Here Aristotle concludes his first Category or Predicament — Essence or Substance. He proceeds to the other nine, and ranks Quantity first among them.[45] Quantum is either Continual or Discrete; it consists either of parts having position in reference to each other, or of parts not having position in reference to each other. Discrete Quanta are Number and Speech; Continual Quanta are Line, Surface, Body, and besides these, Time and Place. The parts of Number have no position in reference to each other; the parts of Line, Surface, Body, have position in reference to each other. These are called Quanta, primarily; other things are called Quanta in a secondary way, κατὰ συμβεβηκός.[46] Thus we say much white, when the surface of white is large; we say, the action is long, because much time and movement have been consumed in it. If we are asked, how long the action is? we must answer by specifying its length in time — a year or a month.
[45] Ibid. b. 21, seq.
[46] Ibid. p. 5, a. 38, seq.
To Quantum (as to Essence or Substance) there exists no contrary.[47] There is nothing contrary to a length of three cubits or an area of four square feet. Great, little, long, short, are more properly terms of Relation than terms of Quantity; thus belonging to another Category. Nor is Quantum ever more or less Quantum; it does not admit of degree. The Quantum a yard is neither more nor less Quantum than that called a foot. That which is peculiar to Quanta is to be equal or unequal:[48] the relations of equality and inequality are not properly affirmed of anything else except of Quanta.
[47] Ibid. b. 11, seq.
[48] Ibid. p. 6, a. 26-35.
From the Category of Quantity, Aristotle proceeds next to that of Relation;[49] which he discusses in immediate sequence after Quantity, and before Quality, probably because in the course of his exposition about Quantity, he had been obliged to intimate how closely Quantity was implicated with Relation, and how essential it was that the distinction between the two should be made clear.
[49] Ibid. a. 36, seq.
Relata (τὰ πρός τι — ad Aliquid) are things such, that what they are, they are said to be of other things, or are said to in some other manner towards something else (ὅσα αὐτὰ ἅπερ ἐστὶν ἑτέρων εἶναι λέγεται, ἢ ὁπωστοῦν ἄλλως πρὸς ἕτερον). Thus, that which is greater, is said to be greater than another; that which is called double is called also double of another. Habit, disposition, perception, cognition, position, &c., are all Relata. Habit, is habit of something; perception and cognition, are always of something; position, is position of something. The Category of Relation admits contrariety in some cases, but not always; it also admits, in some cases, graduation, or the more or less in degree; things are more like or less like to each other.[50] All Relata are so designated in virtue of their relation to other Correlata; the master is master of a servant — the servant is servant of a master. Sometimes the Correlatum is mentioned not in the genitive case but in some other case; thus cognition is cognition of the cognitum, but cognitum is cognitum by cognition; perception is perception of the perceptum, but the perceptum is perceptum by perception.[51] The correlation indeed will not manifestly appear, unless the Correlate be designated by its appropriate term: thus, if the wing be declared to be wing of a bird, there is no apparent correlation; we ought to say, the wing is wing of the winged, and the winged is winged through or by the wing; for the wing belongs to the bird, not quâ bird, but quâ winged,[52] since there are many things winged, which are not birds. Sometimes there is no current term appropriate to the Correlate, so that we are under the necessity of coining one for the occasion: we must say, to speak with strict accuracy, ἡ κεφαλή, τοῦ κεφαλωτοῦ κεφαλή not ἡ κεφαλή, τοῦ ζῷου κεφαλή; τὸ πηδάλιον, τοῦ πηδαλιωτοῦ πηδάλιον, not τὸ πηδάλιον, πλοίου πηδάλιον.[53]
[50] Aristot. Categ. p. 6, b. 20.