A. Of What Sort the Univocity of Being is and to What Things it Extends.

131. As to the first point I say that being is not a univocal assertion in the ‘what’ of all per se intelligibles, because not of ultimate differences, nor of the proper passions of being. (A difference is called ultimate because it does not have a difference - because it is not resolved into a quidditative and qualitative concept, a determinable and determinate concept; but there is only a qualitative concept of it, just as an ultimate genus has only a quidditative concept.)

132. The first claim, namely about ultimate differences, I prove in two ways. First as follows: if differences include being univocally said of them, and these differences are not altogether the same, then they are diverse entities in some respect the same. Such are differences properly, from Metaphysics 5.9.1018a12-13, 10.3.1054b25-27. Therefore, ultimate differences will be differences properly; therefore they differ in other differences. But if these other differences include being quidditatively, the same follows about them as about the former, and so there would be a regress to infinity in differences; or a stand will be made at some differences that do not include being quidditatively, which is the conclusion intended, because they alone will be ultimates [see also n.136 below].

133. Second as follows: just as a composite being is composed of act and potency in the thing, so a composite concept per se one is composed of a potential and actual concept, or composed of determinable and determining concept. Just as therefore the resolution of composite being stops ultimately at simply simples, namely at ultimate act and ultimate potency, which are diverse primarily, such that nothing of one includes anything of the other (otherwise this one would not be act primarily, and that one would not be potency primarily, for what includes something of potentiality is not act primarily) - so in the case of concepts must it be that every concept that is not simply simple [n.71], and yet is per se one, is resolved into a determinable and determining concept, such that resolution stops at simply simple concepts. That is, it stops at a concept that is determinable only, such that it include nothing determining it, and at a concept that is determining only, which does not include any determinable concept. The concept that is determinable only is the concept of being, and the concept that is determining only is the concept of ultimate difference. Therefore, these will be diverse primarily, such that one never includes the other.

134. The second claim, namely about the properties of being [n.131], I prove in two ways. First as follows: a property per se in the second mode A predication is per se in the second mode when the subject falls into the definition of the predicate, as ‘man is capable of laughter’, since laughter is expulsion of sound on the apprehension of the ridiculous, and only a man, a rational animal, has both a mind to apprehend the ridiculous (which is a sort of incongruity apprehended in things) and a physical mouth to expel sound on that apprehension. Angels, by contrast, can apprehend the ridiculous but do not have mouths to produce sound; their laughter is virtual. Brute animals have mouths to produce sound but no apprehension of the ridiculous (at least qua ridiculous). A predication is per se in the first mode, by contrast, when the predicate falls into the definition of the subject, as precisely in ‘man is a rational animal’. ¹⁹ is predicated of the subject (Posterior Analytics 1.4.73a37-b5); therefore, the subject is put in the definition of the predicate as something added (from ibid. and Metaphysics 7.5.1031a2-14). Being therefore falls into the idea of its property as something added. For being does have its own properties, as is plain from the Philosopher in Metaphysics 4.2.1004b10-17, where he maintains that, just as a line qua line has properties, and number qua number, so there are certain properties of being qua being. But being falls into the idea of them as something added; therefore it is not in their quidditative idea as per se in the first mode. This is also confirmed by the Philosopher in Posterior Analytics 1.4.73a34-b5, ‘On the status of principles’, where he maintains that per se predications are not convertible; because if a predicate is said per se of a subject, the converse is not said per se but per accidens. Therefore if this predication ‘being is one’ is per se in the second mode, the predication ‘one is being’ is not per se in the first mode but per accidens as it were, as this proposition ‘what is capable of laughter is man’.

135. Second as follows: being seems to be sufficiently divided (as regard division into the things that include it quidditatively) into uncreated being and into the ten categories and the essential parts of the ten categories. At least it does not seem to have more things quidditatively dividing it, however it may be with these divisions. Therefore if ‘one’ and ‘true’ include being quidditatively, being will be contained under some one of them. But being is not one of the ten categories, as is plain; nor is it of itself uncreated being, because it belongs to created beings. So it would be a species in some genus, or an essential principle of some genus. But this is false, because every essential part in any genus, and all the species of any genus, include some limitation, and so any transcendental would be of itself finite, and consequently would be repugnant to infinite being, and could not be said of infinite being formally - which is false, because all transcendentals state perfections simply and belong to God supremely.

136. Thirdly it can be argued (and herein is confirmed the first argument [n.132] for this conclusion [n.131]), that if ‘one’ includes being quidditatively, it does not include precisely being, because then that being would be its own property. Therefore it includes being and something else. Let that something else be a; either then a includes being or it does not. If it does, ‘one’ would include being twice, and there would be an infinite regress. Or, wherever a stop will be made, let that last thing, which belongs to the idea of ‘one’ and does not include being, be called a: the ‘one’, by reason of the included ‘being’, is not a property [of being], because the same thing is not a property of itself, and consequently that other included thing, which is a, is primarily the property, and is such that it does not include being quidditatively. And so, whatever is primarily a property of being does, thereby, not include being quidditatively. The term ‘one’ states a property of being (it states being as undivided). So if ‘being’ belonged to the quiddity of ‘one’, and if therefore the predication ‘one is being’ were per se in the first mode with ‘being’ falling into the definition of ‘one’, then the ‘being’ which falls into the definition of ‘one’ would be the definition of a property of being, and being would be a property of itself. So if, to avoid this, ‘one’ is said to include being and something else in its definition, as in ‘one is undivided being’, then the something else, namely ‘undivided’, either includes being in its definition or it does not. If it does, then ‘undivided’ is defined as ‘undivided being’ and wherever ‘undivided’ appears one can replace it with the definition ‘undivided being’. Consequently, to say ‘one is undivided being’ is to say ‘one is undivided being being’, and then to say ‘one is undivided being being being’, and so on ad infinitum. So if, alternatively, one makes a stop at ‘undivided’ and does not define ‘undivided’ as ‘undivided being’, and if therefore in the definition of one as ‘undivided being’ the ‘being’ is excluded from the definition of ‘undivided’ but is still included in the definition of ‘one’, then this ‘one’ is, after all, not the relevant property of being but rather the ‘undivided’ is, and this ‘undivided’ cannot now, ex hypothesi, include ‘being’ in its definition. ²⁰