Page:Mind (New Series) Volume 6.djvu/168

 152 L. T. HOBHOUSE : square was drawn in white chalk on a blackboard or in black lead on white paper, but was no more and no less a square in either case. Now here the attributes B and C are them- selves modifications of A. A no longer appears in quite the same character twice over. Thus to take an instance as before from the world of geometry, a curve of the second degree is a conception which can be rendered algebraically by a certain general form of equation. To this equation in its general form no real curve corresponds, and though it expresses certain qualities or relations of actual curves it seems impossible to form any adequate conception of the curves themselves as curves except by what we may call disjunctive illustration. If in the general equation the sum of certain coefficients is determined as negative the curve will be an ellipse ; if as positive it will be a hyperbola ; if as zero a parabola. The general expression is here a form to be filled in, which does not acquire positive and intelligible meaning until filled in. It is related to intelligible conception as the word to the sentence. And since the form can be filled in in more than one way the general is here equivalent to the disjunctive. Further, though the form has to be filled in, and though the net result will differ according to the way in which we fill it in, it remains in all cases the same form. The general equation holds whether certain coefficients have a positive, negative, or zero value. Each curve is a special and peculiar modification of identical elements. True, the re- lation of general and specific is in this case so organic, that we cannot adequately conceive the one without the other in some one of its forms. The 'modification' is not a real process applied to a real element and developing it in time into a new form. But the reality expressed by the phrase is the nature of the resemblance or characteristic affinity between the curves, as it presents itself upon ultimate analysis. The two or more contents resemble one another not in a vague or unanalysable sense, but in a way which may be accurately represented by saying that each presents a peculiar differentiation of a common quality. Lastly the disjunction involved is no longer indefinite. And here we have another point of contrast with the abstract quality. For if ' square ' is to be interpreted disjunctively, there is no end to the alternatives. A square drawn in chalk or pencil, or cut out of paper or cardboard, or formed in any way you please will do equally well, the nature of the material leaving the squareness quite unmodified. In other words the concept as abstract does not contain "the prin-