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Notes
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.
- ↑ De Gen. et Corr. I. 1. 7.
- ↑ De Cœlo, III. 2. 7.
- ↑ Vide Trendel. Comment.
- ↑ Metaphysica, IV. 6. 24.