Chapter X: Introduction: I--Relation of Berkeley's Philosophy to Other Systems (3)

We may be unable to decide for any of the alternative data, but we work out all the possible arguments as hypotheses, and so are prepared in a degree for all the possible events. A person is seen approaching our residence, but we cannot discern whether it is A. B., who is a bore, or C. D., who is an entertaining companion. We argue rapidly--'If it is A. B. _I shall have a bad half-hour_, for he always wearies me; if it is C. D. _I shall have an agreeable distraction_, for he is very amusing.'

According to the syllogists, the dilemmatic premises are a statement of alternative data and the choice of one of them, and the inference is the rejection of the remainder: or the rejection may be given as matter of fact and the selection as conclusion. In neither case have we argument.

From the moment we select a datum the remaining data are of no import to us, and they need not be mentioned. The selection of one datum is logically identical with the rejection of the rest, and this is therefore not a conclusion from that.--'Do you take tea or coffee?'--'Tea, please.'--'Then I conclude you do not take coffee.'--A person who would 'conclude' in this fashion would be justly deemed irrational. The choice of the tea is a fact, and the rejection of the coffee is the same fact otherwise expressed, so that the rejection cannot be a rational conclusion.--'My doctor sends me off every winter to Nice, Algiers, or Egypt; but I never go to Algiers or Egypt.'--There is no occasion to say, 'therefore you go to Nice'; that has been already announced as a matter of fact and is not susceptible of inference. For the sake of verbal emphasis we might remark, 'So it is to Nice you go', but this is not logically requisite.

Whately's examples of this kind of theorem are exactly of the model just given.--'Either the earth is eternal, or the work of chance, or the work of an intelligent Being; it is not eternal, nor the work of chance, _therefore_ it is the work of an intelligent Being.' This is put forward in all gravity as a specimen of reasoning. It is plain that if we know the premises as matters of fact, we also know the proposed conclusion as a matter of fact. There is no occasion to reason about it.

The Aristotelian hypothetical can be reduced to arithmetical subtraction. Suppose we put five balls into a bag and afterwards take out three without seeing the remainder: is the judgment that two balls remain in the bag a logical inference? No--it is matter of fact. Since we last perceived the objects they have undergone diminution, but that does not confer on what is left of them the imaginary character proper to a rational conclusion. What remains is as much fact--recollected but not imaginary fact--as before the subtraction.

Whately's next example is--'It is either spring, summer, autumn, or winter; but it is neither spring nor summer; therefore it is either autumn or winter.' This is aggravated fallacy. Not only is it mere subtraction, but the remainder is _perceived_--not recollected, as in the preceding case. The actual season of the year is a known fact, and is not rendered more certain by an inference drawn from the absence of some other season. Arguments have no validity as against matters of fact, and add nothing to their authority. Fact is above, and independent of, argument. The example just cited may be paralleled thus--'The cards in my hand are either spades, hearts, clubs, or diamonds; but they are neither spades nor hearts; therefore they are either clubs or diamonds'.--I _see_ that they are either clubs or diamonds: the perceptual judgment renders the rational--imaginary--judgment superfluous. Reason is intended to supplement experience--not to supersede it.

XX--DEBATE

The purpose of debate is to determine the goodness or badness of an argument by general logical criticism and knowledge of the matter. This is not dialectic, but takes place after the dialectician has declared that a given theorem is valid argument. If then its conclusion is repugnant to us we may seek to stigmatise it--or remove a stigma as the case may be--by going behind the argument to the composition of the judgments that enter into it.

Let us take the case of Caesar being proved to be a tyrant in a society that punishes tyranny with death. There are two ways in which he may be saved or his punishment mitigated.

We are not bound to take the first precedent that is offered from which to generate a conclusion. We grant that Caesar resembles the general notion 'tyrant,' but we ask if he does not resemble in an equal or greater degree some other person or class in regard to whom capital punishment is no just treatment. Does he resemble a 'successful and patriotic general'--a 'benevolent monarch'--a 'wise legislator'--a 'virtuous man'? All these resemblances are compatible with his being a tyrant in some senses of the word. Let us not condemn Caesar for what may be a merely technical offence--the usurpation of authority--if in other respects he is an admirable man. So an opportunity must be given to Caesar or his advocate to suggest other precedents, yielding a different conclusion, by which to complete our imperfect knowledge of the case. Socrates, when he was brought under the class 'perverters of youth'--which also yielded the conclusion 'death'--suggested as an amendment that he should be classed under 'national benefactors,' with the conclusion 'maintenance for life at the public expense.'

It is not enough that we can say of a case that it 'is' this or that, and so proceed to draw the conclusion bound up in that classification. 'Is' in the case means likeness to the precedent, and one 'is' is good only when no better can be found.

If after having weighed the alternative precedents it appears clear that Caesar resembles tyrants more than any other class of persons, the prospect looks bad for him. But there is still a chance of escaping the worst penalty. It turns on the meaning of the word 'all,' which in logic generally introduces a proposition to which no exception has been found--the misnamed and misleading 'universal.'

Logicians do not hesitate to say that in this connection it means 'all possible, known or unknown, past or future individuals of the class.' They suppose, or talk as if they supposed, that at some fixed date in our life we enter into possession of our general ideas, and that no subsequent experience can modify them. Hence the moment it is admitted that Caesar is a tyrant, he is supposed to come under the rule of a stereotyped general idea with inflexible consequences.

This is not quite so. 'All' does not mean 'all possible' but 'all known up to the present time, _exclusive of the case under discussion_.' Our general or average ideas are the plasmic product of the individuals we have actually known--not a unit more. And as that idea is liable to be modified by every new individual examined, it is possible that on examining Caesar we may find reason to change our general idea, to the extent at least of dividing it into two species, the tyrants who deserve death and the tyrants who deserve some milder punishment, and that we shall resolve to bring Caesar under the latter species. Thus if the idea threatens to hang Caesar, on the other hand Caesar may burst the idea, and his case establish itself as a new precedent. That is how general ideas multiply--by a sort of fission.

In the proposition 'tyrants deserve death' as first proposed, we are dealing with the old general idea, and--as regards all individuals except those from which it was drawn--the proposition is little more than a hypothesis. The idea is itself on trial. Until Caesar is examined we do not fully know how the general tyrant is in future to be defined. Our examination of Caesar is a part of our education on the subject of tyrants. In judging we learn, and the general idea which remains _after Caesar is examined_ is that by which he is to be judged.

If our idea of tyrant remains unshaken after the trial of Caesar, and if he is found to resemble that class more than any other, then--and not till then--are we compelled to pass on him the judgment associated with the definition of tyrant.

An argument based on a particular or solitary precedent is criticised on the same principles. We seek to prove either that the case is not sufficiently like the precedent to justify the application, or that the applicate is not a property of the precedent. If we make good either of these propositions, we prevent the suggested conclusion from being fastened on the case.

The syllogistic dialecticians do not admit alternative precedents or reconstruction of general ideas: their terms and figures are not adapted to express such notions. Hence they cannot evade a conclusion whose premises are correctly given. They have an axiom to the effect that a judgment must be absolutely true or absolutely false--a door must be open or shut, it cannot be ajar; every colour is white or black, it cannot be green or grey, and so on. Now in practical reasoning we may and constantly do admit premises and reject the conclusions they dialectically involve. We look at the question 'from another point of view.' This means that while admitting there is some ground for bringing a case under a certain precedent, we contend that on the whole it is preferable to bring it under another precedent with a different conclusion. The proposed handle _may_ fit the vase somehow, but we think another sort of handle will suit it better. Or--rather than accept an objectionable conclusion--we will divide our idea. This is degree in truth. And that is the elastic method on which we reason in actual affairs. Logicians give a false account of reason, and so their systems are neglected and their authority is never recognised in real debates.

CATEGORIES

XXI--CATEGORIES OF SUBSTANTIALISM, AND OTHERS

A Category is primarily a class of Judgments. Since arguments are composed of judgments, a category is also a class of arguments; that is to say, the argument follows the classification of the judgment. This is not the practice of syllogists, who have categories for judgments only, the arguments being classified according to verbal expression.

I distinguish six categories--two Natural and four Artificial. The judgments of a natural category concern experience presented in a synthesis whose composition is due to the noumenal mind; the categories corresponding to this definition are--

Inherence--
Association.

An artificial category is so called because the synthesis is formed by the subjective mind.

The first category of this kind is

Perspection--

which is an artificial arrangement of objects according to a figurative interpretation of certain appearances they present.

The second artificial category I will call

Concretion--

as it is an ideal cohesion of experiences never wholly perceived at once. These two categories are those chiefly responsible for the realistic mode of thought.

The third artificial category is that which is called in science causation, but it is only

Sequence,--

that is, a series of phenomena sufficiently coherent to afford a basis for inference, but not necessarily or energically connected. Hume and others have conclusively proved that such phenomena are not causally related.

Finally there is

Causation--

in the proper sense of the word, that is, the relation between energic mind and its effects. This is the category of human affairs generally, and of all the Cosmic that we explain by analogy with the Human. It is the only exhaustive explanation of phenomena, and so is the category which philosophy would substitute for the rest. When we can truly resolve things into effects analogous to human actions, we have reached the highest standpoint from which they can be viewed. _Realistic_ anthropomorphism is the first and rudest explanation of things: _idealistic_ anthropomorphism is the last and most refined.

The artificial categories are all formed on analogies supplied by the natural, since the intellect is incapable of imagining anything absolutely original.

Each category may include judgments of other categories in a subordinate relation. Inherence and concretion enter to some extent as auxiliaries into all the others. A group category may be treated as an individual object for certain purposes, and an individual as a group of properties. In the one case a fictitious unity is created, in the other a real unity is imaginatively dissolved. But in general the categories are sufficiently distinct and may be considered as mutually exclusive. They will be separately analysed and exemplified.

The term category is used in common logic to signify the final classes into which _judgments_ can be arranged. To this minor use only is the category applied. It does not either denote a classification of _arguments_ or a distinct province of ideas whose origin and validity should be a matter of investigation. In Greek and modern logic arguments are distinguished solely by their verbal expression--never by the character of the judgment that enters into them. Treated in this superficial and haphazard way, the categories necessarily play a quite insignificant part in philosophy.

The oldest known set of categories is that quoted by Aristotle in his Metaphysic as being held by a sect of Pythagoreans. It consists of the following series of contraries--

Bound. Infinity.
Odd. Even.
Unity. Plurality.
Right. Left.
Male. Female.
Rest. Motion.
Straight. Crooked.
Light. Darkness.
Good. Bad.
Square. Oblong.

Aristotle's own categories are the following:--

(1) _Essence_ or _Substance_, as man, horse:
(2) _Quantity_, as two cubits long:
(3) _Quality_, as white, erudite:
(4) _Relation_, as double, half, greater:
(5) _Place_, as in the Agora:
(6) _Time_, as yesterday:
(7) _Posture_, as standing, sitting:
(8) _Having_ (Condition?), as to be shod, armed:
(9) _Action_, as he is cutting, burning:
(10) _Passion_, as he is being cut.

This list can be reduced to one half the number. Quantity, Quality, Posture, Condition are kinds of _Attribute_ or _Property_ of the Substance. Place and Time are valid. Action and Passion are both referable to causation. Non-causal sequence or consecution (as day following night)--one of the commonest judgments--is not mentioned.

The Stoics reduced Aristotle's ten categories to four--Substratum or Substance, the Essential Quality, Manner of being, and Relation.

Ka[n.]áda, a Hindu philosopher, has six categories--Substance, Quality, Action, Genus, Individuality, and Concretion or Co-inherence.

Plotinus was acquainted with the Aristotelian and Stoic lists and offers as his own:--(1) Fundamental forms of the _Ideal_--Being, Rest, Motion, Identity, Difference; (2) Categories of the _Sensible_--Substance, Relation, Quality, Quantity, Motion.

Descartes recognised but two final categories, the Absolute and the Relative.

Kant has an elaborate scheme of categories, which he considered to be, not merely classes of judgments, but innate power of the mind by which we are moved to form the judgments. They are the following:--

I. _Of Quantity._ Unity, Plurality, Totality.
II. _Of Quality._ Reality, Negation, Limitation.
III. _Of Relation._ Of Inherence and Subsistence
(_substantia et accidens_).
Of Causality and Dependence
(cause and effect).
Of Community (reciprocity between
the active and the passive).
IV. _Of Modality._ Possibility, Impossibility, Existence,
Non-existence, Necessity,
Contingency.

Sir William Hamilton's categories were Being, Being by itself, and Being by accident.

Categories have also been proposed by Spinoza, Locke, Wolff, Leibnitz, Herbart, Mill, and others. No two of them are alike. They are not formed on any definite principle, but are individual opinions as to the most convenient way to classify judgments[13].

XXII--INHERENCE

An object being given by perception we develop our knowledge of it, first by narrowing our focus of attention so as to perceive parts and single attributes of the object; next by widening our attention so as to include several objects in one view. The first process is Analysis or Abstraction; it informs us what attributes co-inhere to constitute the object. The second is Synthesis or Grouping, by which we learn the relations of one thing to others. These operations comprise all we know about a thing, for it can have no attributes which are not either internal or external.

Practical analysis means cutting a thing to pieces or dissolving it, and this has a certain value because it multiplies objects. But it does not increase our knowledge of the first thing. On the contrary, by destroying a thing we render a knowledge of it impossible. The analysis which gives knowledge is Metaphysical Abstraction--an attention concentrated on the parts of a thing without destroying their connection with the other inherent parts. The metaphysical elements may be quite different from the mechanically divisible parts. They are generally a species of things which could not exist alone, such as red, blue, straight, curved, square, round, acid, sweet, insipid, fragrant, sharp, hot, heavy, dull, loud, bright, and a multitude of properties of that abstract kind.

For many of these--at least for the description of them--a comparison of two or more things is essential. A sound is heard to be loud by comparison with another which is low or soft; a knife is known to be blunt by experience of another more sharp, or the same knife in a sharper condition. But comparison does not alter the essential character of abstract attention--it serves merely as an incitement to it. Difference between qualities otherwise alike whets our attention to a finer discrimination.

The properties recognised by each sense are easily distinguished in the bulk from those of another sense. Colour is distinct from Figure in a more marked degree than red from blue or square from circular. Fine degrees of Sound may be difficult to discriminate, but not the difference between a sound and a smell or a taste.

Still broader contrasts give rise to an artificial but sometimes useful kind of attribution--the negative. When we do not know much concerning the positive characteristics of a thing, it is something to know that it has _not_ this or that property. What Thought is, positively, few people know, but they are able to say (with a little prompting) that it is un-extended, im-material, im-ponderable, and so forth. This comparison re-acts on the thing better known, and so we call visual objects 'extended' from their dissimilarity to thoughts. But for that there would have been no occasion to notice the abstract extension of visual objects. The term 'visual object' would have tacitly included extension. There must be great and general ignorance of a thing to excuse the negative attribution: it is not allowable to speak of plants as non-metals, or sheep as non-horses, but a large class of animals is called in-vertebrate. In this case the negative property serves to bar a possible inference that all animals are vertebrate, since those we know best are so.

The judgment in this category is a consciousness of the attributes making up a thing, or so much of it as interests us. 'Cleopatra's Needle is an obelisk of granite, about sixty-eight feet high, and is carved with hieroglyphics.' If we go on to say that it stands on the Thames Embankment, we shift into the category of association. The relation of an object to its place is different from that of one inherent attribute of the object to another, or to the whole.

The properties of a general idea are defined in this category. The synthesis is natural or noumenal, the artificiality of the idea consisting merely in the omission of some of the concrete properties. 'Garden rhubarb [in general] has broadly cordate leaves, strongly veined beneath; the footstalks are long, thick, and fleshy, with a channel above; its growth is exceedingly rapid.' These are properties inherent in a unity not of our making. The botanist changes into the category of sequence when he says, 'the stalks are used for tarts and made into jam.'

In a complicated object or general idea some of the judgments we treat as inherent may be inferences in other categories used subordinately. 'The ancient Persians had remarkably thin and weak skulls. They were good horsemen and archers, courageous and spirited in battle. They wore a tunic and trousers of leather.... They were quick and lively, keen-witted, capable of repartee, ingenious, and--for Orientals--far-sighted. They had fancy and imagination, a relish for poetry and art, and they were not without a certain power of political combination.' Some of these properties might have been perceived objectively, but not the possession of fancy and imagination, which could only be known by inference in causation--here used to complete a coherent unity. The historian employs causation as a principal category when he tells us that 'their bards did not touch the chords which rouse what is noblest and highest in our nature.' The thought implied in touching chords--the notion of will directing action--is a different judgment from the perception of an inherent permanent attribute.

The argument in this category consists in ideally completing an imperfect object by comparison with a similar object, or the idea of a similar object. Suppose we have studied thoroughly one or more rhubarb plants, and then see a plant with broadly cordate leaves, footstalks long, thick, and fleshy, and having a channel above. In the time at our disposal we cannot ascertain if its growth is exceedingly rapid, but we are justified in inferring that it is, and that the plant we are examining is in all other respects rhubarb. If the Egyptian obelisks we have seen were sculptured with hieroglyphics throughout their length, and we see an obelisk part of which is underground, it is a rational inference that that part also is sculptured.

We have proved that certain samples of aluminium have a specific gravity of 2·6, and then see a metal--of specific gravity unknown--which has all the other properties of aluminium: we may confidently infer that this metal also would, if tested, show a specific gravity of 2·6.

For purposes of reason it may be necessary to compare things that cannot be brought physically together. When this happens we generally compare them in _idea_, or the idea of one with the other as object. When great accuracy is required and the idea--which is always rather vague--cannot be relied on, we have recourse to mediate comparison. _Standards_ are employed. These are manageable or portable objects with which principal things are separately compared by way of effecting indirectly a comparison between them. Standards can only mediate comparisons between _abstract_ properties, for if they contained all the concrete properties of the compared objects they would, by supposition, be as unmanageable as the latter. We have standards for length in rules, scales, tapes, chains; the balance is a standard for weight. There are also scales for pitch of sound, varieties of colour, degree of light, heat, atmospheric pressure, and probably some others for special purposes.

Indirect comparison is not in itself inference; or if inference it is subordinate and preparatory to some more important conclusion. A coin is weighed and concluded to be _light_, but this is only a datum in determining the more important question whether it is a forged coin or not.

XXIII--ASSOCIATION

In this category we widen the attention so as to include several objects in one act of perception.

The first result of this diffusion of attention is to lessen the brilliancy of objects. Our attention is a light which is intensified when narrowed and concentrated--enfeebled when dispersed over several objects. The observation of a group amounts practically to observing the objects in rapid succession. At a given moment we perceive only one thing well, or it may be only a small part of a thing, but we have a dull sense of other things adjacent, which we have just seen and may immediately see again in any order we please. That is all that is meant by perception of a group.

To distinguish this category properly from the next we must consider the group of objects as divested of depth or distance outwards. It is to be regarded as a flat surface standing a few feet from us, the objects in it having absolutely the dimensions they appear to have. This is in fact their _real_ magnitude, for the supposed real magnitude is a matter of theory, and means the perceptual magnitude taken under certain conditions of observation. The real magnitude is constantly changing, so for practical convenience in determining size, etc., we refer all objects to one condition of observation--that in which they can be touched as well as seen.

In metaphysic we are not obliged to recognise this convention. If an object a mile off appears to be an inch high, it is an inch high as really as if it were in a photograph or picture and materially represented of that height. The mystery of the change of size in objects is not explained or reasoned away by any device for overcoming some of its practical inconveniences. It depends on the degree of energy with which minds affect each other.

A group has properties which an object has not; or, if this be not strictly the case, we may say that the properties we look for in a group are not those we distinguish in a single object. The special properties of a group are _positions_. It is unnecessary to say 'relative' positions, for position cannot be otherwise than relative. Position cannot be defined by reference to anything more simple. What is meant is intuitively known to everybody. But let us take a concrete example--a man with a horse and cart standing on a bridge. Each object in this group has a position towards the other objects. The bridge is _over_ the river and _under_ the cart; the cart is _upon_ the bridge and _behind_ the horse; the man is _in_ the cart; the horse is _before_ and _outside_ of the cart, it is _near_ one end of the bridge, _far_ from the other, and _between_ the two extremities. These are the principal positions in a natural group or association, by which is meant the objects we can see (or are supposed to see) simultaneously, and whose mutual positions we are considering.

The use of observing positions is the same as that which moves us to all rational study, namely, its value in prediction. We can reason from one object to another in a group just as we reason from one property to another in an object.

Suppose our perception of a landscape is interrupted for a moment, and when we next endeavour to perceive it we find we only perceive a portion of it, the rest being 'hidden' by an intervening object. As far as we are concerned the hidden part has been annihilated. We only remember what was there. But this recollection is also a preconception of what we may be able to cause to appear again, either by removing the obstructing object, by waiting till it has been removed, or by walking round and standing between it and the landscape.

If this be too close to mere recollection, we have pure reasoning when from the general appearance of a group we imagine generally some concealed part of it not before seen. A procession of people dressed in mourning is usually accompanied by a hearse: from perceiving the people only on a certain occasion we predict the hearse. The sound of a steam-whistle enables us to imagine a train in a certain locality, though fog or other obstruction may prevent our seeing it. The scent of flowers prepares us for finding them somewhere near us. From smoke we predict the nearness of a chimney. The trail of an animal is a clue to his position.

The judgment in this category is therefore a consciousness of position, such as those mentioned above. The argument is a completion of one association by comparison with another--the expectation of similarity in groups.

_Movement._ All judgments as to _change_ of position in objects come under this category. It takes at least two things arranged in a group to produce the perception of movement. If there were but one thing in our field of observation we could not say whether it moved or not, for there would be nothing which it would pass, or leave, or approach. It would appear to stand still. There is, however, more in movement than depends on mere perception.

All movement is due to energy either in the observer or in the other mind acting upon his. Energy is not a generalisation of moving things, nor a property, nor a relation, though all these may be signs of energy. The most abstract idea of movement is _Motion_. It may be defined as a series of positions.

_Number._ If we treat a group as a large loose object we shall perceive in it certain properties not strictly positional. Number is one of these.

A group of three coins has not the same practical value as a group of six or sixty, and we are thus obliged to notice the difference and distinguish degrees of this property by names--hence Arithmetic.

_Flat Space_ or space of two dimensions is another property of a group. Grouped objects have frequently intervals between them. Such intervals are negations of perception--interruptions or discontinuities of experience. But by abstraction we can reduce the objects bounding an interval to a geometrical line, and so give a sort of positive existence to the interval. Thus we talk of a hole or of darkness as if they were true objects, and measure them by standards of length.

If we abstract the boundary lines from a space we get the idea 'intervalness,' which is the right name for two-dimensioned space. This abstract idea is nearly the same as abstract size. Space is interval without bounds--size is object without contents. Space and size are equally _nothing_ intrinsically or in their own right, but they have been reached by different modes of refining away the positive qualities associated with them, and this difference of origin is slightly suggested by their names. Spaces have a use in perception similar to _rests_ in music--they relieve the attention and give contrast and vigour to the next positive object.

XXIV--PERSPECTION

This is the first of the artificial categories. It is an ideal treatment of an associated group to facilitate a certain kind of reasoning.

Reason--let me repeat--is the imaginary extension of experience by comparison with more complete experience of a similar kind. By reasoning in inherence we complete single objects; by inference in association we complete groups. These two categories demonstrate that a natural group consists of fragments of objects, and fragments of other natural groups which are possible but not yet developed. A hill is partly concealed by a house, the house partly concealed by a tree, the tree by a stone fence, the fence by a growth of ivy. A river disappears at a curve and is lost to view; we know from experience of other rivers that under certain conditions we might perceive the river further on as a feature in several more landscapes. As we gaze at an association of objects these possible completions occur to us--not fully or definitely but sufficiently to convince us that the group might be developed into many other groups, and into a multitude of objects of forms different from those we actually perceive. By our hypothesis the observer has always been stationary, the objects have moved to and fro but not from near to far. Their real dimensions have remained unaltered, and nothing has occurred to suggest that they ever appear of other dimensions. In short we are gazing on a piece of stage-scenery.

But there is another element in perception. We and all other real (mental) beings are part of the cosmic force. We are co-creators of what we perceive--limited gods, not machine-men as the scientific people would have us believe. But for our power of affecting each other and our readiness to receive impressions from other minds, there would be no perception--no material objects. We (that is, all sentient beings) could, by unanimous resolution, annul the material creation--blot out the universe of objective things in a moment. United to and implied in this general power is the particular power of modifying our world without destroying it. We can redistribute the active and passive forces so as to produce other perceptual effects than those present at a given moment. And we habitually do this to some extent. Within a limited scope our world is plastic as dough, and we knead it to any form we please. For example, we exert energy to change our place, and immediately the group before us breaks up and undergoes metamorphosis. Some objects disappear altogether, and entirely new objects present themselves. Some become smaller, others larger; some fractional forms fill out to completion, some integers undergo curtailment, others separate into several distinct objects. In a few minutes the first group has dissolved into a second, which may merge into a third, and so on indefinitely.

In contemplating these phenomena we discern a third form of completeness and incompleteness, distinct from those that enter into inherence and association. Hence a new type of reasoning--another category: the Perspective.

It will be convenient to suppose that the modifications to which it refers are solely due to the observing mind, as the most conspicuous and comprehensive really are, but some of the minor perspective changes are due to the noumenon of the object.

We have first to get a criterion of perspective perfection. What this shall be is to some extent a matter of convention. The standard I shall adopt is, that an object of a nature to be perceptible to all the senses would be most perfect if within reach of touch. If it can be heard it is then heard at its loudest--this is correct enough for our purpose,--if it can be seen it is then seen at its largest and brightest. This is Perspective Completeness at the Tactual Range. It means the closest contact of noumenon and subject, compatible with clear definition in perception.

Now let us exert energy and disarrange a group. Those things that were or might have been tangible in the former position, are no longer so, but they may still be seen, heard, or even smelt. The bright colours have however somewhat faded, the size has shrunk, some of the details are lost. Here is a lapse from perspective completeness. It is indicated, not as in the first two categories by mechanical cutting away of mass and circumstance, but by deterioration all over the object. We seem to be thrown out of focus in relation to it, and the perspective degradation may increase until the object has dwindled to a speck and finally disappears altogether.

The judgment in this category consists in observing the kind and degree of degradation to which things are liable in perspection. In addition to change in size, brightness, detail and loudness, which have been already mentioned, occultation as in the second category can be used as an indirect datum. An object which eclipses another is invariably more perfect perspectively than the object eclipsed. The motion of objects has also to be taken into account. As objects degrade their movements slacken, and recover power as the objects are restored.

By attending to all these indications and checking each by the rest, we have the elements of a fairly accurate inference as to comparative perspective condition. We have constant practice in this sort of thought with frequent opportunities of verifying our conclusions; penalties are annexed to failure and rewards to success. It is no wonder then that in the course of years we become expert in judging of perspective condition, so that when confronted with a natural group we can estimate almost instantly the degree in which each object falls short of perspective integrity.

The result of this practice is that on perceiving a natural group of many objects, we graduate them according to the perspective deterioration which each exhibits, and for greater precision we figure the perspective difference as an interval between the objects--an imaginary interval modelled on the true interval of association. The object on a distant horizon is visually as near as the ground we can touch by stooping, but in this imaginary group the former is placed at the far end of the line and the latter at the near end, and between them are ranged the other objects each at a point corresponding to what we suppose to be its perspective distance. That is how a landscape acquires depth. Space outwards is an ideal imitation of real lateral interval. It is the measure and expression of perspective defacement.

From what has been said it follows that the near objects will be relatively large, clear, and lively in motion, while the far will be small, dull, and slow, but this rule is liable to many exceptions which can only be learnt by experience.

On the analogy of the other forms of inference--which consist in completing imperfect things by reference to others more perfect--the essence of an argument in perspection is the power to imagine an object which is perspectively defective, brought up to the tactual range and displaying all the qualities it would possess in that position. This is done by comparing it with the idea of the same or a similar object experienced at the tactual range; and is done for an ulterior purpose, like all other intellectual operations. A great part of our material happiness consists in the exercise of the short senses (taste, touch and smell), and the chief use of perspective reasoning is to enable us to judge of the energy required to bring a distant object near for close perception. We have therefore to observe our energic fluctuations in conjunction with perspective change, if we would extract the utmost practical benefit from this category. The perspective inferences are none the less useful after we discover that they are not intuitions, and that the completeness we imaginatively assign to distant objects has no existence until we exert the corresponding energy.

A landscape being rendered perspective we can determine the perspective state of any new object that may enter it, by reference to the objects adjoining it, and this though the object be of a species quite unknown to us and which therefore, by itself, would afford no clue to its perspective distance.

The imaginary interval we place between objects of different perspective effacement, can be expressed in terms of exact lateral measurement. This is done by developing and measuring the associative groups represented in the perspective group. Supposing we wish to get an exact definition of the perspective condition of a mountain relative to a certain station, we can, from that station, develop all the natural groups up to the mountain (walk over the ground) and measure the lateral intervals and masses disclosed. The total measurements will be a definition of the mountain's perspective distance in terms of true associative distance. That is what we mean by saying a mountain is ten miles off. It is not _really_ ten miles off--it is not an inch off. But to render it tactually perfect we should have to expend an amount of energy equal to 17,600 times the energy required to move from one associative object to another a yard apart from it laterally. If we practise the mileage scale in conjunction with the perspective indications, we may acquire the art of expressing in miles, though not measured, the distance of objects estimated from purely perspective data, but few can do this with any near approach to exactness[14].

The realistic three-dimensioned space is a combination of the true interval of association and the false interval of perspection. This generates an idea resembling the capacity or vacancy in a room or vessel, and thus it is supposed that objects occupy a sort of universal room without walls, floor, or ceiling. It is however the enclosing objects which make a room, and when they are abstracted there remains nothing. The universal room is therefore nothing--a myth. It is a useful working theory for common purposes, but in philosophy it is superfluous and obstructive.

In the definitions of geometry no difference is made between the depth of a landscape and the 'third dimension' of any small cubic object. They are both called 'third dimension' or 'cubic dimension.' Yet they are inferences of different categories, and neither is real. The former, as we have just seen, is the imagined redintegration of objects perspectively shrunk and defaced. The latter is the imaginary completion of a thing having many surfaces or facets, only one of which can be shown at a time.

_Sky Perspection._ The effect produced on our mind by the observation of celestial objects, reveals at once the artificiality of cubic space. Clouds in their form and movements are somewhat like earthly things--vapour or mountains,--and so we conceive them partially graduated in distance and floating in a concavity. But whether they are a mile off, or twenty miles off, few of us can tell.

When we contemplate the sun, moon and stars, our realism is completely at fault. These we cannot modify at will, and they move too slowly and present too uniform an aspect to cause the perspective effect. Since we have never seen them at the tactual range we know not to what degree they are perspectively incomplete; hence they appear without relative distance--distance being simply a metaphor of perspective effacement. If 'cubic space' is real, let the realists tell us why we do not see it in the sky--why we do not arrange the stars behind each other according to their calculated distances. This question is unanswerable realistically, but idealistically it presents no difficulty. The sky is not spaced, because the conditions are wanting under which the illusion of terrestrial space is formed in the intellect.

By close instrumental attention to the moon and planets a slight parallax is observable, and on the analogy of terrestrial parallax astronomers are able to calculate what they call the distance of these bodies. Perhaps their calculations are right, but the magnitudes are not conceivable as associative distance, being so much greater than we have any experience of. We take them to mean that the heavenly bodies are extremely degraded, perspectively speaking. Their noumena are in contact with our minds, for this is essential to perception, but if astronomical calculations are correct the contact is infinitely slight, compared with what it would be, supposing--to speak realistically--we could go to the stars or they could be brought to us.

Berkeley's _Theory of Vision_ and _Dialogues_ are occupied with the analysis of perspection. The arguments he uses to show that distance outwards is not real are in the main those given in this section.

XXV--CONCRETION

If we take a cricket-ball in the hand and turn it round we shall perceive a series of discs. Only one of these can be seen at a time, but if we perceive and remember the whole series we shall be able to infer all from the perception of one in a similar object. The same occurs with other cubical or solid objects. This is a form of ideal construction different from any we have yet considered. It differs from inherence in that the object which we conceptually put together is never objectively perceived as a whole. It is an imaginary whole constructed in the intellect out of fragmentary experience. It differs from association on the same grounds; the latter can be all perceived at once in forming the judgment. It differs from perspection in that the imperfection of experience is due to curtailment, not to general deterioration. What we actually see may be perspectively perfect. It differs also from the next category in that the series of perceptions can occur in various orders of succession.

_The 'backs' of Things._ We talk of the back of a thing, but nobody has ever seen a back. Things have no backs in the popular sense of the word. When we turn round a back to perceive it, it is then a front. Everything is a flat upright surface, and its appearance of solidity can be imitated on a surface known to be flat, and with nearly the same illusive completeness as in the original object. In turning things round we merely change the surface; we are exercising our power to alter primary consciousness.

When two persons perceive the 'same' object from contrary directions, the sameness means that the two objects proceed from the same cause, or can be reduced to the same general idea. But the objects are numerically distinct. By a similar turn of speech we say that A and _a_ are the same _letter_, but they are evidently distinct and dissimilar objects. If we hold a thing before a mirror and see what is termed its back, we produce a new object resembling the first in some respects but without its resistance.

Resistance is a negative term signifying the limit of our power to alter primary experience. Where our power ceases resistance is said to begin, and we meet with resistance when we apply a power inadequate to the desired effect.

Dr. Johnson's solitary experiment in idealistic philosophy has been often related. He struck a post, and because it did not disappear he thought he had disproved Berkeley's statement that material objects exist only in the perceiving mind. The experiment merely showed that all means are not adequate to change all primary experience. Had he shut his eyes, or turned a corner, or occupied his attention with other matters, the post would have vanished. He chose improper means and therefore met with 'resistance.' No idealist believes we can change our primary experience by any capricious and frivolous means[15].

_Geographical Concretion._ The knowledge of large geographical areas is an artificial construction without objective reality.

Our experience is, literally and exactly, a series or sequence--a flux or stream. It is composed of objects or of groups, according to the width of our attention. If we travel over a large tract of country the experience is a train of objects or views, which follow each other continuously but for interruptions in attention. If we were bound to think of things in the order in which they were experienced, we should have to imagine our topographical consciousness as a long ribbon of views, like the pictures of a panorama. Supposing we travelled hither and thither over one county, it would appear to us as a straight strip of land which might be several hundred miles long. If we again traversed the ground, but in another order, we should have another strip resembling the first, but also differing from it, and it would be necessary to keep the two from being confused in our mind. If several persons traversed the same ground but in divers directions, they would each retain a different recollection of it, and it would be extremely hard for any two of them to agree as to the order in succession of any portion of the ground traversed.

Our experience of the natural group suggests a mode of treating our geographical experience which overcomes many of these inconveniences. We find that we can traverse (either bodily or by the eye) a single landscape in a thousand directions, and retain a memory of it without any reference to these directions. What we remember is the mutual positions of the objects, not the order in which they were observed. As this greatly facilitates the memory of one group, we apply the same principle of synthesis to the succession of groups composing our geographical experience. We dismiss from our minds the order of observation, and construct instead an imaginary group of associated objects or places having mutual positions. It is imaginary, for no one has ever seen as a co-existent synthesis the objects of a county, not to speak of a country or continent. Substituting for memory of succession, a memory of position, there grows up in our mind a large co-existent image of a country on the model of a single group, which affords all the advantages as regards economy of energy which we enjoy by virtue of comprehending a natural group in one act of consciousness.

Take an instance of this economy. Suppose a man travelled from London to Oxford, then to Exeter, then to Portsmouth, then to Brighton, and afterwards desired to return to London. If he, acting on a mistaken conception of truth and disdaining instruction from others, persisted in remembering the objects perceived on his journey as--what they no doubt literally were--a continuous series, he would be unable to imagine any way of returning to London except by reversing the order of his journey. If on the other hand he carried in his mind an image of the ground in question, with the mutual position of the places, it would enable him to _foresee_ that London was to be reached by journeying northward from Brighton, in far less time and at far less cost than by returning the way he came. Thus does conceptual position, when it is correctly imagined, prove its superiority to the order of experience. And we say that the ideal picture is truer than the crude memory,--not that it is really so if natural order is a test of truth, but because it is the least onerous, which is our practical standard of truth. The only object of knowledge being the wise management of energy, that sort of knowledge must be considered truest that enables us to have the feelings we desire at the least cost. In one sense truth means the quickest and easiest way of passing from one state of consciousness to another preconceived state.

It may be objected to the above example as a valid deduction from an imaginary synthesis, that the relation of London to Brighton is now a certainty, whereas an inference can be no more than a probability. The reply is, that if a man has already traversed the route in question, it is to him an actual experience and his idea of it is ever afterwards a memory, not an inference. But until it is actually perceived it must be imaginary, and therefore slightly problematical. Although a man is convinced that others are not deceiving him in saying a place is to be reached in a certain way, he cannot be absolutely sure that he fully understands the directions given, in other words, that his image of the route corresponds to their perception of it. There probably never is exact similarity between one man's primary experience and another man's idea of it. It may even be doubted whether there is ever exact similarity between a man's own primary experience and his subsequent idea of it.

The geographical synthesis is founded on actual exploration supplemented by inference. The mutual position of some important places are determined and serve as precedents for a multitude of minor positional deductions. _A_ is twenty miles north of London, _B_ is ten miles south of London, hence _A_ is thirty miles north of _B_. The mileage is determined by imagining the synthesis developed into natural groups and measured laterally. Other scales are the time spent in travelling between the places, or the money it costs, or the distance delineated on a map.

Though the geographical concretion may be modelled on the association, we cannot treat it perspectively, for the places being purely ideal (except the one we are at), the ideal image is not liable to deterioration by weakened perception. It may suffer degradation by forgetfulness, but that has nothing to do with perspection.

_Sphericity of the Earth._ The geographical synthesis is not always formed on the pattern of a natural association. That is the first and most obvious shape to give it, and for thousands of years it appears to have answered the topographical needs of mankind. But as exploration extended it was found that the associative theory did not in some cases afford true preconception. If we travel far enough in any fixed direction we shall return to the point from which we started. This could not have been predicted from a synthesis formed on the model of a landscape. Such a return however takes place in the objects denominated spheres, and so the spherical instead of the flat form has been conceptually given to the geographical concretion. That is all that is meant by saying that the world is round. There is no world, as the mystical realist--projecting outwards his mental synthesis--imagines. There is only a scheme of spherical positions in the intellect, which facilitates the recollection of places and enables us to foresee the shortest and easiest way of reaching--_i.e._ experiencing places. The concretion is true inasmuch as the prediction is found to coincide with real experience. But that by no means implies that the places exist except when perceived in minds.

XXVI--SEQUENCE

Sequence is a series most resembling a procession of objects in a natural group (second category). It differs therefrom in that the objects cannot be seen together. It differs from concretion in that the order in which the objects appear cannot be altered, or if they are human and alterable we cease to treat them as a sequence. They no longer have the predictive value which moves us to form artificial groups of objects.