Dun Scotus On The Question Of Whether A Material Substance Of Its Very Nature Is Singular: An Inquiry Into The Principle Of Individuation

John Duns Scotus (ca. 1266-1308) and William Ockham (ca. 1285-1347) are the central figures in the medieval discussion on the nature of universals and virtually define the realist/nominalist controversy of the 14th century. In dealing with the ontological status of universals, one is necessarily drawn into a discussion of the nature of individuation wherein particulars are accounted for. This necessity is due to the particular nature's seeming participation of some degree in the universal itself. One' s convictions regarding the nature of the relation between the particular and the universal will determine one's view of the ontological status of universals ¹. Inextricably linked to the question of the relation of particulars to universals is the question of how rational beings arrive at the notion of such universals. For again, if it can be determined that such common concepts as "human nature" have as their basis some corresponding reality within the individual, the claim for the existence of universals is greatly supported.

Scotus' position, which has come to be known as Moderate-Realism , advocates a three-tiered existence of natures such as "human nature". The ontologically prior mode of existence is that wherein human nature is of itself neither universal or particular, but indifferent to each. A second mode is that whereby the nature is itself made particular through existence in reality through contraction via an individual difference. And the third mode is existence in the intellect whereby the concept is universally predicable of numerically multiple particulars. This triad allows Scotus to maintain that (i) "human nature", for example, does exist in the particular human whereby real commonality is accounted for, (ii) that our concept of universals corresponds to actual instances of nature, both undetermined and determined with respect to singularity, and (iii) that universals have a real ontological status ² independent of the intellect's concept or the particular's nature..

Ockham's position differs from Scotus' most centrally on the former's refusal to concede the ontologically prior existence of "human nature". More precisely, Ockham's own ontology does not allow for the existence of instances of nature outside that of the particular nature, which he views as incapable of possessing any real commonality with the potential of being shared or transferred to other particulars. This restriction of natures greatly impacts the way in which the other two modes of existence, namely, concept and particular nature, may be understood. Regarding cognition of universals, it must now be admitted that, rather than allowing for the concept's correspondence to an ontologically prior "human nature", the mind derives its concept from the particular. Therefore, the inquiry turns to the manner in which the intellect derives or arrives at the notion of universals from its encounter with the particular. Is it that the mind perceives a reality within the particular which it understands to be universal or common "nature"? Ockham will answer no, since the particular by definition is particular and is of itself not common, nor will the unity of the particular nature allows for a distinction ³ through which a commonality might be sought. Instead, he will claim that the intellect, through the nature of its own operation, assigns concepts or names to particulars. Therefore, any concept pertaining to universals is simply the result of the natural activity of the mind, and the content of that concept need not be sought in existing natures. For this reason, Ockham's position has come to be referred to as Nominalism or Conceptualism.

Scotus sets out his theory of individuation in Book Two, distinction three of his Oxford Lectures ⁴ . His treatment involves the presentation of six questions, each of which addresses its own alternative theory of individuation. The attempt is made to refute the first five, following which Scotus presents his own theory, the sixth, as alone plausible. This paper will examine Scotus' refutation of the first question, in which he argues against the position that "natures of themselves are singular". It will be in the context of this discussion that Scotus must defend the three-tiered ontology of natures outlined above.

The Question

"The first question then is whether a material substance by its very nature is a 'this,' that is, singular and individual." ⁵ As stated above, Scotus recognized that the nature's real existence in the particular differed from the same's existence in the mind or as ontologically prior. This existence in the particular is characterized by the nature's contraction through an individual difference into what no longer can be considered completely universal. The undetermined nature and the individual difference "contract" and create in the particular a numerical unity in which no real distinction between the initial two is possible. Scotus will, however, posit a formal distinction, which is made only in the intellect, yet corresponds to the ontologically prior status of human nature. The individual nature itself remains unintelligible, due to the intellect's inability to conceptualize such a radical individuator. The formal distinction, though intellect-dependent, corresponds to actual metaphysical constituents of the individual nature.

This intellect-dependent quality of human nature in the individual is by no means unique to Scotus. In fact, the theory which Scotus will here attempt to refute takes as its foundation the converse of this same observation, namely, that it is only within particular substances that we see any instance of human nature. Whereas the existence of human nature is not cognized outside the individual, we may rightly attribute nature to the particular, such that once the individual is accounted for, we have accounted for the nature. Scotus explains, "Some say to this question that there is no intervening cause between the nature of a thing and its singularity. One should not look for any further reason between the nature and its singularity, but those causes of a thing which gives existence to its nature also account for its singularity (and these are the concurrent causes of a thing: agent, matter and form, and final cause)." ⁶ These Aristotelian causalities mentioned here are sufficient in explaining the particular nature due to the fact that natures are found only in individual substances, and therefore once the individual substance is accounted for, so also will be the nature.

Ockham agrees with this explanation of causality, since it is commonly understood that whatever pertains to an individual substance is either form, matter or a composite of these two. He points to the conclusion that, given the fact that the particular is a unity within which no real distinctions are found, any formal distinction such as Scotus posits, must have as its underlying reality, if it is not to simply derive from the intellect, something of either form, matter, or a composite of these two. He writes, "Therefore we must say with the Philosopher that in a particular substance nothing whatsoever is substantial except the particular form and the particular matter or a compound of matter and form. Hence, we must not imagine that in Socrates we have human nature or humanity distinct in any way from Socrates, to which is added an individual difference that 'contracts' this nature.... Every essence and quiddity and everything substantial, if it really exists outside the mind, is either simply and absolutely matter or form, or a compound of them, or is a separate immaterial substance, according to the teachings of the Peripatetics." ⁷

It is clear, however, to all except the extreme-realists , that nature is not to be found in the individual as a part of the individual's substance and possessing matter, form, or a composite thereof. For in that case, Socrates would be no more an individual as he would be human nature, since the whole (Socrates) in which real distinctions exist cannot be truly designated by any one distinct part. It is also clear that human nature as a universal is intellect-dependent, while the nature of the individual is neither universal of itself ⁸ nor intellect-dependent. For this reason it is argued that the ascription of "universal" or "common" to human nature is only in a qualified sense. And, "since 'to be universal,' therefore, is only 'to be' in a qualified sense, it will pertain to a thing because of the intellect, whereas 'to be singular' is 'to be' in an unqualified sense; hence it will pertain to a thing of itself, of its very nature." ⁹

The claim here, then, is that the particular is all that is given, and the particular is clearly a matter-form composite to which certain things pertain in an unqualified sense and others in a qualified sense. When we speak, therefore, of what pertains to the individual substance per se , we must restrict our discussion to only those things which pertain in an unqualified sense. The individual, then, is seen both to possess existence as a particular and its own nature, such that existence as a particular necessarily entails one's nature, and the real instance of nature necessarily entails existence as a particular. It would seem then, that the notion of a "universal" nature is not to be sought within the particular as a constituent of being. Instead, such a notion should be relegated solely to the intellect, a relegation which disallows both real distinction and formal distinction between singularity and universal nature within the particular. "That which is the cause of the nature of the thing in question is also that by which it is individuated; and in this sense the nature of itself is singular." ¹⁰

Scotus does not, however, view the individual as anything other than a per se unity which is both one and indivisible. This one per se unity, though, may possess more than one formal principle whereby the unity exists. Scotus finds two such formal principles at play in every particular, namely, those of the undetermined or specific nature and the individuator whereby the nature is contracted into its particular existence. These two formalities, when discerned by reason, account for the formal or virtual distinctions contained within "one thing which is virtually or pre-eminently as it were two realities." ¹¹ Thus the argument raised by Ockham pertaining to the matter/form composite of substantial entities is conceded by Scotus with the understanding that the positive individuating principle is a formal perfection whereby the nature, undetermined as to singularity or universality in its ontologically prior existence, is determined and thereby perfected into a particular existence. Given this ontology, Scotus necessarily expects to find within the instance of particular nature a formal principle whereby the undetermined becomes determined. The second element of Ockham's argument, namely, that intellect-dependent notions of particulars ought not be attributed to them per se , will be taken up directly by Scotus in his refutation of the question under consideration.

Scotus will present a three-fold argument against the view that the nature in and of itself accounts for singularity. First, an epistemology will be laid out whereby any act of intellection must be understood to be caused by an object of the intellect. This causal relation between object and act must be established by Scotus if he is going to insist that intellect-dependent notions such as his formal distinction deserve to be attributed to the nature of the particular. Secondly, Scotus will introduce his distinctions of greater and lesser unities, through which he attempts to demonstrate the necessity of positing some lesser unity within the particular through an argument pertaining to opposites. Lastly, he will explain his three-tiered understanding of natures based on Avicenna's infamous claim that "equinity is just equinity".

Causal Relation of the Object and Act of the Intellect

Scotus begins his critique of the theory that natures of themselves are particular, by underscoring the causal relation between objects of the intellect and acts of the intellect. He writes, "The object of the intellect is prior by nature to the act by which it is understood, for the object is the cause of the act... or if it is not the cause of the act, all admit that it precedes the knowledge of itself." ¹² Here Scotus insists that any concept held by the intellect is triggered by an actual object perceived by the mind. In particular, what is here being claimed is that the distinction which the mind makes between the particular and its nature must have behind it some underlying reality. This distinction is in fact a distinction of two concepts within the intellect, implying the need for two underlying distinct objects, namely, the formal principles of nature and the individuator. Scotus writes, "In such notions as these, does the intellect, I ask, have as the object something in it? If not, we have a mere fiction of the mind. If it is the same thing, the object of both concepts is identical unless you admit that one and the same extra-mental thing formally generates two objects in the intellect. And in this case it does not seem that the thing or anything of the thing is the object of my knowledge, but rather something produced by the thing. But if the intellect knows something different in each concept, then our thesis is granted, since a difference is there prior to the concept." ¹³

Here the point is made that if the causal relation between object and concept is denied, the reliability of reason is jeopardized. For if no object is required for a concept to be formed, says Scotus, then such concepts are fictitious and correspond to nothing real. This also holds true for the case in which the mind has one object yet forms two distinct concepts. The second concept would then be necessarily fictitious and void of information pertaining to the real world. Or perhaps that single object is somehow causing the intellect to perceive two distinct concepts although no distinction truly exists in the object. If such is the case, it must be concluded that the intellect is merely being manipulated by an unusual causal power within the object . And this does not seem to be the case. The alternative to these views is that distinct concepts will necessarily have distinct underlying objects. Formal distinctions, therefore, although they derive from particulars containing no real distinction, nevertheless must be said to correspond to distinct formal realities (and in this case principles) within the particular , if indeed such formal distinctions are conceptualized.

Ockham agrees that, "In creatures no extra-mental distinction of any kind is possible except where distinct things exist" ¹⁴ , but claims that this ultimately entails a real distinction between "really distinct things", even when a formal distinction is sought. He presents the following syllogistic proof: "This nature is not formally distinct from itself; this individual difference is formally distinct from this nature; therefore this individual difference is not this nature." ¹⁵ The point here made is that formal distinctions amount to real distinctions when scrutinized, and as shown above, positing the nature and individuator as really distinct entities within the particular is a position easily shown to be false. Here, then, Ockham tries to flush out Scotus' formal distinction theory by pushing Scotus' own sensitivities toward the necessary per se unity of the particular.

The first premise of Ockham's argument insists that, if indeed the particular nature is a per se unity, whole and not composite of real distinctions, the nature cannot be said to be distinct, formally or otherwise, from itself. Scotus himself would likely concede this point, but would be careful to define nature as a per se unity constituted by two formal principles. By this qualification he is able to maintain that the intellect conceives the particular nature as unity, as Ockham seems to here intend it, whereby, for example, Socrateity is understood as a real substance. But Scotus will also allow for the intellect to conceive both distinct formalities whereby that unity is constituted. To the formal principle of nature is then ascribed universality (Socrate's human nature), and to the other singularity ¹⁶ (Socrateity and not Petrinity). This results in Scotus offering three concepts stemming from the per se unity. But such will necessarily be the case given the formal construct of the particular unity. Scotus will not disallow the intellect a concept pertaining to the unity itself, for if the mind does not primarily conceive the unity, the case for formal distinctions would be self-evident. In addition to this concept, the intellect, within or below the per se unity of the particular, conceives two formal distinctions pertaining to two formal principles. This triad, then, takes place on two levels, with the concept arising from the reality of the unity forming the apex, as it were, under which fall the dual formal principles of which the apex is actually constituted.

The apex, or particular nature, then, as Ockham points out in the first premise of his syllogism, is not formally distinct from itself . The second premise is that the individual difference is formally distinct from this nature. Here also, Scotus may concede with the provision that by nature here is meant the formal principle of nature and not the per se unity. As mentioned above, Ockham's first premise views nature as specifically and exclusively the particular substance, since for him there are no constituents other than nature and existence (and matter and form). Given that this particular nature is understood as per se unity by both Scotus and Ockham, both clearly understand that if anything is said to be of the particular substance yet in addition to the particular nature, a real distinction is evidenced. This is precisely the result Ockham is intending to conclude with, with the aim of demonstrating that Scotus' formal distinctions are in fact real distinctions within the particular nature.

But as in the first premise, the second premise can be conceded without a resulting real distinction being evidenced if certain necessary qualifications are made, namely, "the [formal principle of] individual difference is formally distinct from [the formal principle of] this nature". This qualification removes the tension between the per se unity and any addition element (such as the individuator). For in Scotus' perspective, no such tension exists, as the per se unity is just that, and comprises the entire particular nature. Nor would the individual difference be understood to be formally distinct from the particular nature, for the latter's existence derives from the former. Rather, the formal distinction is to be made between the two formal principles constituting the existence of the particular nature. In Scotus' understanding, a formal distinction between the individualtor and undetermined nature in no way jeopardizes the per se unity. For is it precisely the interaction of these two whereby the per se unity is actualized. And what accounts for the unity cannot at the same time cause a disunity or real distinction. Therefore, whereas Ockham's syllogism concludes that a formal distinction is untenable and that a real distinction has been demonstrated, Scotus' formal distinction seems to have remained intact.

Where then, is Scotus' first point of refutation left standing? It will be recalled that in order to secure an isomorphic relation between concept and reality, a necessary causal relation between object of the intellect and act of the intellect was claimed. And expansion of this claim includes the implication that distinct concepts arising from one object must also, then, stem from two distinct realities or formalities within that object. In that object in which no real distinctions are made, such as the nature of the individual, the presence of two concepts, namely that of the particular and of universal human nature, points to the presence of formalities within the single object. Ockham's initial syllogism failed in that it pitted one formal constituent against the object itself, while denying the existence of the second formal constituent, namely, the undetermined human nature. Although this syllogism in no way encompasses Ockham's argument against the possibility of formal distinctions ¹⁷, it is that argument which claims to demonstrate the implausibility of Scotus' position using precisely the argument Scotus offers in refutation of the position held by Ockham ¹⁸ .

Scotus then applies this in order to demonstrate the need for positing, first, a concept of singularity in the mind, and then, a reality or formality corresponding to that singularity. First, the intellect either has a concept of singularity or it doesn't. If the latter, it must be held that the intellect knows particulars only through universals. But whereas particulars do not really exist as universals but particular substances, one's knowledge, derived solely from universals, cannot be said to correspond to things as they really are in existence, a conclusion which is unacceptable. Scotus here implies, then, that concepts pertaining to singularity are indeed grasped by the mind, whereby particulars are known. This conclusion is also acceptable to Ockham, since for him, the nature is itself the singular, and the intellect's sole source of information pertaining to particular substances and universals ¹⁹ is derived from the intellect's encounter with the particular.

The difference lies, of course, in the fact that Scotus, in addition to the concept pertaining to singularity, will insist, contrary to Ockham, that the mind likewise has a concept pertaining to the common nature, which must be attributed to a real object or formality. Ockham grants that the mind has a concept of the human nature but will insist that it is derived from the natural activity of the intellect as it encounters the particular nature. As is perhaps abundantly clear, Ockham does not concede the real existence of universals.

Scotus, then, has begun his refutation by establishing an epistemological foundation whereby he may infer formal realities from concepts. This is indeed a necessary prerequisite to any further discussion, for Scotus' entire theory of individuation rests squarely on the shoulders of formal distinctions. Underlying the formal distinction is Scotus' ontology of three-tiered existence of things ( res ) whereby, real things may exists in reality as particular, in the mind as universal, or as undetermined. Ockham does not share this ontology, and limits existence of real things to that of particular substances existing in reality. Thus, for Ockham, there is no need nor foundation for formal distinctions, nor for an individuator, for there is no undetermined nature in need of contraction. Scotus' project of isolating a positive formal principle which serves as the individuator finds its significance in this context in that, if such an individuator is found, its presence would necessarily imply the existence of such an undetermined nature of which it is the individuator. Conversely, if such an formal principle of individuation is found to not exist or to be irrelevant through a more plausible explanation of particular natures, Scotus' entire ontology is brought into question. Having, then, established a correspondence between object and concept whereby cognition of the formality is possible and reliable, Scotus moves on to the second argument in which he attempts to demonstrate the plausibility, if not necessity, of positing a unity which is lesser than numerical unity.

Greater and Lesser Unities

"I also argue in a second way. Anything whose proper unity is less than numerical unity, is not numerical unity." ²⁰ This simple statement begins the second argument presented by Scotus against the theory in question. Here, he will attempt to demonstrate that there exists within the particular different levels of unity. These unities, if shown to be other than identical point to differing digress of unity, the highest of which is understood to be numerical unity. Scotus will then introduce a second line of argument in which he will show that the particular possesses opposite characteristics, a fact which necessitates greater and lesser unities. His goal is to demonstrate the existence of a lesser unity within the particular and then identify that lesser unity with a real human nature within the particular. His most controversial claim in this argument is that this human nature within the particular still maintains some potentiality with respect to being shared or being transferred to other members of the species. This, of course, will catch the attention of Ockham, as we will observe.

This argument seems to assume an implication of the first, namely, the intellect has concepts which correspond to real objects. Scotus is here building a case based on observations or concepts pertaining to differing unities within the particular. Numerical unity is at once self-evident to the intellect, for once the thing in question is ascertained as existence, the most general notion possible, numerical unity is immediately implied, since all substances existing in reality are particulars. Numerical unity here refers to that unity whereby the particular nature of one substance is radically diverse from other substances of the same and another species, and is incapable of numerical multiplication. An illustration may be found in the idea of perfectly identical twin, such that they are identical in every detail pertaining to nature and body. Yet no matter how identical they are, the two will never be one numerically. This is because the numerical unity of each substantial being existing in reality is incapable of being shared or transferred. Therefore, numerical unity is by far the greatest unity as it remains such regardless of any possible circumstance.

Scotus also understands the intellect as possessing the concept derived from the formal principle of undetermined human nature, from which we understand a common human nature. This concept of itself then exists as a universal which is predicable of other members of the species. The underlying reality of this concept, when applied to the particular, is the formal principle of the undetermined nature, which, after contraction through an individual difference, becomes a constituent part of the particular. This formal reality, then, according to Scotus, is the common nature within the particular. This common nature contains a unity of its own, but a unity which is "less than" numerical unity. For whereas the latter necessarily implies a mode of existence and in incapable of being contradicted, the lesser or specific unity does not necessarily imply particular existence and is capable of being numerically multiplied through contraction of various individuators. Numerical unity pertains to our understanding of individuals as particulars, and specific unity pertains to our understanding of the nature possessed by that individual.

Scotus' claim that, "Anything whose proper unity is less that numerical unity, is not a numerical unity," simply implies that the specific unity of which the intellect is aware of is other than the numerical unity whereby individuals are distinguished, and this fact points to two unities rather than a two-fold implication of numerical unity. The significance of this argument is this. Those holding the view that nature in and of itself is singular must ascribe to that singularity all that pertains to the nature of the particular. For adherents to this view, the only instance of nature is found in the particular substance existing in reality. Therefore, anything which is to be said of particulars per se must be located exclusively in that unity whereby the particular is found to exist in reality, a unity which we have rightly identified as numerical unity.

This, however, creates an interesting backlash, for to say that numerical unity is the only unity possessed by the particular is to ascribe no other unity than what is possessed by all particular objects. For whereas numerical unity is necessarily present in every particular substance existing in reality, everything which exists has numerical unity. But it is certainly seems the case that the intellect immediately apprehends some particulars as belonging to a unity other than numerical unity, whereby we are able to say that this particular is of the same general nature as that particular. Along these same lines the intellect makes distinction between the general natures of particulars such that certain particulars are deemed of a different sort that others. To Scotus, this observation is quite clear, and therefore is able to offer such an argument established on numerical unity and unity less than numerical unity. However, he will not speak of these lesser unities as unities whereby two or more particulars are found to be similar. It is this unity, of course, whereby Scotus believes we make classifications and comparisons. But his immediate project is to demonstrate the presence of these two unities with the particular nature.

Scotus next claims that "the same thing is not consistent with the opposite of itself" ²¹ , whereby he means to demonstrate the necessity of there being two unities in order to accommodate for the presence of opposites within the particular substance. These opposites are numerical unity and numerical multiplication, both of which are found in respective unities within the particular. As stated above, numerical unity is necessitated by existence in reality and is incapable of numerical multiplication. The specific nature within the particular, however, was said to be capable of numerical multiplication. If only one unity exists within the particular, namely numerical unity, it would not be compatible with that quality of the specific nature whereby the nature is determinable regarding other particulars. For numerical unity is not compatible with numerical multiplication. In the case that a unity less that numerical unity is not conceded, Scotus supplements this argument with a seven-fold argument ²² whereby he attempts to demonstrate that such a unity exists. Scotus concludes that a unity less than numerical unity must exist in order to accommodate these opposites within the particular. Since lesser unities may possess qualities of which the greater unity of itself is incompatible, the capacity for numerical multiplication does not interfere with the particular's numerical unity.

Ockham, however, sees a serious flaw in this argument, so serious, in fact, that Adams considers it "fatal to Scotus' theory". ²³ Specifically, he sees inconsistency between Scotus' claim here that even in reality the specific nature retains its capacity for numerical multiplication, and another statement mentioned in the discussion of the first argument, namely, that the nature and individual difference are not really distinct but are distinct only formally. These two claims seem to clash, given Scotus' early statement ²⁴ that, "If one pair of opposites pertains to something of itself, the other pair of opposites is incompatible with the thing itself." It was upon this very premise that Scotus has proceeded with his entire attempt at demonstrating the necessity for a greater and lesser unity wherein the opposites of numerical unity and multiplication could be accommodated within the particular.

Ockham believes that if this be the case, Scotus ought also to concede the following modification: "Whenever one pair of opposites really pertains to something in such a way that the thing is truly and really denominated from it, whether they pertain to it of itself or through something else (this fact remaining unchanged), the other of the opposites does not really pertain to it, but will be absolutely denied of it." ²⁵ This, however, makes a common nature, capable of numerical multiplication, an impossibility within the particular and its numerical unity. For although Scotus is willing to claim a formal distinction between the undetermined nature and the individual difference, he must nevertheless maintain that both these formalities pertain to the particular nature per se . Therefore, given Ockham's modification, the opposites of numerical unity and multiplication, both attributed to per se constituents of the particular nature, cannot both exist within the same particular. And whereas Scotus has rightly identified numerical unity as the greater, that opposite pertaining to the lesser unity is that which will be denied by the particular nature. And that lesser opposite is the universal human nature. Ockham writes,

"His claim that a multiplicity opposed to the greater unity can, without contradiction, stand together with the lesser unity seems incompatible with his other claim that the nature and the individual difference do not really differ. For when any two are really the same, whatever can, by divine power, really be one of them can be the other. But this individual difference cannot be numerically many really distinct things. Therefore, neither can the nature, which is really the same as the contracting difference, be many really distinct things. Nor, consequently, can it be any thing other than the contracting difference. Thus, the nature is not without contradiction compared to numerical multiplicity." ²⁶

The Undetermined Nature

Scotus concludes his refutation of the theory that natures of themselves are singular, with a brief defense of the existence of the undetermined nature. As stated above, Scotus maintains a three-tiered ontological status for the existence of natures, which he understands to exist as particulars in reality, as universals in the intellect, and as undetermined. This last mode of existence, the undetermined, is that which is contracted by the individual difference whereby a particular nature exists, and that which, when grasped by the intellect, is capable of being predicated of numerically many, that is to say, is universal. It is clear, then, that the undetermined nature is the storehouse from which all natures, as Scotus sees them, flow.

Scotus begins by affirming the statement of Avicenna that "Equinity is just equinity; of itself it is neither one nor many, universal nor singular" ²⁹. Here Avicenna describes equinity as of itself neither a particular nor universal. As has been made clear from the discussion above, equinity as particular would necessitate its existence in the real world. Therefore, for Avicenna to claim that it is not particular, would necessarily prohibit it from being understood as an extra-mental object or reality. By universal we may simply understand "concept" of the intellect, regardless of how one wishes to account for that concept. Thus, by denying equinity universal quality, Avicenna also prohibits equinity as such from being defined as a concept of the intellect. Nor, says he, is equinity to be understood numerically, whether one, as pertains to particulars, or many, as pertains to universals. Equinity of itself, then, is neither simply the particular in reality nor simply the universal in the intellect. Equinity of itself somehow exists independently to these qualifications.

Scotus applies Avicenna's statement to his theory of natures, wherein the undetermined nature is understood to exist in an ontologically prior state, and thereby serves as the direct source of both the nature in reality and in the intellect. Regarding this he writes, "The mind understands the nature of stone for what it is in itself and not as universal or particular or singular; so in its extra-mental existence stone is primarily neither one nor many numerically, yet it has its own proper unity which is less than the unity pertaining to a singular." ³⁰ Here Scotus understands the undetermined nature to be that reality which unifies the specific nature of particulars of the same species, as well as the intellect's concepts of such. It is precisely upon this understanding that Scotus attributes universal characteristics to the nature within the particular as we have seen in his argument from geater and lesser unities. The change in status from undetermined to particular nature is accounted for through the individual difference's contraction of the former into the latter. And the change from undetermined nature to universal concept is accounted for through the mind's activity which takes hold of the concept and then embellishes it with further knowledge gained of the particulars through experience. In this way, Scotus, as did Aquinas, finds in Avicenna's statement a powerful explanatory system upon which great portions of the ontological and epistemological frameworks of all three of these thinkers rests.

Ockham, however, doubts this entire scenario, and raises questions as to how "equinity" is to be understood in Avicenna's statement. If equinity stands for the concept, Avicenna's statement is clearly false, since it would not then be indifferent with respect to being particular. Or if by equinity is meant particular horses, the statement is again found to be false, for then it would not be indifferent with respect to being universal. Ockham does not seem able to imagine what alternative status we can reasonably give equinity wherein it is neither one nor many, neither particular nor concept nor being of reason. He writes, "It seems that besides the supposition for the concept and for the particular thing, it would be necessary to assume a third in which term supposits for the quiddity that is absolutely indifferent to each." ³¹ And indeed, such a supposit is hard to fathom, for what seems to be described here is merely a state of potentiality whereby actualities are formed, whether in the mind or in the extra-mental world. But Scotus does not refer to this undetermined nature as in potentiality to a determined existence, but rather seems to allude that it is indeed a mode of existence in and of itself, such that equinity proper is that undetermined nature. Scotus could perhaps avoid the brunt of Ockham's effective argument regarding per se contradictories, if it is conceded that the undetermined nature stands in potentiality to the nature determined with respect to individuality. This would allow Scotus an avenue for developing a causal relation whereby the particular nature "participates" in a common nature, but would not allow him to claim the particular nature itself possesses a specific nature capable of numerical multiplication. It was precisely this latter insistence which Ockham's argument exposed as implausible, given his modification of the initial premise. The notion of potentiality might also have ramifications pertaining to the individuator, for rather than merely contracting the undetermined into a determined particular, one must speak of actualization of the undetermined into the determined, and this through the individuator. The primary role of the individuator then would be that of "actualizer", rather than "contractor". This however, seems plausible, for when asked, "what is the actuality?", one may answer, "a particular nature numerically one". And when asked, "what is this an actuality of?", one may answer, "human nature," which of itself maintains the ontologically prior status Scotus is wont to ascribe to it. The particular nature could then be considered "common" in the sense that each particular nature is an actualization of the common undetermined potential nature by means of an individuator whereby singularity is accounted for. Ockham, however, would necessarily continue to debate even the potentiality approach, as it continues to presuppose an ontologically reality independent of particulars and concepts. This potentiality approach would also entail the liklelihood that a formal distinction would remain btween the individuator and nature within the particular. But as long as Scotus maintains his three-tiered ontology, such a formal distinction need not be avoided.

Thus Scotus concludes his refutation of the first rival theory pertaining to the theory of individuation. For the most part, this has been a battle of radically differing ontologies, from which very different presuppositions are derived. These diverse presupposition have appeared throughout the arguments presented above, and find very little common ground. And although an examination of this argument brings into clear focus the role of one's ontological presupposition, challenging the validity of such, it remains highly probable that neither Scotus nor Ockham would forsake their respective ontologies based on the outcome of this argument. But we are clearly the wiser in the exercise.