CHAPTER XV.
THE CONDITIONS OF KNOWLEDGE
EX PARTE SUBJECTI.

II. -- THE INTELLECT.

§ 267. By its functions, its powers of abstraction, of generalisation, of relational judgment and inference, the faculty of intellect is evidently distinct in nature from that of sentience. As a cognitive faculty, if our causal theory is to hold good, it must be, of course, a potentia passiva. But it is not merely a potentia passiva; it is in another aspect active, and hence is called an intellectus agens. The intellectus passiva or possibilis is simply the intellect considered as passively receptive of forms or species derived from the phantasm or sense-impression and ultimately from the objects. The functions of the intellectus agens, on the other hand, are many. Knowledge is gradually built up by a slow process in which analysis, synthesis, induction and deduction, postulation and verification all play a part. But just as a building cannot be constructed by merely beating the air with hammer and chisel and trowel, but postulates materials as well as tools, so our intellectual activities would be useless unless somehow they could obtain material upon which to work. We must get ideas from somewhere, for it is upon ideas and their relations that the whole superstructure of knowledge is built. Hence, the first intellectual function which we must discuss is that of apprehension or abstraction, for it is by this that our ideas in the first place are formed.

§ 268. Apprehension must not be confused with conception, which is a much more complex process, implying often both judgment and inference. Apprehension is simply the process by which from the phantasm, image or sense-impression, the idea is obtained. Now the phantasm is concrete, particular, complex, and rich with a multifarious detail; whereas the idea is abstract, general, and, in the first instance, simple. The idea, therefore, is something different from the phantasm. Hence, the phantasm does not of itself determine the actus of the intellectual potentia; but some process of abstraction is involved in which the universals implicit in sense-impressions are apprehended. It is the individual which is presented in sense-perception; but the individual, being complex, cannot be known all at once. We have to attend first to one aspect, then to another, all of them simple at first, yet corresponding to some aspect of objective reality, because, though the phantasm does not itself per se and simpliciter determine the idea, it does so impelled, as it were, by attention and controlled by the selective activity of the intellect.

§ 269. Thus knowledge begins with elementary notions such as existence, being, unity, quality, change, duration, extension, direction, distance, on the objective side; and psychical existence, thought, sensation, volition, activity, etc., on the subjective side. All these notions, and others besides, are both simple and ultimate for us; by which I mean, not that they cannot be analysed metaphysically or logically defined, but that in origin they are ultimate, since they are ideas which we apprehend directly in experience. Such ideas are often vague at first, and consequently are regarded by some as bare and empty. Yet in spite of their alleged bareness and emptiness, and the unquestionable difficulty there is in defining them, they are more valuable for knowledge than any phantasm, for they have something which the phantasm has not, viz., meaning or objective significance. The phantasm is a picture which means nothing except to an outside observer. The idea is significance itself, for in it we know the object and are aware that we know.

The significance of the idea in a sense is unique and peculiar to the product of intellectual activity, which alone has conscious 'objective reference.' But it presupposes correspondence between the idea and the objective entity that is signified by that idea. This correspondence is due to the fact that the idea is derived from the phantasm. For the phantasm, as we have seen, corresponds with reality; and in the phantasm the idea is implied, though it does not exist there as such, but has to be analysed out, so to speak, in abstraction. When, therefore, in an act of intellectual apprehension, the phantasm determines the idea, it communicates to it that objectivity which itself unconsciously possesses on account of its own determination by the object. In short, the idea has meaning and objective significance, because it corresponds with reality; and it corresponds with reality because through the phantasm it is itself determined by reality.

§ 270. It may seem, perhaps, that in this somewhat complex metaphysical analysis I have been guilty of the Kantian error of splitting up the mind into innumerable water-tight compartments. But this is not so. For, in the first place, my account of cognition is far less complex than (v.g.) the physiologist's account of digestion; and since things are complex, and especially Man, complexity is no argument against truth. Secondly, the faculties and functions I have been describing are not contained, like so many pills within a box. On the contrary, they presuppose that the mind is one; and unless the mind were one, and unless in sense-perception thought and sensation functioned together, no matter how many faculties we had they could not give us knowledge. Some have said that sense-perception is a form of inference; but I reject this view precisely because it seems to divide sense-perception into two processes, whereas for consciousness it is one. The perception of a complex object implies inference in the past; and possibly to an outside observer perception itself would appear like an inference, since in it thought formulates what sense-data implicitly contain. But this is not what we ordinarily understand by an inference, nor is it for consciousness an inference at all.

§ 271. There are ideas, however, which are obtained by a process still more analogous to that of inference; and yet they are ideas which for us are simple and ultimate. Among the simple ideas which I enumerated above, almost all belonged to the level of accidents or phenomena, and all were directly apprehended in the data of experience. But there are other ideas which seem to involve an intellectual function which is something more than mere abstraction. I refer to such ideas as substance, cause, and purpose. Substances, causes and purposes are implicitly contained in the data of sense-experience; but they are not contained in the same way as quality, change, extension. They are presupposed as the metaphysical conditions of the accidents and accidental modifications to which sense-data directly correspond. It has been suggested, indeed, that the notion of substance is given in self-consciousness, causality in the influxus of the will into action, and purpose in conscious striving after an ideal. Indeed, it will hardly be disputed that purpose is revealed directly in the data of our inner experience. But in regard to substance and causality the question seems to be more doubtful. Hume's analysis revealed no 'sensations' of which they could be regarded as 'faint copies;' and many since Hume have declared themselves unable to find any data to which they correspond. On the other hand, we are certainly conscious of ourselves as real individuals, and again are certainly conscious of active processes as well as mere states of consciousness. We all know what we mean by activity, volition, control, self-determination, responsibility. And that certain 'something' which we call self-conscious activity has a dual aspect, which is not adequately expressed by the notion of antecedent and consequent, but is adequately expressed by the notion of cause and effect. Hence, while in external perception succession is all that is given, self-conscious activity implies something more than mere succession, and it seems to be from this that the notion of causality is derived. But, in any case, we know what is meant by a cause, for, if we did not, it would be impossible to talk rationally of metaphysical conditions and logical presuppositions; in fact, we could scarcely reason at all. Granted, however, that we have some such notion, it is not difficult to see how causes, substances and purposes alike are implied in the data of objective as well as in subjective experience.

§ 272. Thus, Causality is implied in change, which is a notion derived directly from objective (as well as subjective) experience. Change involves a transition from not-being to being; and since not-being of itself cannot give rise to being of which it is the negation, we infer a something which causes the change. Change, like incompleteness and limitation, implies a something beyond itself, a something to which that change and that limitation is due. Thus far every man goes, for every one talks of causes and seems to talk of them rationally and to understand what they mean. But to determine precisely what is the cause of any particular event, or to determine whether events in general presuppose an ultimate cause or an ultimate ground is quite a different matter, and one with which the plain man is hardly concerned.

Substance, too, is a notion which every one possesses and which he uses in almost every judgment that he makes. It is implied in the 'this,' which he takes as the subject of his propositions; and experience itself forces him to recognise that the 'this' is one and yet many; that it exists and is permanent, and yet is subject to change. All accidents, qualities, appearances, modifications, when considered in the concrete, are referred to some individual, either to something outside us or to the self; and this predication of accidental differences of a substantial ground is not an arbitrary process but a process which is forced upon us by experience. Qualities are given in combination; and though we cannot predicate them until we have formed an idea of each in distinction from the rest and an idea also of the unity which they presuppose, as soon as these ideas have been formed, we are constrained by experience itself to combine them in the way in which we do. Things qualitatively different and spatially distinct from their neighbours manifest within themselves structural differences. They have many qualities, all of which are localised in the same objective thing. Experience compels us to affirm that a thing is a unity in difference, and the concept of unity in difference is, as we have seen, but another form of the concept of substance and accident. Or, again, looking at the matter from a different point of view, and applying our notion of causality, we may say that things are one, because they act as if they were one. And in general this principle is true. Actio sequitur esse, for there is nothing else from which it can proceed. The actor who successfully impersonates Macbeth can do so only in so far as he has the same nature as Macbeth, the same passions, the same love of power, the same hatred of all that stands in his way; though in ordinary life he may keep these passions in check. A many-sided activity proceeding from what is spatially one implies that it is really and substantially one, or, in other words, that its activities are held together by a unity of ground or form. Thus the recognition of substantial unities, no less than the recognition of real causes, is forced upon us by experience itself; and is due to the fact that there are real causes and real substances which determine directly or indirectly the content of our thoughts.

§ 273. On the other hand, among material things, it is difficult to distinguish what are substantial unities from what are not; or better, perhaps, it is difficult to locate the substantial unity. Is a lump of sugar a substantial unity? Certainly it is substantial, for it unites within itself sweetness, hardness, whiteness, and other properties characteristic of carbon compounds. But is it one substance or many? It would seem that it is many, for it consists of innumerable particles, cohering together, yet in reality distinct and individual, and each possessing the characteristics that belong to what we call sugar. But it hardly behoves the metaphysician to distinguish between one substantial unity and another, provided he can show that his concept of substance is in general valid, and can state clearly what he understands a substance to be. A body which consists of parts and possesses properties relatively distinct and mutually independent, yet held together and controlled by some one principle or form which makes each and all the parts different from what they would be, were they really distinct and separate, and which causes them to act as one -- as in the case of a man, an animal, a plant, and even an atom as conceived in the electron theory of J. J. Thompson -- is certainly a substance. But if the parts of a body are really divided and merely cohere together by mutual attraction or by some external force, then that body is not a substantial unity, but an aggregate of substantial unities which interact. It is, however, for the physicist and the chemist, not the metaphysician, to draw the line between substantial unities in the concrete.

§ 274. The ideas of substance, cause, being, existence, quality and such like simple and ultimate ideas are, then, objectively valid, and unless they were valid and were strictly derived from and determined by objects themselves, through the mediation of sense-perception, knowledge itself would be a farce. It is impossible to trace with anything approaching accuracy or certainty the development of these ideas, or even to ascertain in what order they are first derived, for we cannot live again the period of infancy and youth. Still, in analysing more complex notions, we arrive finally at simpler notions which cannot be further analysed, nor yet defined, but which none the less have meaning and significance. To define a straight line is impossible, for it throws us back at once upon direction; and direction, though it can be illustrated and pictured, since it is contained in the data of experience, is for us an ultimate notion which we understand and are constantly using, but are unable to define.

§ 275. Every abstract notion, whether ultimate or not, represents but an aspect of the real thing, and so is incomplete. It has positive content, but it also implies a relation to something else; and often enough if we wish to define it we can do so only by reference to something else. For the realist, however, this does not mean that ideas and their relations are structural differences or appearances which emerge within the universe as a whole and imply an immanent Ground; but that the plan or design according to which the universe is constructed and according to which changes in it take place, is rational and intelligible, and may be known by us because it is implied in the finite objects which are presented to our minds in experience. We saw in the last chapter how each individual thing has a purpose; how action was an attempt to realise this purpose; how purposes were co-ordinated and subordinated one to another; how, in short, the universe formed a systematic and teleological, though not an organic, whole. We saw also that this systematisation did not destroy the real unity of the individual thing; and again that, though all things are inter-related, a relation is not a physical nexus implying an immanent Ground, but rather an ordo belonging to the individual things in so far as they imply and express a rational plan, just as a building implies and expresses the plan which existed in the mind of the architect. Now this inter-relatedness and systematic connectedness is a characteristic of all aspects of reality abstract as well as concrete; and, therefore, is to be found in every science. Not only are things interconnected and inter-related, but so also are their qualities and attributes when considered in general and apart from their manifestation in this or that object. And what I have said above about relations in the concrete applies here also. The relation is implied in its terms, and as soon as the terms are known the relation is recognised.

§ 276. Let us take Geometry as an example. What is its object? A number of abstract entities, points, lines, angles, figures, planes, solids, all of them systematically related and inter-connected, yet each having positive content of its own from which its relations arise. An angle is not a line, nor a line an angle; yet an angle cannot be defined apart from a line, while the line being an ultimate notion cannot be defined at all. A line, you say, is the locus of a moving point; and an angle (if plane) the space included between two intersecting straight lines. But what is a locus? What a point? What intersection? What motion? Sooner or later you must come back upon an ultimate notion, the meaning of which you know by a sort of intuition, for you have derived it direct from experience. It does not matter much what notions you call ultimate in geometry, and your choice will depend largely upon your point of view;^{1} but sooner or later your analysis must come to an end, and you will be forced to admit that there are certain notions which you can indicate but cannot define, like the boy who said that a kick was when you hit a man with your foot. Indeed, there is something to be said for the old-fashioned way of defining (v.g.) a circle as " When you take a line in a plane such that any point in it is equi-distant from a given fixed point that line is called a circle." Such a definition brings out the fact that we know what a circle is long before we are able to define it, and that our knowledge is derived directly from experience where circles exist, not exactly, but approximately in the configuration of actual bodies. Geometry, like every other science, starts with certain ultimate notions which are obtained direct from experience. These notions have innumerable implications, because there is an indefinite number of other notions to which they are related. But once you have got your notions the relation between them is fixed and determined because it was already implied in the content of the notions themselves.

This, you say, is true, so far as notions are concerned; but it is true because the notions are arbitrarily defined, and not because they are derived from experience. On the contrary, notions in geometry are never arbitrarily defined, but are always determined in the last instance by experience. You may choose the entities in regard to which you are going to formulate your definition; but, this done, your definition is fixed and necessary, for it is already implied in the notion itself and in the entity in regard to which you are going to define it. Thus, instead of defining a circle as a line which lies in a plane such that, etc., you may define it as the locus of a moving point, etc., or again as a particular case of an ellipse in which the foci coincide, or, again, as a conic such that all its conjugate diameters are at right angles to one another. But whatever entities you may choose as the terms in regard to which your circle is to be defined, the relation between the circle and those terms is fixed. You cannot define it as you like, but must define it in accordance with your pre-conceived, though undefined, notion of a circle. Nor does your definition change or mutilate or intrinsically modify your pre-conceived notion of a circle. It amplifies it, if you like; but it does not alter it or show that it was self-discrepant. It merely means that you know more about a circle, and more about geometrical entities in general, and their relations one to another.

§ 277. Geometrical science, then, has for its object a number of entities systematically related. Our notions of these entities are derived ultimately, and in many cases directly, from experience, and the relations between these entities are determined by the entities themselves; but not vice versa, or, at least, not in the same rigid sense. For it is no more true to say that relations react upon and are intrinsically modified by the nature of the entities they relate, than it is to say that the nature of a grain of corn is intrinsically modified by the fact that it is intended as food for man. Both statements are guilty of a hysteron proteron. Nevertheless, geometry is concerned chiefly with relations, since its aim is to discover the rational plan of the universe which they express. This, in fact, is the aim of all science, no matter with what aspect of reality it is concerned. Every science is an attempt to discover the rational plan of the real world, in so far as concerns the particnlar kind of entity which it takes as its object. And in every case the entities belonging to this particular kind or class will be extremely numerous and often extremely complex. Hence, as the relations between them will share in their complexity, the general method adopted in order to manifest this rational plan, is again common to all sciences. The physicist, the chemist, the naturalist, and the mathematician alike endeavour to show that the relations between any two entities, no matter how complex, are deducible from a few first principles or general laws in which both entities and relations are comparatively simple, and thus to grasp in synthesis the structure, or plan, of that particular aspect of reality with which they have to deal and the co-ordination of its manifold and intricate parts.

§ 278. But although the aim of all sciences is to know, and to know means to reconstruct a system of ideas which shall correspond to a system of objective entities, different sciences differ considerably not only in the way in which they set about this work of reconstruction, but also in the degree of completeness which as yet they have attained. The reason of this difference is not far to seek. It is simply that some sciences are more abstract than others. I have said that to know the nature of any two entities is to know the relation between them. Whence it follows that the more abstract an entity is the sooner it is known, because in it, if I may say so, there is less to know. The concrete, moreover, includes the abstract, and a knowledge of the concrete implies a knowledge of the abstract ; for, as we have seen, it is by abstraction that all knowledge begins. Hence abstract sciences such as arithmetic, algebra, geometry, not only precede, but are presupposed by more concrete sciences such as mechanics and dynamics, while these in turn precede and are presupposed by the still more concrete physical and natural sciences. The physicist is not concerned merely with configurations which are external and directly apparent to the senses, but with the inner structure of things, with the relations which hold between the various potentiae and qualities that are comprised within the unity of the concrete individual. And he is concerned with these potentiae not as static, but as dynamic and active. "Ever since physical science began in the atomic theories of the Greeks," says Professor Larmor, "its main problem has been that of unravelling the nature of the underlying correlation which binds together the various natural agencies."^{2} The physicist has to deal with the complex causes which produce 'quality' of sensation, and 'quality' of sensation does not analyse its object, but presents it in synthesis. He has to deal with phenomena and their transmutations, but those phenomena and their transmutations are particular, detailed, complex, and do not at once reveal their inner nature and their component parts, still less their causes or their presuppositions. In a word, the physicist does not, like the mathematician, take as the object of his enquiry simple entities, the nature of which is at once apparent, but complex entities which have first to be analysed, and which cannot be analysed directly.

§ 279. From the complex nature of the object of physical science follows an important consequence: the physicist has no axioms. An axiom is a self-evident truth, one which is not only per se nota quoad se, but also per se nota quoad nos. It is a proposition expressing a relation between two entities, but the nature of the entities in this case, being simple and extremely abstract, it is apprehended at once by the intellect; for the relation is, according to our theory, implied in its terms and arises immediately the nature of those terms is apprehended.

From the intellectual nature of the soul itself [says Aquinas] it follows that immediately man knows what is a whole and what is a part, he knows that the whole is greater than the part; and so on for other (axioms). But what a whole is and what a part is, he can only know by means of species intelligibiles received from phantasmata; and on this account Aristotle shows (toward the end of the Posterior Analytics), that the knowledge of axioms (principia) comes to us via the senses.^{3}

An axiom, then, comes to us from experience, and, like all knowledge, is determined ultimately by the nature of its object; but it presupposes that the nature of objects between which an axiomatic relation is seen to hold, be extremely simple otherwise it could not be per se nota quoad nos, but would have to be discovered by means of analysis and inference. This simplicity, therefore, being absent, in the case of physical objects for the reasons above explained, physical science has no axioms of its own, and consequently has to adopt a different method from that of the mathematician. It has no self-evident first principles in regard to the correlation of natural agencies, from which to deduce the systematic structure and interdependence of the objects which constitute the physical world and so to manifest its rational plan. Hence in place of axioms, it substitutes general principles which in origin, at any rate, were 'postulates.'

When we come to treat of the epistemological value of cognition, the 'pragmatic' attitude which is now so commonly taken up in regard to the methods and presuppositions of physical science will be more fully treated. It will be sufficient, therefore, if I now discuss the foundation of the Newtonian laws upon which the science of Mechanics has been built. Two remarks, however, must be premised in regard to the objective necessity of physical laws in general.

§ 280. In the first place, all the relations between objects existing in the physical world are necessary, i.e., given the objects, the relations follow as a necessary consequence, and did we know the nature and structure of the objects we should at once know their relations. But this necessity is only hypothetical, for it is conceivable that physical objects might have been different in structure to what they are and so have been connected by different laws. The co-existence of certain attributes, properties, or natural agencies is not a metaphysical necessity, except in so far as one attribute, property or agency is implied in, or presupposes another; and we have no reason for supposing that this is the case in regard to all physical properties and agencies. There is an element of contingency, therefore, in the physical world. The laws which govern the actions of physical objects are necessary, given the existence of those objects and given the Divine concursus; but the structure of those objects is a fact which has to be discovered by experiment and observation, or deduced from provisional hypotheses and postulates which lead to conclusions that correspond with known facts. Secondly, there is no reason a priori (so far as I can see) why an object should not tend gradually to increase or decrease, to development or to decay. True, one can hardly suppose that things tend to corruption of themselves, i.e., in virtue of this positive and existential nature, for this would contradict the Spinozistic axiom that every being tends to persevere in esse suo, and strives to realise a definite end or purpose. But all finite and contingent beings presuppose Divine conservation and concursus; and we might suppose, I think, that this was gradually withdrawn; provided always that the withdrawal was regular and according to knowable laws, so that our human demand for knowledge might not be frustrated. On the other hand, the principle of Causality that 'every event must have a cause,'^{4} and the further principle that the effect must resemble its cause and be contained in it, either formaliter or eminenter, is axiomatic, and follows from the very nature of 'being' and of 'change.' In so far, then, as conclusions in Mechanics or in Physical Science are based upon this principle, they are true a priori; but, as we shall see, the Newtonian laws, though they presuppose the principle of Causality, are in reality based upon another principle less axiomatic, and so have to seek for verification a posteriori.

§ 281. The first law of motion states that "every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state." Is this an axiom or a postulate? Motion is a fact, and so is rest, at least comparative rest; but it does not seem to me to be necessary that motion, once begun, should tend to continue, still less that it should continue in a straight line rather than in a circle or in any other kind of line. If it does so, it is a fact; but I hardly think that it follows from the nature of motion or from the nature of a moving body. For it is conceivable that things might tend to move progressively faster or slower, given an efficient cause, and yet the laws which governed this motion might be knowable.^{5} The law of inertia, as stated above, is, to my mind, not a self-evident truth, but a general physical principle which we know to be true because the conclusions which follow from it have been sufficiently verified in experience.

The second law of motion -- "rate of change of momentum is proportional to force and takes place in the straight line in which the force acts" -- seems, on the other hand, to be but a particular application of the law of causality. Change of momentum or of quantity of motion, like every other change, implies a cause, and to attribute motion to a 'force' is but to give a name to a particular kind of cause since 'force' is defined as "whatever changes the state of rest or uniform motion of a body." Assuming, then, that the first law of motion is true, i.e., that moving bodies do not of their own accord tend either to increase their speed or to come to a standstill, the second law is a necessary consequence; the 'change' in the body's state of motion or rest must be proportional to its cause, and since the force or cause ex hypothesi acts in a straight line the change of motion must take place in the same line.

§ 282. It is to be observed, however, that this law says nothing about the nature of force. It may be attractive or repulsive or both or neither. Again, metaphysically, if it produces a real change, it must be something real. But physicists prefer to abstract from the reality of force, and, since they do not know its nature, to define it as the space-rate at which energy is transformed (W = 1/2 Mv²/h); or the time-rate at which momentum is generated (W = Mv/t). These definitions, however, are not strictly definitions at all. For an equation tells us nothing about the nature of entities, but simply expresses a relation between certain quantities known or unknown. W signifies not the entity 'force,' but the quantity of force or the number of units of force. Similarly, if energy is defined as "capacity for doing work" 1/2 Mv² is not kinetic energy as such, but quantity of kinetic energy expressed in terms of a certain unit. Hence the above equations do not tell us that force is a spacerate, but the equation (W = 1/2Mv2/h) affirms that the number of units of force (e.g., gravity) is equal to the ratio of two other numbers, viz., the number of units of kinetic energy to the number of distanceunits, or the height. Similarly, the equation (W = Mv/t) expresses merely a relation of equality between quantity of force on the one hand, and the ratio of momentum (i.e., quantity of motion) to time (i.e., a certain number of time-units) on the other. A mathematical equation, therefore, is not really a definition, but merely a statement that the quantities denoted by certain symbols are equal to certain other quantities denoted by other symbols. Hence, to infer that force and other physical entities are not real because they can be expressed as 'ratios,' 'rates,' or quotients is illogical; for it is not the entity itself which is so expressed or 'defined,' but the quantitative value of that entity as measured by its effects. The existence of agencies capable of changing motion is presupposed by the fact that motion is changed; and though as yet we do not know what the agencies are, but only their 'values' as measured by the change they actually produce, it is hardly logical to infer from this that they are not real.

§ 283. The third law of motion -- action and reaction are equal and opposite -- has also been used as an argument against the reality of force on the ground that it is inconceivable that the objects upon which we act should resist our actions with a force equal in quantity to that which we exercise upon them. This second kind of 'inertia,' however, so far from being inconceivable, seems to be only another example of the more general principle omne ens perseverare in esse suo. For if this principle is true, clearly every being will resist force attempting to change its state, and will offer a resistance proportionate to the vigour of the attempt made. In other words, the effect produced in one body will be the measure of the force which has been brought to bear upon it, and the force which was required to produce that effect will be the measure of the resistance or inertia that called it forth.

The doctrine of Conservation of Energy is really implied in the second law of motion, and hence may also be regarded as a particular case of Spinoza's famous axiom. Indeed, we may say that both Mechanics and Physics presuppose the truth of that axiom; for the first law of motion is a statement to the effect that states of motion and rest tend to persevere. Could we, then, regard Spinoza's axiom as a self-evident truth, it might be possible to show that the fundamental principles of Mechanics are necessary a priori; but, as I have said, Spinoza's axiom is not strictly necessary, except when we consider 'being' purely in the abstract. It is true that a self-existent being must 'persevere in esse suo;' and it is true that all beings, whether self-existent or not, tend so to persevere in so far as they have being. But it is not true that all being does persevere in esse suo, for if it did, not only would the sum of potential and actual energy be constant, but they would be respectively constant, i.e., there would be no transformation of energy nor any other kind of change. Change, in fact, presupposes (1) energies which exist, but are not actual and yet strive to become so; (2) that these energies are of a different order, or at least of a different degree of strength, such that one energy may be able to realise itself at the expense of another; (3) that these energies are finite, contingent and essentially dependent upon a supreme Being both for their existence and their activity; and (4) that, being dependent, their sum is not necessarily, though it may be de facto, constant. Hence, although the doctrine omne ens perseverare in esse suo and the laws of motion in which it is applied to mechanical actions and changes, are true in that they express a tendency which is characteristic of all existent beings, they are not necessarily true; for a gradual decrease or a progressive increase of motion, force, energy, and dependent 'being' in general is not metaphysically impossible. As laws, then, which express the co-ordination of physical forces and motions, the mechanical principles formulated by Newton need verification in experience; a verification which they seem actually to have received, at any rate, in the realm of Astronomy.

§ 284. This need for a verification process in the case of the principles of physical science does not invalidate, but rather confirms our general doctrine for scientific induction involves not only judgment and inference, but also apprehension, abstraction, and to some extent at least that intuitive insight by means of which we recognise the relations that hold between abstract notions. In the first place, the notions involved in Newton's laws, motion, rest, uniformity, a straight line, force, action, reaction, etc., are all derived from experience through the phantasm or sense-impression. They are all abstract notions, yet have meaning, and signify entities existing objectively in the real world. True, the notions of force and energy are derived from inner rather than from outer experience; but just as the intellect apprehends that substance is implied and presupposed by unity in difference, so also it recognises that force and energy are presupposed as the metaphysical conditions of change and motion. And, again, just as we found that it was difficult to 'locate' substance, so to speak, in regard to material and inanimate things; so also it is difficult to locate a 'force,' if by 'force' is understood the real cause of motion while neither the notion of force nor that of substance tells us anything in regard to the nature of particular forces or particular substances. Secondly, we found that the first and third laws of motion, as well as the doctrine of Conservation of (material) Energy, might be regarded as particular cases of a more general principle, expressing the relation between two simple entities ens and perseverare. This relation, however, did not seem to be necessarily valid in regard to an ens contingens, but merely to express its natural tendency. Consequently, as Spinoza's axiom, not being itself strictly axiomatic, cannot impart to mechanical principles an axiomatic character, the human intellect is forced to seek for verification elsewhere. This it does by means deduction and by a careful process of observation, experimental or otherwise, and generalisation leading to the formulation of empirical laws with which the conclusions of our deductive reasoning may be compared.

Of the nature of reasoning little need be said,^{6} except that, whether syllogistic or not, it is but a more complex form of that intuitive judgment by which we recognise the relations that hold between different entities, the entities here being not ideas, but other judgments. Doubtless, reasoning often involves postulation, or rather is a result of postulation. But postulation itself is merely a name for a complex process which includes the activity both of intellect and will. Of intellect, because a postulate is a judgment, uncertain perhaps, as judgments often are, and possibly abstract, but still a judgment and therefore an intellectual act. Of will, because we desire to ascertain the truth of our tentative judgment; whether the relation we apprehend really holds to the concrete. Again, experiment may be involved; but experiment is merely perception, combined with action, and its function is quite subordinate to the intellectual end we have in view. So, too, is the will in so far as it co-operates in cognition. It transforms an idea into a purpose; it keeps the mind fixed on that purpose; and directs all its activities to the realisation of that purpose but beyond this it has no legitimate influence in the sphere of cognition.

§ 285. We may now sum up the main characteristics of the Aristotelico-Scholastic, or Causal Theory of Knowledge. Ex parte objecti the conditions of human knowledge are finite individual objects, each a unity of ground amid structural difference; each independent of its neighbours in regard to its existence, but possessing attributes identical in nature with theirs; each forming part of a rational plan and manifesting in an imperfect way the attributes of the Deity to whom it owes its existence and upon whom it depends; each striving to realise itself and to bring to act the potentiality of matter in itself and in other objects; and thus capable of producing in them effects like in form to the activity from which they proceed. Ex parte subjecti the conditions of human knowledge are that man should be one, organic, sentient, active, and rational. Through his body he is brought into contact with external things which manifest their nature in their activities. The form of the psychophysical processes which take place in his brain and in his organs of sense is determined by the activity of these objects (or, again, by internal changes within the organism) and hence the species sensibilis corresponds to some characteristic of the objective real thing. But knowledge proper is obtained only in ideas and in the judgments in which these ideas are combined. The content of an idea, therefore, must be determined by the object, and this takes place primarily in simple apprehension, which is one aspect of human perception. The combination of these ideas in judgment must also be determined by the object, and this takes place in the empirical or a posteriori judgment in which relations of co-existence and sequence are apprehended, and again in the axiomatic or a priori judgment in which relations between simple entities are apprehended as necessary because implied in the nature of the entities themselves. But the intellect, besides apprehending the many in the one, also apprehends the one in the many and so is able to subsume. Subsumption is characteristic both of judgment and of (syllogistic) inference. In judgment a particular entity is subsumed under a universal idea, and in the syllogism a particular relation is subsumed under a general principle or law. The idea corresponds with some real entity in the objective world or in the self; the judgment corresponds with some relation holding between these entities in that they imply a rational plan; systems of ideas, complex concepts, theories, correspond with the systematic co-ordination and correlation of real things; always provided and in so far as reality itself is their determining cause.

§ 286. Truth, then, consists in a relation of correspondence between the idea or judgment and the thing. It is an adaequatio intellectus et rei. 'Cognition' includes all acts whether of the perceptual or purely intellectual order by means of which this relation is brought about. Knowledge is the possession of true ideas (or systems of ideas), whether actually functioning in consciousness or existing only per modum habitus. Error is a positive difformity between the idea and the thing, and we may say in general that it is due to association, to an influxus voluntatis, or to some other subjective influence which causes assent to be given before the object has had time or opportunity itself to determine the content of thought. Error will be discussed later in the chapter on the Criteria of Error. It should, however, already be clear that the primary aim of one who seeks for truth should be to allow reality itself to determine the content of thought, and that the primary function of criteria of truth will be to distinguish cases in which the sense impression, the id quo percipitur, and the idea or concept, the id quo intelligitur, has been objectively determined from cases in which it has not.

{1} Compare Staudt Geometrie der Lage (or any modern Geometry) with the older Euclidian theory.

{2} Encyclopaedia Britannica, vol. xxxviii., article Energetics."

{3} Summa Theologica, I. p. 2, q. 51, ad 1. and cf. Maher, Psychology, 5th edit., p. 290.

{4} Or better, perhaps, Quidquid contingenter existit habet causam sui efficientem."

{5} If motion is a positive quality it must tend, according to Spinoza's axiom, to persevere in its being but if it is a continuous change, it postulates a continuous cause.

{6} For a discussion of the nature of judgment and reasoning from the Aristotelian point of view cf. Maher, Psychology, chap. xii. and xv. and for the logical aspect of the same, Joyce, Principles of Logic, chap. iii. and xii.