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Suppose we start from the explosion—and changes or movements are not only apt to attract attention first, but, when recognized as events and not as abstracts personified, they call for some supplementing beyond themselves—then in this case we may search for the agent at work or for the object affected, but not for both at once. Moreover, if we find either, a complete judgment at once ensues: “The enemy explodes,” or “The mine is exploded.” The original judgment is really due to a synthesis of these two. But, when the results of former judgments are in this manner taken up into a new judgment, a certain “condensation of thought” ensues. Of this condensation the grammatical structure of language is evidence, though logical manipulation—with great pains—obliterates it. Thus our more complex judgment would take the form—“The enemy is now mine-exploding” or “The mine is enemy-exploded,” according as one or other of the simpler judgments was made first. An examination of other cases would in like manner tend to show that intellectual synthesis is always—in itself and apart from implications—a binary synthesis. Wundt, to whom belongs the merit of first explicitly stating this “law of dichotomy or duality”^[1] as the cardinal principle of discursive thinking, contrasts it with synthesis by mere association. This, as running on continuously, he represents thus—A — B — C — D — . . . ; the synthesis of thought, on the other hand, he symbolizes by forms such as the following:—

		$\scriptstyle {\overbrace {\quad \quad \quad } }$				$\scriptstyle {\overbrace {\quad \quad \quad } }$
$\scriptstyle {\overbrace {\quad } }$		$\scriptstyle {\overbrace {\quad } }$		$\scriptstyle {\overbrace {\quad } }$		$\scriptstyle {\overbrace {\quad } }$		$\scriptstyle {\overbrace {\quad } }$
AB	;	AB		CD	;	AB		C	$\scriptstyle {\overbrace {\quad } }$ DE;	&c.

Thus, Socrates is a philosopher; the philosopher Socrates discovered a method; the philosopher Socrates discovered the dialectical method; &c. The point is that the one thing attended to in an intellective act is the synthesis of two ideas, and of two ideas only, because, as only one movement of attention is possible at a time, only two ideas at a time can be synthesized. In that merely associative synthesis by which the memory continuum is produced attention moves from A to B and thence to C without any relation between A and B being attended to at all, although they must have relations, that of sequence e.g. at least.

“Difference,” says Hume, “I consider rather as a negation of relation than anything real or positive. Difference is of two Difference and Likeness. kinds, as opposed either to identity or resemblance. The first is called a difference of number, the other of kind.” The truth seems rather to be that difference in Hume's sense of numerical difference^[2] is so far an element in all relations as all imply distinct correlatives. To this extent even identity—or at least the recognition of it—rests on difference, that form of difference, viz. which is essential to plurality. But absolute difference (i.e. diversity) of kind may be considered tantamount not, indeed, to the negation, but at least to the absence of all formal relation. That this absolute difference—or disparateness, as we may call it—affords no ground for relations becomes evident when we consider (1) that, if we had only a plurality of absolutely different presentations, we should have no consciousness at all (cf. § 11); and (2) that we never compare—although we distinguish—presentations which seem absolutely or totally disparate, as e.g. a thunderclap and the taste of sugar, or the notion of free trade and that of the Greek accusative. All actual comparison of what is qualitatively different rests upon at least partial likeness. This being understood, it is noteworthy that the recognition of unlikeness is, if anything, more “real or positive” than that of likeness, and is certainly the simpler of the two. In the comparison of sensible impressions—as of two colours, two sounds, the lengths or the directions of two lines, &c.—we find it easier in some cases to have the two impressions that are compared presented together, in others to have first one presented and then the other. But, either way, the essential matter is to secure the most effective presentation of their difference, which in every case is something positive and, like any other impression, may vary in amount from bare perceptibility to the extremest distance that the continuum to which it belongs will admit. Where no difference or distance at all is perceptible there we say there is likeness or equality. Is the only outcome, then, that when we pass from ab to ac there is a change in consciousness, and that when ab persists there is none? To say this is to take no account of the operations (we may symbolize them as ac→ab:c, ab→ab:o) by which the difference or the equality results. The change of presentation (c) and absence of change (o) are not here what they are as merely passive occurrences, so to put it. This is evident from the fact that in the former there is positive presentation and in the latter no presentation at all. The relation of unlikeness, then, is distinguished from the mere “position” or fact of change by (1) the voluntary concentration of attention upon ab and ac with a view to the detection of this change as their difference, and by (2) the act, relating them through it, in that they are judged unlike to that extent. The type of comparison is such superposition of geometrical lines or figures (as, e.g. in Euclid I. iv.): if they coincide we have concrete equality; if they do not their difference is a line or figure. All sensible comparisons conform essentially to this type. In comparing two shades we place them side by side, and passing from one to the other seek to determine not the absolute shade of the second but its shade relative to the first—in other words, we look out for contrast. We do not say of one “It is dark,” for in the scale or shades it may be light, but “It is darker”; or vice versa. Where there is no distance or contrast we simply have not two impressions, and, as said—if we consider the difference by itself—no impression at all. Two coincident triangles must be perceived as one. The distinction between the one triangle thus formed by two coinciding and the single triangle rests upon something extraneous to this bare presentation of a triangle that is one and the same in both cases. The marks of this numerical distinctness may be various: they may be different temporal signs, as in reduplications of the memory-continuum; or they may be constituents peculiar to each, from which attention is for the moment abstracted, any one of which suffices to give the common or identical constituent a new setting. In general, it may be said (1) that the numerical distinctness of the related terms is secured in the absence of all qualitative difference solely by the intellectual act which has so unified each as to retain what may serve as an individual mark; and (2) that they become related as “like” either in virtue of the active adjustment to a change of impression which their partial assimilation defeats, or in virtue of an anticipated continuance of the impression which this assimilation confirms.

It is in keeping with this analysis that we say in common speech that two things in any respect similar are so far the same. Identity. This ambiguity in the word “same,” whereby it means either individual identity or indistinguishable resemblance has been often noticed, and from a logical or objective point of view justly complained of as “engendering fallacies in otherwise enlightened understandings.” But apparently no one has inquired into its psychological basis, although more than one writer has admitted that the ambiguity is one “in itself not always to be avoided.”^[3] It is not enough to trace the confusion to the existence of common names and to cite the forgotten controversies of scholastic realism. We are not now concerned with the conformity of thought to things or with logical analysis, but with the analysis of a psychological process. The tendency to treat presentations as if they were copies of things—the objective bias, as we may call it—is the one grand obstacle to psychological observation. Some only realize with an effort that the idea of extension is not extended; no wonder, then, if it should seem “unnatural” to maintain that the idea of two like things does not consist of two like ideas. But, assuming that both meanings of identity have a psychological justification, it will be well to distinguish

1. Wundt, Logik; eine Untersuchung der Principien der Erkenntniss (2nd ed., 1893), i. 59 sqq.
2. Hume's numerical difference, that is to say, is really distinctness, not quantitative difference.
3. Cf. J. S. Mill, Logic, bk. i. ch. iii. § 11, and Examination of Hamilton, 3rd ed., ch. xiv. p. 306, note; also Meinong, “Hume-Studien” II., Wiener Sitzungsberichte (Phil. Hist. Cl.). ci. 709.