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The Cambridge History of English and American Literature in 18 Volumes (1907–21).
Volume X. The Age of Johnson.

XIV. Philosophers

§ 6. His analysis of “Philosophical Relations”

The “philosophical relations,” under his analysis, fall into two classes. On the one hand, some of them depend entirely on the ideas compared: these are resemblance, contrariety, degrees in quality and proportions in quantity or number. On the other hand, the relations of identity, space and time, and causation may be changed without any change in the ideas related; our knowledge of them thus presents an obvious difficulty, for it cannot be derived from the ideas themselves. Hume does not take much trouble with the former class of relations, in which this difficulty does not arise. He is content to follow on Locke’s lines and to think that general propositions of demonstrative certainty are, obviously, possible here, seeing that we are merely stating a relationship clearly apparent in the ideas themselves. He does not ask whether the relation is or is not a new idea, and, if it is, how it can be explained—from what impression it took its rise. And he gives no explanation of the fixed and permanent character attributed to an idea when it is made the subject of a universal proposition. It is important to note, however, that he does not follow Locke in holding that mathematics is a science which is at once demonstrative and “instructive.” The propositions of geometry concern spatial relations, and our idea of space is received “from the disposition of visible and tangible objects”; we have “no idea of space or extension but when we regard it as an object either of our sight or feeling” (i.e. touch); and. in these perceptions, we can never attain exactness: “our appeal is still to the weak and fallible judgment which we make from the appearance of the objects, and correct by a compass or common measure.” Geometry, therefore, is an empirical science; it is founded on observations of approximate accuracy only, though the variations from the normal in our observations may be neutralised in the general propositions which we form. Hume does not apply the same doctrine to arithmetic, on the ground (which his principles do not justify) that the unit is something unique. He is thus able to count quantity and number in his first class of relations and to except algebra and arithmetic from the effect of his subtle analysis of the foundations of geometry. In his Enquiry concerning Human Understanding, however, he deserts, without a word of justification, the earlier view which he had worked out with much care and ingenuity, and treats mathematics generally as the great example of demonstrative reasoning. In this later work, in which completeness is sacrificed to the presentation of salient features, he speaks, not of two kinds of relations, but of “relations of ideas” and “matters of fact”; and, in each, he seeks to save something from the general ruin of the sciences to which his premises lead. The last paragraph of the book sets forth his conclusion:

  • When we run over our libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames; for it can contain nothing but sophistry and illusion.
  • This passage, startling and ruthless as it sounds, is chiefly remarkable for its reservations. It was easy to condemn “divinity or school metaphysics” as illusory; they had for long been common game. But to challenge the validity of mathematics or of natural science was quite another matter. Hume did not temper the wind to the shorn lamb; but he took care that it should not visit too roughly the sturdy wethers of the flock. Yet we have seen that, according to his principles, mathematics rests upon observations which fall short of accuracy, while natural science, with its “experimental reasoning concerning matter of fact,” depends upon the relation of cause and effect.

    The examination of this relation occupies a central position in both his works; and its influence upon subsequent thought has been so great as, sometimes, to obscure the importance of other factors in his philosophy. He faced a problem into which Locke had hardly penetrated, and of which even Berkeley had had only a partial view. What do we mean when we say that one thing is cause and another thing its effect, and what right have we to that meaning? In sense perception, we have impressions of flame and of heat, for instance; but why do we say that the flame causes the heat, what ground is there for asserting any “necessary connection” between them? The connection cannot be derived from any comparison of the ideas of flame and of heat; it must come from impression, therefore; but there is no separate impression of “cause” or “causation” which could serve as the link between two objects. What, then, is the origin of the connection? To use the terminology of the Enquiry, since cause is not a “relation of ideas,” it must be a “matter of fact”—an impression. But it is not itself a separate or simple impression; it must, therefore, be due to the mode or manner in which impressions occur. In our experience, we are accustomed to find flame and heat combined; we pass constantly from one to the other; and the custom becomes so strong that, whenever the impression of flame occurs, the idea of heat follows. Then, we mistake this mental or subjective connection for an objective connection. Necessary connection is not in the objects, but only in the mind; yet custom is too strong for us, and we attribute it to the objects.