Leibniz's New Essays Concerning the Human Understanding Part 5

So much for Leibniz's polemic. Its meaning is that s.p.a.ce and time have significance only with reference to things and events, that they are the intellectual, the ideal side of these objects and occurrences, being the relations which give them order and unity. A s.p.a.ce which is not the s.p.a.ce of objects, which is not s.p.a.ce in and through objects, is an inanity; it is not spirit, it is not matter; it is not a relation of either. It is nothingness magnified to infinity, and then erected into existence. And all for nothing; for it does not enable us to account for a single concrete fact of experience. For this we must have recourse to relations and orders of existence. s.p.a.ce is therefore to be defined as the order which makes it possible for objects to have situation; time as that which makes it possible for events to have dating,--not as if they were actually prior to them, and although nothings in themselves, yet capable of giving concrete determination to things, but as _actually_ the relations themselves, and as _ideally_ necessary for the coherent experience of co-existent objects and of connected events. As Leibniz puts it epigrammatically: "s.p.a.ce is the order of possible constants; time the order of inconstant possibilities."

We have finished the exposition of the views of Leibniz about matter and material facts. One question, however, remains to be discussed,--a question which Leibniz's contemporary critics would not allow him to pa.s.s over in silence, even had he been so disposed. What is the reality of matter, of motion, of s.p.a.ce, and of time? Since they are, as Leibniz says, only phenomena, not absolute realities, what distinguishes them from dreams, from illusions? What distinguishes sensible phenomena from capricious fantasies, and gives them reality?

Leibniz begins his answer by pointing out that the mere fact that bodies are phenomena does not make them unreal. To say that anything is phenomenal is to say that it is sensible; but "the senses make no declaration regarding metaphysical matters" such as truth and reality. The senses, in a word, only inform us that the experiences are there for the senses, that they are sensible. What is the ultimate nature of the sensible or the phenomenal, what is their reality, is a question wholly outside the province of sense. The questions of ultimate nature, of reality, are questions of metaphysics, and hence are to be decided by the reason, not by the senses. And Leibniz goes on to say that the truthfulness of the senses, since it concerns only the sensible, consists in the reciprocal agreement of sensible facts, and in that we are not deceived in reasoning from one to another. An isolated sense-experience could not be said to be either true or false, real or illusory. It would be true that it was experienced, and that is all that could be said about it. But since our experiences are not thus separated, but have a certain order, there arises what we may call sensible reality and illusion. When the order between two facts remains the same "in different times and places and in the experience of different men," we call these facts real. If, however, our experience cannot be repeated by ourselves or by other men when the same conditions (that is, connections) are present, it is unreal, or false. It is thus "the _relation_ of phenomena which guarantees truth of fact regarding sensible objects." Constancy, regularity, justify us in ascribing reality; chaotic change and lack of orderly connection are a sign of unreality. Even our dreams have a reality; for they have their connections and place in experience. If we understood their connections we should even be able to explain their apparent lack of connection with the rest of experience. Leibniz thinks that both the Academicians and Sceptics and their opponents erred in attempting to find greater reality in sensible things than that of regular phenomena. Since our observations and judgments upon sensible phenomena are of such a nature that we can predict future phenomena and prepare for them, we have all the reality in them that can be had or asked for. Even if it be granted possible (as it must be on this basis) that, metaphysically speaking, sense-experience is only a connected dream, it yet has a sufficient reality; for we are not deceived in the measures taken with reference to phenomena, provided that we act on the ground of their observed harmonies and relations. Thus while we are obliged to admit that our senses inform us that there are hard, pa.s.sive, extended, indivisible things, not perfectly continuous and not intellectual in their nature, and we know on metaphysical grounds that this information is not correct, we cannot say that our senses deceive us, for sense makes no statements regarding such matters. It is our reason that errs if it takes the information that the senses give as if it were a declaration of reason itself. Sensible things have all the reality necessary for this range of experience,--_practical_,--such regularity of co-existence and sequence as allows us to act without being led astray.

But if we regard sense-phenomena not merely in their connection with one another, but in their dependence upon the absolute realities, we have still better justification for their comparative reality. These phenomena are consequences of necessary and eternal truths. One endowed with a perfect knowledge of such truths would be able to deduce, _a priori_, the phenomena from them. The reality of sensible phenomena thus consists not merely in their connection with one another, but in the fact that they are connected as the laws of the intelligible world require. They follow not only rules of co-existence and sequence; but these rules may be brought under general laws of motion, which in turn may be deduced from geometrical principles. These latter, however, are _a priori_; they are truths which are grounded in the very intelligence of G.o.d. The sensible has its basis in the ideal. To state the same fact in another way, all sensible phenomena occur in time and s.p.a.ce; or rather, time and s.p.a.ce are the orders, the relations, of phenomena occurring and existing. But, as we have just seen, time and s.p.a.ce are ideal. A relation, as Leibniz points out, being neither attribute nor accident, cannot be _in_ the things which it relates, as their possession. In his own words, it cannot be conceived as if it had one leg in one object, the other leg in the other. A relation is not a material bond, running through or cementing objects; it is ideal, existing in the mind. And while it is true that s.p.a.ce and time are the relations of objects and events, it is also true that if all objects and events were annihilated, s.p.a.ce and time would continue to have their ideal existence in the intelligence of G.o.d as the eternal conditions of phenomena. They thus form the links between absolute reality and the reality of sensible existence. The principle of sufficient reason forms another link. It may be recalled that in discussing Leibniz's theory of volition we found that the will of G.o.d in relation to the sensible world is always determined by the choice of the better; that in this consists the controlling reason and regulative principle of all that occurs and exists. Thus for every fact in the sensible world there is connection with "metaphysical," or absolute, reality, not only through the medium of the intellectual relations of time and s.p.a.ce, but through the dynamic intermediary of the divine will acting in accordance with the divine reason. Sensible facts have, then, a reality, but a dependent one. There would be no _contradiction_ involved if they were not what they actually are.

We may sum up the matter by saying that the reality of sensible phenomena consists in the constancy of the mutual order in which they exist, and in the dependence of this order upon the divine Intelligence and Will. In this respect, at least, Leibniz resembles the young Irish idealist, Berkeley, who only seven years after Leibniz wrote the "New Essays" composed his "Principles of Human Knowledge," urging that the immediate reality of sense-phenomena consists in their "steadiness, order, and coherence," "in a constant uniform working," and that this "gives us a foresight which enables us to regulate our actions for the benefit of life." It was Berkeley also who wrote that their ultimate reality consists in their being ideas of a Divine Spirit. This was six years before the death of Leibniz. Yet it does not appear that Berkeley knew of Leibniz, and the only allusion to Berkeley which I have found in the writings of Leibniz shows that Leibniz knew only of that caricature of his views which has always been current,--that Berkeley was one who denied the existence of any external world. What he writes is as follows: "As for him in Ireland who questions the reality of 'bodies,' he seems neither to offer what is rational, nor sufficiently to explain his own ideas. I suspect that he is one of those men who are desirous of making themselves known through paradoxes."

CHAPTER IX.

SOME FUNDAMENTAL CONCEPTIONS.

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 pa.s.sive 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 pa.s.sive 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 pa.s.sive 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 const.i.tutes 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 ident.i.ty and diversity. These relations are of course to Locke thoroughly external. It is "relation of time and place which always determines ident.i.ty." "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 ident.i.ty of man. The ident.i.ty of an organism, vegetable, brute, or human, is its continuous organization; "it is the partic.i.p.ation of the same continued life, by constantly fleeting particles of matter in succession vitally united to the same organized body." _Personal_ ident.i.ty is const.i.tuted by a similar continuity of consciousness. "It being the same consciousness that makes a man be himself to himself, personal ident.i.ty depends on that only." It "consists not in the ident.i.ty of substance, but in the ident.i.ty of consciousness." It will be noticed that Locke uses the notion of ident.i.ty which he has already established to explain organic and personal unity. It is the "_same_ continued life," "_ident.i.ty_ of consciousness," that const.i.tute them. We are, hence, introduced to no new principle. Ident.i.ty 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 ident.i.ty 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 ident.i.ty 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 "ident.i.ty 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 const.i.tutes the 'Ego' in those individuals who think." "Except for the soul, there is neither the same life nor any vital union." As to personal ident.i.ty, Leibniz distinguishes between "physical or real" ident.i.ty and "moral." In neither case, however, is it a unity which excludes plurality, an ident.i.ty 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 ident.i.ty of the individual, while _apperceptions_ (that which is consciously apprehended of past experiences) const.i.tute the moral ident.i.ty and make manifest the real ident.i.ty." 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 const.i.tute 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 ident.i.ty as well. As he expresses it in one place: "The self (_soi_) is real and physical ident.i.ty; the appearance of self, accompanied with truth, is personal ident.i.ty." But the essential point in either case is that the ident.i.ty 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 ident.i.ty.

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 s.p.a.ce, 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 _quant.i.ty_, 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 G.o.d, 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 s.p.a.ce, 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 s.p.a.ce, time, and number, and of an infinite s.p.a.ce, 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 quant.i.ty. Quant.i.ty is that which is essentially capable of increase or decrease. There is then an infinity of quant.i.ty; there is no quant.i.ty which is the absolute limit to quant.i.ty. Such a quant.i.ty would be incapable of increase, and hence contradictory to quant.i.ty. But an actual infinite quant.i.ty (whether of s.p.a.ce, 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 quant.i.ty of any kind is absurd and self-contradictory. But what does this prove, except that the notions of quant.i.ty and infinity are incompatible with each other, that they contradict each other? Hence, instead of the infinite being a mode of quant.i.ty, it must be conceived as essentially distinct from and even opposed to quant.i.ty. 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 s.p.a.ce, time, nor number which is infinite; and that it is only true that however great be a s.p.a.ce, 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 s.p.a.ce 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 quant.i.ty, if they are taken as true wholes." "We deceive ourselves in trying to imagine an absolute s.p.a.ce 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 quant.i.tative 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 a.s.signable, [that is, of a certain definite quant.i.ty]; every line is the same. 'Infinites'

and 'infinitesimals' signify only quant.i.ties 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 a.s.signed. Or we are to understand by the infinitely little, the state of vanishing or commencing of a quantum after the a.n.a.logy 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 G.o.d." 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 quant.i.ty. Only the infinite without parts is one, and this is not a whole [of parts]: this infinite is G.o.d."

It cannot be admitted, however, that Locke has given a correct account of the origin of the notion of the quant.i.tative 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 s.p.a.ce. According to Leibniz, this repet.i.tion, however long continued, can give no idea beyond itself; it can never generate the idea that the process of repet.i.tion 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 repet.i.tion 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 ident.i.ty 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, ident.i.ty and diversity, and infinity, and that this principle is that of spatial and temporal relation. Infinity is conceived as quant.i.tative, as the successive addition of times and s.p.a.ces; ident.i.ty and diversity are oneness and difference of existence as determined by s.p.a.ce and time; substance is the underlying static substratum of qualities, and, as such, is considered after the a.n.a.logy of things existing in s.p.a.ce 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 G.o.d; in the objective continuity of the world, and the personal ident.i.ty of man, and in the true infinity of G.o.d. 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, ident.i.ty, and infinity are conceived of by mechanical categories, or measured by the sensible standard of s.p.a.ce 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 ident.i.ty 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 s.p.a.ce 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 s.p.a.ce and time, and not as conditioned by them.

CHAPTER X.

THE NATURE AND EXTENT OF KNOWLEDGE.

The third book of Locke's Essay is upon words and language; and in the order of treatment this would be the next topic for discussion. But much of what is said in this connection both by Locke and by Leibniz is philological, rhetorical, and grammatical in character, and although not without interest in itself, is yet without any especial bearing upon the philosophical points in controversy. The only topics in this book demanding our attention are general and particular terms; but these fall most naturally into the discussion of general and particular knowledge. In fact, it is not the terms which Locke actually discusses, but the ideas for which the terms stand. We pa.s.s on accordingly, without further ceremony, to the fourth book, which is concerning knowledge in general. Locke defines knowledge as "nothing but the perception of the connection and agreement, or disagreement and repugnancy, of any of our ideas." These agreements or disagreements may be reduced to four sorts,--Ident.i.ty, or diversity; Relation; Co-existence, or necessary connection; Real existence. The statement of ident.i.ty and diversity is implied in all knowledge whatsoever. By them "the mind clearly and infallibly perceives each idea to agree with itself and be what it is, and all distinct ideas to disagree; _i. e._, the one not to be the other." The agreement of relation is such knowledge as the mind derives from the _comparison_ of its ideas. It includes mathematical knowledge. The connection of co-existence "belongs particularly to substances." Locke's example is that "gold is fixed,"--by which we understand that the idea of fixedness goes along with that group of ideas which we call gold. All statements of fact coming under the natural sciences would fall into this cla.s.s. The fourth sort is "that of actual and real existence agreeing to any idea."

Leibniz's criticism upon these statements of Locke is brief and to the point. He admits Locke's definition of knowledge, qualifying it, however, by the statement that in much of our knowledge, perhaps in all that is merely empirical, we do not know the reason and connection of things and hence cannot be said to _perceive_ the agreement or disagreement of ideas, but only to feel it confusedly. His most important remark, however, is to the effect that relation is not a special kind of knowledge, but that all Locke's four kinds are varieties of relation. Locke's "connection" of ideas which makes knowledge is nothing but relation. And there are two kinds of relation,--those of "comparison" and of "concourse." That of comparison states the ident.i.ty or distinction of ideas, either in whole or in part. That of concourse contains Locke's two cla.s.ses of co-existence and existence. "When we say that a thing really exists, this existence is the predicate,--that is to say, a notion connected with the idea which is the subject; and there is connection between these two notions. The existence of an object of an idea may be considered as the concourse of this object with me. Hence comparison, which marks ident.i.ty or diversity, and concourse of an object with me (or with the _ego_) are the only forms of knowledge."

Leibniz leaves the matter here; but he only needed to develop what is contained in this statement to antic.i.p.ate Berkeley and Kant in some of the most important of their discoveries. The contradiction which lies concealed in Locke's account is between his definition of knowledge in general, and knowledge of real existence in particular. One is the agreement or disagreement of _ideas_; the other is the agreement of an idea _with an object_. Berkeley's work, in its simplest form, was to remove this inconsistency. He saw clearly that the "object" was an intruder here. If knowledge lies in the connection of _ideas_, it is impossible to get outside the ideas to find an object with which they agree. Either that object is entirely unknown, or it is an idea. It is impossible, therefore, to find the knowledge of reality in the comparison of an idea with an object. It must be in some property of the ideas themselves.

Kant developed more fully the nature of this property, which const.i.tutes the "objectivity" of our ideas. It is their connection with one another according to certain _necessary_ forms of perception and rules of conception. In other words, the reality of ideas lies in their being connected by the necessary and hence universal relations of synthetic intelligence, or, as Kant often states it, in their agreement with the conditions of self-consciousness. It is not, I believe, unduly stretching either the letter or the spirit of Leibniz to find in that "concourse of the object with the ego" which makes its reality, the a.n.a.logue of this doctrine of Kant; it is at all events the recognition of the fact that reality is not to be found in the relating of ideas to unknown things, but in their relation to self-conscious intelligence. The points of similarity between Kant and Leibniz do not end here. Leibniz's two relations of "comparison"

and "concourse" are certainly the congeners of Kant's "a.n.a.lytic"

and "synthetic" judgments. But Leibniz, as we shall see hereafter, trusts too thoroughly to the merely formal relations of ident.i.ty and contradiction to permit him such a development of these two kinds of relation as renders Kant's treatment of them epoch-making.

The discussion then advances to the subject of degrees of knowledge, of which Locke recognizes three,--intuitive, demonstrative, and sensitive. Intuitive knowledge is immediate knowledge,--recognition of likeness or difference without the intervention of a third idea; it is the most certain and clear of all knowledge. In demonstrative knowledge the agreement or disagreement cannot be perceived directly, because the ideas cannot be put together so as to show it. Hence the mind has recourse to intermediaries. "And this is what we call reasoning." Demonstrative rests on intuitive knowledge, because each intermediate idea used must be immediately perceived to be like or unlike its neighboring idea, or it would itself need intermediates for its proof. Besides these two degrees of knowledge there is "another perception of the mind employed about the particular existence of finite things without us, which, going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, pa.s.ses under the name of knowledge."

Leibniz's comments are again brief. The primitive truths which are known by intuition are to be divided into two cla.s.ses,--truths of reason and of fact. The primitive truths of reason are necessary, and may be called identical, because they seem only to repeat the same thing, without teaching us anything. A is A. A is not non-A. Such propositions are not frivolous or useless, because the conclusions of logic are demonstrated by means of identical propositions, and many of those of geometry by the principle of contradiction. All the intuitive truths of reason may be said to be made known through the "immediation" of ideas. The intuitive truths of fact, on the other hand, are contingent and are made known through the "immediation"

of feeling. In this latter cla.s.s come such truths as the Cartesian, "I think, therefore I am." Neither cla.s.s can be proved by anything more certain.

Demonstration is defined by Leibniz as by Locke. The former recognizes, however, two sorts,--a.n.a.lytic and synthetic. Synthesis goes from the simple to the complex. There are many cases, however, where this is not applicable; where it would be a task "equal to drinking up the sea to attempt to make all the necessary combinations. Here the method of exclusions should be employed, cutting off many of the useless combinations." If this cannot be done, then it is a.n.a.lysis which gives the clew into the labyrinth. He is also of the opinion that besides demonstration, giving certainty, there should be admitted an art of calculating probabilities,--the lack of which is, he says, a great defect in our present logic, and which would be more useful than a large part of our demonstrative sciences. As to sensitive knowledge, he agrees with Locke that there is such a thing as real knowledge of objects without us, and that this variety does not have the same metaphysical certainty as the other two; but he disagrees regarding its criterion. According to Locke, the criterion is simply the greater degree of vividness and force that sensations have as compared with imaginations, and the actual pleasures or pains which accompany them. Leibniz points out that this criterion, which in reality is purely emotional, is of no great value, and states the principle of the reality of sensible phenomena which we have already given, repeating that it is found in the _connection_ of phenomena, and that "this connection is verified by means of the truths of reason, just as the phenomena of optics are explained by geometry."

The discussion regarding "primitive truths," axioms, and maxims, as well as the distinction between truths of fact and of reason, has its most important bearing in Locke's next chapter. This chapter has for its t.i.tle the "Extent of Human Knowledge," and in connection with the sixth chapter, upon universal propositions, and with the seventh, upon axioms, really contains the gist of the treatment of knowledge. It is here also that are to be considered chapters three and six of book third, having respectively as their t.i.tles, "Of General Terms," and "Of the Names of Substances."

To understand Locke's views upon the extent and limitations of our knowledge, it is necessary to recur to his theory of its origin. If we compare what he says about the origin of ideas from sensations with what he says about the development of general knowledge from particular, we shall find that Locke unconsciously puts side by side two different, and even contradictory, theories upon this point. In the view already given when treating of sensation, knowledge originates from the combination, the addition, of the simple ideas furnished us by our senses. It begins with the simple, the unrelated, and advances to the complex. But according to the doctrine which he propounds in treating of general terms, knowledge begins with the individual, which is already qualified by definite relations, and hence complex, and proceeds, by abstracting some of these qualities, towards the simple. Or, in Locke's own language, "ideas become general by separating from them the circ.u.mstances of time and place and any other ideas that may _determine_ them to this and that particular existence." And, still more definitely, he says that general ideas are framed by "leaving out of the _complex_ idea of individuals that which is peculiar to each, and retaining only what is common to them all." From this it follows that "general and universal belong not to the real existence of things, but are the inventions and creatures of the understanding." "When we quit particulars, the generals that rest are only creatures of our own making... . The signification they have is nothing but a relation that by the mind of man is added to them." And in language which reminds us of Kant, but with very different bearing, he says that relations are the workmanship of the understanding. The abstract idea of what is common to all the members of the cla.s.s const.i.tutes "nominal essence." This nominal essence, not being a particular existence in nature, but the "workmanship of the understanding," is to be carefully distinguished from the real essence, "which is the being of anything whereby it is what it is." This real essence is evidently equivalent to the unknown "substance" of which we have heard before. "It is the real, internal, and unknown const.i.tution of things." In simple or unrelated ideas and in modes the real and the nominal essence is the same; and hence whatever is demonstrated of one is demonstrated of the other. But as to substance it is different, the one being natural, the other artificial. The nominal essence always relates to sorts, or cla.s.ses, and is a pattern or standard by which we cla.s.sify objects. In the individual there is nothing essential, in this sense. "Particular beings, considered barely in themselves, will be found to have all their qualities equally essential to them, or, which is more, nothing at all." As for the "real essence" which things have, "we only suppose its being without precisely knowing what it is."

Locke here presents us with the confusion which, in one form or another, is always found in empiricism, and which indeed is essential to it. Locke, like the ordinary empiricist, has no doubt of the existence of real things. His starting-point is the existence of two substances, mind and matter; while, further, there is a great number of substances of each kind. Each mind and every separate portion of matter is a distinct substance. This supposed deliverance of common sense Locke never called into question. Working on this line, all knowledge will consist in abstraction from the ready-made things presented to us in perception, "in leaving out from the complex idea of individuals"

something belonging to them. But on the other hand, Locke never doubts that knowledge begins with sensation, and that, therefore, the process of knowledge is one of adding simple, unrelated elements. The two theories are absolutely opposed to each other, and yet one and the same philosophical inference may be drawn from each; namely, that only the particular is real, and that the universal (or relations) is an artificial product, manufactured in one case by abstraction from the real individual, in the other by compounding the real sensation.

The result is, that when he comes to a discussion of the extent of knowledge, he admits knowledge of self, of G.o.d, and of "things,"

only by a denial of his very definition of knowledge, while knowledge of other conceptions, like those of mathematics, is not knowledge of reality, but only of ideas which we ourselves frame. All knowledge, that is to say, is obtained only either by contradicting his own fundamental notion, or by placing it in relations which are confessedly artificial and superinduced. It is to this point that we come.

The proposition which is fundamental to the discussion is that we have knowledge only where we perceive the agreement or disagreement of ideas. Locke then takes up each of his four cla.s.ses of connection, in order to ascertain the extent of knowledge in it. Our knowledge of "ident.i.ty and diversity extends as far as our ideas," because we intuitively perceive every idea to be "what it is, and different from any other." Locke afterwards states, however, that all purely identical propositions are "trifling," that is, they contain no instruction; they teach us nothing. Thus the first cla.s.s of relations cannot be said to be of much avail. If we consider the fourth kind of knowledge, that of real existence, we have an intuitive knowledge of self, a demonstrative knowledge of G.o.d, and a sensitive knowledge of other things. But sensitive knowledge, it must be noted, "does not extend beyond the objects _actually present_ to our senses." It can hardly be said, therefore, to a.s.sure us of the existence of _objects_ at all. It only tells us what experiences are being at the time undergone. Furthermore, knowledge of all three (G.o.d, self, and matter), since of real being, and not of relations between ideas, contradicts his definition of knowledge. But perhaps we shall find knowledge more extended in the other cla.s.ses. And indeed Locke tells us that knowledge of relations is the "largest field of our knowledge." It includes morals and mathematics; but it is to be noticed that, according to Locke, in both of these branches our demonstrations are not regarding facts, but regarding either "modes" framed by ourselves, or relations that are the creatures of our minds,--"extraneous and superinduced"

upon the facts, as he says. He thus antic.i.p.ates in substance, though not in phraseology, Hume's distinction between "matters of fact" and "connections of ideas," in the latter of which we may have knowledge, but not going beyond the combinations that we ourselves make.

This leaves one cla.s.s, that of co-existence, to be examined. Here, if anywhere, must knowledge, worthy of being termed scientific, be found. This cla.s.s, it will be remembered, comprehends our knowledge concerning substances. But this extends, according to Locke, "a very little way." The idea of a substance is a complex of various "simple ideas united in one subject and co-existing together." When we would know anything further concerning a substance, we only inquire what other simple ideas, besides those already united, co-exist with them. Since there is no _necessary_ connection, however, among these simple ideas, since each is, by its very simplicity, essentially distinct from every other, or, as we have already learned, since nothing is essential to an individual, we can never be sure that any idea really co-exists with others. Or, as Locke says, in physical matters we "can go no further than particular experience informs us of... . We can have no certain knowledge of universal truths concerning natural bodies." And again, "universal propositions of whose truth and falsehood we have certain knowledge concern not existence;"

while, on the other hand, "particular affirmations are only concerning existence, declaring only the _accidental_ union or separation of ideas in things existing." This particular knowledge, it must be recalled, is, in turn, only sensitive, and thus extends not beyond the time when the sensation is had.

We are not surprised then at learning from Locke that regarding bodies "we are not capable of scientific knowledge." "Natural philosophy is not capable of being made a science;" or, as Locke elsewhere states it, knowledge regarding the nominal essence is "trifling" (Kant's a.n.a.lytic judgment); regarding the real essence is impossible. For example, when we say that all gold is fusible, this means either simply that fusibility is one of the ideas which we combine to get the general idea of gold, so that in making the given judgment we only expand our own notion; or it means that the "real" substance gold is always fusible. But this is a statement we have no right to make, and for two reasons: we do not know what the real substance gold is; and even if we did, we should not know that fusibility _always_ co-exists with it. The summary of the whole matter is that "general certainty is to be found only in our ideas. Whenever we go to seek it elsewhere, in experiment or observations without us, our knowledge goes not beyond particulars."

It has been necessary to give an account of Locke's views at this length because it is in his discussion of the limitations and extent of knowledge that his theory culminates. While not working out his sensationalism as consistently as did Hume, he yet reduces knowledge to that of the existence of G.o.d and ourselves (whose natures, however, are unknown), and to a knowledge of mathematical and moral relations, which, however, concerns only "the habitudes and relations of abstract ideas." We have now to see by what means Leibniz finds a wider sphere for certain and general knowledge by his theory of intellectualism than Locke can by his sensationalism.

Leibniz's theory of knowledge rests upon a distinction between truths of fact, which are _a posteriori_ and contingent, and truths of reason, which are _a priori_ and necessary. In discussing his views regarding experience, we learned that, according to him, all judgments which are empirical are also particular, not allowing any inference beyond the given cases experienced. Experience gives only instances, not principles. If we postpone for the present the discussions of truths of reason, by admitting that they may properly be said to be at once certain and universal, the question arises how in matters of fact there can be any knowledge beyond that which Locke admits; and the answer is, that so far as the mere existence and occurrence of these facts is concerned, there is neither demonstrative nor general knowledge. But the intelligence of man does not stop with the isolated fact; it proceeds to inquire into its cause, to ascertain its conditions, and thus to see into, not merely its actual existence, but its _possibility_. In Leibniz's language: "The real existence of things that are not necessary is a point of fact or history; but the knowledge of possibilities or necessities (the necessary being that whose opposite is not possible) const.i.tutes demonstrative science." In other words, it is the principle of causality, which makes us see a fact not as a mere fact, but as a dependent consequence; which elevates knowledge, otherwise contingent and particular, into the realm of the universal and apodictic. Underlying all "accidental union" is the real synthesis of causation.