Therefore the relation between content or matter of knowledge, and the form which is its general characteristic as knowledge, is of this kind. We can either study the objects of knowledge directly as we perceive them, or indirectly, as examples of the way in which we know. As studied for their own sake, they are regarded as the matter or content in which the general form of knowledge finds individual realisation. In botany, for instance, we have a large number of actual plants classified and explained in their relation to one another. A botanist is interested directly in the affinities and evolution of these plants, and in the principles of biology which underlie their history. He pushes his researches further and further into the individual matters that come to light, without, as a rule, more than a passing reflection upon the abstract nature of the methods which he is creating as his work proceeds. He classifies, explains, observes, experiments, theorises, generalises, to the best of his power, solely in order to grasp and render intelligible the region of concrete fact that lies before him. Now while his particular results and discoveries {48} constitute the “form” or knowable properties of the plant-world as the object of botanical science, the science which inquires into the general nature of knowledge must treat these particular results as “mere matter”—as something with which it is not directly concerned, any more than the art which makes a statue is primarily and directly concerned with the chemical and mechanical properties of marble. The “form” or knowable properties with which the general science of knowledge is directly concerned, consists in those methods and processes which the man of science, developing the modes in which common sense naturally works, constructs unconsciously as he goes along. Thus, not the nature and affinities of the plant-world, but classification, explanation, observation, experiment, theory, are the phenomena in virtue of which the organised structure of botanical science participates in the form of knowledge, and its objects become, in these respects, objects of logical theory.
Hence some properties and relations of objects, being the form or knowable structure of the concrete objects as a special department of nature, correspond to the mere matter, stuff, or content of Knowledge in general, while other properties and relations of objects, being their form or knowable structure as entering into a world of reality displayed to our intelligence, correspond to the form of Knowledge as treated of by a general inquiry into its characteristics, which we call Logic. It is just as the qualities or “forms” of the different metals of which knives can be made are mere matter or irrelevant detail when we are discussing the general “form” or quality of a good knife, {49} whatever its material. A reservation on this head appears in the following section.
Form of Knowledge dependent on Content
2. For the form of Knowledge depends in some degree upon its matter. It is very important to realise this truth; for if Logic is swamped by being identified with the whole range of special sciences, it is killed by being emptied of all adaptation to living intelligence. What is called Formal Logic par excellence in all its shapes, whether antiquated as in Hamilton’s or Thomson’s Formal Laws of Thought, or freshly worked out on a symbolic basis as by Boole and others, has, it appears to me, this initial defect, when considered as a general theory of Logic. As a contribution to such a theory, every method which will work undoubtedly has its place, and indicates and depends upon some characteristic of real thought. But in the central theory itself, and especially in so short an account of it as must be attempted in these lectures, I should be inclined to condemn all attempts to employ symbols for anything more than the most passing illustration of points in logical processes. All such attempts, I must maintain, share with the old-fashioned laws of Identity, Contradiction, and Excluded Middle the initial fallacy of representing a judgment by something which is not and cannot be in any way an adequate symbol of one. If, in order to get at the pure form of Knowledge, we restrict ourselves to very abstract characteristics in which all knowledge appears, very roughly speaking, to agree, and which can be symbolized for working purposes by combinations of signs which have not the essential properties of ideal contents, then we have ab initio substituted for the judgment something which is a very {50} abstract corollary from the nature of judgment, and may or not for certain purposes and within certain limits be a fair representative of it. We cannot and must not exclude from the form of Knowledge its modifications according to “matter,” and its nature as existing only in “matter.”
In fact, the peculiar “form” of everything depends in some degree on its “matter.” A statue in marble is a little differently treated if it is copied in bronze. A knife is properly made of steel; you can only make a bad one of iron, or copper, or flint, and you cannot make one at all of wax. Different matters will more or less take the same form, but only within certain limits. So it is in Knowledge. The nature of objects as Knowledge—for we must remember that “form” in our sense is not something put into the “matter,” something alien or indifferent to it, but is simply its own inmost character revealed by the structural relations in which it is found capable of standing [1]—depends on the way in which their parts are connected together.
[1] The example of the marble statue may seem to contradict this idea; and no doubt the indifference of matter to form is a question of degree. But the feeling for material is a most important element in fine art; and in knowledge there is only a relative distinction between formal and material relations.
Let us compare, for example, the use of number in understanding objects of different kinds.
Suppose there are four books in a heap on the table. This heap of books is the object. We desire to conceive it as a whole consisting of parts. In order to do so we simply count them “one, two, three, four books.” If one is taken away, there is one less to count; if one is added, there is one more. But the books themselves, as books, are not {51} altered by taking away one from them or adding one to them. They are parts indifferent to each other, forming a heap which is sufficiently analysed or synthesised by counting its parts.
But now instead of four books in a heap, let us think of the four sides of a square. Of course we can count them, as we counted the books; but we have not conceived the nature of the square by counting its sides. That does not distinguish it from four straight lines drawn anyhow in space. In order to appreciate what a square is, we must consider that the sides are equal straight lines, put together in a particular way so as to make a figure with four right angles; we must distinguish it from a figure with four equal sides, but its angles not right angles, and from a four-sided figure with right angles, but with only its opposite sides equal; and note that if we shorten up one side into nothing, the square becomes a triangle, with altogether different properties from those of a square; if we put in another side it becomes a pentagon, and so on.
These two things, the heap of books and the square, are prima facie objects of perception. We commonly speak of a diagram on a blackboard or in a book as “a square” if we have reason to take it as approximately exact, and as intended for a square. But on looking closer, we soon see that the “matter,” or individual attributes, of each of these objects of our apprehension demands a different form of knowledge from that necessary to the other. The judgment “This heap of books has four books in it” is a judgment of enumerative perception. The judgment “The square has four sides” is a judgment of systematic necessity.