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Part IV: Accidents Beyond Quantity

As shown in our discussion of quantity, various types of accidents may be quantifiable, but they are not on that account to be regarded as mere quantities. This distinction between quantity and the accidents it modifies is lacking among several modern schools of thought, ranging from seventeenth-century mechanism to much of modern analytic philosophy. The reduction of all reality to quantity has become especially popular since the mid-nineteenth century, with the advent of scientism, the notion that physical science can account for all of reality, and the spread of the peculiar Victorian idea that objectivity is an intellectual virtue. These two tendencies favor a philosophy that regards quantity as real, while all else is just subjective perception. This results in a failure to distinguish mathematical models from the more complete reality they represent only partially. We have already commented on the ontological incoherence of quantity without substance. We will now examine the categories of accident beyond quantity, in both their quantitative and non-quantitative aspects.

Space and Time

We have seen that the notion of quantity presumes at least an abstract space to act as a medium of pluralization for iterations of abstract entities. Any world that has real individuations of substance will necessarily need a real space if they are to co-exist in a way that they can be a plurality or merge to form a greater substance. Spatial extension appears to be intimately related with the part to whole relationship (though this is not the only sense of part to whole), so that space would seem to be the principle of pluralization of individuated substance.

In classical and medieval philosophy, the category of quantity was usually conceived in terms of spatial extension, so that in natural philosophy it was virtually synonymous with geometric volume. With the advent of Cartesian and Newtonian mechanics in the seventeenth century, this tendency to regard quantity as spatial extension became more pronounced, despite the fact that new analytic tools made geometric proofs less essential to mathematics. At the height of seventeenth- and eighteenth-century mechanism, most natural philosophers defined all matter as extension. For philosophical materialists, from Hobbes to La Mettrie, this meant that everything is extension. Theistic mechanists, by contrast, circumscribed the omnipresence of extension with important caveats. Descartes held that all matter was extension, but regarded mind as an altogether different sort of substance, a res cogitans. Pascal agreed with most mechanists that all qualitative phenomena are reducible to geometric quantity, but he rejected Cartesian attempts to define the categories of matter, extension, and quantity in terms of one another.

Newton conceived of matter and its dynamical relations as being mediated by space, a uniform and infinite void whose properties most closely resembled the immaterial, infinite, and unchanging God. Unlike Descartes, who denied the possibility of a void since everything but mind was material extension, Newton made space independent of matter, so it was practically a substance unto itself. This was a departure from the classical and medieval tradition, which did not consider "space" as a substantial entity separate from matter, but instead contemplated "place" or "position" as accidents of substance. Classical philosophy did contain some indication that "place" might exist independently of matter. In Ptolemaic cosmology, the earth is situated in a physically special place at the center of the universe toward which all heavy objects naturally fall. Newton's space, though independent of matter, is perfectly uniform, with no intrinsically special places.

Einstein's theory of relativity has challenged earlier conceptions of space, even threatening to abolish the category altogether. The empirical validation of special and general relativity, however, should not be taken as proof of the metaphysical interpretation that space is curved or that "space-time" is a single irreducible entity. For one thing, the standard interpretation of relativistic space-time is incompatible with quantum mechanics, which clearly distinguishes space and time. For another, Einstein was not altogether consistent in his metaphysical treatment of space, sometimes regarding it as a void, and other times as a deformable substance.

Natural philosophers of the Scholastic age were generally quicker than their modern counterparts to recognize that empirical validation of a mathematical model does not necessarily mean that the model provides a true picture of physical reality. For example, astronomers of the early sixteenth century used three different models - epicycles, elliptics, and logarithmic tables - to calculate celestial motions. None of these models were considered to reflect physical reality, for the physics of the time asserted that the heavenly bodies moved in concentric crystalline spheres, which was incompatible with real motion in epicycles or elliptics. When Copernicus proposed his heliocentric model, astronomers understandably regarded it as just another valid computational model and nothing more, since it contradicted physics as it was then understood. It remained for Galileo and Newton to provide an alternative theory of mechanics that could validate Copernicanism as more than a mathematical model that preserves the phenomena or "saves the appearances." To take a modern example distinguishing mathematical models from physics, in quantum mechanics the same physics can be described by the conceptually disparate yet mathematically equivalent Heisenberg and Schrodinger pictures, which respectively use matrix algebra and wavelike differential equations.

Even when a mathematical model truly does reflect an aspect of physical reality, this does not mean that the modeled physical properties are quantities and nothing else. A mathematical model, by necessity, can only describe the quantitative aspects of properties; it would be fallacious to infer that no non-quantitative aspects need exist. Ironically, those analytic philosophers who disparage metaphysics as mistaking our way of thinking for reality commit precisely this blunder in their interpretation of quantitative models of reality. Blinded by scientism, they follow physicists in naively ascribing ontological reality to mathematical models. If this results in conceptual incoherence, as is often the case in quantum mechanics, they claim to have made a profound discovery that invalidates any conceptual intuition to the contrary. As a perusal of modern theoretical physics will show, disparagement of common sense is not the exclusive domain of metaphysicians.

It remains to be seen to what extent relativity is a mathematical model and to what extent it depicts physical reality. We are prevented from accepting it completely as the latter due to several points of incoherence. The most egregious of these is to be found in general relativity, which treats space-time as something that can be "warped" by matter, as though it were a substance, contrary to the relativistic thesis that there is no Cartesian plenum or aether. If space-time is warpable, it is effectively an aether, a medium through which objects move. Aside from the incoherence of whether space-time is a substance or not, both special and general relativity treat space and time by a single pseudo-metric, from which it is invalidly inferred that space and time are different aspects of the same thing, seen from different reference frames. This analysis considers only the quantitative or extensive aspects of space and time, when there is certainly more to time than extension, as evidenced by its asymmetry with respect to forwards and backwards, a fact captured neither by Newtonian nor relativistic mechanics, both of which are time-reversible. The fields of physics that do capture time asymmetry - quantum mechanics and statistical mechanics - treat time as a parameter that tracks the evolution of all physical observables, including spatial position. The asymmetry of time is indicated not by its own properties, since it is modeled as a simple extensive variable, but from the properties of the observables evolving with respect to time.

The supposed integration of space and time is first introduced by special relativity, which regards "space-time" as a vector space defined by the Minkowski pseudo-metric s2 = x2 + y2 + z2 - c2t2. This geometry is an artifact of the Lorentz transformation v' = (1 - v2/c2)-1/2, under which Maxwell's electrodynamic equations are invariant, while they fail to remain the same under the simple Galilean transformation x' = x + vt. One of Einstein's most daring intuitions was his inference that classical kinematics was just a low-velocity approximation of the Lorentz transformation, which rendered all laws of physics invariant, including those of mechanics. Applying this intuition mathematically, coupled with the fact that the speed of light is invariant under the Lorentz transformation, a new relativistic kinematics is generated, with empirically verifiable results such as the famous mass-energy equivalence relation E = mc2. The mathematical and empirical fruitfulness of special relativity is unquestionable, and Minkowski "space-time" is certainly a mathematically accurate model of relativistic dynamics. This does not mean that Minkowski space-time is a true picture of physical reality, as we have seen from the use of mathematics in Ptolemaic astronomy and quantum mechanics. The formal interdependence of space and time simply means that a magnitude of spatial displacement is necessarily tied to the magnitude of temporal duration, but this link between the quantitative aspects of space and time does not tell the whole story about space and time. Space and time may be quantifiable, but they are not merely quantities.

The hypothesis of a necessary interdependence between space and time was known even to classical and medieval philosophers, many of whom regarded time as merely a measure of motion through space. Indeed it is far from obvious that there could be any such thing as time independent of spatial motion. All time is reckoned by counting motions assumed to be identical, such as swings of a pendulum, revolutions of celestial bodies, or vibrations of an atom. We may sense time elapsing independently of observing any moving object, but our own internal movements might generate this sensation, as we can only think sequentially from one thought to the next. Still, it would seem that time is not utterly dependent on space, since in everyday life, the duration of time elapsed does not depend strictly on the magnitude of motion, as we perceive that things can move across different quantities of space in the same amount of time.

At relativistic speeds, however, the velocity of an object does affect its experience of time, though not in the way we would expect if time were merely a measure of motion. Rather than speeding up in time, a high-speed particle is actually slowed down in time (though not linearly) as it approaches the speed of light, and photons have no experience of time at all. This, at any rate, is the most common colloquial explanation of "time dilation" in special relativity. We encounter limitations to this interpretation when we ask what it could possibly mean for time to "speed up" or "slow down." Without delving into the validity of the "twin paradox" and other relativistic oddities, we might ask at a more basic interpretive level whether this "slowing down" of time might alternatively be characterized as a slowing down of the intrinsic motion of the particle. This interpretation is consistent with the idea that time is a measure of motion, and we would say that a particle with an external velocity approaching the speed of light has a diminishing rate of intrinsic motion, with the limit being that of utterly changeless photons. This explanation might account for why relativistic time is so different from quantum mechanical time; they are measuring different aspects of motion. Neither the relativistic variable 't' nor the quantum parameter 't' is time or even a complete representation of time, but these are variables that measure motion differently, capturing different aspects of time. Quantum mechanics measures the evolution of wavefunctions, so its "time" parameterizes this development. Relativity instead measures time by external observations of events from a distance, based on the transmission of light signals in a vacuum. This extrinsic notion of time would be distinct from the quantum mechanical parameterization, though both are related in some way to metaphysical time.

The distinction between space and time is more apparent when we consider not their quantitative aspects, but the different ways they relate to substances. "Place" is an inherent accident of a substance, if space is absolute; otherwise, it is a relative accident with respect to some other substance. Yet relative accidents, such as relative position, velocity, and acceleration, only have meaning if we specify a common time for the objects bearing these accidents. Time seems to be a more transcendent category than the other accidents, including space. Some of the most basic ontological theses presume the specification of time. For example, we have already considered how contrary accidents may not be held in the same respect at the same time. The logic of time is different from that of other accidents, since it specifies a principle of non-contradiction of accidents. A substance can endure through time, having contrary accidents at different times. There is no contradiction as long as the possession of these accidents is not simultaneous. Each passing instant of time requires the manifestation of one or another accident.

An apparent counterexample to this account might be seen in quantum mechanics, where the wavefunction between measurements seems to individuate the simultaneous manifestation of contrary properties, in a "superposition of states." In reality, as I have shown elsewhere, the probabilistic formalism of quantum mechanics presumes the mutual exclusivity of orthogonal states, so it is inconsistent to use the wavefunction as an example of violating non-contradiction. So far is the possession of contrary accidents from physical possibility (conveniently, "mixed states" can never be observed), we cannot even conceive of it, as we have to visualize two contrary states in rapid succession. Our mind, which operates in time as does matter, must obey the law of non-contradiction, as it cannot harbor contrary concepts in the same way simultaneously. Time distinguishes successive states of substances; as each real state is defined, it cannot be in contradiction with itself.

Here we arrive at another mystery, perhaps central to the enigma of time. The past is clearly defined and non-negotiable, and no instant can carry internal contradictions. The same is true of the present, but what of the future? It is no contradiction to regard contrary accidents as possible futures, as the future is, from our perspective, not yet definite. Yet a purely relativistic notion of time cannot give us any real distinctions among past, present and future (due to the relativity of simultaneity), though we know for certain that things past are non-negotiable. How can we avoid the conclusion that all things are equally certain and fixed in a strongly deterministic sense, unless we respect the reality of past, present and future? There is no way to arrive at any meaningful probabilistic or statistical mechanics if the three parts of time are objectively indistinguishable. In order for there to be real activity, it is necessary for there to be a real present where one among many possibilities is realized, to be fixed forever in the past. Time is the medium of action.

When we understand that time is the medium of action, we can appreciate the origin of a pseudo-category postulated by modern physicists: the event. This is nothing other than the spatiotemporal coordinates of an act. An action, in the sense of change, by logical necessity occurs at a definite moment in time, and because of the commonly held natural principle against action at a distance, physicists are justified in further specifying natural acts as confined to a locality in space. In fact, the whole structure of relativity would break down if we admitted action at a distance. The difference between relativistic and classical notions of spatiotemporal events is that in relativity we can only speak of a present with respect to a given worldline trajectory; we cannot objectively declare distant events to be simultaneous. Though intuitively challenging, there is nothing here to contradict the reality of past, present, and future, but these are only experienced locally. Simultaneity paradoxes are limited in that they can never result in a future event preceding a past event in a temporal loop. Treating "events" as an ontological category mistakes geometry for reality, as an "event" in the physicist's sense is not really an "event" in the common sense of an action or happening, but it is only the spatiotemporal coordinates of an action. To reduce physical reality to spatiotemporal "events" is to commit the error of mistaking a geometric model for substantial reality, in an attempt to reduce all reality to constituents of a space-time continuum or perturbations of that continuum. Such an account somewhat inconsistently regards space-time as a substance or a sort of force field.

Philosophical discussion of space and time can be extricated from the relativistic muddle when we recognize that general relativity is really describing a warpable gravitational force field, embedded in true, potentially infinite space. This true space, a sort of meta-space, is not observable empirically, since everything is in relative motion and we have no absolute reference point. We can only see motion along the contours of gravitational fields at the cosmological level. As a convenient mathematical tool, much as we use radial coordinates for revolving bodies, we may regard these contours as those of "space" itself, since all matter must follow these contours.

True space, the philosopher's space, is Euclidean, as a consequence of the fact that space is not a substance. Space considered as an abstract mathematical model might be Euclidean or non-Euclidean, but such contours can have no meaning for a metaphysical plenum. Perhaps it would be better to say that true space is neither Euclidean nor non-Euclidean, but uniform and potentially infinite. The Euclidean model best exemplifies these characteristics, but it is only a mathematical model, not a real space.

In special relativity, a Euclidean metric is assumed for the spatial coordinates, and only the treatment of time results in the unusual Minkowski pseudo-metric s2 = x2 + y2 + z2 - c2t2. This metric was derived in order to deal with the kinematic or dynamical relations described by special relativity; it is an artifact of physics rather than a metaphysical necessity. Nonetheless, the effects of special relativity such as time dilation and Lorentz contraction appear to be quite real, and they raise important questions about the relationship between space and time. Even if we acknowledge that metaphysical space is Euclidean (and for special relativity, even the physicist's "space" is Euclidean, as gravitational contours are ignored) and that time has objective local reality of past, present, and future, it does not follow that space and time can be modeled as a simple four-dimensional Cartesian space, nor even that it is meaningful to speak of distant events as objectively simultaneous. We must distinguish the intuitively difficult from the metaphysically impossible, despite the fact that physicists have mistaken the mathematically expressible for the metaphysically possible, placing little value on the role of intuition or philosophic logic, believing these to be biological or mental limitations of humans, rather than genuine limitations on metaphysical possibility.

The locality of the present has important implications, but we will leave this for a treatment of metaphysics. For now, it suffices to identify space and time as distinct fundamental categories of accident, despite some physicists' attempts to conflate the two. Space is a medium that makes possible the individuation of substance, while time makes possible the individuation of successive actions and qualities in the same substance. Space and time are both linked directly to substance, so there is no strong a priori reason to expect simultaneity in spatially distant objects. Space and time are accidents of substance that we only know how to measure relatively, often using bizarre mathematical models that should not be identified with space and time themselves.

Relational Accidents or Relations

Place and time, we have seen, may be predicated directly of substance, yet we only know how to measure them relative to the position of another object or the time of another action. Spatiotemporal measurements are but one case in an entire class of accidents that are predicable only in relation to the property of another substance. These relational accidents, which we may call simply "relations," may be of two general types. Some relations are capable of inhering directly in a specific subject, yet only in relation to the property of another subject. These are called "relatives" in classical philosophy, examples of which include "double" and "half," which are predicable of a specific object, yet can be defined only by reference to another object. Other relations are not predicable of a specific subject, yet may be conceived as a sort of higher order accident relating two or more accidents. For example, the distance between two objects is a relation between the positions of each object, and is not inherent in one or the other object or position. Both types of relational accidents or "relations," we should emphasize, are more narrowly conceived than "relation" in formal logic or semantics, for we are only concerned with "relations" that are predicable of a subject or subjects with reference to another accident of some substance. The hierarchy of relational accidents is depicted below, to be elaborated in what follows.

If we admit that accidents can co-exist in the same reality, we are faced with the possibility that these accidents can be related to one another, and these relations themselves may be considered a sort of accident. However, it is not always clear what is the subject of such a relation. In the case of classical relatives, such as "double," we can see in the statement "x is double of y," that "double" is primarily predicated of x, for y is not "double" anything in this statement. Yet "x is double" is incomplete in meaning, and cannot correspond to any ontological entity, without y to serve as a reference point for doubling. Thus a relative R of the form "x is R of y" is predicable of x, yet in a way that is necessarily modified by y. Both x and y are subjects of R, yet R may be said to inhere more directly in x. With other relations, such as distance, we have seen above, the relation R(x,y) is not directly predicable of one or the other subject, but it is a meta-accident of two subjects. "The distance from Boston to New York" is not directly predicable of either city.

In both kinds of relations, we presume the existence of at least two accidents that serve as subjects. We may indirectly speak of relations between substances, but these are only possible by virtue of accidents that admit of relation. "The distance from Boston to New York," though nominally predicable of substances, is predicated of these cities only by virtue of their accidents of place, which more directly admit of the distance relation. Since our "relations" are really relational accidents, they do not encompass the broader logical sense of the term, where a relation is simply any semantic function that admits two or more predicates. By the standards of formal logic, anything that relates two or more things is a relation, which would include the relationships between universals and particulars, substances and accidents. This is not what we mean by "relation," a term we confine to the sense of a relational accident, an ontological entity whose reality is grounded in the co-existence of the accidents it relates.

When dealing with relational accidents or relations, it is useful to clarify if they are relating universal accidents (properties) or individuated accidents (tropes). Aristotle neglected to refer back to this basic distinction when examining each of the nine categories of accident. Modern discussions of ontology usually regard relations themselves as strictly universal, though the accidents they relate may be universal properties or individuated tropes. In analytic philosophy, relations are represented as predicate functions, and their only formal distinction from existential properties is that they can receive two or more predicates rather than only one. This substitution of formal logic for ontology results in a loss of information, as it suppresses some important distinctions between properties and relations.

Relations differ from other accidents in that they cannot inhere in a subject as a single individuation, independently of other subjects or tropes. It would seem, then, that a relation cannot be a trope, but this does not follow, since it is not necessary for a trope to be a well-defined substantive entity. The distance |A - B| between concrete objects A and B is certainly an instantiation of the generalized relation, "distance," so we may regard |A - B| as a trope, even though it is not a physical entity. The modern analytic assumption mistaking physical reality for all reality renders the recognition of individualized relations impossible.

Yet relations differ from other accidents even when considered as universals, to the extent that they are denied entry into the class of "properties" that encompasses all other accidents in modern ontology. This distinction between property and relation may be justified on the ground that an object may "bear" properties, but it does not, on its own, "bear" a relation. Be that as it may, a relation is still truly an accident, since it is "in a subject" in the formal sense we discussed previously. "In a subject" means it pertains to the subject, not as a part, and cannot exist separately from the subject. The uniqueness of relations consists in that they are necessarily accidents of composite subjects. The distance |A - B| pertains to the objects A and B, not as a part of these objects, yet it cannot exist separately from them. Once we admit that the objects A and B exist with defined spatial properties, the distance |A - B| must also exist.

The distance is certainly ontologically real even from a physical perspective, since A and B may have measurable properties that depend on their relative distance. As we discussed previously, in physics one more commonly knows only the relative properties of substances, not any absolute values, the latter having proved to be largely irrelevant to the nature of physical interaction.

There is a general type of relation, classically called a relative, which seems to inhere in a single subject, though it can only be defined with respect to multiple subjects. Some examples are "double," and "half," "master" and "slave." In the first pair, the relation seems to qualify a particular accident (trope), though it is actually defined with respect to some other accident. For example, in a half teaspoon of sugar, "half" qualifies the quantity of sugar, but only by reference to another quantity, a hypothetical whole teaspoon of sugar. There need not be an actual whole teaspoon of sugar in existence for the half teaspoon to exist, so the "half" is not ontologically dependent on any particular whole, but it is necessary for it to be at least hypothetically possible for a whole teaspoon to exist, or the "half" would have no referent. Thus the individuated "half" is ontologically dependent only on the universal "whole teaspoon." More generally, relatives such as "double" and "half" may be expressed in the form Rxy, or "x is R of y," where x is an individual accident, R is a relative, and y is a universal accident. (Type I in figure above) The first variable x may also represent a universal accident when expressing generalized relations.

The other type of relative, of which "master" and "slave" are examples, also seems to inhere in a single subject, though it can only be defined with respect to another subject. The use of grammatical substantives (nouns) for this pair does not preclude us from using these terms to describe accidents, as we have shown throughout that classical ontology is not dependent on grammar. "Slave" describes the state (a type of accident yet to be discussed) of a particular individual, so it is predicable only of that individual, though it is necessary for the slave to have a master by which his slave status is defined. We would not say slavery in any way inheres in the master, nor is it predicable of the master, who on the contrary embodies the very opposite of the slave state. A relative of this type might be expressed in the form Rxy, or "x is R of y," where x is an individual subject (a substance or accident), R is the relative, and y is an indeterminate subject. (Type II in figure above) So, when we say, "Homer is a slave," we really mean, "Homer is the slave of some master." There is a necessary linkage between R and y; each relative R has a corresponding predicate y that is necessary in order for R to be applicable to any subject x. Without a master (y), no man can be a slave.

Note that we are using modern predicate logic somewhat differently from the custom of analytic philosophers, since we take care to specify which ontological class each variable may represent. We do not regard all two-place predicate relations as logically similar. As such, our logic is not a matter of mere syntactic form, but it is truly a language of reality rather than semantic possibility. In another work, we will explore more thoroughly the distinction between symbolic logic and the ontologically grounded logic of the classical tradition.

Relatives and other relations may admit of contrariety, degree, and reciprocation. These attributes are not all the same in scope. Reciprocation and contrariety are limited to two-predicate relations of the form "x is R of y," or higher-predicate relations of the form "(x1, x2, x3...) is R of (y1, y2, y3...)." Relations of any predicate form may admit of degree, but relatives of the two types discussed previously (double/half and master/slave) do not generally admit of degree.

For a relation R to admit degrees means that we can say something is "more R" or "less R," so R is quantifiable intensively or extensively. In order for the relation to be quantifiable, it is necessary, though not sufficient, for at least two of its predicates to admit degree. The distance relation, for example, is quantifiable, since the properties it relates, namely positions, are measurable. If only one predicate varied by degree, the degree of the relation would only depend on that one predicate, being independent of all others and hence not truly a degree of relation.

The relatives "master" and "slave" do not admit of degree, for a slave is a slave regardless of how many or what kind of masters he has. The indeterminacy of y in the expression "x is R of y" for relatives of this type precludes the possibility of making R vary in degree. The relatives "double" and "half" likewise do not admit of degree, since the y in "x is R of y" is a fixed whole, unvarying in degree. Other relatives of this type, however, might admit degree. For example, "x is the inferior of y," has this form, where x is a subject and y is a universal accident, and both x and y can have varying magnitudes.

Contrariety and reciprocation of relations are closely linked. When we say a relation A is capable of reciprocation, we mean that the following statements hold:

(x is A of y) ⇒ (y is B of x) for some relation B
(y is B of x) ⇒ (x is A of y)

For either of these statements to hold non-trivially, we must presume asymmetry in relation A; in other words, Axy != Ayx. This is the case for all relatives, as well as many other types of relations. If the relation is symmetric, then both statements would hold trivially, as A = B.

It remains to be seen whether all two-predicate relations have an inverse. Given the relation A's asymmetry, we might simply define an arbitrary relation B that inverts the predicates. Even if this were always valid, the second statement nonetheless would not necessarily follow from the first. For example:

x is the father of y ⇒ y is the son of x
y is the son of x !⇒ x is the father of y

The second implication does not hold, since x could be the mother of y. Thus father and son may be inverse relations, yet not fully reciprocal. This is because the relation of being a son admits more than one possible type of predicate, from the mother or the father. Aristotle insists that all relatives, if given properly, are predicated in relation to correlatives (x and y) that reciprocate. If this is so, it would seem that the relation of son is not here given properly, and we should instead distinguish in "son" two relations, "fathered," and "mothered," or alternatively, we may abstract from gender, leaving "parent" and "offspring."

Why should we insist that relatives be defined in a way that admit reciprocation? For one thing, such a formulation guarantees that we relate only essential accidents; that is, accidents that differentiate the species. For example, if we were to define the relative "slave" as "slave of a man," this would be improper, since what is essential to "slave" is being "the slave of a master." Since the definition of a thing is the expression of its essence, only the last expression truly defines the relative "slave." As it happens, such an expression can be reciprocated. Similarly, "offspring of a parent" is essential to "offspring." More generally, when any reciprocal relation is predicated of two real subjects, the relation is also real, being bound to essential properties.

Nonetheless, there may yet be real relatives that do not admit of reciprocation. This appears to be the case for relational accounts of knowledge and perception. The relations "being knowable," "being perceptible," and "being measurable" appear to have no reciprocals. We may say, "x is perceptible by y," but y is not necessarily the perceiver of x. Here the difficulty arises from the fact that we are describing a potential relation rather than an actual one. If we admit that the potentialities of measurability, perceptibility, and knowability are real, or at least that the knowable or perceptible accidents are real, than we must admit that "being knowable," etc. are real relations, despite the fact that they have no reciprocals. These are asymmetric, as they seem to inhere more in the first predicate rather than the second. For a color to be perceptible, it would seem that virtually any perceiver whatsoever, even a hypothetical one, would suffice. If we grant that perception and knowledge may be considered independently of any definite substance that is the perceiver or knower, then there could indeed be a class of relatives that have no definite reciprocal, namely those relations defining potential knowledge and perception. (Type III in figure above)

The concept of relation as relational accident does not include parts of a whole. For relational accidents, being is the same as being related to something else. No slave can be a slave without a master; there can be no distance except with respect to two objects. As for relations of perception and knowledge, a taste might be perceptible without an actual perceiver, but a potential perceiver, at least, is necessary. With parts of a whole, by contrast, the being of the part is distinguishable from its union with the whole. A head can truly be a head, or a hand truly a hand, independently of considering the body to which they belong. A part is at least potentially separable from the whole, if not actually. The whole is not intrinsically necessary for a hand or any part of a substance to be (though it may be physically necessary). Parts of wholes are divisions of substances, so it would be a mistake to classify them among relational accidents, which take accidents as their subjects. Nonetheless, relations may relate properties (such as mass, volume, magnitude or intensity) of parts and wholes, as when we say a cup is half of a pint.

Relations in the sense we have discussed are truly accidents, as they are "in a subject" in the formal sense, with the distinction that this subject must be ontologically composite. They are predicated most directly of accidents, though they are predicable of substances in an indirect sense. The "relatives" of the Aristotelian tradition are a special sort of relational accident that is more directly predicable of one subject than the other, though it is ontologically dependent on both. The primary subject (x) of a relative may be a universal or individuated accident, while its secondary subject (y) may be a universal accident, an indeterminate subject, or an indefinite potential. Due to the lack of concreteness of these secondary subjects, the relative may be said to truly inhere in its primary subject when this is an individual. Yet, moving beyond the classical tradition, we recognize there can be ontologically real relations among two or more accidents, even determinate tropes, without inhering in one or the other subject. These meta-accidental relations should nonetheless be distinguished from the broadest semantic or logical sense of "relation," as they are confined to relations among ontological accidents.

Quality

A quality, in the most general sense, is something in virtue of which a subject possesses some characteristic. This cannot be true of quantity with regard to its subject, since quantity only modifies an existing attribute, so it depends existentially on that attribute and cannot be its source. We would not say that fire is hot by virtue of having a particular magnitude of heat, but rather that the magnitude of heat is a measure of how hot the fire is. The thing measured is ontologically prior or at least coequal to the magnitude of the measurement. Qualities have greater ontological independence than quantities, since they are the "stuff" that quantity measures and the means whereby other accidents may be possessed by a subject.

A quality answers the question quale, "what sort is it?" or "what kind is it?" A subject without any accidents could not belong to any kind, but quality differentiates essences into kinds, whereas quantity only pertains to iterations or extensions of the same kind. However, as substances might contain multiple qualities, only some of which are essential to the species in which the substance is being considered, we may identify each quality as "essential" or "accidental" with respect to a species. The traditional term "accidental quality" is an unfortunate choice, since all qualities are accidents; "incidental quality" would be a less equivocal term. By "essential qualities" and "accidental qualities," we mean only that the former differentiate or characterize the species being considered and the latter do not. We will not consider here the difficult question of which species are truly natural and which are arbitrary classifications (except to illustrate concepts), but consider all species merely as a priori possible modes of classification.

Influenced by mechanistic physics and chemistry, many modern philosophers and scientists have discarded the category of quality, under the pretext that qualities are all reducible to quantitative properties. In fact, even on its own terms, mechanism does not reduce all accidents to quantity, as the mechanical properties themselves (acceleration, force, mass, etc.) are not quantities (though they are quantifiable), but are qualities or relations. Indeed, early mechanists such as Galileo did not hesitate to describe mechanical properties as qualities. It was only by a later change of terminology that mechanists restricted the name 'quality' to "secondary" properties such as color, taste, smell, and other sensory perceptibles, thought to be reducible to mechanical properties. Even if this reduction were correct, there could still remain "primary qualities" among the mechanical properties themselves.

The possibility of reducing some qualities to others was known to ancient and medieval philosophers, several of whom recognized an explicit distinction between primary and secondary qualities. Democritus, the first atomist, undoubtedly influenced modern mechanists with his distinction between real properties - the shape, disposition, and situation of atoms - and merely conventional properties, such as color, sound, and taste. Aristotle, in his theory of perceptibles, distinguished "common sensibles" (aistheta koina) and "particular sensibles" (aistheta idia). The former included perceptions of the qualities of shape, extension, movement and rest, while the latter consisted of the psychological qualia of color, taste, et cetera.

The most important distinction among classical qualities, in light of modern treatments of the question, is Aristotle's class of "primary differences" (protai diaphorai), explicated in his treatment of tactile sensibles. Tactile sensibles, according to Aristotle, are manifestations of heat and cold, wetness and dryness, which are the "primary differences" underlying all other tactile sensations, such as rough and smooth, hard and soft. This is a clear example of subjective perceptibles being reducible to only a few real physical qualities. Many of the medieval Scholastics elaborated this distinction between primary and secondary sensibles (prima sensibilia and secunda sensibilia). St. Albert the Great, St. Thomas Aquinas, and St. Bonaventure, in particular, all articulated a distinction between primary and secondary qualities (qualitates primae and qualitates secundariae, with the latter being reducible to the former.

Early Scholastics such as Robert Grosseteste (c. 1175-1253) believed that intensive perceptibles were not subject to mathematical analysis, but John Duns Scotus articulated the possibility of quantifying quality, and later Scholastic philosophers further elaborated this concept of intensive magnitude. I have shown elsewhere that intensive magnitudes admit at best of a very impoverished type of quantity, lacking extensive addition.

Early modern mechanists such as Galileo and Gassendi believed that the only real qualities were mechanical, while all others were secondary. It became customary among later mechanists to speak of mechanical properties in distinction from "qualities," by which they meant only secondary qualities of perception. Since many Aristotelean primary qualities, such as heat and cold, wetness and dryness, were now considered to be secondary qualities, it is understandable how the entire class of "qualities" came to be regarded as secondary, when in fact mechanists themselves admitted several qualities. Real properties, according to Descartes, included flexibility, movement and extension, the first of which is a quality in the classical sense.

Since all the properties admitted by mechanists, including space and time, were measurable as extensive quantities, it became customary to regard the measurable qualities of mechanics as "quantitative," while qualities of merely intensive magnitude were regarded as "qualitative." This dichotomy persists in modern language, when we speak of "quantitative" and "qualitative" observations. In fact, even a quantitative observation presumes the existence of some quality (or some measurable relation, space or time) that is being measured. The formulae of modern physics still presume qualities as their predicates. Newton's force law F = ma does not mean force is mass or acceleration or a combination of the two, but only that the magnitude of force is proportional to the magnitude of mass and acceleration. We will not consider here whether the qualities of Newtonian mechanics are reducible to more fundamental qualities or relations, or even if reductionism has been overstated with regard to chemistry and biology. Instead, we will simply note that the category of quality has by no means been rendered irrelevant by modern science, which implicitly assumes its reality.

John Locke restored the Scholastic terminology of primary and secondary qualities in his theory of psychology, articulating this distinction in the more familiar terms of subjectivity and objectivity. Primary qualities are existent of themselves, independent of any observer, while secondary qualities are particular to the mind of the perceiver, and have no existence outside the mind, though they may be indirectly generated by primary qualities. Thus the qualia of "green" seen in the mind's eye does not inhere in a leaf, but is generated in the mind indirectly as the result of light of a certain frequency being reflected off the leaf. Locke's belief that the sole locus of secondary qualities is the mind does not inevitably follow from mechanism, which only requires that they be reducible to quantifiable properties.

It is not our purpose here to determine which qualities are primary and which are secondary, nor which perceptibles have extra-mental reality. Rather, we shall articulate a robust a priori theory of qualities that encompasses all the possibilities considered above. For this end, it is more appropriate to have a fundamental division of qualities that does not depend on whether they are primary or secondary, but enables us to consider each in the abstract, before analyzing whether it is even feasible to reduce one to another.

As we stated at the beginning, a quality modifies a substance's existence by giving it a certain kind of essence, or form, to use Aristotelian terminology. St. Thomas Aquinas made use of this fact to give an elegant account of quality and quantity, saying that quality inheres in a substance through its form, whereas quantity inheres in a subject through its matter (a term signifying the principle of individuation). While we will not justify here the metaphysical division of essence into matter and form, this account of quality harmonizes nicely with the fact that it answers the question, quale, "What kind is it?", since the form of a substance defines what kind of essence it is, or its quiddity (that which it is). Quantity, on the other hand, presumes likeness in kind, so that to have more or less of a thing does not alter the kind, but in fact, by measuring quantity, we regard the subject of measurement as being of a common kind. I can only count apples and oranges together if I regard both indistinguishably as fruit or some more generic kind of object. Quantity regards substance with regard to extension and iteration, but quality regards it with respect to its kind, distinguishing it from other substances.

Aristotle identified four types of qualities, though he allowed that there may be other possibilities. The four classes of quality are:

  1. states and conditions (or habits and dispositions)
  2. natural capacity and incapacity
  3. affective qualities or affections
  4. shape or external form

Many modern commentators have complained that these classes are so thoroughly dissimilar that they do not merit being lumped together into a single category called "quality." As we shall see, each of these classes have all the features we have indicated of qualities: (1) a subject possesses other accidents in virtue of these; (2) they differentiate essences into kinds, answering the question "what kind is it?"; (3) they inhere in a substance through its form rather than its matter. Further, St. Thomas Aquinas offers a metaphysical motivation for the four classes of quality, though it is doubtful that Aristotle himself thought of any such scheme. The classes may be distinguished according to the "mode of determination of the subject to accidental being," which may be taken in regard to:

  1. the very nature of the subject;
  2. action and
  3. passion resulting from its natural principles (matter and form);
  4. quantity.

In the Categoriae, Aristotle uses attributes of man to exemplify each of the different types of qualities, apparently on the assumption that man is the most perfect substance, having the greatest variety of qualities. Instead of restricting our examples to man, we will consider each class of qualities as applied to the broadest possible scope of subjects, extending to inanimate entities. We will also show how the four types of quality correspond to the four modes of relating a subject to accidental being. These four types will be examined in order of increasing difficulty. (4, 2, 3, 1)

The shape or external form of a substance is its spatial or geometric distribution. When we distinguish substances only with regard to their shape, we effectively regard them as homogeneous. In other words, we are considering only how the quantity of a substance, in the geometric sense, is distributed, without regard for intrinsic characteristics of the substance itself. We may consider several equal quantities of the same substance, yet distinguish how that quantity is distributed in each. Thus "shape" is the mode by which a substance participates in quantity. Shape, of itself, presumes the existence of space, but not of time. Consequently, this type of quality is, of itself, devoid of movement, as is quantity.

Shape is a quality since it is the mode by which a substance is distributed in space, so the properties of that substance are accordingly distributed, meaning that accidental being is manifested in accordance with shape. Thus shape has the first feature of qualities, namely that it is a means by which a substance may participate in accidental being.

It is clear that shape possesses the other features of quality, if we take care to distinguish shape from quantity. One might object that shape does not distinguish substances into kinds, since it is only a modification of quantity. To this we may reply that shape does not modify mere magnitude, which is quantity, but rather the arrangement of substance. A round stone differs from a flat stone, even if they are equal in volume. Thus shape distinguishes kinds, and it inheres in the subject through its form. Indeed, geometric shape is the most primitive and archetypal notion of form.

If we were to admit no other quality besides shape or external form, we would have a crude atomism similar to that of Democritus. This purest form of materialism reduces all reality to simple bodies of varying shapes, making extension of homogeneous matter the only accident of being. In fact, even Democritus recognized that this is an insufficient account of reality, as it is necessary to include the dynamical properties of these atoms. Materialists familiar with modern physics would further admit that, even considered statically, fundamental particles have real properties other than spatial distribution.

Modern physicists and philosophers generally admit the existence of various natural capacities or dispositional properties, by which we mean the capacity to act in a certain way. While there may be dispute as to which capacities are reducible to others, no one argues that these are all reducible to shape or external form. Indeed, that would be impossible, as spatial form is static, so by itself it can not constitute a capacity to act, though it might be a necessary condition for the manifestation of such a dispositional property. Natural capacities are qualities, for they are clearly a means by which a substance can possess other accidents, as they are dispositional. They distinguish substances into "real" kinds (with the caveats discussed previously regarding the reality of kinds), as a soluble salt is different in kind from an insoluble salt. Consequently, natural capacity inheres in a subject through its form, even though it may result from both matter and form.

A natural capacity, being a capacity to act, is a quality that makes possible certain actions. As such, all natural capacities are dispositional rather than occurrent (such a distinction is inapplicable to shape, which is static). An "occurrent quality" is really an action (which we will see in Part V is a relation) made possible by a quality, which is itself dispositional. Although qualities of natural capacity are dispositional, it is in the act of occurrence that they fully realize their being, for it is through such acts that they may bring about other accidents that depend on them. For example, a flammable material has the capacity to be ignited, and when it is actually ignited it can manifest characteristic qualities of heat and color. Although the material is no less flammable when it is not ignited, it cannot manifest dependent qualities unless the act of ignition occurs.

Some have sought to find a basis for the dispositional/occurrent distinction in modal or probabilistic logic, but in fact modal logic expresses the result of the existence of real disposition, and cannot serve as its basis. In other words, it would be backwards to say that something has the real disposition of flammability because it is possible for it to ignite. Rather, it is possible for it to ignite because it has the disposition. The outcomes described by modal logic are the result of the disposition, not its foundation.

Affective quality deals with a substance's determination with regard to passion - that is, how it is acted upon. The most common examples of affective qualities are perceptibles, but these have come into disrepute since the advent of Locke's philosophical psychology. Modern thinkers no longer regard the quale of "redness" perceived in our mind's eye as inherent in the perceived rose, but consider it an artifact of the mind. In support of this view, they invoke not only mechanistic physics, but consider that the same object might not generate the same perceptible in different minds. Even if the true locus of sensory qualia is the mind rather than external objects, the existence of perceptibles is in no way mitigated. If sensory qualia are indeed artifacts of the mind, then the mind's sensitive faculty is their subject, and the light from the rose is a stimulus indirectly acting upon the mind, producing the quale of red that we see. This account of perceptibles as produced by the external object's act upon the mind is an inversion of the classical account, where the mind's act of perception acts upon the external object. In either case, the perceptibles are truly affective, the only distinction being that in the classical account their subject is the external object, while in the modern account their subject is the mind.

Affective qualities might be the most quintessentially "qualitative" properties, in our modern sense of the word, as they are almost completely removed from the concept of quantity, admitting only of intensive magnitude. Each quale differentiates a kind, and it clearly inheres in form rather than matter, as it has nothing to do with quantity, though it may admit of intensive magnitude. We may recognize colors as having "more" or "less" brightness, but how could we conceivably reduce the qualitative aspects of "red" or "blue" to mere quantity? Modern physics misses the mark by explaining color in terms of light frequency, for this ignores the qualitative aspects of color, as blue is clearly not a more intense red. A neurophysiological account of the generation of qualia might reduce some of these to compositions of more basic qualia. For example, the "secondary colors" are composites of primary colors, and the sensation of burning is a composition of the sensations of warmth and the thermal pain associated with freezing. There is nothing incoherent about reducing secondary qualities to primary qualities, but it is another matter altogether to reduce these to pure quantity.

Despite the eminently qualitative nature of affective qualities, many modern philosophers have followed Locke in attempting to regard affective qualities as secondary qualities, derivative of quantifiable mechanical properties in the perceived object. While there might be no absurdity in regarding affective qualities as secondary qualities, it is hardly intelligible that the diversity of qualia should be reducible to purely quantitative derivations, as the distinction among qualia is in kind, not in quantity. This illogical reduction is unnecessary, at any rate, in the case of perceptibles, as we can regard these as affective qualities of the mind stimulated by an external object, as discussed above.

More broadly, affective qualities may include non-perceptibles, as long as they determine the mode in which an object is acted upon. Properties such as classical magnetism and gravity may be considered as both natural capacities and affective qualities, since they determine both how a body acts and how a body is acted upon. This broader view of affective qualities contrasts with Aristotle, who restricted them to sensibles and other perceptibles related to "affections of the soul." Nonetheless, there is no a priori obstacle to postulating non-perceptible affective qualities, and indeed this broader definition comports nicely with the Thomistic account of the four kinds of qualities.

An affective quality is dispositional, in that it determines the mode by which a substance may receive an act or be acted upon. Like a natural capacity, it requires a certain action in order to be manifested occurrently. A color is perceptible even if no one actually perceives it, yet its dispositional potential is fully realized only when it is actually perceived. Affective qualities, however, differ from natural capacities in their relation to the act of occurrence, for affective qualities do not make possible the act that they passively receive. They always depend on some extrinsic factor in order be realized occurrently.

Lastly, we consider states and conditions (or habits and dispositions, as they were known to Scholastics), which are qualities determining a subject's accidental being with regard to its nature, according to St. Thomas Aquinas' definition. In order to discuss such qualities, it is necessary to make definitions and hypotheses about nature that would need to be later justified in a treatise on natural philosophy if we are to uphold these qualities as metaphysical realities rather than mere a priori possibilities.

Nature is a source or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not in virtue of concomitant attributes. (Physics I, 8)

In Aristotle's natural philosophy, a "nature" is an inherent principle of motion or change. It is essentially teleological, since any such principle is necessarily directed toward an end, or it would not be a motive principle at all. Thus there is necessarily teleology in the class of states and conditions, and a sense of metaphysical good and evil (distinct from the moral sense), whereby a disposition or condition is "good" to the extent that it is in accordance with the subject's nature. Since conditions (dispositions), like natural capacities and affections, may change with respect to time, Aristotle additionally identifies a state (habit) as a condition that is held for an extended period of time.

According to Aristotle, "natures" are possessed only by simple bodies, living beings, and intellectual souls, each of which contain an internal principle of motion. As this view is considerably broader than most modern anti-essentialist accounts of nature, we will adopt this hypothesis as embracing the widest range of a priori possible natures and corresponding states and conditions. We will briefly examine the basis for regarding each of these three classes as having "natures," and their implications regarding states and conditions.

Aristotle assumed that all inorganic matter was governed in its motion by the "simple bodies" or elements that composed everything. The "end" of each element was its natural place, with earth gravitating toward the center of the universe, and fire rising toward the heavens. Modern physics would significantly reform this view, but some basic principles remain the same. Instead of four elements, we identify fundamental particles, which gravitate toward the center of the earth only locally, not globally. More generally, particles do not move toward a natural "place," but instead follow an inertial contour along spacetime, as affected by gravitation. With inertial mechanics, the telos of a simple body is not a fixed end-point, but is defined by a direction along a contour. In both ancient and modern systems, the intrinsic motion of bodies is blind, unguided by any form of perception. A simple body deviates from its natural path only by being acted upon by an external force. We might consider that molecules also have principles of motion, since they are not mere composites of fundamental particles, but in the act of bonding they reconfigure the very nature of the bound electrons, effectively creating a new essence or nature. If this account is correct, the principle of motion for molecules would be the same as that for simple bodies.

Aristotle only considered the nature of simple bodies with regard to spatial motion, since he supposed that the simplest bodies were merely quantities of homogeneous substance, defined only by their spatial extension. The nature of such bodies could not be the principle of any change save local motion, as only spatial extension was essential to simple bodies. In actuality, we recognize that fundamental particles have other dynamical principles such as angular momentum, charge, and spin, so there multiple aspects of a particle's nature, expressed as several distinct principles of motion or change. These natural principles are not limited to changes in space, but can include any self-induced change in properties, as expressed by the particle's time-dependent wavefunction. These aspects of a fundamental particle's nature are more than mere natural capacities, to the extent that they are principles of change arising from essential characteristics of the particle.

We do not know how much of the "nature" of fundamental particles is really just a natural capacity contingent upon some deeper, hidden attributes. It may very well be that even fundamental particles are reducible to simple bodies, each of which may be considered in its dynamic degrees of freedom, be they spatial or some other dimension. The principle of motion or change for each simple body would be considered with respect to that primary medium of its being, its degrees of freedom.

The other two proposed subjects of "natures," living beings, and intellectual souls, are more controversial, owing to the dominant tendency of materialist reductionism in modern biology. The idea that biology is reducible to the physics of simple bodies is a gross assumption, not at all merited by our crude understanding of ontogeny and practically non-existent knowledge of abiogenesis. The supposition that life may "emerge" as a stochastic phenomenon, analogous to the "emergent properties" of non-linear dynamics, is equally gratuitous, and misunderstands chaos theory as generating ontologically distinct categories. These cultural myths require more extensive treatment in separate essays; for now, we shall content ourselves with understanding what it would mean for living things and intellectual souls to have natures.

At a glance, living things appear to have intrinsic principles of motion that are not obviously derivable from the natures of simple bodies. If living things truly have a characteristic principle of motion or change, we may see this in growth and reproduction, which is common to all organisms. Growth does not just mean increase in size via nutrition, but includes ontogeny or biological development. In the case of most individual organisms, the ontogenic principle has a definite end-point in the adult form, though there may be accidental deviations from this form, as in birth defects or variations in development caused by chemical influences. Despite this degree of variability in individual development, its telos or end more closely resembles a definite form than an indefinite progress in some direction. Thus it is meaningful to speak of developmental "defects" for those organisms that fail to develop the proper adult form (ignoring accidental attributes). Even materialist scientists who deny teleology in nature use this language all the time, tacitly admitting a teleological aspect to ontogeny.

Discussions of evolutionary theory, to this day, often conflate ontogeny with phylogeny, but if we avoid this error, we will find that even a non-teleological and continuous descent of species from one another would not abolish "essentialism" in the individual. Taking neo-Darwinian theory as a supposition, we would have to admit that there exists a phylogenetic continuum from say, Eohippus to Equus, or even from a bacterium to Equus, but this does not mean that a modern horse does not have an ontogenic nature. Given its zygote, it has a very real tendency to develop into Equus rather than Eohippus; if it did otherwise, we would rightly regard it as a highly defective horse. Phylogeny comes into play only in the reproductive act, by which the offspring zygote may have a slightly different ontogenic nature than that of its parents, but it still has its own nature.

Reproduction may also be posited as a teleological process expressing the nature of an organism. Here the telos may not be as sharply defined as it is in ontogeny, for there is no expectation that the offspring should exactly resemble the parent. Moreover, if neo-Darwinism is correct, there would seem to be no real distinction between essential and non-essential traits of an organism, so there can be no clear idea of what would constitute a successful replication of the parents. Reproduction is perhaps a misnomer, as a successful procreative act might not replicate the nature of the parent, but indeed it may be advantageous for the offspring to deviate from that nature. "Advantage" or "fitness" in biology means increasing the likelihood of survival long enough so the offspring in turn may procreate. While we can certainly see a telos in surviving long enough to mate as often as possible (though this is not a sharply defined end-point), it is not at all clear what would constitute a successful reproduction, without reference to the eventual success of the offspring and their descendants. True success in procreation, if it does not mean passing on an essential nature (fixed within some range of accidental variability), cannot be determined until long after the fact, if indeed ever. Most biologists, nonetheless, would consider a procreative act successful if it produces viable offspring that are at least potentially capable of mating with existing organisms (or reproducing asexually). The telos of reproduction, then, is producing viable offspring, even if the offspring differs from the parent in nature.

If neo-Darwinism is incorrect, and some type of saltational phylogenetic transition is necessary for all but the lowest orders of taxonomy, then essentialism would be preserved in reproductive acts among individuals in such a species (or genus, or whichever taxonomic group was phylogenetically semi-isolated). The telos of reproduction could then be understood to include reproducing the essential traits (which define the species or genus) of the parents in the offspring, while permitting variability in the accidental traits. On our time scale, at any rate, the essentialist model holds quite nicely, since neo-Darwinian phylogenetic changes are imperceptibly slow if they occur at all. Thus, in the span of human history, we can always expect horses to beget horses, and the same for other species.

We cannot give an extensive examination of materialist biology here, but it suffices to observe that the natural principles of life, growth and reproduction have no analogue in the natural principles of simple bodies. Indeed, the teleology of organisms is fundamentally different from that of simple bodies. Whereas simple bodies only have "tendencies" to move or be at rest in particular directions, carried only by their inertia or other intrinsic properties, living organisms each grow toward a definite form, and then either propagate that form, or at least propagate enough traits for the offspring potentially to grow to some other definite form and generate its own offspring. This difference in teleology alone should give us pause before supposing that biology might be reducible to physics. Indeed, metaphysicians from antiquity through the early modern period have seen the teleology of nature as an insurmountable proof of the irreducibility of biology. Modern evolutionary theory does not abolish ontogenic teleology, and it only modifies reproductive teleology rather than nullify it. The supposition that these teleologies can somehow "emerge" from stochastic processes deserves critical examination, which we will pursue in another essay.

Given that the viable adult form of the organism is its telos, it becomes meaningful to speak of whether an organism is healthy or sick, fit or injured, sane or insane, and other normative judgments. All these assessments of the state or condition of an organism define good or bad with respect to the viably functioning adult form. We may speak of such states or conditions in terms of whether it increases or decreases the organism's ability to grow, survive, and propagate. Aristotle defines the metaphysical good as "dispositions of the perfect to the best, and by perfect I mean that which is disposed in accordance with its nature." This sort of teleology, which exists even in plants and primitive animals, does not suppose mental intentionality in nature, but simply defines the good as those states or conditions that help manifest an organism's telos, regardless of whether these conditions are achieved by mental intention.

In many animals, there are apparently varying degrees of behavioral intentionality. The exercise of these intentional faculties, be they instinctive or cognitive, provides another medium for states or conditions that may influence the manifestation of an organism's nature. We can speak of a "mad dog" as one whose mental state impedes its ability to function according to its ontogenic form. We might even equivocally speak of animals as being "wise" or "unwise" depending on whether their intentional behaviors favor their biological success. This would only be equivocal usage, since when we call a human "wise" we expect a conceptual understanding of what he is doing. More commonly, we may speak of animal behavior as "natural" or "unnatural," as animals in captivity lose their habits from the wild, so that they would be less biologically fit if they returned there. Yet we should not speak of animal behaviors as metaphysically good or bad simply and absolutely, but we must consider the environment in which the animal finds itself. Behaviors that are advantageous in one environment may be disadvantageous in another, so an animal that behaves "unnaturally" from an ontogenic perspective may actually be favoring its likelihood of reproducing, and is therefore behaving naturally from a reproductive perspective. Natural principles coming in conflict with each other in a single subject is not only possible, but is in fact a common occurrence. Many animals have instinctive behaviors that do not optimize their reproductive outcomes, and humans are especially familiar with how the various faculties of the mind may conflict in their goals.

This brings us to the last subject of states and conditions, which is the intellectual soul. In humans, the subject of intellection is also the subject of lower mental faculties shared by various animals, a confusion that has led many to suppose that intelligence might be nothing more than a highly efficient form of animal cognition. While so-called "evolutionary psychologists" (formerly called sociobiologists) often use the term "intelligence" to refer to cognition, philosophers have historically understood intelligence to mean something quite different. The intellect is the faculty of understanding or regarding something as true or false. This is a perfectly abstract faculty, irreducible to a mere processing of signals. Indeed, what goes under the name of "information theory" is really "signal theory," as modern computer scientists clumsily conflate ideas with their arbitrary representations, erroneously regarding the latter as "information." There is nothing complex about the intellect as such; it is in fact incredibly simple. All the complexity of human thought is to be found in the cognitive processes in the brain, but an inanimate process cannot be the subject of a judgment of truth or falsehood. We will treat the notion of the mind as an epiphenomenon of matter at length in another work. Here we will content ourselves with expressing what is meant by an intellectual soul.

An intellectual soul has both intellect and will, not to be confused with cognition and appetite in animals. The intellect is distinct from cognition in that it does not merely process the phantasms of the mind, but rather understands the idea represented by a phantasm, effectively uniting the idea with itself. The most complicated cognitive algorithms only relate means to ends, but there is no understanding involved. Enamored with the magic of silicon, many believe that artificial replication of human intelligence is possible in principle. Of course, if this were so, it would also be possible in principle to create such an artificial intelligence by a system of pipes with pressure valves (serving as logic gates) or billions of people transmitting signals via flash cards to each other, creating a collective intelligence. The widespread failure, or studied refusal, to recognize the incoherence of this position comes in part from a failure to examine what intelligence is qualitatively, instead of naively assuming that mathematical representations provide complete depictions of reality. We have noted earlier that mathematical relations, when applied to reality, actually presume the existence of qualities or other predications, so it is not cogent to invoke the mathematics of science as a proof that everything is quantitative. The fallacy of a purely quantitative ontology is most evident in discussions of artificial intelligence or emergent intelligence from collective processes. Not only do practitioners of this science not have the answers, but they fail to grasp the question.

Volition or will in an intellectual soul differs from animal appetite in that it acts posterior to an intellect that understands, rather than in response to the sensitive faculties alone. Humans, of course, possess lower appetites in addition to will, and it is not always clear to what extent we are influenced by them in each act. This confusion of faculties has lent plausibility to the supposition that will is nothing more than another appetite. Yet there are clearly cases, as in abstract reasoning, where we will on the basis of abstract ideas, that would be unintelligible to apply to inanimate matter or any complex system of signal processing. In modern theories of the mind, human volition is not distinguished from animal appetition because of an inability to understand these faculties except in terms of inputs and outputs. Since both human volition and animal appetition seem to be non-deterministic or "random," they are treated indistinguishably. This account of free will as randomness is incoherent, as it does not suffice to be random in order to be free. We do not regard electrons as free-willed, though they exhibit non-deterministic behavior. This simplistic input-output explanation of mind fails to grasp anything beyond determinism and randomness, and leads to the absurd conclusion that to achieve free will it is only necessary to introduce random variation in computer algorithms. This electronic alchemy suffers from a failure to understand its goal, supposing intelligence to be just a set of algorithms and random variations.

The disparity between the intellectual soul and its evolutionary counterfeits is most evident when we consider the telos of the intellectual soul as it actually exists. For the intellect, the telos is Truth, for it only accepts what it regards as true, and rejects (or accepts the negation of) that which it regards as false. It can do nothing else, for to understand something is to regard it as true. The will, when acting according to a strictly intellectual nature, chooses in accordance with what is presented to it as Truth. Thus the Good that the will pursues must coincide with Truth. Our apprehension of the Good includes moral ideals of how a person ought to behave, embodied in virtues such as Justice, Prudence, Temperance, and Fortitude. We also apprehend certain rights (droits, derechos, or directives) that tell us what we ought to do or ought to recognize in others.

Those who deny that the intellectual soul is ontologically distinct from brute animals must also deny that Truth and the Good have any existence outside of material contingency. The materialist must conceive of truth only as an animal apprehends practical realities. Indeed, many philosophers of science have asserted that science is not concerned with truth, but only with practical realities that yield fruitful results. Many scientists, no doubt, would beg to differ with this interpretation of their profession, and indeed human experience universally affirms that people care deeply about Truth, and are often willing to die for their ideals if necessary, which hardly seems apt if they are concerned with practical results. Philosophers, mathematicians, and theologians spend years trying to understand things that may never have any practical implications. Faced with a tidal wave of evidence against them, reductionist evolutionary psychologists must explain away these realities as secretly motivated by some adaptive advantage, or else they are a defect that evolution will eventually remove. Dawkins, Dennett and others have built a cottage industry on these "just-so" stories.

The problem for reductionism is even more acute when faced with the anthropologically universal love of moral ideals, even when the pursuit of these principles leads to impractical results. Evolutionary psychologists must either reduce all morality to closet utilitarianism or disparage it as a defect or a useful delusion to keep the masses happy. Once again, wild speculation on the behavior of australopithecines is supposed to rationalize away the inconvenient reality of impractical ethics. Of course, if there is no ideal Good (or at least an ideal tendency, if the Good is not a fixed end-point), then our idealist ethics is chasing a chimera. This creates a dilemma for reductionists, at least those who are not nihilists, for if there is no teleological Good, talk of rights and morals becomes nonsense, except in a utilitarian sense. Many materialists have tried to reduce morality to utilitarianism, but in practice even materialists reject utilitarianism, valuing people based on an intuitive sense of their worth, practicing honesty even when it is impractical to do so, and rejecting utility in favor of idealism in countless other ways. Rather than regard all that we hold dear as a lie, most materialists simply accept existing morality uncritically, eschewing only those principles that are distasteful to them, while regarding the basic virtues and rights of man as "self-evident" or "rational" truths, an implicitly Platonic view. For those of us who easily recognize the incoherence of Platonic materialism, yet do not regard moral ideals as useful fictions, we must hold that the Good really does exist.

Aristotle conceived of the telos of human will as being man's own happiness or felicity, as though the pursuit of the Good was equivalent to the pursuit of happiness, or possibly even subservient to it. While many people might subvert the pursuit of the Good to the pursuit of happiness or even of base pleasure, giving credence to a sort of utilitarian reductionism, for others the pursuit of happiness is subordinated to the pursuit of the Good, which is loved for its own sake. We see this attitude in Stoicism and Christianity, while the former attitude is contained in Epicureanism and modern utilitarianism. Whichever is the correct order of priority depends on congruence with Truth, for we may believe that Truth and the Good are united, not merely because we assume the will acts posterior to the intellect (an assertion requiring demonstration), but because it would be absurd to say something is good without also thinking it in accordance with truth.

With intellectual souls comes the knowledge of good and evil, described in Genesis as a divine power, the use of which is fraught with danger when placed in mortal hands. The telos of intellectual souls is the True and the Good, both of which have been conceived as aspects of Divinity. If our natural tendencies toward truth and goodness indeed lead toward an Absolute end, that end would certainly be God. Thus all intellectual and moral activity tends toward God, and the man who would reject God yet continue to pursue truth and goodness to a limited degree is in contradiction with his natural end, for he will only pursue goodness and truth up until a certain point, beyond which he will go no further. He makes an intermediate end his ultimate end, preferring the lesser good over the greater and thus acting contrary to his nature. We can see the intellectual aspect of this self-imposed limitation when scientists disregard metaphysics and theology as worthless, concerning themselves only with the corporeal world. They impose arbitrary limits to their inquiries and to their zeal for truth. In the moral sphere, a man might love creatures without loving the Creator who sustains their being, so he limits his love to contingencies. Only when man has no limits on his zeal for the True and the Good can he even have the possibility, however fantastic, of realizing his natural end. Even should he never attain union with God, he must ever yearn for that union if he is truly to be an intellectual or spiritual soul.

Atheism, unbelief, and even spiritual sloth effectively truncate humanity, making a man less than what his nature would direct him to be, as he pursues lesser goods instead of the Absolute Good for which his soul was made. The paradox of man is that his natural end requires a supernatural God, and without God man is less than what his nature would make him, so he is conflicted. Man without God, either through ignorance or antipathy, tries to satisfy himself with lesser goods while his soul urges him to still greater things. If he were to curb this urge and find contentment in lesser pleasures ("the life fit for cattle," as Aristotle disparaged it), he might avoid misery, but only at the expense of never fully being a man. The fullness of humanity, or of any intellectual soul, is to be realized only in God; the one who denies this is doomed to contradiction with his nature, to be resolved either by misery or by quiet acquiescence in a semi-bestial state. As there are many more Epicureans than nihilists, most unbelievers have chosen the semi-bestial state, ironically adding credibility to their view that man was never anything more than a sophisticated brute.

Habits and dispositions characteristic of an intellectual soul are defined as "good" and "bad" with regard to the soul's ends of Truth and the Good. In this regard, we may speak of moral habits, such as virtues and vices, or intellectual habits, such as various types of knowledge and ignorance.

Our discussion of habits and dispositions has required some speculation about natural philosophy and philosophical psychology. We do not presume to have solved these issues with ontology, but rather we are constructing our ontology in the broadest possible way to encompass all of the a priori possibilities of inanimate, animate, and intellectual natures.

Continue to Part V


© 2008 Daniel J. Castellano. All rights reserved. http://www.arcaneknowledge.org

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