense of necessary connection is confined, I think, to our _waking_ consciousness. Of course there are degrees between waking and dreaming; but I should be inclined to set up the presence or absence of judgment as a very fair test of those degrees. We say that a man is _awake_ in as far as he is aware (i) of a reality which is not his mere course of consciousness, and (ii.) of the same reality of which other {36} people are aware; _i.e._ in as far as he identifies his present perception with a reality, and that the real reality. It is said that surprise, _i.e._ the sense of conflict between expectation and the reality, is absent In dreams, and in a very remarkable passage Aeschylus identifies the life of the savage in his (imaginary) primitive state with a dream-life, considered as a life of sensuous presentation, in which the interpretative judgment of perception was absent. With extraordinary profoundness, in portraying this all but animal existence, he strikes out all those relations to the objective world by which man forms for himself a system that goes beyond the present, so as to leave the stream of presentation without any background of organised reality. [1]

[1] I quote from Mrs. Browning’s Translation of the _Prometheus Bound_, which seems close enough for the present purpose.

“And let me tell you, not as taunting men,
But teaching you the intention of my gifts,
How first, _beholding, they beheld in vain.
And hearing, heard not, but, like shapes in dreams_,
Mixed all things wildly down the tedious time,
Nor knew to build a house against the sun
With wicketed sides, nor any woodwork knew,
But lived, like silly ants, beneath the ground,
In hollow caves unsunned. There came to them
No steadfast sign of winter, nor of spring
Flower-perfumed, nor of summer full of fruit.
But blindly and lawlessly they did all things,
Until I taught them how the stars do rise
And set in mystery, and devised for them
Number, the inducer of philosophies.
The synthesis of letters, and besides,
The artificer of all things, Memory,
That sweet muse-mother.” _Pr_., v. 445, ff.

The expression “seeing saw not, and hearing heard not” appears to suggest the contrast of presentation and objective perception.

{37} It may be asked, “Why should not a man form for himself a system which interprets his own perception, but is discrepant from the system of every one else? Should we in that case count him as awake?” Yes, he would be awake, but he would be mad. Suppose, being a common man, he interprets all his perceptions into a system which makes him out to be King of England; in such a case he cannot be set down as dreaming, because he is alleging a connection which goes beyond his present perception, and has, ostensibly, been propounded as an interpretation of it into a systematic order of things. He has in short _a_ world, but he has broken away from _the_ world, and therefore we pronounce him mad. A completely new vision of life may cause a man to be thought mad. [1]

[1] See Browning’s _Epistle of Karshish_.

The whole world, then, of our waking [1] consciousness may be treated as a single connected predicate affirmed as an enlargement of present perception. All that we take to be real is by the mere fact of being so taken, brought within an affirmative judgment.

[1] I do not mean to say that judgment and consciousness of a world can be wholly absent in dreams, and often no doubt they are distinctly present. But in those dreams, in my own experience the normal ones, which leave behind a mere impression that unrecognisable images have passed before the mind, judgment and the sense of reality must surely have all but disappeared. I am inclined to think that dreams are very much rationalised in recollection and description.

_Comparison with world as Will_

5. To further illustrate the relation of what, in our permanent judgment, is distinctly thought, what is dimly thought, and what is implied, let us look for a moment at what we may call “the world as will.” This is _not_ the doctrine of Schopenhauer in his work, _The World as Will and Idea_, {38} although the two conceptions have something in common. His is a metaphysical doctrine, in which he says that the fundamental reality of the Universe must be conceived as Will. We have nothing to do with that. We are speaking merely of what the world is for us, and for us it is not only a system of reality but a system of purposes. Our world of will is a permanent factor of our waking consciousness, just as much as our world of knowledge. Now our will is made up of a great number of purposes, more or less connected together, just as our knowledge is made up of a great number of provinces and regions more or less connected together. And just as in our knowledge at any moment much is clear, much is dim, much is implied, and the whole forms a continuous context, so it is with our purposes.

When, for example, one stands looking at a picture, one’s immediate conscious purpose is to study the picture. One also entertains dimly or by force of habit the purpose to remain standing, which is a curious though common instance of will. We do not attend to the purpose of walking or standing, yet we only walk or stand (in normal conditions of mind) as long as we will to do so. If we go to sleep or faint, we shall fall down. Purpose, like judgment, is confined to the waking consciousness.

But further; the purpose which one entertains in standing to look at a picture is not really an isolated pin-point of will. It is uppermost in the mind at the moment in which we carry it out, but it is only the uppermost stratum, or perhaps rather the present point attained upon a definite road, within an intricate formation or network of purposes, which taken together constitute the world of will. The purpose of looking {39} at a picture shades off into the more general purpose of learning to take pleasure in what is good of its kind, which is again set in a certain place within the conception of our life and the way in which we desire to spend it, and our purposes throughout every particular day are fitted into one another, and give a particular setting and colour to each other, and to each particular day, and week, and year.

Now less or more of all this may be clearly in the mind when we are carrying out a particular momentary aim. But it is quite certain that in a human life the particular momentary aim derives its significance from this background of other purposes; and, if they were to fall away, the distinct momentary purpose would change its character and become quite a feeble and empty thing.

Thus we have, in our world of will, a parallel case which illustrates the nature of our world of knowledge. There is the clear will to look at the picture, the dim will to continue standing, and the implied will to carry out certain general aims, and follow a certain routine or course of life, which gives the momentary purpose its entire setting and background.

I have spoken of the will in order to illustrate the judgment, because the dim and implied elements are perhaps more easy to observe in the case of the will. Almost all our common waking life is carried on by actions such as walking and sitting, which we hardly know that we will, but which we could not do if we did not will them. And also the greater part of our life is rather within a sphere of will which has become objective for us in our profession, interests, and ideals, than a perpetual active choice between {40} alternatives such as brings the act of volition before us in the most striking way. Just so it is with judgment. Our speaking and writing is a very small part of our judging, just as our conscious choice between alternatives [1] is a very small part of our willing.

[1] I do not for a moment suggest that our “conscious choice” is ultimately different in kind from our habitual persistence in a course of life. I only take it as an instance in which we fully attend to our volition.

_Distribution of Attention_

6. Thus the world of knowledge and the world of will must each of them be regarded as a _continuum_ for the waking consciousness. Whenever we are awake, we are judging; whenever we are awake we are willing. The distribution of attention in these two worlds is very closely analogous. In both, it is impossible to attend to our whole world at the same moment. But in both, our world is taken as being a single connected system; and therefore (i.) attention shades off gradually from the momentary focus of illumination into less and less intensity over the other parts of the continuous judgment or purpose; but (ii.) that which is _in_ the focus of attention depends for its quality upon that which is less distinctly or not at all in the focus of attention. And as attention diminishes in intensity, the implication of reality does not diminish with it. In other words, in spite of the inequality of attention, the reality of our whole world is implied in the reality of which at any moment we are distinctly aware. But being distinctly aware of reality is another name for judgment.

Now the common logical judgments which we shall have to analyse and classify are simply those parts of this continuous affirmation of consciousness which are from time {41} to time separately made distinct. Each of them therefore must be regarded as a partial expression of the nature of reality, and the subject will always be Reality in one form, and the predicate reality in another form. The ultimate and complete judgment would be the whole of Reality predicated of itself. All our logical judgments are such portions and fragments of this judgment as we can grasp at the moment. Some of these gather up in a system whole provinces of reality, others merely enlarge, interpret, or analyse the content of a very simple sense-perception. We shall not go far wrong in practice if we start from this judgment of Perception as the fundamental kind of Judgment. The real subject in Judgment is always Reality in some particular datum or qualification, and the tendency of Judgment is always to be a definition of Reality. We see the parts of Judgment most clearly in such thoughts as “This is blue”; “This is a flower”; “That light is the rising sun”; “That sound is the surf on a sandy shore.” In these we can plainly distinguish the element of presentation and the interpretative construction or analytic synthesis which is by the judgment identified with it.

{42}

LECTURE III THE RELATION OF LOGIC TO KNOWLEDGE

_Meaning of “Form”_

1. I spoke of the whole world, which we take to be real, as presented to us in the shape of a continuous judgment. It is the task of Logic to analyse the structure of this Judgment, the parts of which are Judgments.

The first thing is then to consider what sort of properties of Judgments we attend to in Logic. It is commonly said that Logic is a formal science; that is, that it deals with the form, and not with the content or matter of knowledge.

This word “form” is always meeting us in philosophy. “Species” is Latin for form, as εἶδος and ἰδεα [1] are Greek for form. The form of any object primarily means its appearance, that which the mind can carry away, while the object as a physical reality, as material, remains where it was. It need not mean shape as opposed to colour; that is a narrower usage. The Greek opinion was no doubt rooted in some such notion as that in knowing or remembering a thing the mind possessed its form or image without its matter. Thus the form came to stand for the knowable shape or structure which makes a thing what it is, and by which we recognise it when we see it. This was its species or its idea, the “image,” as it is used in the phrase, “Let us make man in our own image.” So in any work of the hands {43} of man, the form was the shape given by the workman, and came out of his mind, while the matter was the stuff or material out of which the thing was made.

[1] [= “eidos” and “idea”. Tr.]

The moment we contemplate a classification of the sciences, we see that this is a purely relative distinction. There is no matter without form. If it was in this deep sense without form, it would be without properties, and so incapable of acting or being acted upon. In a knife the matter is steel, the form is the shape of the blade. But the qualities of steel again depend, we must suppose, upon a certain character and arrangement in its particles, and this is, as Bacon would have called it, the _form_ of steel. But taken as purely relative, the distinction is good _prima facie_. Steel has its own form, but the knife has its form, and the matter steel can take many other forms besides that of a knife. Marble has its own form, its definable properties as marble (chemical and mechanical), but in a statue, marble is the matter, and the form is the shape given by the sculptor.

Now applying this distinction to knowledge in general, we see that all science is formal, and therefore it is no distinction to say that Logic is a formal science. Geometry is a formal science; even molecular physics is a formal science. All science is formal, because all science consists in tracing out the universal characteristics of things, the structure that makes them what they are.

The particular “form,” then, with which a science deals is simply the kind of properties that come under the point of view from which that science in particular looks at things. But a very general science is more emphatically formal than {44} a very special science. That is to say, it deals with properties which are presented in some degree by everything; and so in every object a great multitude of properties are disregarded by it, are treated by it as matter and not as form. In this sense Logic is emphatically “formal,” though not nearly so formal as it is often supposed to be. The subject-matter of Logic, then, is Knowledge _qua_ Knowledge, or the form of knowledge; that is, the properties which are possessed by objects or ideas _in so far as they are members of the world of knowledge_. And it is quite essential to distinguish the form of knowledge in this sense from its matter or content. The “matter” of knowledge is the whole region of facts dealt with by science and perception. If Logic dealt with this in the way in which knowledge deals with it, _i.e._ simply as a process of acquiring and organising experience, then Logic would simply be another name for the whole range of science, history, and perception. Then there would be no distinction between logic and science or common sense, and in trying to ascertain, say, the wave-length of red light, or the cab-fare from Chelsea to Essex Hall, we should be investigating a logical problem. But we see at once that this is not what we mean by studying knowledge as knowledge. Science or common sense aims at a particular answer to each problem of this kind. Logic aims at understanding the type and principles both of the problem and of its answer. The details of the particular answer are the “_matter_ of fact.” The type and principles which are found in all such particular answers may be regarded as the form of fact, _i.e._ that which makes the fact a fact in knowledge.

Jevons appears to me to make a terrible blunder at this {45} point. He says [1]--“One name which has been given to Logic, namely the Science of Sciences, very aptly describes the all-extensive power of logical principles. The cultivators of special branches of knowledge appear to have been fully aware of the allegiance they owe to the highest of the sciences, for they have usually given names implying this allegiance. The very name of Logic occurs as part of nearly all the names adopted for the sciences, which are often vulgarly called the ‘ologies,’ but are really the ‘logics,’ the ‘o’ being only a connecting vowel or part of the previous word. Thus geology is logic applied to explain the formation of the earth’s crust; biology is logic applied to the phenomena of life; psychology is logic applied to the nature of the mind; and the same is the case with physiology, entomology, zoology, teratology, morphology, anthropology, theology, ecclesiology, thalattology, and the rest. Each science is thus distinctly confessed to be a special logic. The name of Logic itself is derived from the common Greek word λόγος, which usually means _word_, or the sign and outward manifestation of any inward thought. But the same word was also used to denote the inward thought or reasoning of which words are the expression, and it is thus probably that later Greek writers on reasoning were led to call their science ἐπιστήμη λογική, or logical science, also τέχνη λογική or logical art. [2] The adjective λογική, being used alone, soon came to be the name of the science, just as Mathematic, Rhetoric, and other names ending in ‘ic’ were originally adjectives, but have been converted into substantives.”

[1] _Elementary Lessons_, p. 6.

[2] [= “logos”, “episteme logike”, “techne logike” and “logike”. Tr.]

{46} This account of the connection between the name “Logic” and the terminations of the names of the sciences appears precisely wrong. Whatever may have been the exact meaning of the expression “Logic,” or “Logical curriculum,” [1] or “art,” or “science” when first employed, there can be no doubt that the word logical had a substantive reference to that about which the science or teaching in question was to treat. The term “logic,” therefore, corresponds not to the syllables “logy” in such a word as “Zoology,” but to the syllables “Zoo,” which indicate the province of the special science, and not its character as a science. Zoology means connected discourse (λόγος) about living creatures. Logic meant a curriculum, or science or art dealing with connected discourse. The phrase “Science of Sciences,” rightly interpreted, has the same meaning. It does not mean that Logic is a Science which comprises all the special sciences, but that Logic is a Science dealing with those general properties and relations which all sciences _qua_ sciences have in common, but omitting, as from its point of view matter and not form, the particular details of content by which every science answers the particular questions which it asks. It is wild, and most mischievous, to say that “every science is a special logic,” or that “biology is Logic applied to the phenomena of life.” This confusion destroys the whole disinterestedness which is necessary to true scientific Logic, and causes the logical student always to have his eye on puzzles, and special methods, and interferences by which he may teach the student of science how to perform the concrete labour of research. We quite admit that {47} a looker-on may _sometimes_ see more of the game, and no wise investigator would contemn _a priori_ the suggestions of a student like Goethe, or Mill, or Lotze, because their author was not exclusively engaged in the observation of nature. But all this is secondary. The idea that Logic is a judge of scientific results, able to pass sentence, in virtue of some general criterion, upon their validity and invalidity, arises from a deep-lying misconception of the nature of truth which naturally allies itself with the above confusion between Logic and the special sciences.

[1] πραγμάτεια [= pragmateia Tr.]. See Prantl, i. 545.

Therefore the relation between content or matter of knowledge, and the form which is its general characteristic as knowledge, is of this kind. We can either study the objects of knowledge directly as we perceive them, or indirectly, as examples of the way in which we know. As studied for their own sake, they are regarded as the matter or content in which the general form of knowledge finds individual realisation. In botany, for instance, we have a large number of actual plants classified and explained in their relation to one another. A botanist is interested directly in the affinities and evolution of these plants, and in the principles of biology which underlie their history. He pushes his researches further and further into the individual matters that come to light, without, as a rule, more than a passing reflection upon the abstract nature of the methods which he is creating as his work proceeds. He classifies, explains, observes, experiments, theorises, generalises, to the best of his power, solely in order to grasp and render intelligible the region of concrete fact that lies before him. Now while his particular results and discoveries {48} constitute the “form” or knowable properties of the plant-world _as the object of botanical science_, the science which inquires into the general nature of knowledge must treat these particular results as “mere matter”--as something with which it is not directly concerned, any more than the art which makes a statue is primarily and directly concerned with the chemical and mechanical properties of marble. The “form” or knowable properties with which the general science of knowledge is directly concerned, consists in those methods and processes which the man of science, developing the modes in which common sense naturally works, constructs unconsciously as he goes along. Thus, not the nature and affinities of the plant-world, but classification, explanation, observation, experiment, theory, are the phenomena in virtue of which the organised structure of botanical science participates in the form of knowledge, and its objects become, in these respects, objects of logical theory.

Hence some properties and relations of objects, being the form or knowable structure of the concrete objects as a special department of nature, correspond to the mere matter, stuff, or content of Knowledge in general, while other properties and relations of objects, being their form or knowable structure as entering into a world of reality displayed to our intelligence, correspond to the form of Knowledge as treated of by a general inquiry into its characteristics, which we call Logic. It is just as the qualities or “forms” of the different metals of which knives can be made are mere matter or irrelevant detail when we are discussing the general “form” or quality of a good knife, {49} whatever its material. A reservation on this head appears in the following section.

_Form of Knowledge dependent on Content_

2. For the form of Knowledge depends in some degree upon its matter. It is very important to realise this truth; for if Logic is swamped by being identified with the whole range of special sciences, it is killed by being emptied of all adaptation to living intelligence. What is called Formal Logic _par excellence_ in all its shapes, whether antiquated as in Hamilton’s or Thomson’s Formal Laws of Thought, or freshly worked out on a symbolic basis as by Boole and others, has, it appears to me, this initial defect, _when considered as a general theory of Logic_. As a contribution to such a theory, every method which will work undoubtedly has its place, and indicates and depends upon some characteristic of real thought. But in the central theory itself, and especially in so short an account of it as must be attempted in these lectures, I should be inclined to condemn all attempts to employ symbols for anything more than the most passing illustration of points in logical processes. All such attempts, I must maintain, share with the old-fashioned laws of Identity, Contradiction, and Excluded Middle the initial fallacy of representing a judgment by something which is not and cannot be in any way an adequate symbol of one. If, in order to get at the pure form of Knowledge, we restrict ourselves to very abstract characteristics in which all knowledge appears, very roughly speaking, to agree, and which can be symbolized for working purposes by combinations of signs which have not the essential properties of ideal contents, then we have _ab initio_ substituted for the judgment something which is a very {50} abstract corollary from the nature of judgment, and may or not for certain purposes and within certain limits be a fair representative of it. We cannot and must not exclude from the form of Knowledge its modifications according to “matter,” and its nature as existing only in “matter.”

In fact, the peculiar “form” of _everything_ depends in some degree on its “matter.” A statue in marble is a little differently treated if it is copied in bronze. A knife is properly made of steel; you can only make a bad one of iron, or copper, or flint, and you cannot make one at all of wax. Different matters will more or less take the same form, but only within certain limits. So it is in Knowledge. The _nature of objects as Knowledge_--for we _must_ remember that “form” in our sense is not something put into the “matter,” something alien or indifferent to it, but is simply its own inmost character revealed by the structural relations in which it is found capable of standing [1]--depends on the way in which their parts are connected together.

[1] The example of the marble statue may seem to contradict this idea; and no doubt the indifference of matter to form is a question of degree. But the feeling for material is a most important element in fine art; and in knowledge there is only a relative distinction between formal and material relations.

Let us compare, for example, the use of number in understanding objects of different kinds.

Suppose there are four books in a heap on the table. This heap of books is the object. We desire to conceive it as a whole consisting of parts. In order to do so we simply _count_ them “one, two, three, _four_ books.” If one is taken away, there is one less to count; if one is added, there is one more. But the books themselves, as books, are not {51} altered by taking away one from them or adding one to them. They are parts indifferent to each other, forming a heap which is sufficiently analysed or synthesised by counting its parts.

But now instead of four books in a heap, let us think of the four sides of a square. Of course we _can_ count them, as we counted the books; but we have not conceived the nature of the square by counting its sides. That does not distinguish it from four straight lines drawn anyhow in space. In order to appreciate what a square is, we must consider that the sides are _equal_ straight lines, put together in a particular way so as to make a figure with four right angles; we must distinguish it from a figure with four equal sides, but its angles not right angles, and from a four-sided figure with right angles, but with only its opposite sides equal; and note that if we shorten up one side into nothing, the square becomes a triangle, with altogether different properties from those of a square; if we put in another side it becomes a pentagon, and so on.

These two things, the heap of books and the square, are _prima facie_ objects of perception. We commonly speak of a diagram on a blackboard or in a book as “a square” if we have reason to take it as approximately exact, and as intended for a square. But on looking closer, we soon see that the “matter,” or individual attributes, of each of these objects of our apprehension demands a different form of knowledge from that necessary to the other. The judgment “_This_ heap of books has four books in it” is a judgment of enumerative perception. The judgment “_The_ square has four sides” is a judgment of systematic necessity.

{52} Why did we not keep the two judgments in the same logical shape? Why did we say “_This_ heap” and “_The_ square”? Why did we not say “this” in both propositions, or “the” in both propositions? Because the different “matter” demands this difference of form. Let us try. “The heap of books has four books in it.” Probably we interpret this proposition to mean just the same as if we had said “This heap.” That is owing to the fact that the judgment naturally occurs to us in its right form. But if we interpret “The heap” on the analogy of our interpretation of “The square,” our judgment will have become false.

It will have come to mean “Every heap of books has four books in it,” and a judgment of perception will not bear this enlargement. The subject is composite, and one, the most essential of its elements, is destroyed by the change from “this” to “the.”

Let us try again. Let us say “This square has four sides.” That is not exactly false, but it is ridiculous. Every square must have four sides, and by saying “this square” we strongly imply that foursidedness is a relation of which we are aware chiefly, if not exclusively, in the object attended to in the moment of judging, simply through the apprehension of that moment. By this implication the form of the judgment abandons and all but denies the character of systematic necessity which its content naturally demands. It is like saying, “It appears to me that in the present instance two and two make four.” The number of sides in a square, then, is not a mere fact of perception, while the number of books in a heap is such a fact.

But you may answer by suggesting the case that an {53} uninstructed person--say a child, with a square figure before him, and having heard the name square applied to figures generally resembling that figure, may simply observe the number of sides, without knowing any of the geometrical properties connected with it; will he not then be right in saying, “This square has four sides”?

Certainly not. In that case he has no right to call it a square. It would only be a name he had picked up without knowing what it meant. All he has the right to say would be, “This object” or “This figure has four sides.” That would be a consistent judgment of mere perception, true as far as it went. It is always possible to apprehend the more complex objects of knowledge in the simpler forms; but then they are not apprehended adequately, not _as_ complex objects. It is also possible to apply very complex forms of knowledge to very simple objects. Most truths that can be laid down quite in the abstract about a human mind could also be applied in some sense or other to any speck of protoplasm, or to any pebble on the seashore. And every simple form of knowledge is always being pushed on, by its own defects and inconsistencies, in the direction of more complex forms.

So far I have been trying to show that objects are capable of being different in their nature as knowledge as well as in their individual properties; and that their different natures as knowledge depend on the way in which their parts are connected together. We took two objects of knowledge, and found that the mode of connection between the parts required two quite different kinds of judgment to express them. Let us look at the reason of this.

{54} _The relation of Part and Whole_

3. The relation of Part and Whole is a form of the relation of Identity and Difference. Every Judgment expresses the unity of some parts in a whole, or of some differences in an Identity. This is the meaning of “construction” in knowledge. We saw that knowledge exists in judgment as a construction (taking this to include maintenance) of reality.

The expression whole and parts may be used in a strict or in a lax sense.

In a strict sense it means a whole of quantity, that is, a whole considered as made up by the addition of parts of the same kind, as a foot is made up of twelve inches. In this sense the whole is the sum of the parts. And even in this sense the whole is represented within every part by an identity of quality that runs through them all. Otherwise there would be nothing to earmark them as belonging to the particular whole or kind of whole in question. Parts of length make up a whole of length, parts of weight a whole of weight, parts of intensity a whole of intensity, in so far as a whole of intensity is quantitative, which is not a perfectly easy question. Wholes like these are “_Sums_” or “_Totals_”. The relation of whole to part in this sense is a very simple case of the relation of differences in an identity, but for that very reason is not the easiest case to appreciate. The relation is so simple that it is apt to pass unnoticed, and in dealing with numerical computation we are apt to forget that in application to any concrete problem the numbers must be numbers of something having a common quality, and that the nature of this something may affect the result as related to real fact, though not as a conclusion from pure {55} numerical premisses. In a whole of pure number the indifference of parts to whole reaches its maximum. The unit remains absolutely the same, into whatever total of addition it may enter.

In a whole of differentiated members, such as a square, all this begins to be different. A side in a square possesses, by the fact of being a side, very different relations and properties from those of a straight line conceived in isolation. In this case the whole is not made up merely by adding the parts together. It is a geometrical whole, and its parts are combined according to a special form of necessity which is rooted in the nature of space. Speaking generally, the point is that parts must occupy certain perfectly definite places as regards each other. You cannot make a square by merely adding three right angles to one, nor by taking a given straight line and adding three more equal straight lines to its length. You must construct in a definite way so as to fulfil definite conditions. The identity shows itself in the different elements which make it up, not as a mere repeated quality, but as a property of contributing, each part in a distinctive way, to the nature of the whole. Such an identity is not a mere total or sum, though I imagine that its relations can be fully expressed in terms of quantity, certain differentiated objects or conceptions being given (_e.g._ line and angle).

I take a further instance to put a sharp point upon this distinction. The relation of whole and parts is nowhere more perfect, short of a living mind, than in a work of art. There is a very fine Turner landscape now [1] in the “Old {56} Masters” Exhibition at Burlington House--the picture of the two bridges at Walton-on-Thames. The picture is full of detail--figures, animals, trees, and a curving river-bed. But I am told that if one attempts to cut out the smallest appreciable fragment of all this detail, one will find that it cannot be done without ruining the whole effect of the picture. That means that the individual totality is so welded together by the master’s selective composition, that, according to Aristotle’s definition of a true “whole,” if any part is modified or removed the total is entirely altered, “for that of which the presence or absence makes no difference is no true part of the whole.” [2]

[1] February 1892. [2] _Poetics_, 8

Of course, in saying that the part is thus essential to the whole, it is implied that the whole reacts upon and transfigures the part. It is in and by this transformation that its pervading identity makes itself felt throughout all the elements by which it is constituted. As the picture would be ruined if a little patch of colour were removed, so the little patch of colour might be such as to be devoid of all value if seen on a piece of paper by itself. I will give an extreme instance, almost amounting to a _tour de force_, from the art of poetry, in illustration of this principle. We constantly hear and use in daily life the phrase, “It all comes to the same thing in the end.” Perhaps in the very commonest speech we use it less fully, omitting the word “thing”; but the sentence as written above is a perfectly familiar platitude, with no special import, nor grace of sound or rhythm. Now, in one of the closing stanzas of Browning’s poem _Any Wife to Any Husband_, this sentence, only modified {57} by the substitution of “at” for “in,” forms an entire line. [1] And I think it will generally be felt that there are few more stately and pathetic passages than this in modern poetry. Both the rhythm and sonorousness of the whole poem, and also its burden of ideal feeling, are communicated to the line in question by the context in which it is framed. Through the rhythm thus prescribed to it, and through the characteristic emotion which it contributes to reveal, the “whole” of the poem re-acts upon this part, and confers upon it a quality which, apart from such a setting, we should never have dreamed that it was capable of possessing.

[1] In order to remind the reader of the effect of this passage it is necessary to quote a few lines before and after--

“Re-issue words and looks from the old mint,
Pass them afresh, no matter whose the print,
Image and superscription once they bore!
Re-coin thyself and give it them to spend,--
It all comes to the same thing at the end,
Since mine thou wast, mine art and mine shalt be,
Faithful or faithless, sealing up the sum
Or lavish of my treasure, thou must come
Back to the heart’s place here I keep for thee!”

We are not here concerned with the peculiar “aesthetic” nature of works of art, which makes them, although rational, nevertheless unique individuals. I only adduced the above examples to show, in unmistakable cases, what is actually meant when we speak of “a whole” as constituted by a pervading identity which exhibits itself in the congruous or co-operating nature of all the constituent parts. In wholes of a higher kind than the whole of mere quantity the parts no longer repeat each other. They are not merely distinct, {58} but different. Yet the common or continuous nature shows itself within each of them.

The parts of a sum-total, taking them for convenience of summation as equal parts, may be called units; [1] the parts of an abstract system, such as a geometrical figure, may be called elements (I cannot answer for mathematical usage), and the parts of a concrete system, an aesthetic product, a mind, or a society, might be called members.

[1] A unit of measurement implies in addition that it has been equated with some accepted standard. If I divide the length of my room into thirty equal parts, each part is a “unit” in the sum-total; but I have not measured the room till I have equated one such part with a known standard, and thus made it into a unit in the general system of length equations.

But every kind of whole is an identity, and its parts are always differences within it.

_Nature of Knowledge_

4. It will be well to sum up here what we have learnt of the nature of knowledge in general, before passing to the definition and classification of Judgment.

Knowledge is always Judgment. Judgment is constructive, for us, of the real world. Constructing the real world means interpreting or amplifying our present perception by what we are obliged to think, which we take as all belonging to a single system one with itself, and with what constrains us in sense-perception, and objective in the sense that its parts act on each other independently of our individual apprehension, and that we are obliged to think them thus. The process of construction is always that of exhibiting a whole in its parts, _i.e._ an identity in its differences; that is to say, it is always both analytic and synthetic. The objects of knowledge differ in the mode of relation between their {59} parts and the whole, and thus give rise to different types of judgment and inference; and this difference in the form of knowledge is a difference in the content of Logic, which deals with the objects of experience only from the point of view of their properties as objects in an intellectual world.

_Conclusion_