Part V: Classical and Modern Pseudo-Categories

Thus far we have only discussed substance, quantity, space, time, relation, and quality, for these alone span the entire ontology of intelligible reality. Naturally, we can not prove that our ontology is absolutely complete, since there may be categories of reality of which the human mind has not conceived nor the senses apprehended, but we can only discuss that which is intelligible. Nonetheless, we will briefly look at other ontological categories proposed from antiquity to the present day, and show how these are either reducible to the six categories named above, or not categories of ontological entities at all.

Aristotle posited nine categories of accident, yet he only discussed five of these (quantity, place, time, relation, and quality) in any detail, while the remaining four - position, state, action and affection (or passion) - were mentioned only in passing as he turned instead to a discussion of contraries, degrees, and other analytical aspects of categorical entities. We will show that these four categories are all reducible to quality or relation. Thus we depart from the traditional enumeration of nine categories of accident, a number that was given a mystical significance by later Pythagoreans who erroneously ascribed the theory to Pythagoras, though the earliest record of this list certainly comes from Aristotle.

Medieval philosophers were not concerned with postulating new ontological categories, but instead employed metaphysical concepts to analyze entities in these categories. These concepts include matter and form, potentiality and act, essence and existence. None of these concepts constitute new ontological categories, but analyze essents in terms of different aspects or modes of being, without necessarily modifying their essences. Scholastic theology did not require new categories either, since spiritual beings were conceived as being of profound ontological simplicity. Angelic beings are form without matter, and God's essence is His existence. Theological analysis required some arcane metaphysical concepts, but not an extended ontology.

In the early modern era, the dominant tendency among mechanists was to reduce the number of categories rather than add to their number. Nonetheless, the few categories they did propose were often pseudo-categories, such as mind, matter, motion, and rest. We will need to account for these with respect to classical ontology.

In the modern era, Kantian and analytic philosophers have proposed their own categorical systems, but these do not even purport to be ontological. Instead, they are psychological, semantic, or syntactic categories. In most cases, they are valid categories, but they represent an entirely different endeavor from what we are establishing with classical ontology. Our answer to the Kantians and the analytic philosophers must come in the realm of epistemology and metaphysics, where we vigorously assert metaphysical realism against the errors of conceptualism and "scientism" (restricting objective reality to physical objects).

There are instances in modern physics where the assertion of a new ontological category might seem to be in order. We shall examine the theories of the four fundamental forces, as well as the ontological possibilities of relativity, quantum mechanics, and string theory, as well as oddities such as antimatter, tachyons, and singularities. More generally, we may look at the relationship between empirically observed objects and physical "laws," as well as the notion of observation.

A defining characteristic of modern science is its assumption of the non-existence of teleology in nature. This is a gratuitous assumption, as modern physical science only examines things with respect to efficient cause, so it is incompetent to judge whether there might also be a formal and final cause. In Aristotelianism, natural efficient causes are identical to the formal and final cause, and this identity accounts for the continuity of past, present and future being. Without this identity, modern science has no rational basis for causality, and is vulnerable to Hume's critique that supposed physical causes are really nothing more than statistical correlations of successive events. Not only does this reduce theoretical physics to mere description rather than explanation, but it abolishes any possible rationalist basis for modern thought, as there is no demonstrable "reason" for anything. Russell and the analytic school took up the Humean program of abolishing causality from science, though most scientists rightly recoil from such a notion, and indeed believe they can account for why things happen, in the sense of efficient causation. Nonetheless, modern theories of causality bizarrely try to eliminate agency, and instead regard "events" as causing other events, as though events were substances. The true ontological status of events therefore needs to be addressed.

Some modern realist philosophers have persuasively suggested that states of affairs are ontologically fundamental, eliminating the need for substance-accident ontology. As we discussed in Part II, such states of affairs are either not simple or they are merely tropes by another name.

Lastly, the distinction between abstract and concrete may be mistaken as delineating ontological categories, but in fact this is a conflation of several classical ontological and metaphysical distinctions, as we discussed in Part II. At its core, abstraction is a mental operation that does not unequivocally distinguish ontological categories.

There may be other postulated ontological categories that we have omitted, but discussion of the pseudo-categories we have named should suffice to give the reader a sense of how to apply similar critical analysis to other proposed categories. A fundamental limitation of category theory is the impossibility of proving that there cannot be other categories of accident, even if the broad applicability of classical ontology gives us a high degree of confidence that it is in fact complete. Without losing sight of this limitation, we may explore how our six-category ontology applies to each of the putative categories mentioned.

Action and Motion

Action is really a kind of relation. Like relations in general, it may inhere in a particular subject or be a meta-accident of multiple subjects. We distinguish these two types of action grammatically with intransitive and transitive verbs. When we say, "The balloon is rising," we consider the action of "rising" as pertaining to the balloon. When we say, "The gardener is cutting the hedges," the act of "cutting" relates the gardener and the hedges, though it may not necessarily inhere in one or the other. Commonly, we do think of the "cutting" in relation to the gardener in an active sense, meaning the gardener is somehow the source of the action, while the hedges are related to the "cutting" passively, as being the recipient or target of the action. Actions are a particular class of relations, and highly important to any system of metaphysics, even if they are not the most ontologically generic category. As relations, actions are predicable of a subject only in relation to another subject, as is clearly the case with transitive actions (i.e., actions properly denoted by transitive verbs). Even intransitive actions are predicable only in relation to another subject, or more precisely, the same subject considered at different times. The balloon can only be rising if its position at a later time is higher than its position at an earlier instant. In fact, all actions, transitive or intransitive, require time as a medium, so we might say that actions are a time-dependent class of relations.

Towards the end of the Categories, Aristotle identifies six kinds of change. Whether he intended this to constitute his discussion of action or not, the six kinds do in fact define all possible types of time-dependent relations of accidents and substance. The six kinds are: generation, destruction, increase, diminution, alteration, and local motion.

Generation and destruction are changes with respect to substance, as substances come into or out of existence (either absolutely or by transforming into another substance) with respect to time. Increase and diminution are changes in quantity (of substance or accident) with respect to time. Alteration is a change in quality (from one quality to another, not just a change in the magnitude of a quality), and local motion is a change in spatial position with respect to time. All the categories are covered, so this account of action is complete at the highest ontological level, though naturally there is much to discuss at more specific levels. Action encompasses all time-dependent relations among substance and accidents. Those actions that pertain to changes in accidents - increase, diminution, alteration, and local motion - were classically called "motion" in a generic sense.

Although local motion, like other types of action, must be a relation, late Scholastic and early modern natural philosophers often regarded the motions of bodies, including dynamical quantities such as velocity and acceleration, as qualities. This erroneous identification of motion as quality arose from a mathematical analogy between the magnitude of qualities and the magnitude of motion. Ironically, this error was held both by Galileo and his late Scholastic adversaries, and it seems to have tainted later conceptions of motion, though Einstein's theory should make it again obvious that motion is purely relational. We will show this in ontological terms.

Local motion is a relation between the positions of a substance at different times. We do not need to resolve whether or not a moving substance continues to be the same substance at a later time, for even if the substance persists in time, motion would still be predicated of at least two subjects, namely the initial and final positions of the substance. The magnitude of motion may be expressed in terms of some distance Δx traversed during some time. The motion itself is not this numeric magnitude (distance or displacement), but the relation between the positions of a substance at different times, which may vary by direction as well as magnitude. A vector, consisting of magnitude and direction, provides a complete account of motion when it is predicated of some substance, space, and time. Considering a substance with position r₁ at time t₁ and r₂ at time t₂, we may express the motion M(r₁, r₂) = r₂ - r₁. By convention, vectors are indicated in boldface. We see from this formula that the motion M may also be represented as a vector.

The velocity can be obtained for an interval of uniform motion by dividing the motion's magnitude by the magnitude of the time interval, while the direction of the motion is that of the velocity which is also a vector v = M(r₁, r₂) / (t₂ - t₁) = (r₂ - r₁) / (t₂ - t₁). Velocity is also a relation, since it is just motion divided by the magnitude of the time interval. Recall that treating time as though it were nothing more than extensive magnitude is at best a highly incomplete account of time. With modern calculus, we can take the limit of the velocity as the time interval t₂ - t₁ approaches zero, giving us an instantaneous velocity. This instantaneous velocity can easily seem like a quality that varies in intensity, as its relational aspect appears to collapse as the space and time intervals approach zero. It may be mathematically convenient to treat velocity as a continually existing quality that varies in magnitude, but in fact instantaneous velocity is predicated of successive instances of motion, albeit infinitely small, for if the time or space interval should become identically zero, there could be no motion, hence no velocity. It would be absurd that velocity should be a true quality, since it is merely a derivative of motion, which is a relation. Nonetheless, the convenience of regarding it as a quality proved irresistible to the late Scholastic and early modern natural philosophers, who were increasingly concerned more with mathematics than ontology.

The conflation of motion with quality was made possible by the development of new approaches to determining the magnitude of qualities. In the late Middle Ages, variation in a quality's degree was understood as a subject participating to a greater or lesser degree in an invariant quality or form, rather than the quality itself varying. This interpretation was true to Aristotle's thought, and indeed consistent with common sense notions of degrees of a quality, which we may regard as similar in kind though varying in intensity. Scotus understood that the idea that a quality may vary in intensity makes possible a sort of magnitude for qualities, which those of his school dubbed "intension." According to Scotus, quality could be increased by the addition of real and distinct similar parts to an existing quality, joining to constitute some definite intensity. This figurative model treats quality as if it were quantity or extension, but Scotus understood that this was a different sort of quantity, what we would today call an intensive magnitude. Scotists would speak of "intension or remission of forms or qualities," where intension and remission meant an increase or decrease in the degree of participation in a quality. These concepts made possible a discussion of the mathematical aspects of qualitative change.

In the early fourteenth century, the Mertonian scholastics of England linked the intension and remission of forms analogically with motion. Motion was conceived as a succession of new positions, with each new position representing a new degree of the motion's intensity. The succession of positions was analogous to a succession of form of different intensities. This purely mathematical analogy, relating magnitude to magnitude, gradually came to take precedence over ontological distinction, as motion became regarded as a quality. This transformation came about as late Scholastic natural philosophers became concerned primarily with mathematical magnitudes, to the neglect of other aspects of ontology.

In this new view, velocity and acceleration as well as motion were regarded as qualities. The intensity of velocity increased with speed, and variations in velocity were variations in qualitative intensity. Some fruitful mathematical analysis arose from purely a priori consideration of motion, velocity, and acceleration, yielding the mean speed theorem and the uniform acceleration of falling bodies well before Galileo. However, since the geometric account of quality was considered only a mental fiction, these mathematical discoveries did not immediately yield a new physics. Accelerated motion was considered to have both extension and intension, being mathematically quantifiable yet not truly geometric. This ambivalent state of affairs might have been avoided if the Mertonians had never lost sight of the fact that motion and its derivatives are relations, not qualities, so we should not fear to describe their magnitudes as purely extensive.

While motion and its derivatives are relations, other dynamical properties might indeed be qualities. In the equation F = ma, acceleration is a relation, mass is likely a quality, and force is likely a relation. We can only justify these judgments about force and mass with an exploration of natural philosophy, but motion is understandable in terms of the simplest categories of ontology, so we can already know that it is a relation.

Affection, Position and State

Having shown that actions are relations, we may examine the remaining Aristotelian pseudo-categories of affection (or passion), position, and state. The first two are reducible to relations, while the last may refer either to qualities or relations.

Affection or passion is but the inverse relation of a transitive action. A thing is not perceptible unless it is possible for something to perceive it; more generally, a thing cannot be acted upon unless it is possible for something to act upon it. Since action, as we have shown, is a type of relation and not sui generis at the most fundamental ontological level, it is not necessary to postulate a separate ontological category for passion. The inverse relation of a relation is also a relation, so passion, like action, is a relation.

Aristotle strangely identifies "position" as a distinct ontological category, giving the examples of "lying" and "sitting." This is not position in the sense of spatial location, which would be the category of "place." Since Aristotle restricted relational accidents to what we call relatives (see Part IV), he was not able to classify "position" as a relation. Position denotes the relative disposition of substances or their parts. We have expounded a much broader concept of what constitutes a relational accident, allowing the inclusion of position as a relation. Position denotes the relative disposition of substances or their parts, so it may be considered a relation among the spatial locations of various substantial parts.

Aristotle posits a fundamental category of accident known as a "state" (not to be confused with the type of quality also known as habit), which refers to accidental disposition, with the examples "shod" and "armed" given. Whereas position gives the relative disposition of substantial parts, the state describes the qualitative disposition of an object, or its relation to certain qualities. Once more, since we have a broader concept of relation than Aristotle, we can include "state" in the category of relation, though sometimes the state is so simple that it is really just a qualitative predication. A state is therefore either a quality or a relation. Note that a state in the Aristotelian sense is a much narrower concept than the modern sense of a "physical state" or a "state of affairs," as it applies only to qualitative disposition.

The principal reason for the collapse of the last four Aristotelian categories is an expansion of the modern understanding of what constitutes a relation, which we no longer restrict to Aristotelian relatives. This broader concept of relation is subject to the criticism that it is a semantic or conceptual category rather than ontological, yet we have shown in Part IV that higher-order symmetric relations among accidents have as much claim to ontological reality as relatives. Indeed, Aristotle's use of these relations under separate categorical names attests to his regard for their reality; neo-Aristotelians differ from the Stygian only in regarding all relational accidents as a single category.

Potency and Act, Essence and Existence, Matter and Form

Medieval philosophy expounded the Aristotelian distinction between potency and act into a well-developed metaphysics, including the distinctions between essence and existence and between matter and form. Although these metaphysical principles are often spoken of as though they were distinct entities composing a whole, this grammatical necessity should not be mistaken for ontology. In fact, none of these distinctions create new ontological categories, since they do not distinguish distinct types of entities, but rather consider the same entity from different aspects of its being.

The concepts of act and potency, underlying the other metaphysical distinctions, denote the realization of being and the capacity for that realization. Any distinction between potency and act is a distinction in whether the being of something is considered as fully realized or only capable of realization. Such a distinction does not create two kinds of entities, but instead considers the same entity as having the fullness of being in some respect or lacking it. Being, we have noted, is not a genus or an entity, but denotes the existential status of an entity. An entity that is somehow actualized in its being does not have something superadded to itself, but it simply manifests itself more fully. The meaning of such a distinction becomes clearer when we consider specific metaphysical examples.

The distinction between potency and act in the order of existence yields the concepts of essence and existence. Essence is that which makes an entity what it is; it is the entity abstracted from its concrete manifestation. A coherently conceived essence has at least the a priori potential to exist, though there are naturally higher degrees of potentiality, such as metaphysical possibility or physical possibility. There is a world of difference between an entity capable of existence and an entity actually existing. To express this distinction, only the latter is said to have existence. Existence is not something superadded to an essence, but rather it is the full realization of that essence. In order to exist, an entity need do no more than manifest its essence. Existence is clearly not a category of entity, but refers to the full manifestation of an entity as opposed to it having only potential being. Essence and existence are mistaken for categories primarily because of the grammatical necessity of referring to them as though they are entities composing a being.

A similar grammatical confusion arises in the discussion of matter and form, which St. Thomas was forced to describe as a "compound," seeming to suggest they are parts of a whole. In fact, as Aquinas takes pains to express in several places, it is impossible for either matter or form alone to constitute the essence of any entity. This implies that matter and form are not two entities composing a single entity, so they are not an ontological division. We can see this from the definition of matter and form, which is potency and act in the order of essence. Corporeal creatures, St. Thomas argues, necessarily must be somehow extended or multiplied in order to admit of individuation. This capability is supported by a material principle that is the basis of extension. Individual corporeal substances also admit of substantial change, as they may change essential properties while still persisting. The material principle of substance is the stuff upon which a substantial change can act. The act of substantial change is completed by a formal principle, defined by the essence of whatever property or kind is to be imposed on the substance. Both material and formal principles are essential to the substance, but neither can constitute the essence of any entity. Individuated matter cannot conceivably exist unless it is determined by some form. The forms of incorporeal entities can be essences, but the form of a corporeal substance requires a material principle in order to be a coherent essence at all. Thus the matter and form of corporeal entities are not themselves entities constituting a whole. Rather, they are principles referring to the same corporeal essence, considered from the perspectives of its capacity for extensive actualization and the determinate realization of its extensive actualization.

Form as considered above ought not to be confused with Platonic forms or Ideas. A Platonic form is a universal, as discussed in Part I, while a Scholastic form is the projection of a universal onto a corporeal substance, determining its mode of material manifestation and acting as a constituent principle of the substance's essence, though it is not itself the essence of any entity.

The various classical theories of metaphysics - Platonism, Aristotelian realism, conceptualism, and nominalism - differ in their interpretation of ontological predication, but are all compatible with the same set of classical ontological categories. Plato differs from Aristotle in the nature of the predicative relationship between universals and individuals, particularly between objects and properties. Realist, conceptualists, and nominalists differ on whether universals really exist a posteriori. These disputes, though significant, do not require any additions to our list of ontological categories.

Considered generally, Aristotelian potency (dunamis) is the "becoming" or "coming-into-being" of a thing, while actuality (entelechia) is fully realized being, or "being-at-an-end." Potentiality and actuality transcend the categories, as they are in some way predicable of entities in every category. Potentiality and actuality are two different ways of looking at the being of an entity, but their distinction does not establish a multiplicity or complexity of entities.

Potentiality and actuality were applied by Aristotle and his commentators to explain the problem of change or motion. Some interpreters have held that Aristotelian motion or change is itself an actuality, while others have held, less plausibly, that it is the transition from potentiality to actuality. St. Thomas Aquinas perhaps touched upon the best solution when he identified motion as simultaneously considering an object with respect to potentiality and actuality. None of these interpretations abolish our conclusions that motion and other types of action are relations, and that potentiality and actuality are different views of the being of the same ontological entity.

Mind and Matter

In the Age of Reason, Descartes and Leibniz identified mind, matter, motion and rest among their ontological categories. We have already shown that motion, a type of action, is a relation. Rest is but the privation of motion, so it is not an entity at all. Further, relativistic mechanics makes it clear that there is no intrinsic quality of "being at rest" or "being in motion," but rather these states are knowable only in relation to the kinetic state of other objects. Being in a state of rest is indistinguishable from being in the same kinetic state as another object, so it is but another form of relation. The ontological status of mind and matter remain to be determined.

Matter was conceived by the Cartesians as corporeal objects, which are but substances in the classical sense. The mechanists' matter should not be confused with Scholastic materia, which is the metaphysical principle of individuation. For Descartes, matter was limited to spatial extension, as it was for Hobbes and practically every materialist philosopher before the age of modern particle physics. Today, subatomic physics renders incoherent the notion that spatially extensive matter is the fundamental stuff of existence. From the perspective of modern physics, Cartesian matter is certainly not ontologically fundamental, but is a complex substance with the accident of quantity or volume. Even abstracting from any theory of physics, Cartesian matter would be a type of substance, and therefore would not require the introduction of a new category.

For Descartes, mind was another type of substance, a res cogitans, which differed from matter in that it is intensive rather than extensive. Intension and extension constitute a complete categorization of quantity, but do not span all of ontological reality. The central error of the mechanists is to reduce all of reality to quantity. Quality and relation are neglected or regarded as secondary characteristics, while substance is apprehended only insofar as it manifests quantity. The division of reality into extensive substance and intensive substance, even if it were accepted, would not correspond to a division between mind and matter. Intension can be grounded in extra-mental reality, as evidenced by the fact that different minds can perceive the same qualities in the same object, while extension is by no means foreign to the mind, but is essential to most forms of conceptualization.

The ontological status of mind is a question for philosophical psychology, but we can see that in any case it is reducible to one or more of the classical categories. It may be a substance, as Descartes and other dualists have held, or a relation, if mind is but the act of thinking, since action is a relation, or a quality, if mind is but knowledge or some other property of the intelligent soul. Mental substance has held a special place in modern ontology since it is problematic for mechanism, as it has no spatial dimensions. Yet mind is not unique in this regard, for if we accept the ontological reality of quality and relation, there are countless entities besides mind that are not spatial. Lastly, modern physics appears to indicate that even corporeal matter, at its most fundamental level, is not spatially extensive, but we will leave that for a discussion of physics.

Conceptual and Semantic Categories

Since the Enlightenment, many philosophers have moved away from categorical realism, denying that our conceptual distinctions can ever be known to correspond to real distinctions. Such philosophers, beginning with Kant, have proposed categorization schemes that are not ontological, but purely conceptual or semantic (linguistic). The proponents of such systems do not purport to be advancing an alternate ontological scheme, but are pursuing an entirely different endeavor. Nevertheless, these purely conceptual or semantic categories may hold significance for ontologists, insofar as psychologistic systems claim to span all of reality as it is understood, even if their internal distinctions do not correspond to real distinctions.

Our advocacy of an ontological system does not compel us to deny the validity of conceptual, semantic, or even syntactic categories, though we must object to conceptualist claims that ontological categorization schemes are invalid, being merely conceptual distinctions posing as real distinctions. Conceptual, semantic and ontological systems of categorization are not mutually exclusive, but may span the same reality on different epistemic levels. Ontological categories are of things that are or may be; conceptual categories are of things as they are understood; semantic categories are of linguistic objects or meanings that express our understanding of things; lastly, syntactic categories are of symbols that we use to communicate these meanings.

It is only natural that our ontological distinctions should also be conceptual distinctions, since we can only discuss that which is intelligible to us. This does not prove that our ontological distinctions are not real, no more than the necessity of expressing concepts through language and symbols reduces conceptual distinctions to mere semantic or symbolic distinctions. There may be conceptual distinctions that do not correspond to ontology, or ontological categories for which we have no conceptual distinctions and cannot discuss, but neither of these facts proves that there cannot be some conceptual distinctions that truly correspond to ontological distinctions. In our discussion of ontological categories, we have always held potentially real entities as our object of study, defining all the a priori conceivable categories of entities that are not reducible to another category. Certainly, our ability to identify the categories correctly depends on whether our concepts reflect genuine understanding of modes of being. This is only possible if the concepts of our intellect can truly grasp possible realities.

Kant departed from the classical Western tradition on an epistemological level, denying that any a priori conceptual distinctions can give us knowledge of ontological reality, or the thing-in-itself (noumenon). Kant believed that other philosophers had erred in pursuing ontological and metaphysical discussions without first critically ascertaining the capabilities of the human intellect. His Critique of Pure Reason expounds an epistemology for a priori knowledge that informs his categorization scheme.

Kant's epistemology begins with the Aristotelian conviction that all human knowledge begins with experience (in the order of time). Following Aquinas, he acknowledges that real objects affect the senses, partly producing representations, and partly arousing our intellect to compare these representations. This does not mean that all our knowledge comes from experience. Indeed, we are capable of a priori knowledge that shows logical necessity or ontological universality, neither of which can be inferred from experience alone, as experience only deals with the contingent and the particular.

An important motivation for Kant was the distinction between analytic and synthetic judgments. The judgment "A is B" is analytic if B is contained in the concept A, so the judgment merely explicates A, while the judgment is synthetic if B is not contained in the concept of A, so the judgment amplifies A. As examples, "All bodies are extended," is analytic, since extension is contained in the concept of body, but "All bodies are heavy," is synthetic, since the notion of heaviness is not contained in the concept of body. Synthetic judgments alone really add to our knowledge and allow us to expand its sphere.

The critical question for Kant is: how are synthetic a priori judgments possible? To expand a posteriori knowledge, one could simply make more observations, but any appeals to experience in justifying a synthetic a priori judgment would mean it is not purely a priori. In mathematics, a priori synthetic judgments invoke clearly apprehended intuitions rather than experience. I would add that intuition is serving the role of experience, and we may regard synthetic a priori judgments as verified when corroborated by many independent intuitions. Kant does not take this route, and in fact he notes that the success of mathematics in generating a priori synthetic judgments is no cause for optimism about the intellect's general capability for such judgment, especially in metaphysics or ontology. He does regard natural science as containing a priori synthetic judgments, such as the law of conservation of matter and Newton's laws of motion. Nonetheless, Kant argues, philosophers have failed to explain how mathematics and the natural sciences can generate a priori synthetic judgments.

Metaphysical and ontological judgments are a practical necessity for even the simplest human intellectual life. Most people rely on common sense concepts for their ontological or metaphysical assumptions, and these are built into our language, but Kant is concerned with attaining certainty that our concepts truly represent the objects of metaphysics. For Kant, like most modern philosophers, ontology is assumed to be contained in metaphysics, as the latter is considered to be a strictly a priori science of things that actually exist. We, by contrast, follow the Scotist distinction that logic and ontology deal with a priori conceivable entities, while metaphysics deals with both a priori and a posteriori analysis of things that actually are, either necessarily or contingently. When discussing Kant, we must keep in mind that he considers ontology a subdiscipline of metaphysics.

Kant disparages what he calls "dogmatic" metaphysics as involving purely analytical judgments and adding no real knowledge beyond elucidating assumed concepts. This caricature of late Scholastic and Cartesian philosophy does not do justice to either school, both of which are rich in synthetic judgments. Indeed, even a truly dogmatic system, such as Christian theology, may allow for synthetic judgments, as two revealed doctrines may, in synthesis, yield some further truth that is not implicitly contained in either. This synthetic process has in fact been historically realized on numerous occasions. From the eternity of the Word (John 1:1) and the begetting of the Word from the Father came the Nicene synthesis that the Word must be of the "same substance" as the Father. Similarly, the Council of Chalcedon synthesized the divinity of the eternally begotten Word with Christ's status as the only Son of God in the baptismal creed, yielding the doctrine that the eternal Word and Christ the man are the same person. Although Kant mischaracterizes traditional metaphysical systems as being purely analytic, he is in any case not concerned with critiquing these systems directly. Instead, he directs his criticism toward how philosophers arrive at metaphysical concepts in the first place.

The critique of pure reason, Kant states, is a critique of the faculty of pure reason, not of systems. He examines the mind's capabilities with respect to attaining a priori knowledge. This critique is a necessary precursor to what he calls "transcendental" knowledge, which concerns the possible a priori modes by which we may attain our knowledge of objects. Thus Kant calls his category theory a "transcendental doctrine of elements," since he is actually concerned with our mode of knowledge.

Kant's epistemology begins with the Scholastic distinction between the sensitive and intellectual souls as sources of human knowledge. Sensibility deals with objects as given to us; this may include a priori representations, even intuitions. Understanding or intellect deals with objects as thought, yet as objects must be given before they can be thought, a doctrine of sensibility is a necessary first step in developing a science of elements or categories.

Following classical concepts of philosophical psychology, Kant identifies sensibility as the mind's capacity for receiving representations by being affected by objects. Intuition is a particular way objects may affect us, so that our apprehension of the object is in immediate relation to the object itself. Since objects are given through sensibility, and intuition comes from given objects, sensibility alone, says Kant, is the source of intuition. Intuitions are thought by the intellect, generating concepts, and all thought is ultimately related to intuitions, which come from sensibility.

Sensation is the effect of an object on our faculty of representation. Intuitions resulting from sensation are empirical, and the objects of such intuitions are appearances or phenomena. Kant discerns in phenomena distinct aspects that can be known a priori or a posteriori. He regards the "matter" of an appearance to be its raw sensation (sights, sounds, smells, etc.) while the arrangement of this sensation is the "form" of the appearance. This ordering or form lies a priori in the mind, and is distinct from sensation itself. Later philosophers might express this insight more strongly, arguing that sensation is "theory-laden." For present purposes, it suffices to observe that the form of an appearance is distinct from raw sensation. For example, "what we see" is not retinal images, which are inverted and doubled, nor mere patches of light, but the appearance of some physical shape with a distribution of color. The form of a phenomenon is an apparent object.

Kant regards a representation as "pure" if it contains no a posteriori sensation, but is solely the "form" of an appearance without "matter." Such "pure intuition" must be completely abstracted from any sensation, as well as from anything that the intellect thinks. Kant holds that there are only two such pure sensible intuitions: space and time.

Since Kant views things from the perspective of our ability to conceptualize objects, he regards space and time as indispensable pure intuitions, rather than as accidents specifying the determinate being of objects. We cannot conceive of any external reality without putting it in a space, so Kant regards space as a necessary condition for the possibility of appearances. Using this psychological approach inverts the ontological order, for though we cannot visualize something without putting it in a space, that is not a basis for making space ontologically fundamental. Kant grounds the form of phenomena in the human mind rather than in the external object, so for him the order of conceptualization is more relevant.

Kant's view of time, much like space, is a non-empirical concept, a pure intuition that provides a necessary form for all appearances. According to Kant, we cannot conceive of anything as actual without conceiving it in time. Time is the form of the inner sense, based on our consciousness of successive experiences, just as space is the form of our outer sense, enabling us to apprehend external objects co-existing. Time, not being limited to outer objects, is a necessary basis for any intuition whatsoever, as all appearances must be conceived in a time-relation.

Space and time are "empirical realities" only in the sense that they have "objective validity" in their description of the phenomena we perceive in our mind, but not in the sense of being something "out there" that really exists as a property of external objects. This is a peculiar way of speaking, since for most people "empirical" and "objective" refer to external reality. In ordinary speech, we would properly say that Kant denies the objective reality of space and time (either as substances or accidents), regarding them instead merely as the basis of our conceptualizations.

We may already see where Kant is headed: since our conceptualizations are grounded in intuitions that have no objective reality, none of our concepts are fully grounded in objective reality. Kant will phrase this in more positive-sounding language, speaking of "empirical" and "objectively valid" concepts when he does not mean to ascribe external reality to these. His emphasis on the primacy of space and time bears only a superficial resemblance to seventeenth-century mechanism, as he regards these as bearing conceptual phenomena rather than actual physical objects.

Proceeding from the assumption that space and time are merely conceptual constructs that tell us nothing of ontological reality, Kant divides concepts, rather than entities, into four kinds, all of which require time (and in some cases, space) as the form of the intuition in which they are conceived. The four categories are quantity, quality, relation, and modality. With respect to each of these four concepts, we may make judgments, which Kant subdivides as follows:

Quantity

• Unity
• Plurality
• Totality

Quality

• Reality
• Negation
• Limitation

Relation

• Inherence and Subsistence (substance and accident)
• Causality and Dependence (cause and effect)
• Community (reciprocity between agent and patient)

Modality

• Possibility - Impossibility
• Existence - Non-existence
• Necessity - Contingency

These are all classical Aristotelian concepts, but arranged differently because Kant is concerned only with conceptual classification, believing that none of these categories tell us anything about ontology. Nonetheless, we see some distinct analogy between his scheme and ours. Kant regards only quality, relation, and modality as describing the content of a judgment, while modality contributes nothing to the content, "but concerns only the value of the copula in relation to thought in general." For similar reasons, we do not regard the different kinds of modality as ontological categories, as they do not have ontological content, but only describe the mode in which entities have being. If we add Kant's three categories of conceptual content (quantity, quality, relation) to his types of conceptual form (space, time), we arrive at the same list of five accidents that we have expounded.

Kant does not really have a new category theory, so much as he re-interprets the meaning of classical categories, denying them ontological status. In Parts I and II, we addressed challenges to the ontological status of universals and particulars, substances and accidents, arguing that our concepts can in fact describe reality. Kant might agree that our list of categories spans the possible concepts of phenomena, but he denies that such categories can give us any knowledge of entities. It seems bizarre, however, that our natural intellect should have an unfortunate blind spot precisely where all of ontological reality lies, and that the sum of all conceivable phenomena should not include possible entities. It is one thing to say that our concepts of the real world may be mistaken or inaccurate in actuality, but another to deny that the concepts of real or potential entities can exist anywhere in the range of human thought. If substance, space, time, quantity, quality, and relation are not realities, then what is? Kant declares this to be unknowable, implying that entities, whatever they are, lie outside the range of all possible concepts of the human intellect. We, on the other hand, contend that a priori concepts of entities span a maximal set of potentially existing entities, and it is the work of metaphysics and physics to determine which of these actually exist. In our view, the human intellect is a link to reality, while in Kant's view the mind is strangely alienated from reality, and thoroughly unequipped to engage it directly.

The impact of Kant and later psychologistic philosophers has led to a greater emphasis on purely semantic or even syntactic categories in modern philosophy. As these categorical systems do not even purport to be ontological, they do not directly concern us. We should note only that our advocacy of an ontological system does not invalidate systems of conceptual, semantic, or syntactic categories, as long as they are regarded solely as such, and do not pretend to supplant an ontological system.

Edmund Husserl (1859-1938) understood that conceptual and ontological categorical systems were not mutually exclusive, and clearly distinguished categories of meanings from categories of objects, also known as formal and material categories, respectively. Being more optimistic than Kant regarding the faculty of human intellect, he held that the two sets of categories were correlated, and knowledge of one could yield knowledge of the other. For Husserl, both formal and material categories were a priori descriptions of possible entities, not necessarily things that actually exist. We have retained this distinction between ontology (a priori) and metaphysics (a posteriori) throughout our discussion, except when discussing Kant, who includes ontology in metaphysics. Husserl's account of material or ontological categories is given the novel term "descriptivist," though this view extends as far back as Scotus, and likely to Aristotle himself. Our account of the categories as a priori possibilities may also be considered descriptivist.

Entities of Modern Physics

In the late nineteenth and early twentieth centuries, Kantian psychologistic philosophy yielded ground to an empiricist realism inspired by the success of the second scientific revolution. The analytic school led by Russell and Whitehead best exemplified this restored confidence that theoretical concepts could be grounded in objective reality. The ability of mathematicians and physicists to make extremely accurate predictions about concrete reality using formal abstractions appeared to justify a realist interpretation of scientific theoretical concepts. Accordingly, the analytic philosophers attempted to reduce metaphysics to mathematical logic grounded in empiricist realism. This project was scuttled by Kurt Gödel's work proving the limitations of symbolic logic, forcing most of the analytic school to turn to a semantic or psychological approach to metaphysics, again grounded in empirical science. The failure of logicism does not disprove a realist interpretation of scientific theories, but it does show the folly of trying to reduce metaphysics to quantitative natural science, as the logical structure of mathematical theory does not suffice to account for all true statements. The error of scientism lead one to accept too readily concepts of theoretical physics as ontologically fundamental. As we shall see, the concepts of physics are reducible to the classical categories or not ontological at all.

Admittedly, the more exotic aspects of theoretical physics and mathematics seem like fruitful ground for new ontological categories unknown to classical philosophers. While there is certainly room for new metaphysical truths to be brought to light by these sciences, thus far they have not yielded knowledge of anything that might not be classified among the classical categories. The most esoteric inherent properties of natural substances are still qualities, while the most mathematically complicated relation is still a relation, regardless of the real accidents of which it is predicated. We will review several basic physical concepts in detail, justifying the reduction of each to a classical ontological category.

We have already shown how matter and motion are substance and relation, respectively, and that rest is but the privation of motion. Nonetheless, some twentieth century philosophers have proposed "inertia" as a category. Inertia is a strange term in physics, being a "property" whereby an object tends to remain in a state of Newtonian rest, which is uniform motion. Though we have said that rest itself is but a privation of motion and not an entity at all, Galilean relativity implies that any body at rest may also be regarded as in uniform linear motion with respect to something else. Thus an inertial state is relational, being equivalent to a state of uniform linear motion. Still, in physics, one speaks of inertia as if it were some underlying property of a substance that causes it to remain in an inertial state, as a sort of resistance to being moved. In this sense, inertia would be a quality, proportionate to its mass. A body's resistance to rotational motion, or "moment of inertia," is further modified by its geometric configuration. As inertia is determined entirely by the spatial distribution of mass, it would appear to be a secondary quality, or at best equivalent to mass.

Einstein's relativity generalizes inertial mechanics, using the Lorentz transformation and imposing an asymptotic speed limit, but despite the absolute value of the speed of light, an inertial state is no less relative than it was under the Newtonian system. A state of inertia still denotes the kinematic state of an object with respect to some frame of reference, so it is still relational. In Einstein's system, mass remains the physical basis for inertial tendency, so inertia in the sense of resistance to motion remains a quality.

The dependence of physical theories on "frames of reference" might lead one to speculate that these frames are ontologically fundamental or at least potentially real. The fact that reference frames can be arbitrarily conceived or constructed is not necessarily proof that they have no bearing on reality; on the contrary, they seem to be an indispensable part of practical physics. A frame of reference is a spatiotemporal coordinate system defined with respect to the kinematic state of a particular object, usually an inertial state. Thus the frame of reference is really a quantification of the relational state of some object. Since it can have no defined existence independent of the object's kinematic state that serves as a reference point, the frame of reference is necessarily a type of relation, whose predicates are the variables defining the kinematic state of the reference object.

Following the theme of relativity, we may revisit the concept of "space-time" discussed in Part IV. Space-time is an abstract mathematical construct that takes the extensive aspects of space and time and relates them to each other via the Minkowski pseudo-metric, which is further modified by the presence of gravitational fields "curving" or "warping" space-time. This "warping" is just a figure of speech, for space-time is not substantial; what is "warped" is the grid or metric we use to represent the quantitative relations among the magnitudes of spatial and temporal displacements. As seen previously, there is more to time than mere extension, so it is certainly ontologically distinct from space, even if the actualization of one form of displacement (spatial or temporal) depends on the other. The pseudo-metric of space-time quantitatively depicts this interdependence, but it is a careless error to use physical or metaphysical dependence as a basis for collapsing categories. Nothing is more common than for entities of different categories to be dependent on each other, as accidents depend on substance, or quantities on qualities and relations, for example. Discoveries regarding the interdependence of the spatial and temporal displacement of physical objects do not warrant a metaphysical merging of space and time, nor a denial of their real distinction.

Momentum, according to Newton, is the "quantity of motion," a product of mass and velocity. This quantity does not change unless the body is acted upon by an outside force. It is common to characterize momentum as an inherent property of a body, yet as we know that velocity is relative, so must momentum be relative. Indeed, according to standard interpretations of relativity, even mass is relative, though one may distinguish rest mass from kinematic mass.

Force has been a building block of physics since Newton, so it is another potential candidate for a new ontological category, as it appears to underlie virtually every physical change, including transfers of energy. Force may be expressed as the time derivative of momentum, or colloquially, the rate of change in momentum. Mathematically, force may be expressed as the spatial derivative of mechanical work, or the gradient of electrical potential or, for conservative forces, the gradient of some arbitrary potential field.

Force adopts the role of physical agency in Newtonian mechanics, though it is apparently not a substance. Forces subject to conservation laws may appear in some sense substantial, yet not all forces are conservative. A substance may act through its accidents, so force could be an accident, as seems likely since it is always associated with a substantial (though not necessarily corporeal) agent, such as a particle or ensemble of particles. A force is only measurable by its effect on some substantial patient, reinforcing the idea that force is an accident and not a substance.

The variability of force suggests that it may not be an essential property of most substances, as it is freely transferred in varying quantities from one substance to another, in which case it would be merely an accidental (incidental or non-essential) quality. In either case, there is no reason to introduce a new category besides quality. We might also note that, dimensionally, force includes mass, which is a quality, suggesting that it too may have a qualitative aspect.

As the magnitude of a force is relative to one's reference frame, force may be considered a relative accident. Still, the different kinds of forces may be distinguished by qualities, such as mass and charge. Though Ernst Mach hoped to show that force had no empirical reality, modern relativity still depends on this concept. Only in the theory of gravitation was Einstein able to replace force with the geometry of space-time, but it is by no means clear that this is not merely a formal substitution.

During the early modern period, the term "force" (Latin: vis) was applied also to what we now call mechanical energy. In particular, Leibniz identified what we now call "kinetic energy" as vis viva, or "living force." Only in the nineteenth century did the term "energy" appear in its modern physical significance. The conservation law of vis viva was superseded by a broader conservation of total energy (kinetic and potential). Mechanical energy was now held to be the basis of all other forms of energy: electrical, magnetic, heat, radiation, etcetera. As energy mediates virtually every physical interaction, it seems a likely candidate for an ontologically fundamental category.

Strangely, energy has seldom been advanced as ontologically fundamental, as physicists have inclined more toward philosophical materialism, even though the concept of energy permeates physics more thoroughly than does matter. Energy subsists even in particles lacking mass or corporeality, making it a more likely physical fundamental than matter. Yet the materialist prejudice of most scientists and philosophers of science, a piece of intellectual baggage retained from the anticlerical origins of the Enlightenment, conflicts with their professed scientism, causing them to implausibly depict space-time as a substance and to view energy as far too ethereal to serve as the basis of physical reality.

The concept of energy in physics is indeed difficult to concretize. Besides the distinction between potential and kinetic energy, the subject is further complicated by the apparent transmutation of energy among mechanical, photonic, thermodynamic, and other forms. In physics, energy is the capacity to do work, which is measured in Newtonian mechanics as the exertion of force over some distance. Conversely, force is quantitatively the derivative or gradient of energy. Energy is a conserved quantity, giving it some apparent claim to physical reality. It may subsist either in potentia or actualized kinetically. The distinction between potential and kinetic was inspired by Aristotle's concepts of potentiality and actuality, as well as energeia, which is the actualization of being, or being-at-work. Kinetic energy corresponds to energeia, while potential energy resembles dunamis.

Despite this similarity, physicists' energy is at best a subclass of Aristotelian energeia, since it refers only to the being of certain physical changes. Nonetheless, energy has broad application to every field of physics, ranging from mechanics through electrodynamics and thermodynamics, and has quantitative convertibility among the different modes, remaining a conserved quantity. The energy of motion may be considered motion-at-work; electrical energy is electricity-at-work; and so on. Energy thus conceived is not a distinct category of entity, but a mode of being for various entities, be they qualities or relations.

Under relativity, there is no definite classical potential, and kinetic energy is relative to the choice of reference frame. Yet both kinds of energy were already relative concepts in Newtonian mechanics, as a consequence of the fact that energy is a mode of being for relative accidents such as motion. Quantum mechanics has a time-energy uncertainty relation that limits the frequency with which a system may change energy states, but neither this nor the quantization of energy states alters the basic ontological status of energy, which is the potential or actual mode of being for various physical qualities or relations.

The four fundamental forces - gravity, electromagnetism, weak and strong nuclear forces - might have aspects of their manifestation involving new ontological categories. The electromagnetic and weak forces have been merged in a formal mathematical sense, but we will treat them separately as their physical manifestations are quite distinct.

Gravity is a conservative force, permitting the construction of a gravitational potential. It is proportionate to mass and utterly dependent upon the presence of mass. As mass was always conserved classically, there was reason to suppose that mass is a measure of how much of a substance there is. Relativity and modern particle physics have abolished this concept, making mass just another relative dynamical property, a measure of a particle's gravitational inertia. Gravity, in general relativity, is conceived anew as a measure of the "curvature" of space-time, in the metaphorical sense described previously. This brings us to a circular definition, where gravity is but the ability of mass to curve space-time, and mass is but gravitational inertia. Clearly it will not do to give a purely geometric or mathematical description of gravity to account for it ontologically. For now, there is no strong reason to depart from the classical assessment that gravity, or heaviness, is a quality of substance.

Electricity and magnetism are both conservative forces. Their dynamical interdependence is expressed classically by Maxwell's equations. Under special relativity, magnetism is a necessary consequence of the presence of electrostatic force, and electricity and magnetism are different aspects of a four-dimensional tensor, so that an electrical force field in one frame of reference is a magnetic force field in another frame. Thus electrical and magnetic force cannot be fundamentally distinct in category.

Electromagnetic fields may be substantial, since they can apparently subsist on their own, particularly in the form of an electromagnetic wave or photon, a wave requiring no medium, as the Michelson-Morley experiment proved. The electrical and magnetic forces, like all forces, are still qualities requiring an agent and recipient, yet the photon is almost certainly a substance, as are the electromagnetic fields that generate photons and other manifestations of electromagnetic force.

Electrical force fields are produced by, or at least necessarily related to, the presence of a quality known as charge. When the charge is moving, a magnetic field is generated. Both the charge and the fields are the basis for the electromagnetic force. Charge is a mysterious property of subatomic particles, which is conserved even under relativity. The electromagnetic field, as far as we know, is also substantial (though not corporeal). Physicists often speak of fields as though they were a property of space, as though space were a substance. If they spoke with more philosophical precision, they would realize that they are really articulating a Cartesian plenum as a field-bearing substance. The possibility of such a plenum is not eliminated by the Michelson-Morley experiment, but neither is there a sound empirical basis for its existence. Nonetheless, there are weighty arguments from Aristotle and Descartes for its necessity, and more recently theoretical physicists have inferred the existence of a "vacuum field," which is really a plenum by another name.

In the Standard Model of particle physics, the electromagnetic, weak and strong nuclear interactions are mediated by particle exchange, possibly eliminating the need for substantial fields. The physical reality of this particle exchange model seems to be supported by the discovery of W and Z bosons, believed to mediate the weak force. Yet the photons and other bosons that mediate forces are virtual, intermediate steps in interactions depicted in Feynman diagrams for purposes of computation and respecting conservation laws. It would be premature to dispense with substantial fields if the mediating particles are merely virtual. Indeed, we might just as coherently say that the particle mediating the interaction is produced by the field rather than the other way around. Regardless of how we interpret the role of virtual particles, there is no need to introduce a new ontological category.