 Fârâbî grants to his implicit opponent that some senses of “one” do presuppose a many as their subject, so that if the one were removed the many would remain. There are two-place senses of “one”, as there are two-place senses of “being”: for instance, we can say “X and Y are one in species”. Or perhaps it is better to say, not that these are two-place senses of “one”, but that they are plural-subject senses, since we can equally well say “X and Y and Z are one in species”. In any case Fârâbî grants that there are several senses of “one” which presuppose a many as their subject. Perhaps surprisingly, Fârâbî includes here not only “one in species” and the like but also “one in number”: he thinks that the appropriate expression is not, e.g., “Aristotle is one in number” but “Plato’s best student and Alexander’s teacher are one in number”. Also perhaps surprisingly, he tries to trace back the other plural-subject senses of “one” to “one in number”, saying for instance that if X and Y are one in species, then the species of X and the species of Y are one in number (#1–#8). Fârâbî also grants that there are some senses even of the one-place predication “X is one” which presuppose, not a plural subject, but still a subject consisting of many parts, so that for X to be one is for X’s parts to be related in an appropriate way. For instance, for X to be one as continuous is for X to have parts whose limits are the same; for X to be one as contiguous is for X to have parts whose limits, while not the same, are kept in contact by some bond; for X to be one as whole as for X to have all the parts it needs in order to perform its activity well (#9–#15). But Fârâbî says that where many things are said to be one, or where something is said to be one in a way presupposing that it has many parts, this sense of “many” and this sense of “one” are not opposite: nothing is predicated of its opposite. Thus the opposite of one-in-number is many-in-number, but the subject of one-in-number is many names or descriptions of the same thing; the opposite of one-as-continuous is discretely many things disconnected from each other, but the subject of one-as-continuous is magnitude. Fârâbî insists equally emphatically that there are senses of “one” that are not plural-subject senses and do not presuppose a subject with many parts, and indeed in some cases contradict having a subject with many parts. One sense of “one” is as “undivided” or “indivisible” (the Arabic phrase, like the Greek word, is ambiguous between these two construals). Or perhaps rather, as Fârâbî suggests at the end of the treatise, all senses of “one” can be traced back in one way or another to being undivided (#95). Certainly there are many ways that something could be divided, and filling them out leads to different senses of one-as-undivided or one-as-indivisible. For instance, as Fârâbî notes, “one” is said of something extended that is divisible but not actually divided; of something that is spatially located but quantitatively indivisible, i.e., a point; of what is not spatially located and is therefore quantitatively indivisible; of what has (or is) a simple quiddity not divisible into parts of a definition such as genus and differentia; and of what is not “divided” between a paronymously named subject X and an X-ness through which it is X (#20–24). Some of these senses of “one”, such as one in the sense of an indivisible point, are never predicated of a many. Something can also be called one because it does not have a partner, i.e., because is the only F, for some predicate F, or if nothing else is F in the same way that it is F; and especially if F is its quiddity, as, e.g., the moon can be called “one” in the sense that there is nothing else of the same species as it (#25, pp.55–6). This sense of “one”, too, does not presuppose any plurality in its subject. Fârâbî also talks about different senses of “one” as “circumscribed” in some way (see below): at least some of these senses do not presuppose any plurality in their subject, and apparently in all these senses, if the subject that is one were stripped of its unity, it would not become many instead. Fârâbî apparently does not say that “one” in such a sense does not have an opposite, but it does not have an opposite that is a sense of “many”: the opposite of “one” in such a sense would be the contradictory, “not one”, but not a contrary or privative “many”.