# Aquinas on One and Many

By Gyula Klima

## INTRODUCTION: THE SYSTEMATIC AMBIGUITY OF THE NOTIONS OF ONE AND BEING

As is well-known, St. Thomas regarded the notion of one as a transcendental notion, convertible with the notion of being, and thus, as surpassing the boundaries of individual categories. On the other hand, the notion of one is also obviously a numerical notion, and so it should belong to the category of quantity, in particular, to the species of discrete quantity. This apparent conflict can easily be resolved by St. Thomas’s distinction between the notion of the one that is the principle of number and the notion of the one that is convertible with being, provided that the distinction itself is clear enough. However, despite the fact that the notion of one in the context of performing simple arithmetical operations, such as adding one, subtracting one, multiplying or dividing by one, is clear, familiar, and absolutely unambiguous and precise, in a metaphysical context it becomes disturbingly vague, or, in any case, as Aquinas’s need to make this distinction shows, far from unambiguous.

Therefore, in an attempt to clarify this puzzling aspect of this notion, I will first show that upon Aquinas’s conception such vagueness and ambiguity of our notion of one is inevitable, arising of necessity from the analogical character of this notion.

To show the essentially analogical character of this notion, I will begin the discussion in the next section with Aquinas’s distinction, starting with the more familiar and more precise member of this distinction, namely, the one as the principle of number. However, despite the fact that the one as the principle of number may be more familiar in our arithmetical practice, it will soon turn out that the more basic, more primary notion is still that of the one that is convertible with being. But given the analogical character of Aquinas’ notion of being, it is no wonder that the latter member of St. Thomas’s distinction will also turn out to be analogical in itself. Indeed, the subsequent semantic discussion of the analogical predication of both the notion of being and that of the one will show the interdependence of the analogical character of both notions: anything that speaks for the analogical character of being eo ipso speaks for the analogy of unity and vice versa.

These considerations will inevitably lead us to the further discussions of the relationships between the notions of being and one, and those of substantiality, identity and simplicity. As these discussions will show, the systematic ambiguities of these latter notions are necessarily entailed by the primarily analogical character of the notions of being and one.

On the basis of these considerations it will be a natural conclusion that the systematic ambiguity of these notions, rather than being their defect, is precisely what allows us to capture the idea of a metaphysical hierarchy of beings of various degrees of perfection. But then the further inevitable conclusion will be that with respect to this hierarchy of beings we have to make a distinction between beings that are more familiar to us (notiora quoad nos) and those that are not such. To those that are more familiar to us we can apply these notions without qualification, with the presumption of the primacy of our ordinary common-sense conceptual framework. However, once we recognize this hierarchy of beings, we shall also have to recognize that considering this hierarchy in itself, regardless of which beings in this hierarchy are more familiar to us, it is only the absolutely simple One on the top of this hierarchy to which these notions can apply in an absolutely unqualified manner. Or rather we should say that they could apply in this way, were it not for the realization that that absolute simplicity cannot really be captured by any one of these notions.

## THE ONE THAT IS THE PRINCIPLE OF NUMBER, AND THE ONE THAT IS CONVERTIBLE WITH BEING

The most elementary application of our notion of a unit occurs in the simple process of counting. For example, when we have the task of counting the number of people in a room, we take the persons one by one, raising the number of persons we have already counted by one at each step, until we reach the last person. In this process, if we “do not lose count”, that is, if we make sure that we never take the same person twice and we do not leave out any one of them, we have to arrive at a definite and precise result. Apparently, nothing can be more exact and unambiguous than this.

But then suppose we need to count the words on this page. Here the word ‘one’ occurs twice in the subtitle. Should we take these occurrences as one word or two words? Clearly, in this case the result of counting will depend on what we take to be the criteria of identity for words, namely, whether we are supposed to be counting type-words, in which case two occurrences of a similar string of letters should be counted as one word, or token-words, in which case such distinct occurrences should be counted as two words[1]. But once the criteria of identity are fixed, again, we have to arrive at a precise, definite result.

However, what if we need to deal with “fuzzier” entities? What if we have to count, say, the number of the clouds in the sky? Obviously, in this case first we need to know just where one cloud ends and the other begins, and then we have to make sure that during the process of counting no two clouds will merge into one, no one cloud will split into two or more clouds, and that no cloud will vanish, nor a new one will come into existence.

As can be seen from this simple example, even if counting in itself is a simple and entirely unambiguous operation, it has some rather complex and far from unambiguous presuppositions. For even if whenever we count something as one, its addition increases the number of the items counted up to that point exactly and unambiguously by one, it is far from being a simple and unambiguous issue just what we can count as one. So, clearly, in this way the precise and unambiguous arithmetical notion of the unit (that serves as the measure of the number of things when we count them one by one), which Aquinas appropriately describes as the principle of number, presupposes the far from unambiguous notion of some being which is undivided in itself and is divided from others, which is the notion of the one that St. Thomas describes as that which is convertible with being. As he says:

«We should realize that there are two sorts of one [duplex est unum]. Namely, there is the one which is convertible with being, which adds nothing to being except being undivided; and this deprives multitude, insofar as multitude is caused by division, however, it does not deprive extrinsic multitude, which the one constitutes as its part, but the intrinsic multitude that is opposed to unity. For just because something is said to be one, it is not denied that there is something outside of it with which it constitutes a multitude, but what is denied is its own division into a multitude. The other sort of one is that which is the principle of number, which to the notion of being adds measurement; and the multitude of this sort of one is a privation, for a number comes to be by the division of the continuum. Nevertheless, multitude does not entirely deprive unity, for after the division of the whole, the part still remains undivided, but it does remove the unity of the whole[2]

The reason why the presupposed, transcendental notion of the one is, indeed, has to be ambiguous, despite the precision of the consequent arithmetical notion, should be clear if we consider the inherent ambiguity of the notion of division. For suppose we have managed sufficiently to separate and distinguish the individual clouds that serve as the units for our counting. But are those alleged units really one? For what is a cloud? A visible aggregate of tiny droplets of water suspended in midair. So one cloud, which we treated as one in the process of counting clouds, upon closer inspection turns out to be just so many droplets of water. Clearly, these many droplets each are distinct, spatially separated individuals, undivided in themselves and divided from each other. So if the clouds appeared to have some sort of unity merely on account of the relative closeness of their parts, namely of the droplets constituting them, we have to say that the droplets themselves have a greater unity, on account of their continuity.

But then, one of course may go further and ask about the unity of those droplets themselves, which after all are just rather densely packed collections of water molecules. And then, in the same way, one may further ask about the molecules, and then the atoms, which, despite their name, are not indivisible, and then the particles of atoms, until we reach the limits of our knowledge, but perhaps still not the limits of divisibility. But, in fact, those further details are already irrelevant from our point of view. Not only because St. Thomas did not and could not have any idea about these lower levels of the organization of matter, but also because no matter what further details modern physicists may come up with, the metaphysical principles constituted by our most universal notions concerning the unity of a whole and the multiplicity of its parts are the same, regardless of such details[3].

But even from this point of view, one may find the idea of these changing perspectives rather disturbing. For the breaking up of what appeared to be units on a certain level into multitudes on a lower level, and, conversely, the recognition of units on a higher level constituted by a multitude of entities on a lower level is clearly dependent on our perspective, on the “degree of resolution” we apply in distinguishing one thing from another, and taking this thing as one, and not as a multitude of several things. But how can it depend on our perspective what counts as one entity or many entities? For even if there may be some sort of ambiguity in how we divide up things into various units depending on our perspective, isn’t reality supposed to be something definite, determinate, regardless of how we look at it?

## ANALOGY AND PREDICATION SECUNDUM QUID

It is at this point that St. Thomas’s insight concerning the convertibility of one and being turns out to be of particular importance. As he writes:

«nothing prevents some things from being many in some respect [secundum quid] and being one in another. Indeed, all sorts of things that are many are one in some respect, as Dionysius says in the last chapter of On Divine Names. But we have to be aware of the difference that some things are many absolutely [simpliciter], and one in some respect, while the case is the reverse with others. Now something is said to be one in the same way as it is said to be a being. But a being absolutely speaking is a substance, while a being in some respect is an accident, or even [only] a being of reason. So whatever is one in substance, is one absolutely speaking, yet many in some respect. For example, a whole in the genus of substance, composed of its several integral or essential parts, is one absolutely speaking, for the whole is a being and a substance absolutely speaking, while the parts are beings and substances in the whole. Those things, however, which are diverse in substance, and one by accident, are diverse absolutely speaking, and one in some respect, as many humans are one people, or many stones are one heap; and this is the unity of composition or order. Likewise, many individuals that are one in genus or species are many absolutely speaking, and one with respect to something, for to be one in genus or species is to be one with respect to reason[4]

So the status of the unity of a thing is dependent on the ontological status of the thing itself. That thing is said to be one absolutely speaking which is a being absolutely speaking. Therefore, even if we may find some unity on a “higher level” of organization, such as the unity of a heap of stones or an army of people, or some multitude on a “lower level”, such as the multitude of the parts of individual stones or of individual humans, if individual stones and individual humans are beings in the absolute sense, then they also are units in the absolute sense, whereas their collections are units only in some respect, and their parts constitute a multitude only in some other respect, with some qualification.

Now, in general, whenever we have to distinguish the predication of some common term simpliciter and secundum quid, that is, without and with some qualification, then this is a sure sign that the term is being predicated analogically of its inferiors. St. Thomas makes this quite clear in the following passage:

«... there are two ways in which something common can be divided into those that are under it, just as there are two ways in which something is common. For there is the division of a univocal [term] into its species by differences by which the nature of the genus is equally participated in the species, as animal is divided into man and horse, and the like. Another division is that of something common by analogy, which is predicated according to its perfect concept [ratio] of one of those that divide it, and of the other[s] imperfectly and with qualification [secundum quid], as being is divided into substance and accident, and into being in actuality and in potentiality ...[5]»

This general feature of analogical predication (regardless of the details of how an analogical concept is formed, and consequently what sorts of analogy may or need be distinguished[6]) betrays a common feature of analogical concept-formation. This common feature is that our analogical notions presuppose a primary, univocal concept arrived at by ordinary abstraction; it is this primary concept which is then further modified somehow in the process of some analogical concept-formation, yielding those further, qualified senses of the term subordinated to this concept which allow the term to be extended and analogically applied to things to which in its primary sense it could not apply without qualification.

If, therefore, the primary, unqualified concept of being is the one that applies to material substances of ordinary human experience, then, in view of the convertibility of the transcendental notion of being with the transcendental notion of one, it is substances of this kind that can be said to be one in the primary, unqualified sense. In general, then, on this account, the primary units in reality, that is, the things that can be said to be one without qualification, should be precisely these substances. Therefore, whenever it takes some further cognitive operation to discover either some further unity that they constitute, or some multitude of other units that constitute them, the units thus discovered can be said to be one only with qualification, just as St. Thomas said[7].

Indeed, the unity such primary substances constitute is either the unity of their collections or the unity of their genera and species. The cognitive operation required to realize the unity of their collections is counting them together, or some other way of viewing them together collectively, based on their order, connections or common function, while the mental operation required to realize the unity of their species and genera is abstraction[8]. On the other hand, the cognitive operation required to recognize the multitude of the parts that constitute primary substances is the discernment of their parts. In this way, since on this conception the account of unity is based on the primary ontological status of primary substances, it will clearly not depend on us what the primary units of reality are, despite the fact that the ways of carving out our units from reality obviously depend on our cognitive faculties.

However, at this point one may object that despite appearances to the contrary, this account in fact ties the issue of what the primary units of reality are even more closely to our cognitive faculties. For the only reason why Aristotelian primary substances are singled out as the primary beings, and thus as the primary units, seems to be that these are the things that are most familiar to us, insofar as they are the primary objects of our cognitive faculties. But, then, if the objects of ordinary human experience are the beings in the primary sense only and precisely because they are the primary objects of our cognitive faculties, then it is apparently the nature of our cognitive faculties that determines what should be regarded as primary beings. However, this may have nothing to do with how things really are in themselves, apart from our cognitive faculties. Indeed, as we get increasingly familiar with objects that are not objects of our ordinary experience through the advance of natural science, we may have more and more evidence to suggest that objects of our ordinary experience may not be the primary units of reality, but rather they are more like the clouds relative to the droplets that constitute them.

## BEING, SUBSTANCE, IDENTITY, UNITY AND SIMPLICITY

Now is it really the case that it is Aristotelian primary substances that are beings in the primary, unqualified sense? And if so, does it really depend on our cognitive faculties what should count as a primary substance?

In a way the issue whether primary substances are the primary beings and thus the primary units is trivial. Primary substances are the primary beings and vice versa, because this is how the two concepts are related, and that is that. A being in the primary sense is one that has an act of being [esse] without qualification. This means that it has its act of being in such a manner that its act of being is not the act of being of something else with qualification. For instance, by this criterion the wisdom of Socrates is not a primary being, for its act of being is the act of being of something else with qualification, namely the act of Socrates’s being wise, that is, Socrates’s being with respect to his wisdom[9]. On the other hand, by the same criterion, Socrates himself has to count as a primary being, since his act of being is not the act of being of something else with qualification, which is shown by the fact that Socrates’s coming to be and ceasing to be simpliciter is not the coming to be and ceasing to be of something else secundum quid. However, the act of being which is the act of being of something else with qualification is what is usually described as the act of something’s being in something else, esse in alio, that is, as accidental being. By contrast, the kind of being that something has absolutely speaking and which is not the act of being with qualification of something else is what is usually described as esse per se, that is, as substantial being. But this is precisely the way in which primary substances are described, namely, as beings whose nature demands this kind of act of being[10]. So whatever is a primary being is a primary substance and vice versa.

The non-trivial issue, however, is just which entities should count as primary beings and hence as primary substances in this sense. Now since primary substances are primary beings, which have their own act of being without qualification, they will also be beings which, if they are generable and corruptible, will have generation and corruption without qualification. Again, this means that their coming to be and ceasing to be is not the coming to be and ceasing to be of something else with qualification. By contrast, the coming to be and ceasing to be of their accidents is their coming to be or ceasing to be with qualification, that is, their change. But then, since their coming to be and ceasing to be with qualification is not their coming to be or ceasing to be simpliciter, these are the entities that are permanent through change. However, permanence through change is nothing but identity across time, or indeed, with respect to merely possible changes, it is identity across possible situations, or as modern philosophers would have it, across “possible worlds”. But since identity is nothing but unity in substance according to Aristotle[11], a changeable primary substance is something that preserves its unity through actual or merely possible changes.

However, with this last remark we seem to have come full circle. For I started the discussion  with trying to clarify the notion of primary unit with reference to the notion of primary being. This then turned out to be equivalent to the notion of primary substance, which however turns out to be describable in terms of identity, and hence of unity, through change. So, apparently, to explain primary unity we have to resort to the notion of primary substance, while in explaining primary substance we have to appeal to the same notion of unity.

But there is nothing vicious in this apparent circularity. For there is a vicious circle of definitions only if a defining term cannot be understood without the term it defines, whereas the latter cannot be understood without the defining term in question. However, this is certainly not the case here. In fact, there is no circularity here at all. The primary distinction is still that between an act of being without and with qualification, which grounds the distinction between substance and accident. The rest, namely, permanence, identity and hence unity through change, is merely a consequence of this primary distinction, indeed, not even concerning all beings or even all substances, but only concerning generable and corruptible substances. These consequences, however, provide further, occasionally better-known indications which may help us to tell substances from non-substances in particular cases. For instance, in some cases it may be evident that certain kinds of things have generation and corruption without qualification, as in the case of living things, while in other cases it may be more obvious what constitutes the unity of a given thing, as in the case of continuous non-living substances.

But of course other cases may still leave us with a number of hard-to-decide questions. For example, consider the question whether the turning of a piece of graphite into a diamond crystal is a substantial or an accidental change. In this case, the answer obviously depends on whether being graphite or diamond are accidental modifications of the same underlying substance, namely, carbon, which never loses its existence and unity during such a metamorphosis, or graphite and diamond should be regarded as substances in their own right, consisting of differently configured carbon atoms, which however, do not preserve their distinct existence and unity in the wholes they constitute. The former solution would tie the identity of a piece of carbon, whether it is in the form of diamond or graphite, to the unity of the collection of carbon atoms that make it up, treating their differences in configuration on a par with a simple accidental rearrangement of individual units in space, analogous to the rearrangement of a flight of aircraft taking up a new formation in the sky. On the other hand, the latter solution would regard a piece of carbon in the form of a diamond crystal as a unified whole in which there are no distinct carbon atoms as such, but which could be generated by unifying previously distinct carbon atoms in the tetrahedral crystalline structure characteristic of diamonds.

Now I certainly do not want to decide this particular question here, which is not so interesting after all. To be sure, modern quantum chemistry speaks rather for the latter position, as opposed to the rather primitive mechanistic picture underlying the former. But then the further details concerning the distinct vs. indistinct character of the carbon atoms making up the whole should rely on further specific considerations belonging to quantum chemistry. What is important from our point of view is that the clarification of the conceptual relations between being, unity, identity and substance gives us important clues as to what are the relevant considerations in discussing particular cases. Whenever it is clear that a certain kind of thing has generation and corruption simpliciter, then that should be the decisive factor. On the other hand, as could be seen in the particular case of the allotropes of carbon, when the question of substantiality needs to be determined on the basis of considerations concerning unity, then the relevant issue will have to be the relative distinction and unity of the parts making up the whole. The less distinct are the parts, the more unified is the whole; but the more unified is the whole, the more it has to be regarded as having its own substantial being, and the less its parts can be regarded as having their own unity and substantial being[12].

So, if we recognize this type of unity in the realm of objects of ordinary human experience, then we have to recognize those objects as primary substances without further ado. Still, even though on this basis we can recognize such objects as primary substances and hence as the primary beings and primary units in an unqualified sense as they present themselves in our experience, this still need not mean that these substances are the absolutely ultimate units and entities in an even further, more basic sense.

For given that the distinctness and multiplicity of the constitutive parts is what is opposed to the simplicity and unity of the whole, which we have just acknowledged to go hand in hand with substantiality and unqualified being, if we recognize that even within the realm of primary substances there are various degrees of the multiplicity of parts and thus of the opposite simplicity of the whole, then we should also acknowledge that even within the realm of primary substances there have to be several degrees in the applicability of the notion of unity. As St. Thomas writes:

«In response we have to say that God is maximally and most truly one. For just as something is related to being undivided, so it is related to unity; since, according to the Philosopher, a being is said to be one insofar as it is not divided. And so those things which are undivided per se are more truly one than those things that are undivided per accidens, as Socrates and a white thing, which are one per accidens. But among the things that are one per se, those which are undivided absolutely speaking are more truly one than those which are undivided in respect of a genus, or species, or some analogy [proportio]. Hence they are not even said to be one absolutely speaking, but one in genus, or in species, or by analogy; but what is absolutely undivided is said to be absolutely one, and that is numerically one. But even among such things there are degrees. For there is something which is such that even though it is actually undivided, still it is potentially divisible, either by a division of quantity, or by an essential division, or by both: by the division of quantity, as something which is one by continuity; by an essential division, as those things which are composed of matter and form, or from the act of being and that which is; or by both divisions as the natural bodies. And that some of these are not actually divided derives in them from something outside of the nature of composition or division, as is obvious in the case of the body of the heavens and the like, which are such that although they are not actually divisible, they are nevertheless divisible by the intellect. But there are things which are indivisible both actually and potentially, and such are of various kinds. For some involve something else in their concept besides the concept of indivisibility, as a point, which besides being undivided involves also position. But there is something which involves nothing else, but is its own indivisibility, as is the unity which is the principle of number; yet this inheres in something which is not this unity itself, namely, in its subject. Whence it is clear that that in which there is no composition of parts, no continuity of dimension, no variety of accidents, and which inheres in nothing, is maximally and most truly one, as Boethius concludes. And hence follows that His unity is the principle of all unity and the measure of all things; for that which is the maximal is the principle in every genus, just as that which is maximally hot is the [principle] of all hot things, as is said in bk. 2 of the Metaphysics, and that which is the simplest is the measure in any genus, as is said in bk. 10 of the Metaphysics[13].»

However, if there are degrees in unity even within the domain of primary substances, that is, primary beings, then there also have to be degrees of being within the same domain. But how can this come about? How can we interpret degrees of being within this domain, once we have agreed that all primary substances are primary beings, that is, things that are said to be beings without any qualification?

## ABSOLUTE BEING AND ABSOLUTE UNITY

To respond to this question we have to consider how we can say both that any primary substance is one and being in the primary, unqualified sense and that only God can be said to be one and being in an absolutely unqualified sense.

The primary, unqualified sense of being is that on account of which any primary substance can be said to be a being without qualification insofar as it is. But for a primary substance to be is for it to have its essence in actuality, that is, for a primary substance to be, absolutely speaking, is at the same time for it to be with respect to its essence. So even the primary, unqualified predication of being implies a certain implicit qualification, namely, the determination of a thing’s substantial being to its own essence[14]. But isn’t this equally true in the case of God? Couldn’t we say that even for God to be is for Him to be with respect to the divine essence, and so also in this case there is a certain implicit qualification, namely, the determination of divine being by divine essence?

To answer this question, we should consider it in the general context of Aquinas’s analysis of the difference between predication secundum quid and simpliciter, distinguishing between diminishing and non-diminishing determinations[15]. To use the common medieval example, if I say: ‘This shield is white with respect to its one half’, this obviously does not entail that the shield is white, absolutely speaking, for its other half may be black. So in this case the qualification is diminishing [determinatio diminuens], in the sense that it “diminishes”, that is, takes away from, the conditions of the absolute, unqualified applicability of the predicate, and this is why the predicate so qualified can apply to something which is not absolutely white, but only in its half. So precisely because the qualification is intensionally diminishing, it is extensionally enlarging. By contrast, if I say: ‘This shield is white with respect to its whole surface’, then the qualification added to the predicate is not diminishing, for this qualification states that the shield is white all over, which is precisely what the absolute, unqualified predicate would say, namely, that the shield is white, so this qualification does not take away anything from the conditions of the strict applicability of the unqualified predicate and hence it applies only to what is white all over, without qualification.

But, further, if I say: ‘This shield is white with respect to its whiteness’, then, again, the qualification added to the predicate does not take away anything from the conditions of its strict, unqualified applicability, whence it applies only to something that is absolutely white, without any limitation. The reason for this clearly is that when the qualification refers to what is signified by the predicate, then the qualification is not diminishing; on the contrary, since the predicate can apply to the subject only in respect of what it signifies anyway, the predicate so qualified can apply only to that to which it applies also in itself, absolutely, without any qualification[16]. So a diminishing qualification has to refer to something which is distinct from what is signified by the predicate, but when there is no such a distinction, then the qualification is not diminishing. But this is precisely the case in the predication: ‘God exists with respect to His divinity’, for God’s existence being the same as His essence, the qualification refers to what the predicate signifies, namely, divine existence, which is divinity, the divine essence. On the other hand, in everything else, i.e., in every created thing, the nature of the thing is not the same as the existence of the thing, and this is why the created nature imposes a certain diminishing, limiting qualification and determination upon the existence of the thing. As St. Thomas says:

«For a created spiritual substance has to contain two [principles], the one of which is related to the other as potency to act. And this is clear from the following. It is obvious that the first being, which is God, is infinite act, namely, having in Himself the whole plenitude of being not contracted to the nature of some genus or species. Therefore it is necessary that His being itself should not be an act of being that is, as it were, put into a nature which is not its own being, for in this way it would be confined to that nature. Hence we say that God is His own being. But this cannot be said about anything else; just as it is impossible to think that there should be several separate whitenesses, but if a whiteness were separate from any subject and recipient, then it would be only one, so it is impossible that there should be a subsistent act of being, except only one. Therefore, everything else after the first being, since it is not its own being, has being received in something, by which its being is contracted; and thus in any created being the nature of the thing that participates being is other than the act of being itself that is participated[17]

So although all created substances are beings in the primary, unqualified sense, this unqualified sense of being is still not, indeed, cannot be, the absolutely unlimited sense of being according to which only God can be said to exist. The reason for this is that everything is said to exist with respect to its essence, for the substantial existence of every thing is precisely the actuality of its essence. But it is only God whose essence is His own existence, so everything else’s essence, being distinct from its existence imposes some diminishing qualification, some limitation upon the sense of being in which only God can be said to exist. So the substantial being of created substances, on account of which the predicate ‘is’ or ‘exists’ applies to them without qualification, for it is the act of being by which they exist simpliciter, is at the same time an act of being which can be signified by the predicate ‘is’ or ‘exists’ only in a sense which can be derived by some diminishing qualification of the sense of the same predicate in which it applies only to God. Therefore, what accounts for the difference between the senses of ‘exists’ in which a creature and God can be said to exist is precisely God’s absolutely undivided unity, that is, God’s absolute simplicity, as opposed to the necessary intrinsic multiplicity of the constitutive parts of any creature. Indeed, it is precisely this intrinsic multiplicity that distinguishes creatures from God as well as from one another, thereby causing the extrinsic multiplicity of the number of creatures, for created substances differ from one another in their essence insofar as their essences are different determinations of their acts of being. Furthermore, when their essence itself is composite, because it comprises both matter and form, the determination it imposes upon the substantial act of being of material substances also allows the numerical multiplicity of individuals within the same species, divided from one another by their designated matter, that is, their matter informed by their dimensions[18].

Now it is individuals of this kind that are the most familiar to us, and so it is the unity and being of these individuals that provides for us the primary, unqualified notions of being and unity. So first it is relative to these individuals that we have to recognize that their integral parts (whether quantitative parts, other accidental parts or even essential parts), their collections, and their species and genera also exhibit some sort of unity and being which is analogous to the unity and being of these primary substances[19].

But once we recognize the analogical character of the applicability of these notions in the realm of created substances, their parts, species, genera and collections, and we also recognize how the created order of these primary beings is determined by their metaphysical unity, on account of which they approach more or less the absolute unity of divine simplicity, we also have to admit that even the being of these is subject to certain qualification and limitation in comparison to the being of He who IS, without any limitation.

And this is why, when he discusses whether ‘He who is’ [qui est] is the most appropriate name of God, St. Thomas says the following:

«… all other names say something determinate and particularized, as ‘[to be] wise’ says [to be] something[20]. But the name ‘He who is’ says being absolutely, not determined by something added [to it] and this is why Damascene says that it does not signify what God is, but it signifies a certain infinite ocean of substance, as it were, something not determinate. Therefore, when we move toward God in the way of removal, first we deny of Him corporeal [attributes], and secondly even intellectual ones, in the way they are found in creatures, such as goodness and wisdom; and then it remains in our understanding only that He is, and nothing more, whence He is there in a sort of confusion. And finally we remove even this being itself, according to the way it is in the creatures; and then He remains there in a sort of shadow of ignorance, and by this ignorance, as it pertains to our present state, we are most appropriately tied to God, as Dionysius asserts, and this is a sort of haze, in which God is said to dwell[21]

So if we try to capture this absolute being in its simplicity, the notion of absolute being we arrive at leaves us with a certain confusion, because of a lack of determinate understanding. On the other hand, as soon as we try to reach a more determinate understanding of divine nature, it is precisely the determinate character of our concepts, and their resulting multiplicity, which will be incompatible with the absolutely unlimited nature and simplicity of divine being. Indeed, even when a determinate concept represents some absolute perfection which in its absolute, unlimited form is nothing but the plenitude of divine being, but which we can find in the creatures only in a limited and determinate manner, the very determinacy of the concept matches the determinacy, and so also the limited character of the perfection in question as it is found in the creatures. For even though the perfection represented by the concept in itself is absolute insofar as by its own nature it does not demand any determination, the way in which it is represented by the concept, as being a perfection which is distinct from other creaturely perfections, involves a multiplicity that is not compatible with the absolute divine simplicity.

But this is precisely the reason why St. Thomas has to claim that although those names which signify such absolute perfections apply primarily to God quantum ad rem significatam, still, quantum ad modum significandi they apply primarily to creatures. As he says:

«We should consider, therefore, that because [the] names [we apply to God] are imposed by us, and we do not know God except from the creatures, [these names] are always defective in their representation with respect to their mode of signifying[quantum ad modum significandi], for they signify divine perfections in the way in which they are participated by the creatures. But if we consider the thing signified [res significata] by the name, which is that which the name is imposed to signify, we find that some names are imposed to signify primarily the perfection itself exemplified by God absolutely, not implying some [determinate] mode in their signification, while others [are imposed] to signify a perfection in accordance with such a mode of participation. For example, every cognition is [primarily] exemplified by divine cognition, and every knowledge by divine knowledge. The name ‘sense’, however, is imposed to signify cognition in the manner in which it is received materially by a power of an organ. But the name ‘cognition’ does not signify a mode of participation in its principal signification. Therefore, we have to say that all those names which are imposed to signify some perfection absolutely are properly said of God, and they apply to Him primarily as far as the thing signified is concerned, although not as far as the mode of signifying is concerned, such as ‘wisdom’, ‘goodness’, ‘essence’ and the like[22]

So, divine simplicity necessarily defies any adequate characterization by us. The only name that could most appropriately express this absolute simplicity by its indeterminacy, the name qui est, leaves us in confusion precisely because of its indeterminacy. On the other hand, any other name that gives us a more determinate concept is inappropriate in its mode of signifying to express divine simplicity precisely because of the determinacy of the concept in question.

Therefore, since the names signifying some absolute perfection apply primarily and absolutely to God only with respect to what they signify, but none of them can properly apply to Him with respect to their mode of signifying, these names can also absolutely be denied of Him:

«… since a name has both a mode of signifying and the thing signified itself, it can always be denied of God either on account of one of these or on account of both; but it cannot be said of God except on account of only of one them. And since the truth and appropriateness of an affirmation requires that all be affirmed, whereas for the appropriateness of a negation it is sufficient if only one of them is lacking, this is why Dionysius says that negations are absolutely true, but affirmations only in some respect [secundum quid]: for only with respect to what is signified, but not with respect to the mode of signifying[23]

Therefore, on the basis of these considerations we have to recognize the following paradox: these names could be predicated only of God in an absolutely unqualified sense (for the perfection they signify can be found only in God in an absolutely unqualified manner), and not of the creatures (for they apply to creatures in an unqualified sense only because it is from them that we abstracted the primary concepts of the perfections these names signify); still, because of the inherent multiplicity in their mode of signifying, reflecting their origin from the multiplicity of creaturely perfections, we can more appropriately deny them than affirm them of God. But it is precisely the recognition of this paradox that helps us gain some insight into the incomprehensible divine unity reflected in created multiplicity[24].

Notes

[1] Actually, even distinct occurrences of type-words should probably be counted as one only if the two occurrences express the same meaning. For example, in the sentence: ‘She hit the bat with a baseball bat’ we should not count the two occurrences of ‘bat’ as the same type-word. Indeed, the two occurrences of this word belong to distinctly numbered dictionary entries. So perhaps also the two occurrences of ‘one’ in the subtitle should be counted as two type-words in accordance with their two intended meanings. But then it would be a further issue to decide how analogical terms, whose meanings according to Cajetan are partly (secundum quid) the same and partly diverse, should be counted. Thomas de Vio Cardinalis Cajetanus: De Nominum Analogia, Rome: Angelicum, 1934, c. 2, n. 8, p. 12.

[2] «Sciendum autem, quod duplex est unum; quoddam scilicet quod convertitur cum ente, quod nihil addit supra ens nisi indivisionem; et hoc unum privat multitudinem, in quantum multitudo ex divisione causatur; non quidem multitudinem extrinsecam quam unum constituit sicut pars; sed multitudinem intrinsecam quae unitati opponitur. Non enim ex hoc quod aliquid dicitur esse unum, negatur quin aliquid sit extra ipsum quod cum eo constituat multitudinem; sed negatur divisio ipsius in multa. Aliud vero unum est quod est principium numeri, quod supra rationem entis addit mensurationem; et huius unius multitudo est privatio, quia numerus fit per divisionem continui. Nec tamen multitudo privat unitatem totaliter, cum diviso toto adhuc remaneat pars indivisa; sed removet unitatem totius QDP q. 3, a. 16, ad 3-um

[3] For detailed discussions of the medieval notions and principles concerning parts and wholes, see Henry, D. P. 1991, Medieval Mereology, Bochumer Studien zur Philosophie, Band 16, B. R. Gruener, Amsterdam-Philadelphia; for a discussion of Aquinas’s views in particular see especially pp. 218-328.

[4] «Respondeo dicendum quod nihil prohibet aliqua esse secundum quid multa, et secundum quid unum. Quinimmo omnia multa sunt secundum aliquid unum, ut dionysius dicit, ult. Cap. De div. Nom.. Est tamen differentia attendenda in hoc, quod quaedam sunt simpliciter multa, et secundum quid unum, quaedam vero e converso. Unum autem hoc modo dicitur sicut et ens. Ens autem simpliciter est substantia, sed ens secundum quid est accidens, vel etiam ens rationis. Et ideo quaecumque sunt unum secundum substantiam, sunt unum simpliciter, et multa secundum quid. Sicut totum in genere substantiae, compositum ex suis partibus vel integralibus vel essentialibus, est unum simpliciter, nam totum est ens et substantia simpliciter, partes vero sunt entia et substantiae in toto. Quae vero sunt diversa secundum substantiam, et unum secundum accidens, sunt diversa simpliciter, et unum secundum quid, sicut multi homines sunt unus populus, et multi lapides sunt unus acervus; quae est unitas compositionis, aut ordinis. Similiter etiam multa individua, quae sunt unum genere vel specie, sunt simpliciter multa, et secundum quid unum, nam esse unum genere vel specie, est esse unum secundum rationem.» ST1-2 q. 17, a. 4.

[5] «Respondeo dicendum, quod est duplex modus dividendi commune in ea quae sub ipso sunt, sicut est duplex communitatis modus. Est enim quaedam divisio univoci in species per differentias quibus aequaliter natura generis in speciebus participatur, sicut animal dividitur in hominem et equum, et hujusmodi; alia vero divisio est ejus quod est commune per analogiam, quod quidem secundum perfectam rationem praedicatur de uno dividentium, et de altero imperfecte et secundum quid, sicut ens dividitur in substantiam et accidens, et in ens actu et in ens potentia: et haec divisio est quasi media inter aequivocum et univocum.» 2SN d. 42, q. 1, a. 3, in corp. Cf.: «Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem.» in Peri lb. 2, lc. 2, n. 3.

[6] Since here we need not consider in detail exactly how an analogical concept is formed, we need not consider what are the different modes of analogy, which is in the focus of the debates concerning Aquinas’s theory of analogy. See McInerny, R.: The Logic of Analogy, Martinus Nijhoff: The Hague, 1961, and McInerny, R.: Aquinas and Analogy, Washington, D.C.: Catholic University of America Press, 1996. Cf. also: Ashworth, E. J.: Analogical Concepts: The Fourteenth-Century Background to Cajetan, «Dialogue», 31, 1992, p. 399.; Ashworth, E. J.: Analogy and Equivocation in Thirteenth-Century Logic: Aquinas in Context, «Mediaeval Studies», 54,1992, p. 94.

[7] Cf.: «Ad secundum dicendum quod nihil prohibet id quod est uno modo divisum, esse alio modo indivisum; sicut quod est divisum numero, est indivisum secundum speciem, et sic contingit aliquid esse uno modo unum, alio modo multa. Sed tamen si sit indivisum simpliciter; vel quia est indivisum secundum id quod pertinet ad essentiam rei, licet sit divisum quantum ad ea quae sunt extra essentiam rei, sicut quod est unum subiecto et multa secundum accidentia; vel quia est indivisum in actu, et divisum in potentia, sicut quod est unum toto et multa secundum partes, huiusmodi erit unum simpliciter, et multa secundum quid. Si vero aliquid e converso sit indivisum secundum quid, et divisum simpliciter; utpote quia est divisum secundum essentiam, et indivisum secundum rationem, vel secundum principium sive causam, erit multa simpliciter, et unum secundum quid; ut quae sunt multa numero et unum specie, vel unum principio. Sic igitur ens dividitur per unum et multa, quasi per unum simpliciter, et multa secundum quid. Nam et ipsa multitudo non contineretur sub ente, nisi contineretur aliquo modo sub uno. Dicit enim dionysius, ult. Cap. De div. Nom., Quod non est multitudo non participans uno, sed quae sunt multa partibus, sunt unum toto; et quae sunt multa accidentibus, sunt unum subiecto; et quae sunt multa numero, sunt unum specie; et quae sunt speciebus multa, sunt unum genere; et quae sunt multa processibus, sunt unum principio.» ST1 q. 11, a. 1, ad 2-um

[8] Note that in modern logic and set theory it is the former operation of forming collective wholes by lumping individuals together that is rather improperly called abstraction, whereas the original Aristotelian notion of abstraction of forming universal wholes by disregarding the individuating conditions of singulars is discussed rather in historically oriented philosophical studies. In fact, the whole issue would deserve separate treatment, but here I cannot go into further details.

[9] Cf.: Klima, G. The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being, «Medieval Philosophy and Theology», 5, 1996, pp. 87-141. The gist of the criterion can be summarized in the following formula: esse simpliciter entis secundum quid est esse secundum quid entis simpliciter.

[10] «Ad secundum dicendum, quod secundum Avicennam in sua Metaph., esse non potest poni in definitione alicuius generis et speciei, quia omnia particularia uniuntur in definitione generis vel speciei, cum tamen genus vel species non sit secundum unum esse in omnibus. Et ideo haec non est vera definitio substantiae: substantia est quod per se est; vel: accidens est quod est in alio. Sed est circumlocutio verae descriptionis, quae talis intelligitur: substantia est res cuius naturae debetur esse non in alio; accidens vero est res, cuius naturae debetur esse in alio. Unde patet quod, quamvis accidens miraculose sit non in subiecto, non tamen pertinet ad definitionem substantiae; non enim per hoc eius naturae debetur esse non in alio; nec egreditur definitionem accidentis, quia adhuc natura eius remanet talis ut ei debeatur esse in alio.” QDL 9, q. 3, ad 2-um. Cf. “Ad secundum dicendum, quod sicut probat Avicenna in sua Metaph., per se existere non est definitio substantiae: quia per hoc non demonstratur quidditas ejus, sed ejus esse; et sua quidditas non est suum esse; alias non posset esse genus: quia esse non potest esse commune per modum generis, cum singula contenta in genere differant secundum esse; sed definitio, vel quasi definitio, substantiae est res habens quidditatem, cui acquiritur esse, vel debetur, ut non in alio; et similiter esse in subjecto non est definitio accidentis, sed e contrario res cui debetur esse in alio; et hoc nunquam separatur ab aliquo accidente, nec separari potest: quia illi rei quae est accidens, secundum rationem suae quidditatis semper debetur esse in alio. Sed potest esse quod illud quod debetur alicui secundum rationem suae quidditatis, ei virtute divina agente non conveniat; et sic patet quod facere accidens esse sine substantia, non est separare definitionem a definito; et si aliquando hoc dicatur definitio accidentis, praedicto modo intelligenda est definitio dicta: quia aliquando ab auctoribus definitiones ponuntur causa brevitatis non secundum debitum ordinem, sed tanguntur illa ex quibus potest accipi definitio.» 4SN, d. 12, q. 1, a. 1a, ad 2-um

[11] Cf. «Philosophus dicit: unum in substantia facit idem, in quantitate aequale, in qualitate simile.» 1SN d. 8, q. 4, a. 3, 2.

[12] Cf. Aquinas's De Mixtione Elementorum, where it is precisely along these lines that Thomas distinguishes what we would describe as a chemical reaction from the simple physical mixing of imperceptibly small parts.

[13] «Respondeo dicendum, quod deus summe et verissime unus est. Secundum enim quod aliquid se habet ad indivisionem, ita se habet ad unitatem; quia, secundum philosophum, ens dicitur unum in eo quod non dividitur. Et ideo illa quae sunt indivisa per se, verius sunt unum quam illa quae sunt indivisa per accidens, sicut albus et socrates quae sunt unum per accidens; et inter illa quae sunt unum per se, verius sunt unum quae sunt indivisa simpliciter quam quae sunt indivisa respectu alicujus vel generis vel speciei vel proportionis. Unde etiam non dicuntur simpliciter unum, sed unum vel in genere vel in specie vel in proportione; et quod est simpliciter indivisum, dicitur simpliciter unum, quod est unum numero. Sed in istis etiam invenitur aliquis gradus. Aliquid enim est quod quamvis sit indivisum in actu, est tamen divisibile potentia, vel divisione quantitatis, vel divisione essentiali, vel secundum utrumque. Divisione quantitatis, sicut quod est unum continuitate; divisione essentiali, sicut in compositis ex forma et materia, vel ex esse et quod est; divisione secundum utrumque, sicut in naturalibus corporibus. Et quod aliqua horum non dividantur in actu, est ex aliquo in eis praeter naturam compositionis vel divisionis, sicut patet in corpore caeli et hujusmodi; quae quamvis non sint divisibilia actu, sunt tamen divisibilia intellectu. Aliquid vero est quod est indivisibile actu et potentia; et hoc multiplex est. Quoddam enim habet in sui ratione aliquid praeter rationem indivisibilitatis, ut punctum, quod praeter indivisionem importat situm: aliquid vero est quod nihil aliud importat, sed est ipsa sua indivisibilitas, ut unitas quae est principium numeri; et tamen inhaeret alicui quod non est ipsamet unitas, scilicet subjecto suo. Unde patet quod illud in quo nulla est compositio partium, nulla dimensionis continuitas, nulla accidentium varietas, nulli inhaerens, summe et vere unum est, ut concludit boetius. Et inde est quod sua unitas est principium omnis unitatis et mensura omnis rei. Quia illud quod est maximum, est principium in quolibet genere, sicut maxime calidum omnis calidi, ut dicitur 2 metaphysic., Et illud quod est simplicissimum, est mensura in quolibet genere, ut 10 metaphysic. dicitur1SN d. 24, q. 1, a. 1.

[14] For this point see Wippel, J. F.: Thomas Aquinas and Participation, in: Wippel, J. F. (ed.): «Studies in Medieval Philosophy», The Catholic University of America Press: Washington D.C., 1987. For the significance of using the preposition ‘to’ in this context, see R.A. Te Velde: Participation and Substantiality in Thomas Aquinas, Brill: Leiden-New York-Köln, 1995, p. 152.

[15] For a more comprehensive discussion of the logical doctrine behind Aquinas’s analysis of this difference (in connection with St. Thomas’s use of the related theoretical apparatus in his theology of the Incarnation) see Klima, G.:Libellus pro Sapiente: A Criticism of Allan Bäck’s Argument against St. Thomas Aquinas’ Theory of the Incarnation, «The New Scholasticism», 58, 1984, pp. 207-219.

[16] According to the medieval logical literature concerning the fallacy secundum quid et simpliciter, the general rule for distinguishing diminishing vs. non-diminishing qualifications is that a qualification is non-diminishing if and only if it refers to a part of the subject which is such that the predicate would apply to the whole subject without qualification only in respect of that part anyway. For references see my paper referred to in the previous note.

[17] De spir. creat. q. un., a.1: «Oportet enim in substantia spirituali creata esse duo, quorum unum comparatur ad alterum ut potentia ad actum. Quod sic patet. Manifestum est enim quod primum ens, quod Deus est, est actus infini­tus, utpote habens in se totam essendi plenitudinem non contractam ad aliquam naturam generis vel speciei. Unde oportet quod ipsum esse eius non sit esse quasi inditum alicui naturae quae non sit suum esse; quia sic finiretur ad illam naturam. Unde dicimus, quod Deus est ipsum suum esse. Hoc autem non potest dici de aliquo alio: sicut impossibile est intelligere quod sint plures albedines separatae; sed si esset albedo separata ab omni subiecto et recipiente, esset una tantum; ita impossibile est quod sit ipsum esse subsistens nisi unum tantum. Omne igitur quod est post primum ens, cum non sit suum esse, habet esse in aliquo receptum, per quod ipsum esse contrahitur; et sic in quolibet creato aliud est natura rei quae participat esse, et aliud ipsum esse participatum.»

[18] Cf. Wippel, J. F.: Thomas Aquinas on the Distinction and the Derivation of the Many from the One: a Dialectic between Being and Nonbeing, «The Review of Metaphysics 38, 1985, pp. 563-590.

[19] See again the text quoted in n. 4.

[20] Cf. In Boethii De Hebdomadibus, lc. 2. nn. 20-35.

[21] «Ad quartum dicendum, quod alia omnia nomina dicunt esse determinatum et particulatum; sicut sapiens dicit aliquid esse; sed hoc nomen qui est dicit esse absolutum et indeterminatum per aliquid additum; et ideo dicit Damascenus quod non significat quid est deus, sed significat quoddam pelagus substantiae infinitum, quasi non determinatum. Unde quando in deum procedimus per viam remotionis, primo negamus ab eo corporalia; et secundo etiam intellectualia, secundum quod inveniuntur in creaturis, ut bonitas et sapientia; et tunc remanet tantum in intellectu nostro, quia est, et nihil amplius: unde est sicut in quadam confusione. Ad ultimum autem etiam hoc ipsum esse, secundum quod est in creaturis, ab ipso removemus; et tunc remanet in quadam tenebra ignorantiae, secundum quam ignorantiam, quantum ad statum viae pertinet, optime deo conjungimur, ut dicit dionysius, et haec est quaedam caligo, in qua deus habitare dicitur.» 1SN d. 8, q.1, a. 1,  resp. 4

[22] «Considerandum est igitur, quod cum nomina sint imposita a nobis, qui deum non nisi ex creaturis cognoscimus, semper deficiunt a divina repraesentatione quantum ad modum significandi: quia significant divinas perfectiones per modum quo participantur in creaturis. Si autem consideremus rem significatam in nomine, quae est id ad quod significandum imponitur nomen, invenimus, quaedam nomina esse imposita ad significandum principaliter ipsam perfectionem exemplatam a deo simpliciter, non concernendo aliquem modum in sua significatione; et quaedam ad significandum perfectionem receptam secundum talem modum participandi; verbi gratia, omnis cognitio est exemplata a divina cognitione, et omnis scientia a divina scientia. Hoc igitur nomen sensus est impositum ad significandum cognitionem per modum illum quo recipitur materialiter secundum virtutem conjunctam organo. Sed hoc nomen cognitio non significat aliquem modum participandi in principali sua significatione. Unde dicendum est, quod omnia illa nomina quae imponuntur ad significandum perfectionem aliquam absolute, proprie dicuntur de deo, et per prius sunt in ipso quantum ad rem significatam, licet non quantum ad modum significandi, ut sapientia, bonitas, essentia et omnia hujusmodi; et haec sunt de quibus dicit Anselmus, quod simpliciter et omnino melius est esse quam non esse. Illa autem quae imponuntur ad significandum perfectionem aliquam exemplatam a deo, ita quod includant in sua significatione imperfectum modum participandi, nullo modo dicuntur de deo proprie; sed tamen ratione illius perfectionis possunt dici de deo metaphorice, sicut sentire, videre et hujusmodi. Et similiter est de omnibus aliis formis corporalibus, ut lapis, leo et hujusmodi: omnia enim imponuntur ad significandum formas corporales secundum modum determinatum participandi esse vel vivere vel aliquam divinarum perfectionum.» 1SN d. 22, q. 1, a. 2 co

[23] «Ad primum igitur dicendum, quod cum in nomine duo sint, modus significandi, et res ipsa significata, semper secundum alterum potest removeri a Deo vel secundum utrumque; sed non potest dici de Deo nisi secundum alterum tantum. Et quia ad veritatem et proprietatem affirmationis requiritur quod totum affirmetur, ad proprietatem autem negationis sufficit si alterum tantum desit, ideo dicit Dionysius, quod negationes sunt absolute verae, sed affirmationes non nisi secundum quid: quia quantum ad significatum tantum, et non quantum ad modum significandi.» 1SN d. 22, q. 1, a. 2, ad 1-um

[24] So, from this point of view, I do not find the contrast between “Neoplatonic henology”, as opposed to “Thomistic ontology” so sharp as some Thomistic scholars, most notably Gilson, would. But this would deserve a separate study. The issue receives intriguing discussion in Taylor, R. C.: Aquinas, the Plotiniana Arabica, and the Metaphysics of Being and Actuality, «Journal of the History of Ideas», (1998), pp. 217-239.