CATEGORIES

Philosophical categories are classes, genera, or types supposed to mark necessary divisions within our conceptual scheme, divisions that we must recognize if we are to make literal sense in our discourse about the world. To say that two entities belong to different categories is to say that they have literally nothing in common, that we cannot apply the same descriptive terms to both unless we speak metaphorically or equivocally.

Aristotelian Theory

The word category was first used as a technical term in philosophy by Aristotle. In his short treatise called Categories, he held that every uncombined expression signifies (denotes, refers to) one or more things falling in at least one of the following ten classes: substance, quantity, quality, relation, place, time, posture, state, action, and passion. By "uncombined expression" Aristotle meant an expression considered apart from its combination with other expressions in a sentence, and he intended his account to apply only to those expressions we now call "descriptive" and "nonlogical." Logical expressions, such as "not," "or," "some," and "every," are excluded; these were called by medieval philosophers "syncategorematic," to distinguish them from the categorematic expressions covered by Aristotle's account of categories.

Each of the ten classes of entities signified constitutes a category, or genus, of entities, and each categorematic expression is said to be an expression in the category constituted by the class of entities it signifies. The nouns "plant" and "animal," for example, signify kinds of substances and are said to be expressions in the category of substance; the nouns "color" and "justice" signify kinds of qualities and are said to be expressions in the category of quality. On the other hand, the adjectives "colored" and "just" signify, respectively, colored and just things (substances) and also connote (consignify) the qualities color and justice. Aristotle labeled such expressions "derivative terms" or "paronyms" and held that instead of signifying substances simply, as expressions in the category of substance do, they signify substances derivatively by connoting accidents of substances.

Although Aristotle implied that his ten categories constitute the ten highest genera of entities and hence the only true genera—the only genera that cannot be taken as species of higher genera—he also implied that it is not essential to his theory that the categories be exactly ten in number or even that they be mutually exclusive and exhaustive. Categories are listed in various of Aristotle's writings, but the list usually stops short of ten without indication that categories have been omitted. He explicitly stated that no absurdity would result if the same items were included in both the category of quality and that of relation. He remarked that the expressions "rare," "dense," "rough," and "smooth" do not signify qualities, since they apply to a substance with reference to a quality it possesses, yet he did not specify in which category or categories these expressions are included. Despite these indications that his theory of categories is not entirely complete, medieval philosophers generally wrote as though Aristotle's list of ten provided a final, exhaustive enumeration of the highest genera of being.

What is essential to Aristotle's theory of categories is that substances be properly distinguished from accidents and essential predication from accidental predication. Any entity, regardless of the category in which it is included, can be an entity referred to by the subject term of an essential predication. "Man is an animal." "Red is a color." "Four is a number." "A year is twelve months." The subject terms denote entities that fall, respectively, in the categories of substance, quality, quantity, and time, and the predication in each case is essential. On the other hand, only entities in the category of substance can be entities referred to by subject terms of accidental predication. There is no such thing as an accident of an accident; accidents happen to substances and not to other accidents. "Red is darker than orange" does not assert something that happens to be, but need not be, true of red; it asserts what is essentially true of red, something that red must always be if it is to remain the color red. "Red is John's favorite color" does not assert anything that may happen to be true of red; rather, it asserts something that may happen to be true of John. To undergo change through time while remaining numerically one and the same thing is what principally distinguishes substances from entities in other categories. If John ceases to regard red as his favorite color, we say not that red has changed while remaining the same color but that John has changed while remaining the same person.

Categorematic expressions, for Aristotle, are technically "predicates," but they are not "predicates" in a sense that keeps them from serving as subject terms in essential predication. The minor term of an Aristotelian "scientific syllogism" occurs only as a subject, though Aristotle gave no examples in which it is a proper name. He regarded the ultimate subject terms in demonstration as common names marking species that are not further divided. Such expressions are still "predicates" in that like more generic terms they are applied to individuals in answer to the question What is it? But proper names are in a class by themselves; they are applied only in answer to the question Who? or Which? and are not "predicates" at all. Yet if proper names are thus not categorematic expressions, they are still fundamental to Aristotle's theory of categories. Without proper names there are no names for the subjects of accidental as distinct from essential predication. Man as such is an animal—"man" names every person indifferently if it names any, and the question of naming which one (or ones) does not arise. But only some man (or men) is (are) snub-nosed, and until the question Which? is answered by a proper name the subject of the accidental predication remains unnamed.

category-mistakes

If we ask what, according to Aristotle's theory, would be the sort of thing often called today a "category-mistake," we must distinguish a mistake that violates what is essential to the theory from a mistake that violates a particular category-difference marked by the theory. Only a mistake of the first kind is strictly a category-mistake. Mistakes of the second kind form a subclass of equivocations. In his Topics (107a3–17), Aristotle listed as one example of equivocation the sentence "The musical note and knife are sharp." That "sharp" is here used equivocally is shown by the fact that a musical note and a knife belong to different categories. A musical note is a kind of sound, and sounds are qualities. (Aristotle argued in On the Soul, 420a25–28, that we speak of the sound of a body as we speak of the color of a body.) A knife is a kind of substance, and one who believes that "sharp" applies in the same sense to musical notes and to knives may be said to have made the category-mistake of confusing a quality and a substance. Yet an appeal to category-differences is not necessary to expose the equivocation, and many equivocations cannot be exposed in this way because there is no violation of a category-difference. Aristotle claimed that the equivocal use of "sharp" in the example is also exposed by the fact (among others) that musical notes and knives are not compared with respect to their sharpness. Two notes may be equally sharp, or two knives, but not a note and a knife. Again, two flavors are equally sharp, but not a flavor and a note or a flavor and a knife. The equivocation in "The flavor and note are sharp" is exposed, although since flavors and sounds are both qualities there is no violation of a category-difference.

The appearance of absurdity produced by an equivocation can always be removed and literal meaning restored by distinction between the different senses of the crucial words. But with a genuine category-mistake there is no literal meaning to restore. In a passage in his Posterior Analytics (83a30–33), where he was discussing features of essential and accidental predication, Aristotle remarked that Plato's forms can be dismissed as mere sound without sense. The point is illustrated by a sentence like "The color white is white." The sentence may seem to make sense if one claims that since the color white is the standard by which we judge things to be white, it is itself white. But the sense is only apparent, because whatever is white remains numerically one and the same object even if its color changes. Such an object cannot be the quality, that is, the color white itself, as we then have the absurdity that the color white changes its color. Plato's theory of forms, as Aristotle interpreted it, makes the mistake of confusing accidental with essential predication. "The color white is the color white" is not an accidental but a trivially true essential predication; it is clearly not what is intended by the Platonic assertion that the color white is white. But the latter is just as absurd as the assertion that sitting sits.

Except in the passage in the Posterior Analytics, Aristotle did not refer to Plato's forms as mere sound without sense. Plato's theory has certain affinities with Aristotle's metaphysical account of substance as a composite of form and matter, and in his Metaphysics, Aristotle criticized Plato's forms, not as sound without sense, but as entities that fail to do the job they should, since they cannot be formal causes (991a11; 1033b26) and lead to an infinite regress (the third-man argument: 990b17). His criticism of the theory of forms receives attention in the history of philosophy mainly in this context of form, matter, and substance, and the passage in the Posterior Analytics that dismisses the forms as sound without sense is generally passed over or dismissed as a result of more than usual hostility toward Platonists. Yet apart from hostility, Aristotle was required by his theory to regard a sentence like "The color white is white" strictly as a category-mistake.

Kantian Theory

Aristotle's theory dominated discussion of categories until the work of Immanuel Kant, where we find a radically new conception of a category. Kant professed in his theory of categories to have achieved what Aristotle had tried but failed to achieve in such a theory. Instead of beginning with uncombined expressions, Aristotle should have started with expressions of statements or judgments. Every statement is universal, particular, or singular in quantity; affirmative, negative, or infinite in quality; categorical, hypothetical, or disjunctive in the relation of its parts; and problematic, assertoric, or apodictic in modality (Critique of Pure Reason, "Transcendental Analytic," I, 2–3). Each of these twelve ways in which judgments are classified in logic corresponds to a function of the understanding indispensable to the formation of judgments, and each such function yields a category, or pure concept of the understanding, in one of the four major divisions of categories: quantity, quality, relation, and modality. The function, for example, of relating subject to predicate in a categorical judgment yields the relational category of substance and accident, and the function of relating antecedent to consequent in a hypothetical judgment yields the relational category of cause and effect.

Kant's conception of substance leads to important departures from Aristotle in the treatment of common names and paronyms. Whether an expression serves as a common name or as a paronym depends on its function in a given statement and not on its signification as an uncombined expression. "Stone," for example, serves as a common name of the substance in which a change occurs in "The stone grows warm," but it serves to specify a kind of change that occurs in a substance in "The sand becomes stone." In the second case "stone" serves as a paronym; it connotes certain properties, such as hardness and solidity, and denotes any substance, such as a certain amount of sand, that acquires these properties. For Aristotle the change from sand to stone is substantial change, or coming to be, rather than alteration; for Kant substantial change is impossible because substance is related to accident as that which undergoes alteration is related to that which becomes and ceases to be. A substance is altered when one of its accidents ceases to be and is followed by another accident, so accidents, not substances, become and cease to be.

With Kant's theory there are no ordinary equivocations that can be exposed as category-mistakes, since categories are pure (formal), as opposed to empirical, concepts. "Substance" and "quality," in Aristotle's theory, are the highest generic terms that apply, respectively, to knives and sounds, so the equivocation in "The knife and musical note are sharp" can be exposed as a confusion of a substance and a quality. In Kant's theory, by contrast, generic terms represent empirical concepts, and an equivocation that confuses genera, as "The knife and musical note are sharp" confuses bodies and sounds, is not a category-mistake but a confusion of empirical concepts. One makes a category-mistake—violates what is essential to Kant's theory—by misapplying a category rather than by mistaking the category in which an entity belongs. The important point is that Kant's categories apply only to phenomena or appearances, not to entities or things in themselves. Every appearance can be judged according to every category and cannot be said to belong properly in one category rather than another. An appearance of red, for example, has extensive magnitude equal to a spatial area and is hence a quantity; it has intensive magnitude as a sensation with a certain degree of intensity and is hence a quality; it is related to further appearances as accident is to substance and effect to cause; and in relation to other appearances it is possible, actual, or necessary.

In Aristotle's theory, on the contrary, a redness is properly an accident in the category of quality; it exists in a substance from which it may be separated in thought but not in being. The extensive magnitude comprising a spatial area is a quantity of the substance and not of the redness; the intensity of the sensation of redness is a quality of the perceiving subject. Questions concerning the cause or the possibility, actuality, and necessity of the redness can be answered only by references to the substance that is said to be red. When the color is separated in thought from the substance the resulting abstract entity, the color red, can be characterized essentially (red, for example, is darker than orange), but to take it as an entity that itself has accidents is to make the category-mistake of confusing a quality with a substance.

To say that the color red is red is, for Kant, to misapply the relational category of substance and accident. Categories can be applied correctly only to phenomena, and in the case of a relational category both terms of the relation must be phenomena. The phrase "the color red" stands for the concept under which appearances of red are subsumed and not for an appearance that may be related to an appearance of red as substance to accident. This sort of category-mistake needs little attention since with Kant's theory there is no compelling tendency of the human mind to confuse a concept with its instances. But there is a natural tendency to make the mistake of applying categories to what are technically, for Kant, ideas and ideals; the former give rise to antinomies of pure reason and the latter to fallacious proofs of God's existence. Platonism in the form that gains a hold on men's minds is the mistake of applying the category of existence to ideals, not the mistake of confusing a concept with its instances. Along with antinomies and fallacious proofs of God, Kant argued for a third kind of category-mistake, a mistake that occurs when categories are misapplied in judgments about a thinking substance; the result is a set of equivocations giving rise to what Kant called "paralogisms of pure reason." These three kinds of category-mistakes are to be exposed not as sound without sense but as illusions to which the human mind is naturally prone.

Post-Kantian Theories

Although Kant's theory of categories marks the single most important development in the subject since Aristotle, his list of twelve categories never acquired anything like the dominant role once held by Aristotle's list of ten. Kant's influence has been to change the conception of how a list of categories should be formed, rather than to provide the list itself. Instead of looking for the highest genera of being, the most universal kinds of entities, one should look for the most universal forms of understanding presupposed in the formation of judgments. The strong influence of Kant is evident in the theories of categories of such philosophers as G. W. F. Hegel, Edmund Husserl, and Charles Sanders Peirce.

Peirce's theory is closely connected with his contributions to logic, but his conception of what constitutes a category is sufficiently Kantian to distinguish his theory radically from the theory usually associated with the development of modern logic.

theory of types

Bertrand Russell originally devised his theory of types as a means of avoiding a contradiction he had discovered in Gottlob Frege's logic, but the theory has profound implications for philosophy in general, and under its influence "category" has come to be used frequently as a synonym for "logical type."

As the theory of types is presented in Principia Mathematica, its cardinal principle (called by Russell the "vicious-circle principle") is that whatever involves all of a collection must not be one of the collection. The class of white objects, for example, includes (and hence involves) all white objects, and to say that this class is itself a white object is to violate the principle and to utter nonsense. The set of entities consisting of all white objects and the class of white objects is for Russell an "illegitimate totality," a set that "has no total" in the sense that no significant statement can be made about all its members. The purpose of the theory of types is to provide a theoretical basis for breaking up such a set into legitimate totalities. A totality is legitimate when and only when all its members belong to the same logical type, and two entities are of different logical types when and only when their inclusion in the same class yields an illegitimate totality. Whenever an entity involves all the members of a given class its logical type is said to be higher than the type of the members of this class. Logical types thus form an infinite hierarchy with individuals at the lowest level, or zero type, classes of individuals at the next level, then classes of classes, and so on. Since to every class there corresponds a defining property of that class, there is an equivalent hierarchy of logical types with individuals again at the lowest level, but with properties of individuals next, then properties of properties of individuals, and so on. "X is a member of the class of white objects" is equivalent to "X is white," and the two sentences "The class of white objects is a white object" and "The color white is white" are equally expressions of a type-mistake or category-mistake and are equally nonsensical.

The theory of types, if true, gets rid of the contradiction Russell wanted to avoid. This contradiction arises when the class of all classes that are not members of themselves is said to be or not to be a member of itself. According to the theory of types the attempt to make either assertion violates the vicious-circle principle and results in nonsense. But if this way of avoiding the contradiction is to be satisfactory, there must be reasons for accepting the theory of types other than the fact that if it is accepted the contradiction it was designed to avoid is avoided. Efforts to find such reasons have carried investigations concerning the theory of types from the sphere of technical issues in mathematical logic into the sphere of philosophical issues in a theory of categories. Developments in both spheres have often proceeded independently, and even though technical work in mathematical logic has developed alternatives to the theory of types (especially to the theory as first stated by Russell), the fact that the theory is not needed to avoid the original contradiction is not in itself conclusive evidence that the theory has nothing to be said for it as a theory of categories.

Russell offered in support of the theory of types the fact that it outlaws not only conditions giving rise to the paradox concerning class membership but also those giving rise to an indefinite number of other paradoxes of self-reference, including the ancient paradox of the liar. But alternative ways of avoiding these other paradoxes have been developed. More serious than its nonuniqueness as a consistent solution to the problems it was designed to avoid is a difficulty intrinsic to the theory itself. Even if the theory is true, there seems to be no way to state it without contradiction. The word type illustrates the point. In stating the theory one uses this word, which is itself a particular entity, with reference to all entities, so one entity is made to involve the collection of all entities. Russell tried to cope with the difficulty by proposing that a difference in logical type be taken as a difference in syntactical function rather than a difference in the totalities to which two entities may be legitimately assigned. Instead of saying that the color white and a table are of different logical types because the latter but not the former can be included in the class of all white objects without forming an illegitimate totality, we may say that the phrases "the color white" and "a table" belong to different logical types because the latter but not the former yields a significant statement when it replaces X in the sentence-form "X is white."

Reference to linguistic expressions rather than entities avoids a vicious-circle fallacy because the hierarchy of types asserted by the theory then includes only the totality of expressions within a given language, not the totality of all entities. But any given statement of the theory must be in a metalanguage whose expressions are not included in the totality of expressions covered by the statement. While the theory can thus never be applied to the language in which it is itself stated, it can always in principle be restated in a further language (a meta-metalanguage) so that it applies to the language in which it was originally stated as well as the language to which it originally applied. Universal application of the theory is thus possible in principle by proceeding up an infinite hierarchy of languages, while the application of the theory to each particular language asserts the existence of an infinite hierarchy of types of syntactical functions within that language. But in neither case is there the simple assertion that the class of all entities comprises an infinite hierarchy of logical types.

The conception of logical type as syntactical function is much easier to maintain when the expressions typed are those of an artificial language, such as a logical calculus, rather than those of a natural language, such as English. Generalization about the totality of expressions in an artificial language is easy because this totality is generated by the rules one must lay down if one is to construct an artificial language in a clear and definite sense. But such relativity to the rules of an artificial language makes it impossible to maintain all that was originally claimed for the theory of types. Russell was originally understood as claiming to have discovered that what appears to be stated by sentences like "The color white is white" and "The class of white objects is a white object" is simply nonsense. But then it seems that the most one can say is that Russell constructed an artificial language (a calculus or formalism) in which the translations of these English sentences are not well-formed formulas. The mere construction of such a language is clearly not the same as the discovery that in point of logic certain apparent statements are really nonsense. The case against Russell's original claim is all the more damaging in view of the fact that formalisms have since been constructed in which translations of certain sentences that are nonsense according to the theory of types are well-formed formulas, and the contradiction the theory of types was designed to avoid does not appear. Enlarging the notion of logical type to include semantic as well as syntactical function does not change the picture. Semantic rules for an artificial language are necessary if one is to do certain things with the language, but these rules, like syntactical rules, are stipulated in the construction of the formalism; addition of such rules in no way furthers the claim to having discovered that certain sentences are nonsense rather than having constructed a language in which they become nonsense.

Categories as Discovered in a Natural Language

The claim to discovery is essential to a theory of categories, and the claim may still be made if types are found among the expressions of a natural language rather than imposed on the expressions of an artificial language. Instead of beginning with the vicious-circle principle as defining a condition we must impose on any language if we want to make sense, we may begin with expressions in the natural language we ordinarily use—expressions with which we assume we make sense, if we make sense at all—and try to determine what differences in type our making sense requires us to recognize in these expressions. This sort of approach is taken by Gilbert Ryle in The Concept of Mind, where he considers expressions we use in talking about mental powers and operations and argues that certain of these expressions cannot belong to the same type or category as others. Ryle's test for a category-difference is a case where one of two expressions cannot replace the other without turning the literal meaning of a sentence into an absurdity. To begin with an obvious case, when "the man" in "The man is in bed" is replaced by "Saturday" the result is clearly an absurd sentence if taken literally. Less obvious cases often go undetected by philosophers and remain a source of philosophical confusion. "He scanned the hedgerow carefully" becomes absurd when "saw" replaces "scanned," although the absurdity disappears when the adverb is omitted. Failure to note that "to see" belongs in the category of "achievement" verbs while "to scan" is a "task" or "search" verb has misled philosophers to posit a mental activity corresponding to seeing that is analogous to the genuine activity of scanning.

For Ryle categories are indefinitely numerous and unordered. The totality of categories is not in principle an infinite hierarchy of types; categories provide no architectonic such as Kant's fourfold division of triads; and there is no distinction setting off one category from all the others as basic regardless of their number, as Aristotle's distinction between substance and accident. There are thus no mistakes that are strictly category-mistakes rather than ordinary equivocations or absurdities. Ryle explains in his article "Categories" that he uses "absurdity" rather than "nonsense" because he wants to distinguish a category-mistake from mere sound without sense. According to Ryle, a category-mistake is not a meaningless noise but a remark that is somehow out of place when its literal meaning is taken seriously; many jokes, he observes, are in fact "type-pranks."

What Is a Theory of Categories?

The above observations suggest that Ryle has no theory of categories at all—no principles by which categories can be determined and ordered. Yet he seems unwilling to give up all claims to a theory of categories. He is especially concerned with countering the impression that category-differences are on a par with differences created by a particular set of linguistic rules. In his article "Categories" he considers briefly the question What are types of? He suggests that instead of saying absurdities result from an improper coupling of linguistic expressions, it is more correct to say that they result from an improper coupling of what the expressions signify. But one must be wary of saying that types are types of the significata of expressions. A phrase like "significata of expressions" can never be used univocally, because such use presupposes that all significata are of the same type. Ryle claims we can get along without an expression that purports to specify what types are types of, since the functions of such an expression are "purely stenographic"; if we want an expression performing these functions, he suggests "proposition-factor" but cautions that to ask what proposition-factors are like is ridiculous since the phrase "proposition-factor" has all possible type-ambiguities.

Ryle seems hardly to have advanced the question of the status of a theory of categories beyond the point where Russell left it. It appears to be just as difficult to establish category-differences by appeal solely to ordinary language as to establish them by appeal solely to an artificial language. J. J. C. Smart points out, in "A Note on Categories," that with Ryle's test of a category-difference we are led to make very implausible (if not absurd) claims about category-differences. When, for example, "table" replaces "chair" in "The seat of the chair is hard," the result seems clearly an absurd sentence. Yet if "table" and "chair" do not belong in the same category, what words do? If the phrase "category-difference" is to have anything like the force it has had from Aristotle to Russell, the claim to having discovered that "table" and "chair" are expressions in different categories is itself absurd. Though Ryle may not want to make the claim, he cannot avoid it and maintain his test of a category-difference.

Yet Ryle, whatever his intentions, may be said to have established the negative point that absurdity alone is never a sufficient test of a category-mistake. Aristotle, Kant, and Russell each began with metaphysical or logical principles that purport to set limits of literal sense; a violation of these principles results either in sound without sense or in intellectual illusion, and in both cases in more than simple absurdity. Ryle appears to want the advantages of a theory of categories and at the same time to avoid the embarrassment of having to defend its principles. Such a theory promises to rid philosophy of many fallacious arguments and contradictions, but the promise is worthless if the principles of the theory are no more tenable than the arguments and contradictions it sweeps away. Aristotle's metaphysics of substance and accident, Kant's transcendental logic, and Russell's elevation of the vicious-circle principle have proved as philosophically debatable as Platonic forms, proofs for the existence of God, and paradoxes of self-reference. It is comforting to believe that such debatable principles can be discarded and that the forms, proofs, and paradoxes can be exposed as category-mistakes by appeal to nothing more than what a man of common sense will recognize as an absurdity in his own ordinary language. But unfortunately our common use of "absurdity" covers too much. One can hardly hope to rid philosophy of Platonic forms with no more argument than the claim that saying the color white is white is like saying the seat of a table is hard.

Ryle also calls attention to another negative point about a theory of categories. The theory cannot have a subject matter in the usual sense. We cannot generalize about all proposition-factors, all entities, or all of whatever it is types are said to be types of as we generalize about, for example, all bodies or all biological organisms. We may say that every proposition-factor is of some type, but we cannot say what it is like regardless of its type as we can say what every body or biological organism is like regardless of its type. Since everything we can talk about is a proposition-factor, we have nothing with which they can be contrasted; we do, however, have things with which to contrast bodies and biological organisms. Ryle sees this point as forcing us to accept a phrase like "proposition-factor" as merely a kind of dummy expression we may use to preserve the ordinary grammar of "type" and "category," although the important thing is not to preserve the grammar but to avoid the error of thinking we can preserve it with other than a dummy expression. If we take "proposition-factor" as a metalinguistic expression applying to factors in a particular language, we succeed in preserving the grammar without a dummy expression, but only at the price of making categories relative to a particular set of linguistic rules. The use of a dummy expression is at least consistent with the claim (which Ryle seems to want to make) that a recognition of absurdity is not relative to the rules of a particular language. We may be said to recognize, regardless of our language, the absurdity of saying that the seat of a table is hard or that the color white is white, although we are unable to give criteria of absurdity.

Aristotle tried to cope with the subject-matter problem by holding that while we cannot generalize about all entities as we can about all bodies or all biological organisms ("being is not a genus," as he put it), we can have a science of being because there is one primary type of being—substance—and every other type exists, by being an accident of substance. Although we have, then, nothing with which to contrast all beings, we can contrast substances with accidents, and the science of substance is the science of being qua being in that conditions for the being of substance are conditions for the being of everything else. A theory of categories may thus be founded on the principle that substances alone can have accidents and all categories other than substance are categories of accidents. For Kant categories do not distinguish beings or entities but a priori forms of understanding, and, unlike Aristotle's beings or Ryle's proposition-factors, these forms comprise not everything we can talk about but only necessary conditions for judgments about objects of experience. The forms stand in sharp contrast with other objects of discourse and constitute a single subject matter belonging to the science of transcendental logic.

Neither Aristotle's nor Kant's theory of categories seems immune to the objection that its subject matter is created rather than discovered. Aristotle's pronouncements about substance and accident and Kant's about forms of understanding each provide principles that yield a scheme of categories, but one may ask whether the pronouncements are anything more than rules for the construction of a certain kind of language—whether the construction of an Aristotelian metaphysics or that of a Kantian transcendental logic provides a theory of categories with anything more than an artificial language within which certain category-differences are established. An answer to this question is proposed by P. F. Strawson in his Individuals. Strawson suggests that theories of metaphysics have tended to be either descriptive or revisionary. A metaphysics is descriptive insofar as it yields a scheme of categories that describes the conceptual scheme we actually presuppose in ordinary language. A theory becomes revisionary to the extent that it leads to a departure from our ordinary scheme. Strawson cites the metaphysical theories of Aristotle and Kant as descriptive, those of René Descartes, Gottfried Wilhelm Leibniz, and George Berkeley as revisionary. While all five philosophers construct special languages, only Aristotle and Kant do so in a way that results in a scheme of categories that describes the conceptual scheme of our ordinary language.

But if in this sense Aristotle and Kant in their theories of categories describe rather than create a subject matter, what they describe is not what they claim as their subject matter. Strawson professes in his own theory of categories to describe the conceptual scheme of our ordinary language, but he does not profess to give principles of being qua being or a transcendental deduction of pure concepts of the understanding. If Aristotle and Kant to some extent describe the scheme Strawson sets out to describe, this achievement was certainly not their primary objective, and since they differ radically at crucial points, as in their views of alteration and substantial change, they can hardly be said in any case to describe the same scheme. One must say, rather, that each offers metaphysical or transcendental hypotheses that purport to account for and establish the necessity of the conceptual scheme underlying common sense. One may of course accept much of what they say in description of their schemes as true of what one takes to be our commonsense scheme and yet reject their hypotheses. With the rejection there is no need to defend the hypotheses' claims to a metaphysical or transcendental subject matter, but one then needs to explain how our commonsense scheme is subject matter for description. A description of common features in the grammars of Indo-European languages is not exactly what Strawson means by a description of the conceptual scheme of our ordinary language. But it can hardly be said that his efforts to distinguish the two descriptions are entirely successful. In some of his arguments he seems to appeal to metaphysical hypotheses of his own and hence to have a theory accounting for, and not simply a description of, the conceptual scheme he claims as his subject matter. In other arguments he seems, like Ryle, to make an ultimate appeal to our commonsense recognition of absurdity.

The construction of a theory of categories as descriptive metaphysics differs, according to Strawson, from what has come to be called philosophical, or logical, or conceptual analysis. But the difference is not "in kind of intention, but only in scope and generality." Strawson describes philosophical analysis as relying on "a close examination of the actual use of words," and while this is "the best, and indeed the only sure, way in philosophy," what it can yield is not of sufficient scope and generality "to meet the full metaphysical demand for understanding." But Strawson does not elaborate the demand and gives no criterion for deciding when philosophical analysis must give way to descriptive metaphysics. He sometimes implies that we may pass imperceptibly from one to the other, and this may be the case if to do descriptive metaphysics is simply to articulate what is presupposed in a given philosophical analysis. But it can hardly be the case if descriptive metaphysics, unlike philosophical analysis, has its own peculiar subject matter—being qua being, pure concepts of the understanding, our commonsense conceptual scheme, or whatever. Philosophical analysis is clarification of thought about a given subject matter, and to articulate the presuppositions of a given analysis is not to analyze a new subject matter but only to push the original analysis as far as we can. In the end we may arrive at distinctions that agree with what philosophers from Aristotle to Strawson have called "category-differences," and there is no harm in using the label if we mean only that the distinctions are ultimate in the analysis we have given and not also that they have to be supported by a hypothesis about a special subject matter. We can hardly make the additional claim without passing beyond the point where we can hope for help from philosophical analysis.

Historical Notes

stoics and neoplatonists

In place of Aristotle's ten categories the Greek Stoics substituted four "most generic" notions or concepts: substratum, or subject; quality, or essential attribute; state, or accidental condition; and relation. The Stoic view, as well as the Aristotlelian doctrine, was criticized by the Neoplatonist Plotinus. In his Sixth Ennead Plotinus argued that the ultimate categories are neither the Aristotelian ten nor the Stoic four but correspond to the five "kinds" listed in Plato's Sophist : being, rest, motion, identity, and difference. The central point for Plotinus was that different categories apply to the intelligible and sensible worlds, the ultimate categories applying only to the former. Plotinus's views on categories figured prominently in medieval discussions only as they were considerably modified by his pupil Porphyry. In Porphyry's short commentary on Aristotle's Categories, generally known as the Isagoge (Eἰσαγωγὴ, "Introduction"), he accepted Aristotle's list of ten but raised Plotinian questions about the way they exist. He noted that categories are genera and asked whether genera and species subsist (exist outside the understanding) or are in the naked understanding alone; whether, if they subsist, they are corporeal or incorporeal; and finally, whether they are separated from sensibles or reside in sensibles. He remarked that these questions are too deep for an introductory treatise, and we have no record of how he thought they should be answered.

boethius

Boethius translated the Isagoge into Latin, along with Aristotle's Categories and On Interpretation. He also wrote a commentary on the Isagoge, offering answers to Porphyry's unanswered questions, and thus began a tradition, which persisted throughout the medieval period, of accepting Porphyry's questions as presenting the fundamental issues for any account of categories. Since genera and species appear most prominently as genera and species of substances, the issues centered first of all in the signification of common nouns taken as names of kinds of substances. The medieval "problem of universals" thus arose from Porphyry's questions about Aristotle's categories, and prominent medieval philosophers, such as Peter Abelard, Thomas Aquinas, John Duns Scotus, and William of Ockham, are known as conceptualists, realists, or nominalists because of their answers to these questions. The important point for a history of theories of categories is that the discussion of the problem of universals by major figures in medieval philosophy occurred within an unquestioned framework provided by Aristotle's theory of categories—in particular, within a framework that presupposed the basic Aristotelian interrelation of substance and accident and essential and accidental predication.

locke and hume

The Aristotelian framework broke down in modern pre-Kantian philosophy. Signs of the breakdown were evident in Thomas Hobbes and Descartes, but its full force appeared in John Locke and David Hume. With Locke's account of substance as an "unknown something" underlying appearances, essential predication in the category of substance becomes impossible, and the signification of common nouns supposed to name kinds of substances can be fixed only by "nominal essences," by conventional factors, rather than by Ockham's "natural signs in the soul." Essential predication, and hence necessary truth, remains possible only when the subjects are things of our own creation ("mixed modes") and not when they are substances in the real world.

The full consequences of Locke's departure from an Aristotelian framework were drawn by Hume. If it is impossible to know what something in the real world necessarily (essentially) is, it is also impossible to know that any one thing in the real world is necessarily connected with another or that any state of a thing at one time is necessarily connected with its state at another time. In other words, not only substance but also causality—an equally if not more fundamental notion (though not recognized as a category by Aristotle)—is made a matter of habit and custom. The stage was set for Kant to answer Hume with a radically new theory of categories.

hegel

Despite the radical differences between Kantian and Aristotelian categories, two basic points of similarity remain: (1) Categories provide form but not content for cognitive discourse about the world and thus serve to distinguish what we can meaningfully say in such discourse from what we may seem to say when we make category-mistakes or misapply categories. (2) Categories presuppose the substance-accident (subject-predicate) form basic to Aristotelian logic. Hegel's philosophy retains neither of these points of similarity, although he adopted the Kantian view that the clue to a system of categories is to be found in logic. But instead of turning to logic as a study of forms of reasoning without regard for content, Hegel turned to logic as a dialectical process in which form and content are inseparable. The essential nature of this process is seen not in the forms under which subject and predicate are brought together in the premises of reasoning to make affirmative, negative, disjunctive, hypothetical, and other types of judgment but in the basic stages through which the process itself repeatedly moves. These stages Hegel called "thesis," "antithesis," and "synthesis," and he took them as interrelating the basic ideas, notions, or principles of reason, which he also called "categories." This interrelation of categories constitutes both Hegel's system of philosophy and what he held to be the "system of reality." The categories, then, are many, and their exact number cannot be determined until the system of reality is fully articulated. Hegel thus marked the beginning of a tradition in modern philosophy, in which "category" means simply any basic notion, concept, or principle in a system of philosophy.

This use of "category" is standard not only among Hegel's progeny of absolute idealists but also among metaphysicians generally, who dissociate themselves from analytical philosophy. The use remains even when there is no vestige of Hegel's threefold pattern of thesis, antithesis, and synthesis as a means of ordering the principles of speculative philosophy. The categorial scheme in Alfred North Whitehead's Process and Reality, for example, is readily understood as dealing with the sort of notions Hegel called "categories" but hardly with categories in the Aristotelian-Kantian sense of setting limits of cognitive meaning, a sense that still survives in analytical philosophy.

peirce

The collapse of Kant's theory of categories is inevitable, according to Peirce, as logic advances beyond the subject-predicate form recognized by Aristotle. So long as statements like "John gave the book to Mary" are not seen as possessing a logical form fundamentally different from and coordinate with the simple subject-predicate form of statements like "John is tall," categories are determined by what may be taken as different forms of this one-subject–one-predicate relation. Aristotle and Kant analyzed the forms differently, but the relation analyzed was the same. With the development of logic beyond Aristotle (a development to which Peirce made significant contributions), statements like "John gave the book to Mary" are recognized as statements with three-place predicates (x gave y to z ) and are different in logical form from statements with one-place predicates (x is tall). Peirce claimed to have demonstrated in his "logic of relatives" that although one-place, two-place, and three-place predicates are basically different in logical form, predicates with more than three places have no features of logical form not already found in three-place predicates.

The demonstration remains one of the more questionable parts of his logic, but Peirce accepted it as proof that in formal logic there are but three fundamentally different types of predicates and hence that there are but three categories. He sometimes referred to his categories as the "monad," the "dyad," and the "polyad," but he preferred the more general expressions "firstness," "secondness," and "thirdness." As genera (or modes) of being, the categories are designated as "pure possibility," "actual existence," and "real generality." A pure possibility stands by itself, determined by nothing but conditions of internal consistency; what actually exists stands in relation to other existences and to some extent both determines and is determined by them; a true generalization is a representation related to other representations, to actually existing things, and to pure possibilities. In his philosophical cosmology Peirce had three universes corresponding to the three modes of being, and in his semeiotic theory, or theory of signs, he developed an extensive classification of signs, with the main divisions triadic, each triad comprising a firstness, a secondness, and a thirdness. Although Peirce's categories thus function architectonically somewhat as Hegel's thesis, antithesis, and synthesis, they serve, as Hegel's triad does not, to set limits of cognitive meaning. Though Peirce did not use the phrase "category-mistake," he said repeatedly in his later writings that nominalism, which he regarded as the great error in the history of philosophy, arises from the failure to recognize real generality as a mode of being distinct from actual existence. In arguing that universals have no actual existence, the nominalist has failed to see that to ask in the first place whether they have such existence is a category-mistake. In his final years Peirce labored to show that the pragmatic criterion of meaning, which he propounded early in his career, is not only consistent with but actually necessitated by his theory of categories.

husserl

The role of categories in setting limits of cognitive meaning figures prominently in the philosophy of Husserl. To determine "primitive forms" or "pure categories" of meaning is the first task of a "pure philosophical grammar." The fundamental form is that of propositional meaning, and other primitive forms, such as the nominal and adjectival, are forms of meaning that belong to constituents of a proposition. After determining these pure categories of meaning, pure logical grammar turns to primitive forms or categories of the composition and modification of meaning (forms such as those exhibited by propositional connectives and modal expressions). In addition to a pure logical grammar, Husserl held, there are a pure logic of consistency (noncontradiction) and a pure logic of truth. The picture is further complicated in that pure logic may be taken as giving rise to a formal ontology and, again, developed into a transcendental logic. A full account of categories requires the full development of logic in all its phases, and in this respect Husserl's view of categories seems reminiscent of Hegel. But at no point (even in formal ontology) did categories cease for Husserl to be purely formal and become inseparable from content. Husserl was careful to distinguish the kinds of nonsense precluded by his categories from nonsense of content (inhaltlich Unsinn ). A phrase like "if-then is round" is nonsense because it violates a category-difference, a condition of meaningfulness established by logic alone; a phrase like "the seat of the table is hard" violates no such condition, and its nonsense arises from a material, not a formal (logical), incompatibility. While at times Husserl's language may suggest what Rudolf Carnap and others have since called "syntactical categories," it should be noted that Husserl had nothing like Carnap's technical distinction between syntax and semantics and that the "syntactical categories" of Husserl's pure logical grammar are in Carnap's sense neither purely syntactical nor semantical.

frege and wittgenstein

In their philosophies of mathematics and logic both Peirce and Husserl remained close enough to Kant not to accord set theory the fundamental role it has come to play in logic and the foundations of mathematics. Frege, although he did not present any of his views under the heading "a theory of categories," did far more than Peirce or Husserl to shape the discussion of categories in the twentieth century. Frege analyzed sense and reference, concept and object (notions fundamental to Peirce's and Husserl's theories of categories) in a way that permitted him to take set theory as basic in mathematics and to define cardinal numbers as classes of classes. Russell's efforts to cope with the contradictory notion of the class of all classes not members of themselves (a notion one seems forced to admit with Frege's analysis) produced the theory of types.

The conclusion suggested by the difficulties encountered in the theory of types, that categories as setting limits of cognitive meaning are not proper subject matter for a theory, was first advanced by Ludwig Wittgenstein. In his early work, Tractatus Logico-philosophicus, Wittgenstein spoke of the limits of cognitive meaning as the ineffable, as what can be shown but not said. In his later writings he repudiated the suggestion that the limits constitute an ineffable subject matter, something to be unveiled but not articulated as a theory by philosophical analysis. Nevertheless, with the assumption of such subject matter philosophical clarity is to be achieved by the construction of an ideal language, a language is stripped of all superfluous symbolism and is hence unable to give the illusion of transcending the ineffable limits of cognitive meaning. But if this assumption is itself an illusion, as Wittgenstein later held, if we can no more show than we can state the limits of all language, then philosophical clarity can be achieved only piecemeal, context by context; there is no short cut via an ideal language. And a fortiori there is no universal scheme of categories to be unveiled, let alone to be established by a theory. Wittgenstein's influence may be seen in the hesitation of Ryle, Strawson, and other present-day analytical philosophers to claim that categories should (or can) have the absolute universality claimed in theories of categories from Aristotle's to the theory of types.

See also Aristotle; Berkeley, George; Boethius, Anicius Manlius Severinus; Descartes, René; Frege, Gottlob; Hegel, Georg Wilhelm Friedrich; Hume, David; Husserl, Edmund; Kant, Immanuel; Leibniz, Gottfried Wilhelm; Locke, John; Peirce, Charles Sanders; Platonism and the Platonic Tradition; Plotinus; Porphyry; Russell, Bertrand Arthur William; Ryle, Gilbert; Smart, John Jamieson Carswell; Strawson, Peter Frederick; Type Theory; Whitehead, Alfred North; Wittgenstein, Ludwig Josef Johann.

Bibliography

standard histories

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newer works

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Anscombe, G. E. M., and P. T. Geach. Three Philosophers. Ithaca, NY: Cornell University Press, 1961. Contains penetrating but difficult discussion applying recent techniques of analysis to problems of categories in Aristotle, Thomas Aquinas, and Frege.

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Manley Thompson (1967)