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.”
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 title 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 titles, “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 circumstances 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 class constitutes “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 constitution 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 classes, and is a pattern or standard by which we classify 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 God, 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 classes of connection, in order to ascertain the extent of knowledge in it. Our knowledge of “identity 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 class 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 God, 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 assure 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 (God, 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 classes. 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 anticipates 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 class, that of co-existence, to be examined. Here, if anywhere, must knowledge, worthy of being
