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      Chapter X.

       The Nature and Extent of Knowledge.

       Table of Contents

      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