Different Senses Of The Same in Metaphysics V.9:
Aristotle differentiates the following two senses of the same, but note that he does not mention any “the same in the appropriate sense.”
1. The same by coincidence, for instance, pale and cultured are the same because they are accidents of the same subject.
2. The same by itself, namely, having the same number of senses as “one.”
"For indeed those whose matter is one in species or in number, and those whose substance is one, are said to be the same. Thus it is clearly that sameness is a kind of oneness/unity of more than one thing or when a thing is treated as more than one thing." (1018a6-9)
Observation:
x and y are the same by themselves (i) if the matter of x and the matter of y are one in species or in number or (ii) if the substance of x and the substance of y are one.
This suggests:
a. Teaching and learning cannot be the same by themselves in the sense of (ii), since the substance of teaching and the substance of learning are different.
b. But teaching and learning are entitled “the same by themselves” in the sense that the matter of teaching and the matter of learning are one in species and in number, since that which teaching and learning belong to is one both in species and in number. Accordingly, that which teaching and learning belong to, i.e., the path, should be regarded as the matter of teaching process and learning process.
Different Senses Of One (Metaphysics V.6):
Since Aristotle mentions that “one” has the same number of senses as “the same by itself”, perhaps he will address what he means by x and y are the same not in the appropriate sense? Here he does mention some of the senses of one are said to be “in the primary sense”!
1. in virtue of the continuity (1016a5-6)
2. the substrate is indivisible in species, for instance, all liquids are said to be one (e.g., oil and wine), because their ultimate substrate is the same, for all these things are water or vapor.
3. the substrate is one in genus. According to Aristotle, there are two senses of “one in genus”:
3.1. "In a way it is very similar to that in which the matter is one" (1016a25-29)
3.2. for instance, the isosceles and equilateral triangles are one and the same figure, because they are both triangles, but not the same triangles.
4. the definition or essence is one
5. one in number: "those whose matter is one." Seems to allow two senses???
5.1. strong sense (i.e., one and the same without qualification): If x and y are one in number, then x and y are one in species.
5.2. weak sense: If x and y are one in number, then the matter of x and the matter of y are one.
The weak sense seems to echo one of the senses of “the same by itself”: x and y are the same by themselves if the matter of x and the matter of y are one in species or in number (Met. 5.9, 1018a6-9).
6. one in analogy: "those which have the same relation as something else to something else."
7. one in the primary sense
7.1. "In most cases x and y are said to be one because x either acts upon or possesses or is acted upon by y, or x is in relation to y, but in other cases those whose substance is one are said to be one in the primary sense. It is either one in continuity or in species or in definition." (Met. 5.6, 1016b7-10)
Observations:
(i) one in number, one in genus, and one in analogy do not belong to the primary sense.
“One in number” as non-primary sense must be taken in the weak sense (4.5.2). For, if it was taken in the strong sense (4.5.1), then it must imply “one in species” and become one of the primary senses. This passage (Met. 5.6, 1016b7-10) supports the weak sense of “one in number”.
(ii) If x and y are said to be one because x either acts upon or is acted upon by y, then x and y cannot be one in the primary sense.
Teaching and learning are one “not in the primary sense”, because teaching and learning have the acting upon and being acted upon relation.
a. If x and y are said to be one because x either acts upon or is acted upon by y, then x and y cannot be one in the primary sense.
b. Teaching and learning are said to be one because teacher acts upon the student and the student is acted upon the teacher.
c. Therefore, teaching and learning cannot be one in the primary sense.
