Chapter IV: Reality as One and Manifold (1)

25. THE TRANSCENDENTAL ATTRIBUTES OR PROPERTIES OF BEING: UNITY, TRUTH, AND GOODNESS.—So far, we have analysed the notions of Real Being, of Becoming or Change, of Being as Possible and as Actual, of Essence and Existence. Before approaching a study of the Categories or _Suprema Genera Entis_, the highest and widest modes in which reality manifests itself, we have next to consider certain attributes or properties of being which reveal themselves as co-extensive with reality itself. Taking human experience in its widest sense, as embracing all modes that are cognitive or allied with consciousness, as including intellect, memory, imagination, sense perception, will and appetite, as speculative, ethical or moral, and esthetic or artistic,—we find that the reality which makes up this complex human experience of ours is universally and necessarily characterized by certain features which we call the _transcendental attributes or properties of being_, inasmuch as they transcend all specific and generic modes of being, pervade all its categories equally, and are inseparable from any datum of experience. We shall see that they are not really distinct from the reality which they characterize, but only logically distinct from it, being aspects under which we apprehend it, negations or other logical relations which we necessarily annex to it by the mental processes whereby we seek to render it actually intelligible to our minds.

The first in order of these ontological attributes is _unity_: the concept of that whereby reality considered in itself becomes a definite object of thought. The second in order is _truth_: which is the conception of reality considered in its relation to cognitive experience, to intellect. The third is _goodness_: the aspect under which reality is related as an object to appetitive experience, to will.

Now when we predicate of any reality under our consideration that it is “one,” or “good,” or “true”—in the ontological sense to be explained,—that which we predicate is not a mere _ens rationis_, but something real, something which is really identical with the subject, and which is distinguished from the latter in our judgment only by a logical distinction. The attribution of any of these properties to the subject does not, however, add anything real to the latter: it adds merely some logical aspect involved in, or supposed by, the attribution. At the same time, this logical aspect gives us real information by making explicit some real feature of being not explicitly revealed in the concept of being itself, although involved in, and following as a property from, the latter.

There do not seem to be any other transcendental properties of being besides the three enumerated. The terms “reality,” “thing,” “something,” are synonymous expressions of the concept of being itself, rather than of properties of being. “Existence” is not a transcendental attribute of being, for it is not co-extensive with reality or real being. And although reality _must_ be “_either_ possible _or_ actual,” “_either_ necessary _or_ contingent,” “_either_ infinite _or_ finite,” etc., this necessity of verifying in itself one or other member of any such alternatives is not a property of being, but rather something essentially rooted in the very concept of reality itself. Some would regard as a distinct transcendental attribute of being the conception of the latter as an object of esthetic contemplation, as manifesting order and harmony, as _beautiful_. This conception of being will be found, however, to flow from the more fundamental aspects of reality considered as _true_ and as _good_, rather than directly from the concept of being itself.

26. TRANSCENDENTAL UNITY.—When we think of anything as one we think of it as undivided in itself. The unity or oneness of being is the undividedness of being: _Unum est id quod est indivisum in se: Universaliter quaecunque non habent divisionem, inquantum non habent, sic unum dicuntur_.(133) When, therefore, we conceive being as undivided into constitutive parts, and unmultiplied into repetitions of itself, we conceive it as _a_ being, as _one_. For the concept of being, formally as one, it does not seem necessary that we conceive being as _divided or distinct from all other being_. This second negation, of identity with other being, rather follows the conception of being as one: being is distinct from other being because it is already itself one: it is a prior negation that formally constitutes its unity, namely, _the negation of internal division or multiplication of itself_: God was truly _one_ from all eternity, before there was any _other_ being, any created being, distinct from Him. The division or distinction of an object of thought from whatever is not itself is what constitutes the notion of _otherness_.(134)

It is manifest that being and unity are really identical, that when we think of being we think of what is really undivided in itself, that once we introduce dividedness into the object of our concept we are no longer thinking of being but of _beings_, _i.e._ of a multitude or plurality each member of which is a _being_ and _one_. For being, as an object of thought, is either simple or composite. If simple, it is not only undivided but indivisible. If composite, we cannot think of it as _a_ being, capable of existing, so long as we think its parts as separate or divided: only when we think of them as actually united and undivided have we the concept of _a_ being: and _eo ipso_ we have the concept of being as one, as a unity.(135)

Hence the scholastic formulæ: _Ens et unum convertuntur_, and _Omne ens est unum_. The truth embodied in these is so self-evident that the expression of it may seem superfluous; but they are not mere tautologies, and in the interests of clear and consistent thinking our attention may be profitably directed to them. The same remark applies to much in the present and subsequent chapters on the transcendental attributes of being.

27. KINDS OF UNITY.—(_a_) The unity we have been describing has been called _transcendental_, to distinguish it from _predicamental_ unity—the unity which is proper to a special category of being, namely, _quantity_, and which, accordingly, is also called _quantitative_ or _mathematical_ unity. While the former is common to all being, with which it is really identical, and to which it adds nothing real, the latter belongs and is applicable, properly speaking, only to the mode of being which is corporeal, which exists only as affected by quantity, as occupying space, as capable of measurement; and therefore, also, this latter unity adds something real to the being which it affects, namely, the attribute of quantity, of which unity is the measure and the generating principle.(136) For quantity, as we shall see, is a mode of being really distinct from the corporeal substance which it affects. The quantity has its own transcendental unity; so has the substance which it quantifies; so has the composite whole, the quantified body, but this latter transcendental unity, like the composite being with which it is identical, is not a _unum per se_ but only a _unum per accidens_ (_cf._ _b_, _infra_).

We derive our notion of quantitative or mathematical unity, which is the principle of counting and the standard of measuring, from dividing mentally the continuous quantity or magnitude which is one of the immediate data of sense experience. Now the distinction between this unit and transcendental unity supposes not merely that quantity is really distinct from the corporeal substance, but also that the human mind is capable of conceiving as real certain modes of being other than the corporeal, modes to which quantitative concepts and processes, such as counting and measuring, are not _properly_ applicable, as they are to corporeal reality, but only in an _analogical_ or _transferred_ sense (2). The notion of transcendental unity, therefore, bears the same relation to that of quantitative unity, as the notion of being in general bears to that of quantified or corporeal being.

(_b_) Transcendental unity may be either _essential_ (or _substantial_, “unum _per se_,” “unum _simpliciter_”), or _accidental_ (“unum _per accidens_,” “unum _secundum quid_”). The former characterizes a being which has nothing in it beyond what is essential to it as such, _e.g._ the unity of any substance: and this unity is twofold—(1) _unity of simplicity_ and (2) _unity of composition_—according as the substance is essentially simple (such as the human soul or a pure spirit) or essentially composite (such as man, or any corporeal substance: since every such substance is composed essentially of a formative and an indeterminate principle).(137)

Accidental unity is the unity of a being whose constituent factors or contents are not really united in such a way as to form one essence, whether simple or composite. It is threefold: (1) _collective_ unity, or unity _of aggregation_, as of a _heap_ of stones or a _crowd_ of men; (2) _artificial_ unity, as of a house or a picture; and (3) _natural_ or _physical_ unity, as of any existing substance with its connatural accidents, _e.g._ a living organism with its size, shape, qualities, etc., or the human soul with its faculties.(138)

(_c_) Transcendental unity may be either individual (singular, numerical, concrete, real) or universal (specific, generic, abstract, logical). The former is that which characterizes being or reality considered as actually existing or as proximately capable of existing: the unity of an _individual_ nature or essence: the unity whereby a being is not merely undivided in itself but incapable of repetition or multiplication of itself. It is only the individual as such that can actually exist: the abstract and universal is incapable of actually existing as such. We shall examine presently what it is that _individuates_ reality, and what it is that renders it capable of existing actually in the form of “things” or of “persons”—the forms in which it actually presents itself in our experience.

Abstract or universal unity is the unity which characterizes a reality conceived as an abstract, universal object by the human intellect. The object of a specific or generic concept, “man” or “animal,” for example, is one in this sense, undivided in itself, but capable of indefinite multiplication or repetition in the only mode in which it can actually exist—the individual mode. The universal is _unum aptum inesse pluribus_.

Finally, we can conceive any nature or essence without considering it in either of its alternative states—either as individual or as universal. Thus conceived it is characterized by a unity which has been commonly designated as _abstract_, or (by Scotists) as _formal_ unity.

28. MULTITUDE AND NUMBER.—The _one_ has for its correlative the _manifold_. Units, one of which is not the other, constitute multitude or plurality. If unity is the negation of actual division in being, multitude results from a second negation, that, namely, by which the undivided being or unit is marked off or divided from other units.(139) We have defined unity by the negation of actual _intrinsic_ dividedness; and we have seen it to be compatible with _extrinsic_ dividedness, or otherness. Thus the vague notion of dividedness is anterior to that of unity. Now multitude involves dividedness; but it also involves and presupposes the intrinsic undividedness or _unity_ of each constituent of the manifold. In the real order of things the _one_ is prior to all _dividedness_; but on account of the sensuous origin of our concepts we can define the former only by exclusion of the latter. The order in which we obtain these ideas seems, therefore, to be as follows: “first _being_, then _dividedness_, next _unity_ which excludes dividedness, and finally _multitude_ which consists of units”.(140)

The relation of the _one_ to the _manifold_ is that of undivided being to divided being. The same reality cannot be one and manifold under the same aspect; though obviously a being may be actually one and potentially manifold or _vice versa_, or one under a certain aspect and manifold under another aspect.

From the transcendental plurality or multitude which we have just described we can distinguish _predicamental_ or _quantitative_ plurality: a distinction which is to be understood in the same way as when applied to unity. Quantitative multitude is the actually separated or divided condition of quantified being. _Number_ is a multitude measured or counted by unity: it is a _counted_, and, therefore, necessarily a _definite_ and _finite_ multitude. Now it is _mathematical_ unity that is, properly, the principle of number and the standard or measure of all counting; and therefore it is only to realities which fall within the category of quantity—in other words, to material being—that the concept of number is properly applicable. No doubt we can and do conceive transcendental unity after the analogy of the quantitative unity which is the principle of counting and measuring; and no doubt we can use the transcendental concept of “actually undivided being” as a principle of enumeration, and so “count” or “enumerate” spiritual beings; but this counting is only analogical; and many philosophers, following Aristotle and St. Thomas, hold that the concepts of _numerical_ multiplicity and _numerical_ distinction are not properly applicable to immaterial beings, that these latter differ individually from one another _not numerically_, but each by its whole nature or essence, that is, _formally_.(141)

29. THE INDIVIDUAL AND THE UNIVERSAL.—We have distinguished transcendental unity into individual and universal (27, _c_). Reality as endowed with universal unity is reality as apprehended by abstract thought to be capable of indefinite repetition or multiplication of itself in actual existence. Reality as endowed with individual unity is reality apprehended as actually existing, or as proximately capable of actually existing, and as therefore incapable of any repetition or multiplication of itself, of any division of itself into other “selves” or communication of itself to other “selves”. While, therefore, the universal has its reality only in the individuals to which it communicates itself, and which thus embody it, the individual has its reality in itself and of its own right, so to speak: when it actually exists it is “_sui juris_,” and as such incommunicable, “_incommunicabilis_”. The actually existing individual is called in Latin a “_suppositum_”—a term which we shall render by the English “thing” or “individual thing”. It was called by Aristotle the οὐσία πρωτή, _substantia prima_, “first substance,” or “first essence,” to distinguish it from the substance or essence conceived by abstract thought as universal; the latter being designated as οὐσία δέυτερα, _substantia secunda_, “second substance” or “second essence”.

Now it is a fundamental assumption in Aristotelian and scholastic philosophy that whatever actually exists, or whatever is real in the sense that as such it is proximately capable of actual existence, is and must be individual: that the universal as such is not real, _i.e._ as such cannot actually exist. And the manifest reason for this assumption is that whatever actually exists must be, with entire definiteness and determinateness, its own self and nothing else: it cannot be capable of division or repetition of itself, of that which it really is, into “other” realities which would still be “that individual thing”. But reality considered as universal _is_ capable of such repetition of itself indefinitely. Therefore reality cannot actually exist as universal, but only as individual.

This is merely plain common sense; nor does the idealistic monism
which appears to attribute reality to the universal as such, and
which interprets reality exclusively according to the forms in
which it presents itself to abstract thought, really run counter
to this consideration; for what it really holds is not that
universals as such are real, but that they are phases of the
all-one reality which is itself _one individual being_.

But many modern philosophers hold that individuality, no less than
universality, is a form of thought. No doubt “individuality” _in
the abstract_ is, no less than universality, an object abstracted
from the data of experience by the mind’s analysis of the latter.
But this is not what those philosophers mean. They mean that the
individual as such is not a real datum of experience. From the
Kantian view that individuality is a purely mental form with which
the mind invests the datum, they draw the subjectivist conclusion
that the world, thus interpreted as consisting of “individuals,”
is a phenomenal or mental product for the objective validity of
which there can be to man’s speculative reason no sufficient
guarantee.

To this theory we oppose that of Aristotle and the scholastics,
not merely that the individual alone is actually existent, but
that as actually existent and as individual it is actually given
to us and apprehended by us in internal and external sense
experience; and that although in the inorganic world, and to some
extent in the lower forms of life, we may not be able to determine
for certain what portions of this experience are distinct
individuals, still in the world of living things generally, and
especially of the animal kingdom, there can be no difficulty in
determining this, for the simple reason that here reality is given
to us in sense experience as consisting of distinct individuals.

At the same time it is true that we can understand these individual realities, interpret them, read the meaning of them, only by the intellectual function of judgment, _i.e._ by the analytic and synthetic activity whereby we abstract and universalize certain aspects of them, and use these aspects as predicates of the individuals. Now, seeing that intellectual thought, as distinct from sense experience, apprehends its objects only as abstract and potentially universal, only as static, self-identical, possible essences, and nevertheless predicates these of the concrete, individual, contingent, actually existing “things” of sense experience, identifying them with the latter in affirmative judgments; seeing moreover, that—since the intellectual knowledge we thus acquire about the data of sense experience is genuine and not chimerical—those “objects” of abstract thought must be likewise real, and must be really in those individual sense data (according to the theory of knowledge which finds its expression in Moderate Realism),—there arises immediately the problem, or rather the group of problems, regarding the relations between reality as revealed to intellect, _i.e._ as abstract and universal, and reality as revealed to sense, _i.e._ as concrete and individual. In other words, we have to inquire how we are to interpret intellectually the fact that reality, which as a possible essence is _universal_ for abstract thought, is nevertheless, as actually existing, _individualized_ for sense—and consequently for intellect reflecting on the data of sense.(142)

30. THE “METAPHYSICAL GRADES OF BEING” IN THE INDIVIDUAL.—What, then is the relation between all that intellect can apprehend in the individual, _viz._ its lowest class essence or specific nature, and its whole nature as an individual, its _essentia atoma_ or individual nature? We can best approach this problem by considering first these various abstract thought-objects which intellect can apprehend in the individual.

What are called the metaphysical grades of being, those positive moments of perfection or reality which the mind detects in the individual, as, for instance, substantiality, materiality, organic life, animality, rationality, individuality, in the individual man—whether we describe them as “phases” or “aspects” or “formalities” of being—are undoubtedly distinct objects for abstract thought. Why does it thus distinguish between them, and express them by distinct concepts, even when it finds them embodied in a single individual? Because, reflecting on the manner in which reality presents itself, through sense experience, as actually existing, it finds resemblances and differences between individually distinct data. It finds in some of them grades of reality which it does not find in others, individual, specific, and generic grades; and some—transcendental—grades common to all. Now between these various grades of being as found in one and the same individual it cannot be denied that there exists a logical distinction with a foundation or ground for it in the individual reality; because the latter, _being more or less similar_ to other individual realities, causes the mind to apprehend it by a number of distinct concepts: the individuality whereby it differs really from all other individuals of the same species; the specific, differential and generic grades of being whereby it is conceptually identified with wider and wider classes of things; and the transcendental grades whereby it is conceptually identified with all others. The _similarity_ of really distinct individuals, which is the _conceptual identity_ of their _qualities_, is the ground on which we conceptually identify their _essences_. Now is there any reason for thinking that these grounds of similarity, as found in the individual, are _really distinct_ from one another in the latter? They are certainly conceptually distinct expressions—each less inadequate than the wider ones—of what is really one individual essence. But we must take them to be all really identical in and with this individual essence, unless we are prepared to hold conceptual plurality as such to be real plurality; in which case we should also hold conceptual unity as such to be real unity. But this latter view is precisely the error of extreme realism, of reifying abstract concepts and holding the “_universale a parte rei_”: a theory which leads logically to monism.(143)

31. INDIVIDUALITY.—The distinction, therefore, between these grades of being in the individual, is a virtual distinction, _i.e._ a logical distinction with a ground for it in the reality. This is the sort of distinction which exists between the specific nature of the individual, _i.e._ what is contained in the definition of the lowest class to which it belongs, and its _individuality_, _i.e._ what constitutes its _nature or essence as an individual_. No doubt the concrete existing individual contains, besides its individual nature or essence, a variety of accidental characteristics which serve as marks or signs whereby its individuality _is revealed to us_. These are called “individualizing characteristics,” “_notae individuantes_,” the familiar scholastic list of them being “_forma_, _figura_, _locus_, _tempus_, _stirps_, _patria_, _nomen_,” with manifest reference to the individual “man”. But though these characteristics enable us to mark off the individual in space and time from other individuals of the same class, thus _revealing_ individuality to us in the concrete, it cannot be held that they constitute the individuality of the nature or substance in each case. If the human substance, essence, or nature, as found in Socrates, were held to differ from the human substance, essence, or nature, as found in Plato, only by the fact that in each it is affected by a different set of accidents, _i.e._ of modes accidental to the substance as found in each, then it would follow that this substance is not merely _conceptually_ identical in both, but that it is _really_ identical in both; which is the error of extreme realism. As a matter of fact it is the converse that is true: the sets of accidents are distinct because they affect individual substances already really and individually distinct.

It is manifest that the accidents which are _separable_ from the individual substance, _e.g._ name, shape, size, appearance, location, etc., cannot constitute its individuality. There are, however, other characteristics which are _inseparable_ from the individual substance, or which are _properties_ of the latter, _e.g._ the fact that an individual man was born of certain parents. Perhaps it is such characteristics that give its individuality to the individual substance?(144) To think so would be to misunderstand the question under discussion. We are not now inquiring into the _extrinsic_ causes whereby actually existing reality is individuated, into the _efficient_ principles of its individuation, but into the _formal_ and _intrinsic_ principle of the latter. There must obviously be something intrinsic to the individual reality itself whereby it is individuated. And it is about this intrinsic something we are inquiring. The individual man is this individual, human nature is thus individuated in him, by something that is essential to human nature as found in him. This something has been called—after the analogy of the _differentia specifica_ which differentiates species within a genus—the _differentia individua_ of the individual. It has also been called by some the _differentia numerica_, and by Scotists the _haecceitas_. However we are to conceive this something, it is certain at all events that, considered as it is really found in the individual, it cannot be anything _really distinct_ from the specific nature of the latter. No doubt, the _differentia specifica_, considered in the abstract, it is not essential and intrinsic to the _natura generica_ considered in the abstract: it is extrinsic and accidental to the abstract content of the latter notion; but this is because we are conceiving these grades of being in the abstract. The same is true of the _differentia individua_ as compared with the _natura specifica_ in the abstract. But we are now considering these grades of reality as they are actually in the concrete individual being: and as they are found here, we have seen that a real distinction between them is inadmissible.

32. THE “PRINCIPLE OF INDIVIDUATION”.—How, then, are we to conceive this something which individuates reality? It may be well to point out that for the erroneous doctrine of extreme realism, which issues in monism, the problem of individuation, as here understood, does not arise. For the monist all plurality in being is merely apparent, not real: there can be no question of a real distinction between individual and individual.(145) Similarly, the nominalist and the conceptualist evade the problem. For these the individual alone is not merely formally real: it alone is fundamentally real: the universal is not even fundamentally real, has no foundation in reality, and thus all scientific knowledge of reality as revealed in sense experience is rendered impossible. But for the moderate realist, while the individual alone is formally real, the universal is fundamentally real, and hence the problem arises. It may be forcibly stated in the form of a paradox: That whereby Socrates and Plato are really distinct from each other as individuals is really identical with the human nature which is really in both. But what individuates human nature in Socrates, or in Plato, is logically distinct from the human nature that is really in Socrates, and really in Plato. We have only to inquire, therefore, whether the intrinsic principle of individuation is to be conceived merely as a negation, as something negative added by the mind to the concept of the specific nature, whereby the latter is apprehended as incapable of multiplication into “others” each of which would be formally that same nature, or, in other words, as incommunicable; or is the intrinsic ground of this incommunicability to be conceived as something positive, not indeed as something really distinct from, and superadded to, the specific nature, but as a positive aspect of the latter, an aspect, moreover, not involved in the concept of the specific nature considered in the abstract.

Of the many views that have been put forward on this question two or three call for some attention. In the opinion of Thomists generally, the principle which individuates _material_ things, thus multiplying numerically the same specific nature, is to be conceived as a positive mode affecting the latter and revealing it in a new aspect, whereas the specific nature of the _spiritual_ individual is itself formally an individual. The principle of the latter’s individuation is already involved in the very concept of its specific nature, and therefore is not to be conceived as a distinct positive aspect of the latter but simply as the absence of plurality and communicability in the latter. In material things, moreover, the positive mode or aspect whereby the specific nature is found numerically multiplied, and incommunicable as it exists in each, consists in the fact that such a specific nature involves in its very constitution a _material_ principle which is actually allied with certain _quantitative dimensions_. Hence the principle which individuates material substances is not to be conceived—after the manner in which Scotists conceive it—as an ultimate _differentia_ affecting the _formal_ factor of the nature, determining the specific nature just as the _differentia specifica_ determines the generic nature, but as a _material_ differentiating principle. What individuates the material individual, what marks it off as one in itself, distinct or divided from other individuals of the same specific nature, and incommunicable in that condition, is the material factor of that individual’s nature—not, indeed, the material factor, _materia prima_, considered in the abstract, but the material factor as proximately capable of actual existence by being allied to certain more or less definite spatial or quantitative dimensions: “matter affected with quantity”: “_materia quantitate signata_”.(146)

In regard to material substances this doctrine embraces two separate contentions: (_a_) that the principle which individuates such a substance must be conceived as something positive, not really distinct from, but yet not contained in, the specific nature considered in the abstract; (_b_) that this positive aspect is to be found not in the formal but in the material principle of the composite corporeal substance.

To the former contention it might be objected that what individuates the specific nature cannot be conceived as anything _positive_, superadded to this nature: it cannot be anything _accidental_ to the latter, for if it were, the individual would be only an accidental unity, a “_unum per accidens_” and would be constituted by an accident, which we have seen to be inadmissible; nor, on the other hand, can it be anything _essential_ to the specific nature, for if it were, then individuals should be capable of adequate essential definition, and furthermore the definition of the specific nature would not really give the whole essence or _quidditas_ of the individuals—two consequences which are commonly rejected by all scholastics. To this, however, it is replied that the principle of individuation is something essential to the specific nature in the sense that it _is_ something intrinsic to, and really identical with, the whole real substance or entity of this nature, though not involved in the abstract concept by the analysis of which we reach the definition or _quidditas_ of this nature. What individuates Socrates is certainly essential to Socrates, and is therefore really identical with his human nature; it is intrinsic to the human nature in him, a mode or aspect of his human substance; yet it does not enter into the definition of his nature—“_animal rationale_”—for such definition abstracts from individuality. When, therefore, we say that definition of the specific nature gives the whole _essence_ of an individual, we mean that it gives explicitly the abstract (specific) essence, not the individuality which is really identical with this, nor, therefore, the whole substantial reality of the individual. We give different answers to the questions, “What is Socrates?” and “Who is Socrates?” The answer to the former question—a “man,” or a “rational animal”—gives the “essence,” but not explicitly the whole substantial reality of the individual, this remaining incapable of adequate conceptual analysis. The latter question we answer by giving the notes that _reveal_ individuality. These, of course, are “accidental” in the strict sense. But even the principles which constitute the individuality of separate individuals of the same species, and which differentiate these individuals numerically from one another, we do not describe as _essential_ differences, whereas we do describe specific and generic differences as _essential_. The reason of this is that the latter are abstract, universal, conceptual, amenable to intellectual analysis, scientifically important, while the former are just the reverse; the universal differences alone are principles about which we can have scientific knowledge, for “all science is of the abstract and universal”;(147) and this is what we have in mind when we describe them as “essential” or “formal,” and individual differences as “entitative” or “material”.

The second point in the Thomistic doctrine is that corporeal substances are individuated by reason of their _materiality_. The formative, specific, determining principle of the corporeal substance is rendered _incommunicable_ by its union with the material, determinable principle; and it becomes individually _distinct_ or separate by the fact that this latter principle, in order to be capable of union with the given specific form, has in its very essence an exigence for certain more or less determinate dimensions in space. Corporeal things have their natural size within certain limits. The individual of a given corporeal species can exist only because the material principle, receptive of this specific form, has a natural relation to the fundamental property of corporeal things, _viz._ quantity, within certain more or less determinate limits. The form is rendered incommunicable by its reception in the matter. This concrete realization of the form in the matter is individually distinct and separate from other realizations of the same specific form, by the fact that the matter of this realization demands certain dimensions of quantity: this latter property being the root-principle of numerical multiplication of corporeal individuals within the same species.

On the other hand, incorporeal substances such as angels or pure spirits, being “pure” forms, “_formæ subsistentes_,” wholly and essentially unallied with any determinable material principle, are _of themselves_ not only specific but individual; they are themselves essentially incommunicable, superior to all multiplication or repeated realization of themselves: they are such that each can be actualized only “once and for all”: each is a species in itself: it is the full, exhaustive, and adequate expression of a divine type, of an exemplar in the Divine Mind: its realization is not, like that of a material form, the actuation of an indefinitely determinable material principle: it sums up and exhausts the imitable perfection of the specific type in its single individuality, whereas the perfection of the specific type of a corporeal thing cannot be adequately expressed in any single individual realization, but only by repeated realizations; nor indeed can it ever be adequately, exhaustively expressed, by any finite multitude of these.

It follows that in regard to pure spirits the individuating principle and the specific principle are not only really but also logically, conceptually identical; that the distinction between individual and individual is here properly a specific distinction; that it can be described as numerical only in an analogical sense, if by numerical we mean material or quantitative, _i.e._ the distinction between corporeal individuals of the same species (28).

But the distinction between individual human souls is not a specific or formal distinction. These, though spiritual, are not _pure_ spirits. They are spiritual substances which, of their very nature, are essentially ordained for union with matter. They all belong to the same species—the human species. But they do not constitute individuals of this species unless as existing actually united with matter. Each human soul has a transcendental relation to its own body, to the “_materia signata_” for which, and in which, it was created. For each human soul this relation is unique. Just as it is the material principle of each human being, the matter as allied to quantitative dimensions, that individuates the man, so it is the unique relation of his soul to the material principle thus spatially determined, that individuates his soul. Now the soul, even when disembodied and existing after death, necessarily retains in its very constitution this essential relation to its own body; and thus it is that disembodied souls, though not actually allied with matter, remain numerically distinct and individuated in virtue of their essential relation, each to its own body. We see, therefore, that human souls, though spiritual, are an entirely different order of beings, and must be conceived quite differently, from pure spirits.

We must be content with this brief exposition of the Thomistic
doctrine on individuation. A discussion of the arguments for and
against it would carry us too far.(148) There is no doubt that
what _reveals_ the individuality of the corporeal substance to us
is its material principle, in virtue of which its existence is
circumscribed within certain limits of time and space and affected
with individual characteristics, “_notae individuantes_”. But the
Thomistic doctrine, which finds in “_materia signata_” the formal,
intrinsic, constitutive principle of individuation, goes much
deeper. It is intimately connected with the Aristotelian theory of
knowledge and reality. According to this philosophy the formative
principle or ἔιδος, the _forma subtantialis_, is our sole key to
the intelligibility of corporeal things: these are intelligible in
so far forth as they are actual, and they are actual in virtue of
their “forms”. Hence the tendency of the scholastic commentators
of Aristotle to use the term “form” as synonymous with the term
“nature,” though the whole nature of the corporeal substance
embraces the material as well as the formal principle: for even
though it does, we can understand nothing about this “nature”
beyond what is intelligible in it in virtue of its “form.” The
material principle, on the other hand, is the potential,
indeterminate principle, in itself unintelligible. We know that in
ancient Greek philosophy it was regarded as the ἄλογον, the surd
and contingent principle in things, the element which resisted
rational analysis and fell outside the scope of “science,” or
“knowledge of the necessary and universal”. While it revealed the
forms or natures of things to sense, it remained itself impervious
to intellect, which grasped these natures and rendered them
intelligible only by divesting them of matter, by abstracting them
from matter. Reality is intelligible only in so far forth as it is
immaterial, either in fact or by abstraction. The human intellect,
being itself spiritual, is “receptive of forms without matter”.
But being itself allied with matter, its proper object is none
other than the natures or essences of corporeal things,
abstracted, however, from the matter in which they are actually
“immersed”. The only reason, therefore, why any intelligible form
or essence which, as abstract and universal, is “one” for
intellect, is nevertheless actually or potentially “manifold” in
its reality, is because it is allied with a material principle. It
is the latter that accounts for the numerical multiplication, in
actual reality, of any intelligible form or essence. If the latter
is material it can be actualized only by indefinitely repeated,
numerically or materially distinct, alliances with matter. It
cannot be actualized “_tota simul_,” or “once for all,” as it
were. It is, therefore, the material principle that not merely
reveals, but also constitutes, the individuation of such corporeal
forms or essences. Hence, too, the individual as such cannot be
adequately apprehended by intellect; for all intelligible
principles of reality are formal, whereas the individuating
principle is material.

On the other hand, if an intelligible essence or form be purely
spiritual, wholly unrelated to any indeterminate, material
principle, it must be “one” not alone conceptually or logically
but also really: it can exist only as “one”: it is of itself
individual: it can be differentiated from other spiritual essences
not materially but only formally, or, in other words, not
numerically but by a distinction which is at once individual and
specific. Two pure spirits cannot be “two” numerically and “one”
specifically, two for sense and one for intellect, as two men are:
if they are distinct at all they must be distinct for intellect,
_i.e._ they cannot be properly conceived as two members of the
same species.

In this solution of the question it is not easy to see how the
material principle, which, by its alliance with quantity,
individuates the form, is itself individuated so as to be the
source and principle of a multiplicity of numerically distinct and
incommunicable realizations of this form. Perhaps the most that
can be said on this point is that we must conceive quantity, which
is the fundamental property of corporeal reality, as being itself
essentially divisible, and the material principle as deriving from
its essential relation to quantity its function of multiplying the
same specific nature numerically.

Of those who reject the Thomistic doctrine some few contend that it is the _actual existence_ of any specific nature that should be conceived as individuating the latter. No doubt the universal as such cannot exist; reality in order to exist actually must be individual. Yet it cannot be actual existence that individuates it. We must conceive it as individual before conceiving it as actually existent; and we can conceive it as individual while abstracting from its existence. We can think, for instance, of purely possible individual men, or angels, as numerically or individually distinct from one another. Moreover, what individuates the nature must be essential to the latter, but actual existence is not essential to any finite nature. Hence actual existence cannot be the principle of individuation.(149) Can it be contended that _possible_ existence is what individuates reality? No; for possible existence is nothing more than intrinsic capacity to exist actually, and this is essential to all reality: it is the criterion whereby we distinguish real being from logical being; but real being, as such, is indifferent to universality or individuality; as far as the simple concept of real being is concerned the latter may be either universal or individual; the concept abstracts equally from either condition of being.

The vast majority, therefore, of those who reject the Thomistic doctrine on individuation, support the view that what individuates any nature or substance is simply the whole reality, the total entity, of the individual. This total entity of the individual, though really identical with the specific nature, must be conceived as something positive, superadded to the latter, for it involves a something which is logically or mentally distinct from the latter. This something is what we conceive as a _differentia individua_, after the analogy of the _differentia specifica_ which contracts the concept of the genus to that of the species; and by Scotists it has been termed “_haecceitas_” or “thisness”. Without using the Scotist terminology, most of those scholastics who reject the Thomist doctrine on this point advocate the present view. The individuality or “thisness” of the individual substance is regarded as having no special principle in the individual, other than the whole substantial entity of the latter. If the nature is simple it is of itself individual; if composite, the intrinsic principles from which it results—_i.e._ matter and form essentially united—suffice to individuate it.

In this view, therefore, the material principle of any individual man, for example, is numerically and individually distinct from that of any other individual, _of itself_ and independently of its relation either to the formative principle or to quantity. The formative principle, too, is individuated _of itself_, and not by the material principle which is really distinct from it, or by its relation to this material principle. Likewise the union of both principles, which is a substantial mode of the composite substance, is individuated and rendered numerically distinct from all other unions of these two individual principles, not by either or both these, but by itself. And finally, the individual composite substance has its individuation from these two intrinsic principles thus individually united.

It may be doubted, perhaps, whether this attempt at explaining the
real, individual “manifoldness” of what is “one” for intellect,
_i.e._ the universal, throws any real light upon the problem. No
doubt, every element or factor which is grasped by intellect in
its analysis of reality—matter, form, substance, accident,
quantity, nay, even “individuality” itself—is apprehended as
abstract and universal; and if we hold the doctrine of Moderate
Realism, that the intellect in apprehending the universal attains
to reality, and not merely to a logical figment of its own
creation, the problem of relating intelligibly the reality which
is “one” for intellect with the same reality as manifestly
“manifold” in its concrete realizations for sense, is a genuine
philosophical problem. To say that what individuates any real
essence or nature, what deprives it of the “oneness” and
“universality” which it has for intellect, what makes it “this,”
“that,” or “the other” incommunicable individual, must be
conceived to be simply the whole essential reality of that nature
itself—leaves us still in ignorance as to why such a nature, which
is really “one” for intellect, can be really “manifold” in its
actualizations for sense experience. The reason why the nature
which is one and universal for abstract thought, and which is
undoubtedly not a logical entity but a reality capable of actual
existence, can be actualized as a manifold of distinct
individuals, must be sought, we are inclined to think, in the
relation of this nature to a material principle in alliance with
quantity which is the source of all purely numerical, “space and
time” distinctions.

33. INDIVIDUATION OF ACCIDENTS.—The rôle of quantity in the Thomistic theory of individuation suggests the question: How are accidents themselves individuated? We have referred already (29, _n._) to the view that they are individuated by the individual subjects or substances in which they inhere. If we distinguish again between what _reveals_ individuality and what _constitutes it_, there can be no doubt that when accidents of the same kind are found in individually distinct subjects what reveals the numerical distinction between the former is the fact that they are found inhering in the latter. So, also, distinction of individual substances is the _extrinsic_, _genetic_, or _causal_ principle of the numerical distinction between similar accidents arising in these substances. But when the same kind of accident recurs successively in the same individual substance—as, for example, when a man performs repeated acts of the same kind—what reveals the numerical or individual distinction between these latter cannot be the individual substance, for it is one and the same, but rather the _time_ distinction between the accidents themselves.

The intrinsic constitutive principle which formally individuates the accidents of individually distinct substances is, according to Thomists generally, their essential relation to the individual substances in which they appear. It is not clear how this theory can be applied to the fundamental accident of corporeal substances. If the function of formally individuating the corporeal substance itself is to be ascribed in any measure to _quantity_, it would seem to follow that this latter must be regarded as individuated by itself, by its own total entity or reality. And this is the view held by most other scholastics in regard to the individuation of accidents generally: that these, like substances, are individuated by their own total positive reality.

When there is question of the same kind of accident recurring in the same individual subject, the “time” distinction between such successive individual accidents of the same kind would appear not merely to _reveal_ their individuality but also to indicate a different relation of each to its subject as existing at that particular point of space and time: so that the relation of the accident to its individual subject, as here and now existing in the concrete, would be the individuating principle of the accident.

Whether a number of accidents of the same _species infima_, and distinct merely numerically, could exist simultaneously in the same individual subject, is a question on which scholastic philosophers are not agreed: the negative opinion, which has the authority of St. Thomas, being the more probable. Those various questions on the individuation of accidents will be better understood from a subsequent exposition of the scholastic doctrine on accidents (Ch. viii.).

It may be well to remark that in inquiring about the individuation
of substances and accidents we have been considering reality from
a static standpoint, seeking how we are to conceive and interpret
intellectually, or for abstract thought, the relation of the
universal to the individual. If, however, we ascribe to “time”
distinctions any function in individuating accidents of the same
kind in the same individual substance, we are introducing into our
analysis the kinetic aspect of reality, or its subjection to
processes of change.

We may call attention here to a few other questions of minor
import discussed by scholastics. First, have all individuals of
the same species the same _substantial_ perfection, or can
individuals have different grades of substantial perfection within
the same species? All admit the obvious fact that individual
differs from individual within the same species in the number,
variety, extent and intensity of their accidental properties and
qualities. But, having the human soul mainly in view, they
disagree as to whether the substantial perfection of the specific
nature can be actualized in different grades in different
individuals. According to the more common opinion there cannot be
different _substantial_ grades of the same specific nature, for
the simple reason that every such grade of substantial perfection
should be regarded as specific, as changing the species: hence,
_e.g._ all human souls are substantially equal in perfection. This
view is obviously based upon the conception of specific types or
essences as being, after the analogy of numbers, immutable when
considered in the abstract. And it seems to be confirmed by the
consideration that the intrinsic principle of individuation is
nothing, or adds nothing, _really distinct_ from the specific
essence itself.

Another question in connexion with individuation has derived at
least an historical interest from the notable controversy to which
it gave rise in the seventeenth century between Clarke and
Leibniz. The latter, in accordance with the principles of his
system of philosophy,—the _Law of Sufficient Reason_ and the _Law
of Continuity_ among the _monads_ or ultimate principles of
being,—contended that two individual beings so absolutely alike as
to be _indiscernible_ would be _eo ipso identical_, in other
words, that the reality of two such beings is impossible.

Of course if we try to conceive two individuals so absolutely
alike both in essence and accidents, both in the abstract and in
the concrete, as to be indiscernible either by our senses or by
our intellect, or by any intellect—even the Divine Intellect—we
are simply conceiving _the same thing_ twice over. But is there
anything impossible or contradictory in thinking that God could
create two perfectly similar beings, distinct from each other only
individually, so similar, however, that neither human sense nor
human intellect could apprehend them as two, but only as one? The
impossibility is not apparent. Were they two material individuals
they should, of course, occupy the same space in order to have
similar spatial relations, but impenetrability is not essential to
corporeal substances. And even in the view that each is
individuated by its “_materia signata_” it is not impossible to
conceive numerically distinct quantified matters allied at the
same time to the same dimensions of space. If, on the other hand,
there be question of two pure spirits, absolutely similar
specifically, even in the Thomistic view that here the individual
distinction is at the same time specific there seems to be no
sufficient ground for denying that the Divine Omnipotence could
create two or more such individually (and therefore specifically)
distinct spirits:(150) such distinction remaining, of course,
indiscernible for the finite human intellect.

The argument of Leibniz, that there would be _no sufficient
reason_ for the creation of two such indiscernible beings, and
that it would therefore be repugnant to the Divine Wisdom, is
extrinsic to the question of their intrinsic possibility: if they
be intrinsically possible they cannot be repugnant to any
attribute of the Divinity, either to the Divine Omnipotence or to
the Divine Wisdom.

34. IDENTITY.—Considering the order in which we acquire our ideas we are easily convinced that the notion of finite being is antecedent to that of infinite being. Moreover, it is from reflection on finite beings that we arrive at the most abstract notion of being in general. We make the object of this latter notion definite only by dividing it off mentally from nothingness, conceived _per modum entis_, or as an _ens rationis_. Thus the natural way of making our concepts definite is by _limiting_ them; it is only when we come to reflect on the necessary implications of our concept of “infinite being” that we realize the possibility of conceiving a being which is _definite_ without being really _limited_, which is definite by the very fact of its infinity, by its possession of unlimited perfection; and even then our imperfect human mode of conceiving “infinite being” is helped by distinguishing or dividing it off from all finite being and contrasting it with the latter. All this goes to prove the truth of the teaching of St. Thomas, that the mental function of _dividing_ or _distinguishing_ precedes our concepts of unity and multitude. Now the concepts of _identity_ and _distinction_ are closely allied with those of unity and multitude; but they add something to these latter. When we think of a being as one we must analyse it further, look at it under different aspects, and _compare it with itself_, before we can regard it as _the same_ or _identical_ with itself. Or, at least, we must think of it twice and compare it with itself in the affirmative judgment “This is itself,” “A is A,” thus formulating the logical _Principle of Identity_, in order to come into possession of the concept of _identity_.(151) Every affirmative categorical judgment asserts _identity_ of the predicate with the subject (“_S is P_”): asserts, in other words, that what we apprehend under the notion of the predicate (_P_) is _really identical_ with what we have apprehended under the _distinct_ notion of the subject (_S_). The synthetic function of the affirmative categorical judgment _identifies_ in the real order what the analytic function of mental abstraction had _separated_ in the logical order. By saying that the affirmative categorical judgment asserts identity we mean that by asserting that “this is that,” “man is rational” we identify “this” with “that,” “man” with “rational,” thus _denying_ that they are _two_, that they are _distinct_, that they _differ_. Identity is one of those elementary concepts which cannot be defined; but perhaps we may describe it as _the logical relation through which the mind asserts the objects of two or more of its thoughts to be really one_.