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.
[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 pass 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,—Identity, or diversity; Relation; Co-existence, or necessary connection; Real existence. The statement of identity 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 class. 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 identity or distinction of ideas, either in whole or in part. That of concourse contains Locke’s two classes 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 identity 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 anticipate 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 constitutes 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 analogue 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 “analytic” and “synthetic” judgments. But Leibniz, as we shall see hereafter, trusts too thoroughly to the merely formal relations of identity 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, passes 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 classes,—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 class come such truths as the Cartesian, “I think, therefore I am.” Neither class can be proved by anything more certain.
Demonstration is defined by Leibniz as by Locke. The former recognizes, however, two sorts,—analytic 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 analysis 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.”