Here are some comments meant to explicate the arguments contained in paragraphs 1-3 of the shaykh’s Al-Shifa’; Ilahiyyat I.7, which is meant to show that the notion of necessity of existence (wajib al-wujud) can’t belong to more than one entity (dhat). I’ll quote the shaykh’s text and then comment accordingly.
The shaykh begins I.7 as follows (tr. modified from Marmura’s):
(1) We further say: necessity of existence must be one. Otherwise, let [us suppose It were] a multiplicity in which each member is a necessary existent. It would then follow that each, with respect to the meaning which is its true nature, either would not differ at all from [any] other [member] or would differ from it. If it does not differ from the other in the meaning that belongs to [itself] essentially, differing from [the other] only in not being it – and this is inescapably a difference – then it differs from it in [something] other than the meaning.
Here the shaykh states the conclusion he initially seeks for: namely, that, assuming the that necessity of existence belongs to more than one entity, it would follow that they would differ from each other by reason of something other than the one meaning i.e., necessity of existence, which they have in common. From this premise, as he’ll show below, certain absurdities result. But for now, why think the assumption of multiple necessary beings entails it? He answers:
This is because the meaning in both does not differ; [but] something has conjoined [with] it, in terms of which it becomes “this” or in “this” (or it was conjoined by the very fact of being “this” or in “this”), while this [thing] that conjoins [with it] did not conjoin with the other. Rather, it is through [what the former has] that [the latter] becomes “that,” or [through] the very fact that “that” is “that.” This is some kind of specification that has attached to that meaning through which there is a difference between the two. Hence, each of the two differs from the other through this, but would not differ from it in [that it has] the same meaning. It would thus differ from it in [something] other than this meaning.
The reasoning involved in establishing the conclusion he seeks is as follows: since the meaning of being necessary of existence is essential to them, and since we’re assuming they are distinct (for, again, they are two not one) – then either they differ from each other with respect to their essential meaning or not. If they don’t, but nevertheless are two and not one, then they must differ by virtue of something other than that meaning. Hence, it must be said that something extra i.e., over and above that meaning has conjoined to one of the two necessary beings in virtue of which it has become a “this” and eh other a “that” i.e., determinate individuals distinct from each other. This additional feature is a feature of one of them but not the other. If it is supposed that they, in addition to their meaning, also have this feature in common, the same outcome will result; namely, since they are two and not one, there must be some other ‘factor’ or ‘thing’ which one has and the other does not. And if this thing is also said to be common, then the process will continue ad infinitum unless one simply admits that one of them has it and the other does not. Otherwise, they’d be just be one, not two. Put another way, it can be said that through the very fact that the first has that additional feature, it is thereby made distinct from the second one, and also that the latter is distinguished from the former by virtue of the former having that feature. This extra feature, by attaching to one of them differentiates the two from each other. Hence, they differ from each other due to it. But they are not different from each other insofar as they have the same nature or meaning i.e., of necessary existence. Hence, as was sought, they must differ from each other by reason of something other than their common meaning i.e., that extra conjoined thing.
(2) [Now], the things that are other than the meaning but which attach to the meaning are the accidents and [unessential attachments]. These [attachments] either occur to the thing’s existence inasmuch as it is that existence ([in which case] it is necessary that everything in this existence must agree, when [in fact] these were supposed to be different – and this is a contradiction), […].
We’ve established that the two necessary beings differ because of something other than their essential meaning. Now, the shaykh argues, the things other than the essential nature or meaning, which distinguish the two, are either accidents a’raadh or lawahiq. Now, they will either occur to one of the two qua its existence as necessary or not. In other words, it will have them simply by virtue of having, or better, being necessary existence or not. If so, then because, as our initial assumption states, the other thing also has necessary existence, these attachments will inevitably attach to it as well – in which case, and against what we established, the two would be one not two. This is a contradiction.
The shaykh continues:
[…] or lawahiq occur to [the thing’s existence] from external causes, not from quiddity itself. It would then follow that, if it were not for that cause, they would not have occurred; and, if it were not for that cause, it would not be different; and, if it were not for that cause, the essences either would or would not be one; and, if it were not for that cause, “this” by itself would not be necessary of existence, [nor] “that” by itself a necessary of existence – [that is], not with respect to existence but with respect to accidents.
That is to say, if the lawahiq do not occur to one of the two because of its very nature or quiddity, then they will necessarily have to occur due to something outside the quiddity or nature. The reason – although implicit in the text and dealt with more fully elsewhere – for this is because that which does not have something by nature receives it from outside its nature. Otherwise, it would always possess it. At this point, the shaykh draws out a number of corollaries all of which go to show a contradiction. These are that (a) the external cause is why the attachments attach to the two; this would mean (b) if it wasn’t for this external cause, one of the two would not in fact be different from the other; (c) the unity of their essences would depend on the external cause; and finally (d) if it was not for this external cause, neither one of them would be, by itself, necessary of existence – one of them because of the presence of the external cause and the other because of its absence.
The shaykh then concludes:
(3) Thus, the necessity of existence of each, particular to each and singled out , would be derived from another. But it has been stated that whatever is necessary of existence through another is not necessary of existence in itself; rather, it is possible of existence. It would then [follow] that, although each one of these [two] is in itself a necessary existent, it is, within its own domain, a possible existent – and this is impossible.
That is to say, the necessity of existence of each would be derived from another i.e., the external cause in question. But this, as the shaykh shows in detail earlier in I.6, is impossible; for a thing cannot be, in the same respect, both necessary in itself and possible in itself. This is another contradiction. Therefore, either the supposed necessary beings will not be two, but one, or they (or at least one of them) will not be necessary but only possible. The upshot of the entire argumentation above is that necessity of existence cannot belong to more than one entity.