Chapter XCI: Section II: The Nature of Abstraction

Your starting-point is good: man, in fact, does not know anything of substances; he knows neither minds nor bodies; he perceives only transient, isolated, internal conditions; he makes use of these to affirm and name exterior states, positions, movements, changes, and avails himself of them for nothing else. He can only attain to facts, whether within or without, sometimes transient, when his impression is not repeated; sometimes permanent, when his impression, many times repeated, makes him suppose that it will be repeated as often as he wishes to experience it. He only grasps colors, sounds, resistances, movements: sometimes momentary and variable, sometimes like one another, and renewed. To group these facts more advantageously, he supposes, by an artifice of language, qualities and properties. We go even further than you: we think that there are neither minds nor bodies, but simply groups of present or possible movements or thoughts. We believe that there are no substances, but only systems of facts. We regard the idea of substance as a psychological illusion. We consider substance, force, and all the modern metaphysical existences, as the remains of scholastic entities. We think that there exists nothing but facts and laws, that is, events and the relations between them; and we recognize, with you, that all knowledge consists, first of all, in connecting or adding fact to fact. But when this is done, a new operation begins, the most fertile of all, which consists in reducing these complex into simple facts. A splendid faculty appears, the source of language, the interpreter of nature, the parent of religions and philosophies, the only genuine distinction, which according to its degree, separates man from the brute, and great from little men. I mean Abstraction, which is the power of isolating the elements of facts, and of considering them one by one. My eyes follow the outline of a square, and abstraction isolates its two constituent properties, the equality of its sides and angles. My fingers touch the surface of a cylinder, and abstraction isolates its two generative elements, the idea of a rectangle, and of the revolution of this rectangle about one of its sides as an axis. A hundred thousand experiments develop for me, by an infinite number of details, the series of physiological operations which constitute life; and abstraction isolates the law of this series, which is a round of constant loss and continual reparation. Twelve hundred pages teach me Mill's opinion on the various facts of science, and abstraction isolates his fundamental idea, namely, that the only fertile propositions are those which connect a fact with another not contained in the first. Everywhere the case is the same. A fact, or a series of facts, can always be resolved into its components. It is this resolution which forms our problem, when we ask what is the nature of an object. It is these components we look for when we wish to penetrate into the inner nature of a being. These we designate under the names of forces, causes, laws, essences, primitive properties. They are not new facts added to the first, but an essence or extract from them; they are contained in the first, they have no existence apart from the facts themselves. When we discover them, we do not pass from one fact to another, but from one to another aspect of the same fact; from the whole to a part, from the compound to the components. We only see the same thing under two forms; first, as a whole, then as divided: we only translate the same idea from one language into another, from the language of the senses into abstract language, just as we express a curve by an equation, or a cube as a function of its side. It signifies little whether this translation be difficult or not; or that we generally need the accumulation or comparison of a vast number of facts to arrive at it, and whether our mind may not often succumb before accomplishing it. However this may be, in this operation, which is evidently fertile, instead of proceeding from one fact to another, we go from the same to the same; instead of adding experiment to experiment, we set aside some portion of the first; instead of advancing, we pause to examine the ground we stand on. There are, thus, fruitful judgments, which, however, are not the results of experience: there are essential propositions, which, however, are not merely verbal: there is, thus, an operation, differing from experience, which acts by cutting down, instead of by addition; which, instead of acquiring, devotes itself to acquired data; and which, going further than observation, opening a new field to the sciences, defines their nature, determines their progress, completes their resources, and marks out their end.

This is the great omission of your system. Abstraction is left in the background, barely mentioned, concealed by the other operations of the mind, treated as an appendage of Experience; we have but to re-establish it in the general theory, in order to reform the particular theories in which it is absent.