Whenever cogitation is employed upon what may be indivisible it is not subject to error, but when engaged upon topics which involve both error and truth, there is a simultaneous combination of thoughts, whereby they are, so to say, individualized; in the way that Empedocles expressed himself, "Now the heads of many creatures budded forth without necks, and then, heads and necks were by affinity made one." It is thus that thoughts, however disconnected, as the incommensurable and the diameter, are by the intelligence joined together. If the question relate to things past or future, the mind, thinking upon time besides, adds it to the other conditions; for error lies ever in the combination, as when the white is said not to be white, the error is in the addition of the negative. Now, it is always in our power to speak of things individually; but then, it is not only true or false that Clem is fair, but equally so that he ever was or ever will be fair. It is the mind which individualizes each subject. But since the indivisible is in the twofold state either of potentiality or actuality, there is nothing to preclude the mind when thinking upon extension, from thinking upon it as indivisible, for it is indivisible, actually, and in time which is indivisible; as time, like extension, is both divisible and indivisible. It may not then be said that the mind thinks upon any subject in each half; for extension exists only in potentiality, unless it have been divided. But the mind, when thinking upon each of the halves separately, divides the time simultaneously, and then time becomes such as the two extensions; and if the mind make a whole of the two halves, it does the same with time in its relation to them. The mind, however, thinks upon the indivisible as species and not as quantity, in an indivisible portion of time and by an indivisible part of Vital Principle; and this neither by accident, nor in so far as the subjects thought upon, or the part by which, or the time in which, it thinks, are divisible, but as they are indivisible. There is, in fact, in such cases a something indivisible, although it may not be separate, which makes time and extension to be one; and which holds good for all continuity, whether of time or extension. Now, the point and every analogous division, and whatever is as the point indivisible, are made known as being privation of something. The reasoning upon other subjects is like this, for were it asked how the mind is to recognise bad or black, it may be answered, that it recognises them in some way by their contraries; but that which recognises them must, in potentiality, be the thing recognised, and be present also in it. If to any one of the senses there is no contrary, then that sense recognises itself, is in activity and separate from all else. An affirmation, like a negation, is something in relation to something, and is always either true or false; but not so with the mind, as it is true when it judges of any thing after its essence, and may not be true when it judges of something in its relation to something else. Thus, the visual perception of any particular object is true, but whether a something white which is seen be or be not a man is not invariably true; and this holds good for abstractions.
Notes edit
Note 1, p. 159. In the way that Empedocles, &c.] The passage cited in support of the above opinion is not very apposite; for Empedocles[1], who had made "nature to be nothing more than the combination of (μίξις) and change among commingled particles," (attraction and repulsion, in other words), is quoted by Aristotle[2] in the words, "many heads of creatures without necks budded forth;" and, as if to turn against him, as it were, his own doctrine, it is added, "they were by affinity joined together." This led Aristotle to the simile in the text, as Empedocles[3] formed things in nature by the combination of individual particles, so may the mind eliminate new by the association of former or admitted ideas; and as, in the verse cited, head and neck lie dissevered, so, in the idea of quantity, there is nothing in common between the measure of the diagonal and the side of the square. Thus, as there is no common measure for the diagonal and the side of the square, they are, in so far, distinct; but although, in themselves, distinct, they can, in thought, be combined and made one. "By diameter may be understood the diagonal which divides the square into two equal triangles; or it may mean the diameter of the circle which is incommensurate with the circumference." In a word, it is by combination that error creeps into our judgments, and falsifies our perceptions.
Note 2, p. 159. It is the mind, &c.] The question of a fact, such as that in the example, is dependent upon the brain rather than the mind, as that organ can combine the individual notices obtained through the senses; but when the mind intervenes, so to say, and judges from what is, of what was or is to be, there is room for error. It is almost puerile to explain that the assertion "something is not white" is not, necessarily, fallacious; and that, if the object be white, the fallacy comes from the addition of the negative. The double sense of indivisibility is to the same purport; extension is clearly divisible, and, therefore, divisibility is made, actually, apparent as a fact; but the mind can realise to itself extension without parts, as indivisible, that is, and in potentiality.
Note 3, p. 160. It may not then be said, &c.] In this version, the term mind is used, and in another, "intelligence," (which is its synonym), as that which thinks, (τί ἑννόει), but the text does not so specify it; and any allusion to halves would but ill-accord with the notion of homogeneity and impassibility assigned to the thinking principle. But no theory which could be framed of the mind would aid in explaining the train of reasoning here; for, independently of the abstruse nature of all mental processes, there is, evidently about it, confusion, arising from the assumption of a something associated with sensibility, which the brain only could rectify.
Note 4, p. 160. The point and every analogous division, &c.] With respect to quantity[4], in relation to indivisibility, "a point which has position, (καὶ θέσιν ἔχον στιγμή) is indivisible, but a line is divisible in one, surface in two, and body in several directions;" and by privation is implied that the point is without length, depth, or breadth; the line without either breadth or depth; and the surface without depth. It is obvious, from what has been said, that every affirmation or negation must, as depending upon sentient impressions, be either true or false; but that the judgment, when deciding upon essential or abiding qualities, may be true, and that, when drawing its inferences from accidental qualities or relations of bodies, it may be erroneous.