In chap.1.2., of the Bidayat al-Hikmah, the Sadrian philosopher Allameh Tabataba’i sets out to prove, by means of three barahin (demonstrations), that the concept of existence is ishtirak ma’nawi i.e., predicated of different existents in a single sense. Here I’ll only give an analysis of the first proof that he adduces for his conclusion. I’ll take up  his other two arguments in the next two series of posts, God-willing.

The first demonstrative argument according to Allameh hinges on the nature of division:

A proof [that the concept of existence is univocal] is that we divide existence into its different categories, such as the existence of the Necessary Being (wujud al-wajib) and the existence of the contingent being (wujud al-mumkin). The existence of the contingent is divided into that of substance (wujud al-jawhar) and that of accident (wujud al-aradh). The existence of substance and the existence of accident are again divided into their various kinds. It is evident that the validity of a division depends on the unity of what is being divided and on its presence in all its divisions.

Cast in syllogistic form, Allameh’s argument it seems to me would look like this:

Major: for a division to be valid, the term divided has to be univocal. Minor: existence can be validly divided i.e., into necessary, contingent, etc. Conclusion: therefore, existence is a univocal predicate.

Let the minor premise be granted, for it seems evident and straightforward. But what is the exact purport of the major? I have formulated it in those terms because Allameh writes that “the validity of a division depends on the unity of what is being divided and on its presence in all its divisions” and, presumably, I take it, by the terms ‘unity’ and ‘presence’ he just means univocity. If that is the case, Allameh is then saying that the term divided must be present in i.e., predicated of, the parts into which it is divided univocally or in the exact same sense. But why? Because otherwise, he implicitly seems to suggest, there would be no bases for the division – for the dividing terms will then be unrelated both to each other and the whole of which they’re parts i.e., the term which they are dividing. Consequently, the division, if the term divided is not related at all to one or more of its parts – which for Allameh just means not applied univocally to them – will be invalid.

To concretize this abstract point, here are examples of both an (1) invalid and a (2) valid division that Allameh may have had in mind: (1) the division of ‘animal’ into ‘man’ and ‘stone’. The reason this division is invalid is because ‘animality’ does not apply to ‘stone’ in any way or sense whatsoever i.e., neither in the sense in which it applies to ‘man’ nor a different one. And here’s an example of a (2) valid division: the division of ‘animal’ into ‘man’ and ‘horse’. The term ‘animality’ is present in man and horse in the exact same sense i.e., univocally; for a man is said to be an animal just as much as a horse is. So the division is valid.

Allameh with this argument wants to show that the same is the case with the term ‘existence’ when it is divided as well. That is, it must apply to its divisions (i.e., necessary, contingent, etc) univocally. If not, then existence cannot be validly divided into them. And were this true, it would in turn undermine many other philosophical commitments, e.g., a proof of God’s existence, that  both Allameh and his interlocutors may share. Also, whatever the divisions of existence are divided into, existence, as well as the proximate genus of which the second divisions (i.e., substance and accident) are parts, must also apply to them univocally.  To recap all the above then, simply put, in any division whatsoever, if it is to be a valid division, the term divided must be present in its parts in the exact same sense.

Having said all that, here are some questions and concerns that one might raise  contra Allameh’s argument. First, does dividing ‘existence’ mean treating it as some sort of a genus, which it is not (as per what is said in chap. 1.1)? Perhaps Allameh would hold that (the concept of ) existence may not fall under any genus, but it itself can be a genus, under which things fall? But this problematic for other reasons; cf. Aristotle’s argument against why being/existence cannot be a genus in the Metaphysics, Bk.III, chap.3, 998b15-35.

Second, and more importantly I think, is the major premise of Allameh’s argument i.e., that in order for a division to be valid the term divided must univocally be said of its parts, necessary i.e., necessarily true? One can plausibly argue in the negative by recourse to (what are technically called) analogical terms, if there are such things – and it seems that there are; for they seem not require the truth of that premise. For example, following what the First Teacher says in Bk.IV, chap.2 of the Metaphysics, suppose the division of the term ‘healthy’ into ‘animal’ and ‘food’ or (to use my example) the division of the term ‘good’ into ‘man’ ‘song’ and ‘day’. It seems that such a division is valid, even though the terms divided aren’t predicated of their parts univocally but rather analogically i.e., in different but nevertheless closely related senses. Given that, the major premise then, due to analogical terms, is not, it seems, necessarily true. Accordingly, the argument as a whole then cannot be demonstrative of its conclusion; for, although it no doubt rules out the concept of existence as being equivocal i.e., predicated in completely discrete senses, it does not rule it out as being analogical.

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