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The fundamental category of Locke, as of all who take simply a mechanical view of experience, is that of substance. He had good reason to be surprised when the Bishop of Worcester objected that Locke wished “to discard substance out of the world.” How can that be so, Locke asks, when I say that “our idea of body is an extended solid substance, and our idea of soul is of a substance that thinks.” And he adds, “Nay, as long as there is any simple idea or sensible quality left, according to my way of arguing, substance cannot be discarded.” Everything that really exists, is, according to Locke, substance. But substance to Locke, as again to all who interpret the universe after sensible categories, is unknowable. For such categories allow only of external relations; they admit only of static existence. Substance, in this way of looking at it, must be distinct from its qualities, and must be simply the existing substratum in which they inhere.

Locke’s account of the way in which we get the idea, and of its nature, is as follows: “All the ideas of all the sensible qualities of a cherry come into my mind by sensation. The ideas of these qualities and actions, or powers, are perceived by the mind to be by themselves inconsistent with existence. They cannot subsist of themselves. Hence the mind perceives their necessary connection with inherence, or with being supported.” Correlative to the idea of being supported is, of course, the idea of the support. But this idea “is not represented to the mind by any clear and distinct idea; the obscure and vague, indistinct idea of thing or something, is all that is left.” Or yet more simply, “Taking notice that a certain number of simple ideas go together, and not imagining how these simple ideas can subsist by themselves, we accustom ourselves to suppose some substratum wherein they do subsist, and from which they do result.” Hence the only idea we have of it is of something which underlies known qualities. It is their “supposed, but unknown, support.”

If we translate these expressions into the ideas of to-day, we see that they are equivalent to the view of the world which is given us by scientific categories when these categories are regarded not merely as scientific, but also as philosophic; that is, capable of interpreting and expressing the ultimate nature of experience. This modern view uses the words “things-in-themselves” (or absolute realities) and “phenomena.” It says that we know nothing of existence as it is in itself, but only of its phenomena. Mind, matter, objects, are all substances, all equally substances, and all have their unknown essence and their phenomenal appearance. Such a distinction between the known and the unknown can rest, it is evident, only upon a separation between reality and phenomena similar to that which Locke makes between substance and qualities. In knowing the latter, we know nothing of the former. Although the latter are called “phenomena,” they do not really manifest the substantial reality; they conceal it. This absolute distinction between substance and quality, between reality and phenomenon, rests, in turn, upon the hypothesis that reality is mere existence; that is, it is something which is, and that is all. It is a substratum; it lies under, in a passive way, qualities; it is (literally) substance; it simply stands, inactively, under phenomena. It may, by possibility, have actions; but it has them. Activities are qualities which, like all qualities, are in external relation to the substance. Being, in other words, is the primary notion, and “being” means something essentially passive and merely enduring, accidentally and secondarily something acting. Here, as elsewhere, Locke is the father of the mechanical philosophy of to-day.

We have already learned how completely Leibniz reverses this way of regarding reality. According to Locke, reality essentially is; and in its being there is no ground of revelation of itself. It then acts; but these actions, “powers, or qualities,” since not flowing from the very being of substance, give no glimpse into its true nature. According to Leibniz, reality acts, and therefore is. Its being is conditioned upon its activity. It is not first there, and secondly acts; but its “being there” is its activity. Since its very substance is activity, it is impossible that it should not manifest its true nature. Its every activity is a revelation of itself. It cannot hide itself as a passive subsistence behind qualities or phenomena. It must break forth into them. On the other hand, since the qualities are not something which merely inhere in an underlying support, but are the various forms or modes of the activity which constitutes reality, they necessarily reveal it. They are its revelations. There is here no need to dwell further on the original dynamic nature of substance; what was said in the way of general exposition suffices. It is only in its relations to Locke’s view as just laid down that it now concerns us.

In the first place, Leibniz points out that qualities are “abstract,” while substance is “concrete.” The qualities, from the very fact that they have no self-subsistence, are only relations, while the substance, as that of which they are qualities, or from which they are abstractions, is concrete. It is, Leibniz says, to invert the true order to take qualities or abstract terms as the best known and most easily comprehended, and “concretes” as unknown, and as having the most difficulty about them. “It is abstractions which give birth to almost all our difficulties,” and Locke’s error here is that he begins with abstractions, and takes them to be most open to intelligence. Locke’s second error is separating so completely substance and attribute. “After having distinguished,” says Leibniz, “two things in substance, the attributes or predicates, and the common subject of these predicates, it is not to be wondered at that we cannot conceive anything in particular in the subject. This result is necessary, since we have separated all the attributes in which there is anything definite to be conceived. Hence to demand anything more than a mere unknown somewhat in the subject, is to contradict the supposition which was made in making the abstraction and in conceiving separately the subject and its qualities or accidents.” We are indeed ignorant of a subject from which abstraction has been made of all defining and characteristic qualities; “but this ignorance results from our demanding a sort of knowledge of which the object does not permit.” In short, it is a credit to our knowledge, not an aspersion upon it, that we cannot know that which is thoroughly unreal,—a substance deprived of all attributes. This is, indeed, a remark which is applicable to the supposed unknowableness of pure Being, or Absolute Being, when it is defined as the absence of all relations (as is done, for example, by Mr. Spencer to-day).

Closely connected with the notion of substance are the categories of identity and diversity. These relations are of course to Locke thoroughly external. It is “relation of time and place which always determines identity.” “That that had one beginning is the same thing; and that which had a different beginning in time and place from that, is not the same, but diverse.” It is therefore easy to discover the principle of individuation. It “is existence itself, which determines a being of any sort to a particular time and place, incommunicable to two beings of the same kind.” He applies this notion to organic being, including man, and to the personal identity of man. The identity of an organism, vegetable, brute, or human, is its continuous organization; “it is the participation of the same continued life, by constantly fleeting particles of matter in succession vitally united to the same organized body.” Personal identity is constituted by a similar continuity of consciousness. “It being the same consciousness that makes a man be himself to himself, personal identity depends on that only.” It “consists not in the identity of substance, but in the identity of consciousness.” It will be noticed that Locke uses the notion of identity which he has already established to explain organic and personal unity. It is the “same continued life,” “identity of consciousness,” that constitute them. We are, hence, introduced to no new principle. Identity is even in personality a matter of temporal and spatial relations.

In the general account of the system of Leibniz it was pointed out that it is characteristic of his thought to regard identity and distinction as internal principles, and as necessarily implied in each other. We need not go over that ground again, but simply see how he states his position with reference to what is quoted from Locke. These are his words: “Besides the difference of place and time there is always necessary an internal principle [or law] of distinction, so that while there may be several things of the same species, there are no two things exactly alike. Thus, although time and place (that is, relations to the external) aid us in distinguishing things, things do not cease to be distinguished in themselves. The essence of identity and diversity does not consist in time and place, although it is true that diversity of things is accompanied with that of time and place, since they carry along with them different impressions upon the thing;” that is, they expose the thing to different surroundings. But in reality “it is things which diversify times and places from one another, for in themselves these are perfectly similar, not being substances or complete realities.”

The principle of individuation follows, of course, from this. “If two individuals were perfectly similar and equal, that is, indistinguishable in themselves, there would be no principle of individuation; there would not be two individuals.” Thus Leibniz states his important principle of the “identity of indiscernibles,” the principle that where there is not some internal differentiating principle which specifies the existence in this or that definite way, there is no individual. Leibniz here states, in effect, the principle of organic unity, the notion that concrete unity is a unity of differences, not from them. It is the principle which allows him at once to accept and transform the thought of Spinoza that all qualification or determination is negation. Spinoza, in spite of his intellectual greatness, conceived of distinction or determination as external, and hence as external negation. But since ultimate reality admits of no external negation, it must be without distinction, an all-inclusive one. But to Leibniz the negation is internal; it is determination of its own being into the greatest possible riches. “Things that are conceived as absolutely uniform and containing no variety are pure abstractions.” “Things indistinguishable in themselves, and capable of being distinguished only by external characteristics without internal foundation, are contrary to the most important principles of reason. The truth is that every being is capable of change [or differentiation], and is itself actually changed in such a way that in itself it differs from every other.”

As to organic bodies, so far as they are bodies, or corporeal, they are one and identical only in appearance. “They are not the same an instant. . . . Bodies are in constant flux.” “They are like a river which is always changing its water, or like the ship of Theseus which the Athenians are constantly repairing.” Such unity as they really possess is like all unity,—ideal or spiritual. “They remain the same individual by virtue of that same soul or spirit which constitutes the ‘Ego’ in those individuals who think.” “Except for the soul, there is neither the same life nor any vital union.” As to personal identity, Leibniz distinguishes between “physical or real” identity and “moral.” In neither case, however, is it a unity which excludes plurality, an identity which does not comprehend diversity. “Every spirit has,” he says, “traces of all the impressions which it has ever experienced, and even presentiments of all that ever will happen. But these feelings are generally too minute to be distinguished and brought into consciousness, though they may be sometime developed. This continuity and connection of perceptions makes up the real identity of the individual, while apperceptions (that which is consciously apprehended of past experiences) constitute the moral identity and make manifest the real identity.” We have had occasion before to allude to the part played in the Leibnizian philosophy by “minute perceptions” or “unconscious ideas.” Of them he says, relative to the present point, that “insensible perceptions mark and even constitute the sameness of the individual, which is characterized by the residua preserved from its preceding states, as they form its connection with its present state.” If these connections are “apperceived” or brought into distinct consciousness, there is moral identity as well. As he expresses it in one place: “The self (soi) is real and physical identity; the appearance of self, accompanied with truth, is personal identity.” But the essential point in either case is that the identity is not that of a substance underlying modifications, nor of a consciousness which merely accompanies all mental states, but is the connection, the active continuity, or—in Kant’s word—the synthesis, of all particular forms of the mental life. The self is not the most abstract unity of experience, it is the most organic. What Leibniz says of his monads generally is especially true of the higher monads,—human souls. “They vary, up to infinity itself, with the greatest abundance, order, and beauty imaginable.” Not a mathematical point, but life, is the type of Leibniz’s conception of identity.

In the order in which Locke takes up his topics (and in which Leibniz follows him) we have omitted one subject, which, however, may find its natural place in the present connection,—the subject of infinity. In Locke’s conception, the infinite is only a ceaseless extension or multiplication of the finite. He considers the topic immediately after the discussions of space, time, and number, and with good logic from his standpoint; for “finite and infinite,” he says, are “looked upon by the mind as the modes of quantity, and are attributed, in their first designation, only to those things which have parts and are capable of increase and diminution.” This is true even of the application of the term “infinite” to God, so far as concerns the attributes of duration and ubiquity; and as applied to his other attributes the term is figurative, signifying that they are incomprehensible and inexhaustible. Such being the idea of the infinite, it is attained as follows: There is no difficulty, says Locke, as to the way in which we come by the idea of the finite. Every obvious portion of extension and period of succession which affects us is bounded. If we take one of these periods or portions, we find that we can double it, or “otherwise multiply it,” as often as we wish, and that there is no reason to stop, nor are we one jot nearer the end at any point of the multiplication than when we set out. “By repeating as often as we will any idea of space, we get the idea of infinity; by being able to repeat the idea of any length of duration, we come by the idea of eternity.” There is a difference, then, between the ideas of the infinity of space, time, and number, and of an infinite space, time, and number. The former idea we have; it is the idea that we can continue without end the process of multiplication or progression. The latter we have not; it would be the idea of having completed the infinite multiplication, it would be the result of the never-ending progression. And this is evidently a contradiction in terms. To sum the matter up, the term “infinite” always relates to the notion of quantity. Quantity is that which is essentially capable of increase or decrease. There is then an infinity of quantity; there is no quantity which is the absolute limit to quantity. Such a quantity would be incapable of increase, and hence contradictory to quantity. But an actual infinite quantity (whether of space, time, or number) would be one than which there could be no greater; and hence the impossibility of our having a positive idea of an actual or completed infinite.

Leibniz’s reply consists simply in carrying out this same thought somewhat further. It is granted that the idea of an infinite quantity of any kind is absurd and self-contradictory. But what does this prove, except that the notions of quantity and infinity are incompatible with each other, that they contradict each other? Hence, instead of the infinite being a mode of quantity, it must be conceived as essentially distinct from and even opposed to quantity. Locke’s argument is virtually a reductio ad absurdum of the notion that the infinite is capable of parts. In the few pages of comment which Leibniz in 1696 wrote upon Locke, this topic of the infinite is one of the few touched upon. His words upon that occasion were as follows: “I agree with Mr. Locke that, properly speaking, there is no space, time, nor number which is infinite; and that it is only true that however great be a space, a time, or a number, there is always another which is still greater, and this without end; and that, therefore, the infinite is not to be found in a whole made up of parts. But it does not cease to exist: it is found in the absolute, which is without parts, and of which compound things [phenomena in space and time, or facts which may be numbered] are only limitations. The positive infinite being nothing else than the absolute, it may be said that there is, in this sense, a positive idea of the infinite, and that it is anterior to the idea of the finite.” In other words, while the infinite is to Locke an indefinite extension of the finite, which alone is positively “given,” to Leibniz the infinite is the positive and real, and the finite is only in and by it. The finite is the negative.

Leibniz amplifies this thought upon other occasions, as in his present more extended examination. “There is no infinite number, line, or quantity, if they are taken as true wholes.” “We deceive ourselves in trying to imagine an absolute space which should be an infinite whole, composed of parts. There is none such. It is an idea which implies contradiction; and all these ‘infinites’ and ‘infinitesimals’ are of use only in geometry, as imaginary roots are in algebra.” That which is ordinarily called the infinite, that is, the quantitative infinite, is in reality only the indefinite. “We involve ourselves in difficulty when we talk about a series of numbers extending to infinity; we imagine a last term, an infinite number, or one infinitely little. But these are only fictions. All number is finite and assignable, [that is, of a certain definite quantity]; every line is the same. ‘Infinites’ and ‘infinitesimals’ signify only quantities which can be taken as large or as small as one wishes, simply for the purpose of showing that there is no error which can be assigned. Or we are to understand by the infinitely little, the state of vanishing or commencing of a quantum after the analogy of a quantum already formed.” On the other hand, the true infinite “is not an aggregate, nor a whole of parts; it is not clothed with magnitude, nor does it consist in number. . . . The Absolute alone, the indivisible infinite, has true unity,—I mean God.” And as he sums up the matter: “The infinite, consisting of parts, is neither one nor a whole; it cannot be brought under any notion of the mind except that of quantity. Only the infinite without parts is one, and this is not a whole [of parts]: this infinite is God.”

It cannot be admitted, however, that Locke has given a correct account of the origin of the notion of the quantitative infinite, or—to speak philosophically, and not after the use of terms convenient in mathematics—the indefinite. According to him, its origin is the mere empirical repeating of a sensuous datum of time and space. According to Leibniz, this repetition, however long continued, can give no idea beyond itself; it can never generate the idea that the process of repetition may be continued without a limit. Here, as elsewhere, he objects that experience cannot guarantee notions beyond the limits of experience. Locke’s process of repetition could tell us that a number had been extended up to a given point; not that it could be extended without limit. The source of this latter idea must be found, therefore, where we find the origin of all extra-empirical notions,—in reason. “Its origin is the same as that of universal and necessary truths.” It is not the empirical process of multiplying, but the fact that the same reason for multiplying always exists, that originates and guarantees the idea. “Take a straight line and prolong it in such a way that it is double the first. It is evident that the second, being perfectly similar to the first, can be itself doubled; and we have a third, which in turn is similar to the preceding. The same reason always being present, it is not possible that the process should ever be brought to a stop. Thus the line can be prolonged ‘to infinity.’ Therefore the idea of ‘infinity’ comes from the consideration of the identity of relation or of reason.”

The considerations which we have grouped together in this chapter serve to show the fundamental philosophical difference between Locke and Leibniz. Although, taken in detail, they are self-explanatory, a few words may be permitted upon their unity and ultimate bearing. It is characteristic of Locke that he uses the same principle of explanation with reference to the conceptions of substance, identity and diversity, and infinity, and that this principle is that of spatial and temporal relation. Infinity is conceived as quantitative, as the successive addition of times and spaces; identity and diversity are oneness and difference of existence as determined by space and time; substance is the underlying static substratum of qualities, and, as such, is considered after the analogy of things existing in space and through time. It must not be forgotten that Locke believed as thoroughly as Leibniz in the substantial existence of the world, of the human soul, and of God; in the objective continuity of the world, and the personal identity of man, and in the true infinity of God. Whatever negative or sceptical inferences may have afterwards been drawn from Locke’s premises were neither drawn nor dreamed of by him. His purpose was in essence one with that of Leibniz.

But the contention of Leibniz is that when substance, identity, and infinity are conceived of by mechanical categories, or measured by the sensible standard of space and time, they lose their meaning and their validity. According to him such notions are spiritual in their nature, and to be spiritually conceived of. “Spiritual,” however, does not mean opposed to the sensible; it does not mean something to be known by a peculiar kind of intuition unlike our knowledge of anything else. It means the active and organic basis of the sensible, its significance and ideal purpose. It is known by knowing the sensible or mechanical as it really is; that is, as it is completely, as a concretum, in Leibniz’s phrase. Leibniz saw clearly that to make the infinite something at one end of the finite, as its mere external limit, or something miraculously intercalated into the finite, was to deprive it of meaning, and, by making it unknowable, to open the way for its denial. To make identity consist in the removal of all diversity (as must be done if it be thought after the manner of external relations), is to reduce it to nothing,—as Hume, indeed, afterwards showed. Substance, which is merely a support behind qualities, is unknowable, and hence unverifiable. While, then, the aim of both Locke and Leibniz as regards these categories was the same, Leibniz saw what Locke did not,—that to interpret them after the manner of existence in space and time, to regard them (in Leibniz’s terminology) as mathematical, and not as metaphysical, is to defeat that aim. The sole way to justify them, and in justifying them to give relative validity to the sensible and phenomenal, is to demonstrate their spiritual and dynamic nature, to show them as conditioning space and time, and not as conditioned by them.