SOURCE: "The Ontology of William of Ockham" in Ockham's Theory of Terms: Part I of "Summa Logicae," by WIlliam of Ockham, translated by Michael J. Loux, University of Notre Dame, 1974, pp. 1-22.

[In the following essay, Loux focuses on some problems inherent in Ockham's use of the terms concrete and abstract.]

The distinctions between singular and general terms, on the one hand, and abstract and concrete terms, on the other, play crucial roles in discussions of ontological issues. Although these dichotomies can be expressed in purely grammatical terms, they have traditionally been thought to point to two over-arching distinctions among things. Philosophers have frequently claimed that the singular-general term distinction is rooted in a distinction between objects that are particulars and objects that are universals; whereas, the distinction between concrete and abstract terms forces us to confront the distinction between substances (minimally interpreted to include material bodies and persons) and the various characteristics they possess or exhibit.

But because they appear to carry these far-reaching metaphysical implications, these grammatical dichotomies receive detailed treatment at the hands of the nominalist. If his theory is to be at all plausible, the nominalist must have the resources for providing a metaphysically neutral account of the singular-general and concrete-abstract dichotomies. In this essay I want to examine William of Ockham's ontology by focusing on his treatment of these distinctions. My aim here is twofold. By examining Ockham's analysis I hope to provide an introduction to the central themes of Part I of the Summa Logicae and to clarify the concept of a nominalistic ontology in general.

I

Like most philosophers in the Aristotelian tradition, Ockham distinguishes between propositions and the terms out of which they are composed. Central to Ockham's analysis of the concept of a term is his distinction between categorematic and syncategorematic terms. We can get at this dichotomy if we distinguish between expressions that do and expressions that do not yield a meaningful proposition when substituted for 'x' in 'This x-es' or 'This is (a/an) x'. The former (including predicate-expressions, proper names, demonstratives, and pronouns) Ockham calls categorematic terms; the latter (including articles, particles, interjections, quantifiers, and truth-functional connectives) he calls syncategorematic terms.¹

It is among categorematic terms that Ockham locates the distinction between singular and general, or employing Ockham's own terminology, the distinction between discrete and common terms. Very roughly, this is the distinction between categorematic terms that can and categorematic terms that cannot function as predicate in subject-predicate propositions, or that at least is the way a contemporary Ockhamist would express the dichotomy. Ockham himself construes the subject-predicate nexus more broadly to include identity-statements, existential propositions, and propositions incorporating either the universal or particular quantifier. Against this broad interpretation of subject-predicate discourse, Ockham tells us that while the discrete term is predicable of just one thing, the common term is predicable of many.

I have indicated that this distinction has traditionally been associated with the distinction between universals and particulars. For the medieval, the view that these two distinctions are related was legitimized by Aristotle's claim that the universal is that which is predicable of many. In a number of medieval philosophers this relation was explicated in terms of the notion of signification. The claim was that while discrete or singular terms signify particulars, common or general terms signify universals.

In medieval semantics, 'signify' was used as a transitive verb linking categorematic terms with their non-linguistic counterparts. Underlying this usage was the notion that categorematic terms are signs of objects, and the concept of a sign at work here was interpreted in psychological terms. A categorematic term is the sign of an object in the sense that the utterance of the expression has the effect of "bringing that object before the mind" of anyone familiar with the conventions governing the language in which the expression is embedded. The fact that signification involves a word-thing relationship suggests that the medieval notion of signification corresponds to the contemporary notion of reference; but in fact, the two concepts are quite different. The contemporary view tends to be that terms refer (or are used to refer) to objects only within the context of a proposition. The medievals, however, held that the signification of a term is a property which it exhibits quite independently of its role in any particular proposition; and they claimed that, at least in the case of univocal terms, the significatum of a categorematic expression is invariant over the various referential uses to which the term is put. Although it is explicitly relational, the medieval notion of signification is probably closer to the contemporary notion of meaning. In contemporary terms, the medievals were claiming that to know the meaning of a categorematic term is to know which object is its significatum.

At any rate, medieval philosophers frequently held that while discrete terms signify particulars, general terms take universals as their significata. This view is attacked throughout the Summa. Ockham wants to claim that a general term like 'man' does not have just one significatum—a universal; on the contrary, 'man' signifies indifferently each of the many individuals of which it can be truly predicated. Thus, knowing what that term signifies does not involve any cognitive relationship with a Platonic entity; it merely involves the ability to distinguish between objects that are and objects that are not men.

Nor do general terms introduce universals when they function as the predicates of subject-predicate propositions. In predicating a general term of an object, Ockham insists, we are not saying that the object exemplifies a universal; we are merely ascribing to the object a name which is common to several things. Thus, in the simplest kind of case (the affirmative, present-tensed proposition where the referent of the subject-term actually exists) a subject-predicate proposition is true if the subject is numbered among the things signified by the predicate term; otherwise, it is false.² The account may become more complex as we introduce into subject-predicate discourse negation, the various modalities, and past and future tenses; but in no case will our account require the existence of any objects other than those that can serve as logical subjects in predication.³

While he insists that general terms do not signify universals and that universals construed as extra-linguistic objects are irrelevant to the analysis of predication, Ockham grants that the distinctions between singular and general terms and particulars and universals, are intimately related. What he wants to deny and what he takes Aristotle to be denying is that the latter distinction lies hidden somewhere beneath the former. Ockham contends that Aristotle's point is that the two distinctions are identical: the only universals are elements in language—terms predicable of many. The mistake is to construe 'universal' as an expression marking out a kind of object in the real order; the term points to a distinction in the logical order, a distinction among linguistic elements.⁴

Ockham does not, however, mean to claim that universals are mere flatus vocis, that they are simply noises or marks on a page. He interprets language more broadly to include, besides spoken and written language, human thinking. The view is that human thinking proceeds by way of a mental language. This language incorporates terms, and like the terms of spoken language they are either categorematic or syncate-gorematic. These mental terms play different roles, but unlike the terms of spoken language they play these roles naturally. They are not items that are conventionally assigned certain linguistic roles. It is rather that mental words—in their intrinsic nature—just are the sorts of things that can play the roles they play.

Ockham describes the mental language, which is the vehicle of thinking, in terms of concepts appropriate to spoken language. Mental language incorporates different parts of speech: names, verbs, adverbs, etc., and the mental terms belonging to these grammatical categories exhibit many of the grammatical features of spoken terms. Thus, mental names exhibit both case and number; whereas, mental verbs exhibit mood, voice, number, etc. Although he wants to describe mental language by employing concepts pertaining to spoken language, Ockham insists on the ontological priority of mental language. For one thing speech is a mere extension of thinking. In this connection Ockham tells us that speech is related to thinking in much the way that writing is related to speech. Written language is an extension of spoken language in contexts where speech is impossible. It involves a complex set of conventions according to which marks on a page perform the same functions as spoken words. In the same way, we want to think out loud, so to speak, and since the elements of mental language cannot be used in this way, we must employ new materials. Unlike the original linguistic elements, these new materials are not in their intrinsic nature suited to play the variety of linguistic roles. We need conventions, then, assigning this or that role to this or that phoneme or string of phonemes. Thus, speech is an outgrowth of thinking: the terms of spoken language are signs that conventionally play the roles naturally played by mental terms. But the ontological priority of mental language comes out in another way. Ockham tells us that preceding every tokening of a linguistic unit in speech there is a mental tokening of the natural sign to which the relevant spoken sign is subordinated. It is plausible to interpret this remark in terms of causation. Mental tokenings, one wants to say, cause the relevant spoken tokenings.

Mental language like spoken language exhibits the distinction between discrete and common terms. Some elements in mental language are appropriate to just one object; whereas, other mental words signify many and, consequently, can function as predicates in mental propositions. Thus, mental words like spoken words conform to Aristotle's characterization of the universal. In fact, the concept of universality applies most properly to mental terms. The common terms of mental language are universals by nature. They are not items to which mere convention attributes universality; of and by themselves, they are just the sorts of things that are predicable of many. Further, it is here that we find the roots of all universality. On the one hand, the common terms of conventional language represent a mere extension of the common terms of mental language: they are mental words thought out loud. On the other hand, the tokenings of mental universals are causally responsible for the physical tokenings of spoken universals: occurrences of mental universals cause occurrences of conventional universals.

But with what objects are we to identify the natural universals of mental language? Here Ockham provides us with a bit of leeway. While pointing to three different accounts he suggests that only one is correct. The first two accounts are not clearly distinguished in Ockham. They agree, however, in exhibiting an act-object analysis of human thinking. On these views, although universals have a merely mental existence, they are numerically distinct from acts of thinking and are construed as the objects of those acts. On the third view, universals are identified with the different acts of thinking themselves. Here, we are to distinguish for example, thinkings-of-a-man from thinkings-of-a-dog. The two are construed as acts intrinsically different from each other, and the universals man and dog are identified respectively with these different mental acts. Ockham expresses a guarded preference for this view:

But all the theoretical advantages that derive from postulating entities distinct from acts of the understanding can be had without making such a distinction; for an act of the understanding can signify something and can supposit for something just as well as any sign. Therefore, there is no point in postulating anything over and above the act of understanding.⁵

Thus, Ockham agrees that we can get below the distinction between discrete and common terms as it manifests itself in external, spoken language; but he wants to deny that what we reach is a distinction between kinds of things in the real order. What we reach on the contrary is the same old distinction now functioning within the context of a new sort of language. To bring out the force of his account, Ockham distinguishes between what he calls first intentions and second intentions. A mental word is a first intention if at least one of the things it signifies is not a mental word; whereas, a mental word is a second intention if it has at least one significatum and is not a first intention. Employing the distinction, Ockham tells us that the mental word universal is a term of second intention.

II

While plausible in isolation, Ockham's account of the role of general terms in predication appears more dubious when we confront the issue of abstract terms like 'paternity' and 'humanity'. Expressions of this sort surely appear to play essential roles in true propositions; but qua playing these roles they would seem to commit us to the existence of abstract entities, objects over and above individual substances like men and trees. But we are committed to Platonic entities in any event, so that there is no reason to strain at a Platonic analysis of predication. Like many reductionists Ockham finds the issue of abstract terms the major obstacle to a thorough-going nominalism. He spends more than half of Part I of the Summa providing an account of their role in language.

In Ockham the term 'abstract' is used in contrast with the term 'concrete'. The distinction here is purely syntactical. It is the distinction between normal predicative expressions like 'man', 'black,' 'animal', and the nouns built from these by the addition in English of suffixes like '-ity', '-ness', '-hood', and '-kind'. The following examples illustrate the contrast in question: 'wise'—wisdom', 'triangular'—'triangularity', 'man'—'mankind', and 'black'—'blackness'.⁶

As a syntactical distinction the dichotomy between abstract and concrete is relatively harmless, but as we have suggested the nominalist is likely to experience problems when he attempts to get at the semantics behind the distinction. These problems stem from what appears to be a perfectly natural interpretation of the dichotomy. It is natural, that is, when confronted with terms like 'wisdom' and 'wise' to say that whereas 'wisdom' signifies some characteristic or quality, 'wise' signifies the individuals who exhibit the quality, signifying besides the characteristic or quality in question. Beginning with examples like this it is easy to generalize. Abstract terms, we are tempted to say, signify abstract entities; their concrete counterparts signify the individuals exhibiting those abstract entities, signifying, in addition, the abstract entities they exhibit.

In Ockham's terminology, this account of abstract and concrete terms amounts to the proposal to treat all abstract terms as absolute and all concrete terms as connotative.⁷ When he introduces this crucial dichotomy, Ockham tells us that while absolute terms have only primary signification, connotative terms have both primary and secondary signification. So far, we have used 'signify' and its cognates very generally. We have said that a categorematic term signifies an object in the sense that it is a sign of the object; and, following the medievals, we have interpreted the notion of a linguistic sign in a psychological idiom. In less overtly psychological terms, we have used the term 'signify' in such a way that a term 'x' signifies an object, a, just in case the use of 'x' has the effect of introducing a into discourse. Henceforth, I shall use the numerical subscript '0' to mark this sense of 'signify'.⁸

As the definition suggests, to say that a term, 'x, signifies₀ an object, a, is to provide very general information about the semantical relationship between 'x' and a. To provide more determinate information, we must employ the distinction between primary and secondary signification. Ockham never defines these notions; but from his use of the terms, it is clear that a term, 'x', signifies primarily (signifies,) an object, a, just in case 'x' signifies₀a and 'a is (an) x' is true. If we employ the term 'predicate' as Ockham does (so that both singular and general terms can function as predicates), we can say that a term signifies₁ all and only those objects of which it can be truly predicated.⁹ Thus, 'man' signifies₁ the various individuals who are men, 'Socrates' signifies₁ Socrates, and 'triangular' signifies₁ all the objects which are triangular.

The notion of primary signification, however, points to only one way in which the use of a term can introduce an object into discourse; for terms can signify₀ objects which they do not signify₁. Suppose that there is such a thing as whiteness, that 'whiteness' signifies₁ whiteness. On that supposition, it seems plausible to think that the use of 'white', in some sense, directs the attention of our audience to whiteness. 'White', we want to say, just means 'object having whiteness'. But, then, 'white' signifies₀ whiteness. It does not, however, signify₁ whiteness; whiteness, to follow a long tradition, is not white; objects having whiteness are. Labelling the style of signification at work here, Ockham says that 'white' signifies secondarily (signifies₂) or connotes whiteness.

The secondary signification of 'white', unfortunately, is not paradigmatic. Most cases deviate from the pattern set out above. Not only does the relationship of signification₂ differ drastically in these cases, but the things that are signified₂ are also very different. Besides qualities like whiteness and wisdom, a term can signify₂ the constitutive parts of an object and even the truth of a contingent proposition. The best our account can be then is very general. Taking advantage of the vagueness of 'object', let us say that a term, 'x', signifies₂ an object, a, just in case 'x' signifies₀a, but does not signify₁a.¹⁰

With these notions under control we are tempted to follow Ockham's lead and define an absolute term as one that signifies₁ whatever it signifies₀ and a connotative term as one that signifies₁ some of the objects it signifies₀ and signifies₂ others among those objects. But while this works well in the case of absolute terms, it fails to capture the notion of a connotative term; for although he defines this notion in terms of both primary and secondary signification, Ockham's subsequent use of the term 'connotative' is such that terms which have significata₂ but no significata₁ can be connotative. Only in connection with simple cases like 'white' does Ockham stipulate that connotative terms have both primary and secondary significata. To take account of this fact, we must state our definitions as follows:

A term, 'x, is absolute just in case the class of objects it signifies₀ is wholly composed of significata₁ of 'x'.

A term, 'x, is connotative just in case at least one of the significata₀ of 'x' is a significatum₂ of 'x'.

We can now apply this distinction to what I have called the "natural" interpretation of abstract and concrete terms. That interpretation, I claimed, has the effect of converting all abstract terms into absolute terms and all concrete terms into connotative terms. In that interpretation a term like 'triangularity' is construed as an expression signifying₁ the abstract entity triangularity and signifying₂ nothing else; whereas, a term like 'triangular' is construed as signifying₁ the objects that have triangularity while signifying₂ the triangularity they have. More generally, the interpretation would claim that in the case of every pair of terms of the form 'F-ness' and 'F, the abstract form, 'F-ness', signifies₁F-ness and the concrete form 'F' signifies₁F-things and signifies₂F-ness.

To construe abstract and concrete terms in this way, I have claimed, is natural. To the extent that it clarifies what surely appear to be genuine refering uses of abstract terms, the construction is even plausible. But while natural and plausible, the interpretation carries with it a Platonic ontology, an ontology replete with abstract entities of every sort. The account offends against our desire for theoretical simplicity and should, if possible, be suppressed. But how? Although the existence of abstract terms is an undeniable fact, are we committed to treating all such expressions as absolute terms? If not, what sort of account is appropriate?

These questions isolate the problems Ockham sets himself in the central sections of the Summa. He is, however, suspicious of anything like a general solution to these problems. Since he thinks that there may be important differences among abstract terms, he insists on examining the issue by cases. What we need is some method for sorting out abstract terms. In this context Ockham fastens on Aristotle's categories. He claims the categories provide us with a natural ordering of abstract terms; they enable us to consider the ontological merits of abstract terms case by case.

Traditionally, Aristotle's categories have been interpreted as a list of the most general kinds to which objects can belong. If this interpretation is correct, there is something incohererit in Ockham's suggestion that we employ the categories as a framework for an investigation seeking to determine the extent of our ontic commitments. The categories in this interpretation are themselves the results of just such an investigation; they represent a list of all the objects to which we are ontologically committed. It is not surprising, then, that Ockham stands opposed to this traditional interpretation of the categories. The categories, he insists, involve a minimum of ontological presuppositions. They are not a classification of non-linguistic objects at all, but an attempt to classify categorematic terms according to what Ockham calls their mode of signification.

Ockham explicates this notion of the mode of signification by focusing on the various questions we can ask about an individual substance like Socrates. More specifically, he focuses on all those questions raised about an individual substance that are susceptible of one-word answers other than 'yes' and 'no'. Each of these questions can be answered meaningfully, even if falsely, by a large number of categorematic terms. Let us think of each such question as collecting all the categorematic expressions which can be meaningfully employed as answers to that question, and let us say that the terms collected by any given question constitute the answer-range of that question.

The answer-range of different questions will tend to overlap. Thus the terms constituting the answer-range of one question will constitute only a segment of the answer-range of another question. The answer-range of 'What color is he?', for example, constitutes only a part of the answer-range of 'How is he sensibly characterized?' The second question, we can say, is more general than the first; its answer-range is broader. We can, then, by moving to ever more general questions, generate answer-ranges that are ever more extensive. Ockham denies, however, that we can proceed to infinity in this manner; he also denies that we can reduce the multiplicity of answer-ranges to an absolute unity. In our search for ever more general questions about substance, we arrive, sooner or later, at ten very general questions. They constitute the most general questions we can raise about substances. Their answer-ranges, Ockham contends, are both mutually exclusive and collectively exhaustive. No categorematic term is included in the answer-range of more than one of these ten questions, and every categorematic term is included in the answer-range of one of the questions. According to Ockham the ten questions are: What is it? (Quid?); How is it qualified? (Quale?); How much is it? (Quantum?); How is it related to other things? (Cuius? or Ad Quid?); What is it doing? (Quid agit?); What is being done to it? (Quid patitur?); Where is it? (Ubi?); When is it? (Quando?); In what position is it? (In quo situ?); What does it have on? (In quo habitu?).¹¹

Ockham identifies the answer-ranges of these ten questions with Aristotle's ten categories. Thus, the answer-range of 'What is it?' constitutes the category of substance; the answer-range of 'How is it qualified?', the category of quality and so on. According to Ockham each of the categories is composed of terms that convey one very general kind of information about substance. Thus all the terms included in the answer-range generated by 'What is it?' convey information about what substances are; whereas, the terms included in the answer-range of 'How is it qualified' convey information about the qualitative determinations of substances. Using Ockham's own terminology, the terms in a given category signify, substance in a particular mode. Terms from the category of substance signify₁ substances essentially or in the mode of substance; terms from the category of quality signify₁ substances qualitatively or in the mode of quality and so on.

But there is a difficulty with this account. Even if we accept the dubious claim that none of the ten questions can be reduced to any other questions in the list, we are likely to wonder just how the scheme accommodates the abstract terms that were the origin of our appeal to the categories. Employing Ockham's technique for classifying terms, we discover that all abstract terms fall under the category of substance. The only one of the ten very general questions that abstract terms can serve to answer meaningfully is the question, 'What is it?' All the other questions require concrete terms as answers. But clearly this is an unfortunate consequence. For one thing, we appealed to the Aristotelian categories because we wanted a framework for sorting out the various abstract terms. If, however, we employ Ockham's interpretative scheme, the categories are useless in this connection. But quite apart from our search for a classification of abstract terms, there is a difficulty surrounding the allocation of abstract terms to the category of substance. Terms in the category of substance supposedly all signify, substances. Indeed, it is precisely because abstract terms do not appear to signify₁ substances but other more problematic entities that we are engaged in the analysis. Abstract terms appear to be absolute, to signify₁ abstract entities, so that allocating them to the category of substance is inappropriate.

Ockham is aware of these difficulties. His response is to deviate from the scheme and simply to stipulate that abstract terms be placed in the same category as their concrete counterparts. He feels that this stipulation provides us with a natural ordering of abstract terms. It is only plausible to assume, he would claim, that the counterparts of terms exhibiting a particular mode of signification will be sufficiently similar to allow a uniform treatment. Furthermore, although Ockham would construe this stipulation as merely provisional, he wants to claim that the ensuing analysis will vindicate his move. In general, it will show that if abstract terms have any place in the system they belong with their concrete forms.

Ockham's treatment of substance focuses in large part on the problem of universals. His concern here is to provide a neutral account of Aristotle's distinction between first and second substances, but in a number of places Ockham examines the relationship between abstract and concrete terms from the category of substance. In these contexts, he attacks a view that is essentially an application of what I have called the 'natural' interpretation of abstract and concrete terms to expressions in the category of substance. On that view, abstract terms from this category signify₁ the essence or nature in virtue of which substances are what they are; whereas their concrete counterparts signify₁ the various individual substances while signifying₂ or connoting their essence. Ockham's attack on this view comes out in a number of arguments that are likely to appear hopelessly mysterious to the contemporary reader.¹² While I do not pretend to understand those arguments in detail, I find a common theme running throughout. Ockham, I want to suggest, is arguing that the proponent of this view can make his account intelligible only if he appeals to the notion of bare substrate. Essentially, Ockham is challenging the proponent of essences to locate the subject or bearer of the postulated essences. That subject must be something such that by adding the essence to it we get, for example, men. It might seem that the relevant subjects are the individual substances in question, but Ockham insists that this will not do. The individual substances already are men, so that there can be no question of adding something to them to make them men. More generally, the subjects of essence cannot be entities to which the sortal predicates in the category of substance apply. Such objects already possess whatever it is that an object needs to be a substance of this or that sort. The subject of essence, Ockham claims, must lie at a level below that at which substance sortals apply. What though would an object from that level be like? It would have to be an entity conforming to Locke's characterization of substrate, a "something I know not what." But surely, we can take Ockham to be claiming, a mysterious entity like bare substrate should play no role in our theory.

As I read him, Ockham is claiming that the proponent of this view is committed to bare substrate because he distinguishes between substance and essence. Ockham's counter is simply to identify the two. But having identified substances and their essences, he cannot construe the relevant abstract terms as expressions signifying₁ (and their concrete counterparts as terms signifying₂) objects distinct from substances. His account of concrete terms from the category of substance is straightforward. Ockham claims they are absolute terms; the only objects they signify₀ are their significata₁—the various individual substances.¹³ Abstract terms, he suggests, present more serious difficulties. The above claim that they do not signify, anything distinct from individual substances suggests that their role is precisely the same as that of their concrete counterparts. But this is to say that they are synonymous with their concrete counterparts, and that is surely wrong. Ockham is fairly liberal in his use of the term 'synonymous'. He claims that two terms 'x' and 'y' are synonymous if and only if (1) 'x' and 'y' are mutually intersubstitutable and (2) 'x' and 'y' are mutually predicable of each other, and as Ockham is quick to point out the abstract and concrete terms in question fail to satisfy either (1) or (2). Thus, in violation of (1), while 'Man runs' is true, 'Humanity runs' is false; and in violation of (2), both 'Man is humanity' and 'Humanity is a man' are absurd.¹⁴

What Ockham feels he needs here is an account of the role of abstract terms from the category of substance that will accommodate his reductive analysis of that category while preserving the conceptual gulf between abstract and concrete. The account he presents is ingenious. Ockham tells us that a term like 'humanity' incorporates one or more syncategorematic elements in its meaning. Here it differs from its concrete counterpart so that, in a quite ordinary sense, the two differ in meaning. Thus, 'humanity' unlike 'man' is what Russell called an incomplete symbol. Its meaning cannot be explicated in isolation—simply by pointing to one or more objects. What we must do if we are to exhibit the meaning of an abstract term like 'humanity' is to indicate the various propositions in which it can occur. Ockham is not altogether clear about the structure of these propositions; but he appears to hold that they all involve the concept of necessity, that (in the case of 'humanity') they incorporate a context of the following sort: 'Men… necessarily.…' Thus 'humanity' is not a device for referring to objects over and above the individuals that are men, but neither is it simply a device by which we refer to men. It is an expression which provides us with an abbreviated way of making claims about what necessarily is true of men qua men.

Thus, even though abstract terms from the category of *substance introduce no new entities, they are not synonymous with their concrete counterparts. But in showing this Ockham provides us with a technique for eliminating from discourse all abstract terms in the category of substance. We cannot simply replace an abstract term, 'F-ness', with its concrete counterpart F', but we can employ the scheme hinted at above. Thus, all contexts of the form 'F-ness…' can be supplanted by modal contexts of the form 'F-things necessarily.…' There are, of course, gaps in Ockham's account. His schema tells us how to handle expressions of the form F-ness', but it would seem that the move from 'F-ness…' to 'F-things necessarily…' will involve changes in one or more expressions occurring in that part of the context 'F-ness…' that is designated by '…'; for presumably at least some of the expressions that are syntactically and semantically suited for predicative union with abstract terms cannot enter into the subject-predicate nexus with concrete expressions.

While it remains incomplete, the schema sketched above highlights the fact that abstract terms from the category of substance do not add to the significative power of language. As the schema shows, abstract terms provide short-hand ways of saying things that could be said exclusively with the use of concrete terms. But since abstract terms from the category of substance do not play purely significative roles, they cannot, strictly speaking, be either connotative or absolute. They do not signify₀ objects at all; they merely point to propositional contexts. Those contexts do, however, incorporate significative expressions—the concrete forms which signify₁ individual substances. This, I take it, is all that Ockham means when, summarizing the results of his account, he tells us that abstract terms from the category of substance signify₁ individual substances. Although he appears to be saying that abstract terms are absolute, he is really just pointing to the possibility of eliminating from language all the abstract terms in the category of substance. While not significative themselves, these abstract terms give way, under analysis, to propositional contexts incorporating terms that signify₁ substances.¹⁵

The category of quality incorporates, in the first instance, all such terms as can meaningfully serve to answer the question, 'How is it qualified?' and in the second instance the abstract counterparts of these terms. The speaker of English is likely to have a difficult time with this category. I have translated the Latin 'Quale?' as 'How is it qualified?', but the two are not really equivalent. English simply has no interrogative with the force of the Latin 'Quale?' The English abstract term 'quality', on the other hand, is more general than its Latin counterpart. In philosophical contexts the term is frequently employed as a general term covering all non-relational properties. But while the Latin term 'qualitas' is more selective, it is difficult to point to the principle of selectivity at work. This category incorporates what to the speaker of English must appear a very heterogenous group of terms. Among its abstract forms there are expressions (like 'sweetness' and 'whiteness') that purport to signify₁ the various sensible properties of objects, expressions (like 'courage' and 'wisdom') that purport to signify₁ overtly dispositional features like virtue and knowledge, and expressions (like 'straightness' and 'curvature') that purport to signify₁ the shape and form of substances.¹⁶

Given the heterogeneity of these terms, we are not surprised to find Ockham rejecting any single account of all the abstract terms in the category of quality. He wants to claim, on the contrary, that while some of the pairs of abstract and concrete terms from this category do conform to the "natural" interpretation outlined above, others do not. For some expressions in this category, then, the abstract-concrete and absolute-connotative dichotomies run parallel. Roughly, the pairs in question are those associated, on the one hand, with the perceptible qualities of objects and, on the other, with dispositional qualities. In both of these cases, Ockham wants to grant that abstract forms signify₁ objects distinct from substances; their concrete counterparts signify₁ the substances exhibiting these objects while signifying₂ the objects they exhibit.

In the case of abstract terms of this sort surface grammar does not altogether mislead us. They appear to signify₁ abstract objects and actually do. Nonetheless, if we attend only to surface grammar we are likely to construe these expressions as discrete terms. They are after all generally employed in this way in ordinary language. But it is very tempting to move from this fact of usage to the claim that terms like 'whiteness' and 'courage' each signify₁ objects that can be exhibited simultaneously by several different objects. Thus, the surface grammar of these terms tempts us to employ the term 'universal' as a term of first rather than second intention, as a term marking a distinction in the real order.

But it takes merely a moment's reflection to see that such a move is unsatisfactory. Suppose, for example, that whiteness were an object exhibited by all white things. Whiteness would, at any given time, be present in each of several non-continuous regions of space; but that Ockham contends is impossible. An object occupying two discontinuous regions of space at any given time would be divided from itself; it would be two objects and not one. The premise at work here is one that recurs in Ockham's treatment of the categories.

Essentially, it is the claim that if at any time, t, an object, a, is in a place, p₁, and an object, b, in a place, p₂ (where p₁ and p₂ are numerically different non-continuous regions, neither of which is a part of the other), then a and b are numerically different objects.¹⁷ But applying this premise in the present case we are forced to conclude that there can be no one object that is present in all white things. Our only alternative, Ockham wants to claim, is to deviate from ordinary usage and to treat absolute terms from the category of quality as common terms. If we follow Ockham's proposal we must say that there are as many whitenesses as there are white things and that each of these is signified₂ by 'whiteness'.

But while Ockham wants to accept at least part of the "natural" interpretation for terms like 'whiteness' and 'courage', he resists a parallel treatment of terms expressive of figure and form. These expressions, he contends, are not absolute terms signifying₁ entities in virtue of which substances are said to be straight, curved, and the like. There simply are no such entities. The form of argument at work here is characteristic of Ockham's treatment of the "natural" interpretation. According to the "natural" interpretation a substance is curved in virtue of possessing the entity curvedness. But is this the end of the story? Ockham thinks not. Even if a substance possesses the relevant entity it can be curved only if its parts are arranged in a certain way. That the parts of the substance be arranged in this way, then, is a necessary condition of the applicability of the predicate 'curved'. Ockham wants to claim, however, that it is also a sufficient condition. Suppose some substance were to lack the relevant entity. That substance nevertheless would be curved provided that its parts are arranged in the requisite way. The absence of curvedness would be irrelevant to the applicability of the predicate 'curved'. But the appeal to that entity is superfluous, and since it is superfluous the account should be avoided. The principle at work here is, of course, the principle of theoretical parsimony that has come to bear Ockham's name. As he says in a different context, "One ought not postulate many things when he can get by with fewer."

But we need an alternative account of expressions associated with figure and form. The concrete terms, Ockham tells us, are connotative. They signif₁ substances and such qualities as can be meaningfully said to have a shape or figure. Qua connotative they signify², but their significata² are not non-linguistic entities. A term like 'curved', Ockham claims, signifies₂ the truth of the contingent proposition which states that the conditions for the applicability of that term are satisfied. The proposition says in effect that the signified₁ substance or quality has its parts arranged in such and such a way.

Sometimes Ockham says that abstract terms expressive of figure and form are connotative terms synonymous with their concrete counterparts; nevertheless this claim runs counter to what seems to be his "official" position. It is I think merely a short-hand way of summarizing his views on figure and form. The "official" view is that abstract forms like 'straightness' and 'curvature' are terms only from a syntactical point of view. Semantically, they are like abstract terms from the category of substance; they are incomplete symbols which can be explicated only in terms of propositional contexts. As in the case of substance-words the relevant contexts appear to involve the modal concept of necessity. An abstract term like 'straightness' is a device for making claims about what is necessarily true of straight objects qua straight. Such terms are all, via the relevant modal contexts, eliminable in favor of the more familiar concrete forms.¹⁸

We have distinguished between terms that are and terms that are not expressive of figure and form. Ockham provides a more manageable criterion for determining when abstract terms from the category of quality are to be construed as absolute. Where 'F-ness' and 'F' are terms from the category of quality which are related as abstract and concrete, Ockahm's criterion tells us that 'F-ness' is absolute just in case it is impossible some object a, which does not satisfy 'F' at t₁ come to satisfy 'F' at t_1+n merely as the result of a change in place. Thus, Ockham wants to construe 'whiteness' as an absolute term, for he holds that an object that is not white cannot come to be white merely by undergoing local motion; but 'straightness', he would hold, is connotative. A curved bow, for example, can become straight merely as the result of the spatial rearrangements of its parts.

Ockham follows Aristotle in distinguishing terms expressive of continuous quantity and terms expressive of discrete quantity. The distinction between continuous and discrete quantities, at least as it functions in Aristotle, is the distinction between quantities (like the line) which have parts that are spatially contiguous and quantities (like the numbers) where the question, 'Where do its parts join?' makes no sense. Ockham and Aristotle both claim that terms expressive of continuous quantity point to the subject matter of geometry; whereas, it is among the terms expressive of discrete quantities that we find the expressions crucial in arithmetic.

Ockham's account of this distinction is, like his analysis of figure and form, reductionistic. He contends that neither geometry nor arithmetic presuppose entities over and above substances and qualities. He presents a large number of arguments in support of this claim. Many of these arguments parallel the argument I outlined in my discussion of figure and form: the relevant entities are useless as explanatory entities and should consequently be eliminated from our theory. Nevertheless, some of these arguments are meant to exhibit intrinsic difficulties in the notion of a uniquely mathematical object. In particular Ockham wants to point to difficulties involved in specifying subjects for these objects.

In the case of geometrical objects he argues that since points, lines, figures, and solids are not themselves substances, they must exist in something else. The obvious candidate here is material substance, but if we look to the case of geometrical points we see that this account is unsatisfactory. Points are indivisible in all dimensions; and according to Ockham, to locate the immediate subject of a point—"where" a point is—is to locate something that is itself indivisible in all dimensions. But since material substance and the parts of material substance are divisible in all dimensions, they cannot function as the subjects of points. The view that would make lines the subjects of points, Ockham also finds unsatisfactory. Lines, he points out, are divisible in one dimension. Besides, lines need subjects; and, according to Ockham, they must agree with lines in being indivisible in two dimensions. But neither material substances nor their parts can be the "where" of lines. Since they are divisible in breadth, surfaces cannot play this role either; but even if they could, surfaces require subjects, subjects that are indivisible in depth; and both material substances and geometrical solids fail to meet this requirement. But in any event geometrical solids require subjects and the only possible candidates here are material substances. We could provide subjects for geometrical solids by stipulating that the subject of a geometrical solid, x, be some material substance that is exactly congruent with x. But if we make this stipulation, Ockham concludes, the need for geometrical solids disappears. Whatever purpose a given solid is meant to serve, the material substance that is its subject serves as well.

A similar difficulty arises in the case of discrete quantities. Where, for example, does the duality of the two men I have just counted exist? According to Ockham it is not a self-subsistent entity: it must exist in some subject. Ockham would agree that in a general way it is easy to specify the subject of this entity—the two men. Difficulties arise when we try to be more specific. The duality of the two men cannot exist in just one of the men; it is the duality of both men. But neither can it exist in both of the men. The men are spatially discontinuous objects; and for Ockham we have seen it is a necessary truth that one and the same object cannot exist in spatially discontinuous subjects.¹⁹

According to Ockham the concrete terms from the category of quantity are, like the concrete forms expressive of figure and form, connotative expressions signifying, substances and qualities while signifying₂ the truth of some contingent proposition. In each case the connoted proposition states that the conditions required for the applicability of the term in question have been satisfied, and invariably these conditions focus on the results of some procedure of measurement or counting. Their abstract counterparts receive the form of treatment that by now should be familiar; they are construed as incomplete symbols to be analyzed in terms of contexts involving necessity. They are simply devices for making statements about what is necessarily true of substances and qualities qua satisfying the various concrete terms from this category. To speak then of continuous quantities is simply to make claims about substances and qualities qua long, triangular, etc., and to speak of discrete quantities is to speak of substances and qualities qua enumerable as two, three, four, etc. But, then, neither geometry nor arithmetic require entities over and above substances and qualities; the subject matter of mathematics is wholly constituted by these objects qua satisfying the relevant quantitative predicates.

When Ockham introduces the categories he tells us that there is no interrogative in Latin that is syntactically suited to collect all and only the concrete terms from the category of relation; thus, when he deals with the category in isolation he attempts to provide a more detailed analysis of relative expressions. He tells us that the various concrete forms in the category come in pairs such that an object, a, can satisfy one of the predicates from the pair only if there exists some other object, b, such that a satisfies the relevant predicate with respect to b and b in turn satisfies the other predicate in the pair with respect to a.²⁰ 'Father' and 'son' are examples. If an individual is to be a father there must be some other individual whose father he is, and that individual in turn must be his son.

Philosophers have frequently claimed that the individuals a and b, which pairwise satisfy expressions of this sort, are themselves related or relatives and that there is some third entity that serves to bring them together, to relate them. Ockham rejects out of hand the suggestion that some third entity is involved here. That object would have to exist in something. If we focus on the case of a father and son we see that the relevant entity could not exist in just one of these men, for it supposedly brings the two of them together. Neither could it exist in both men, for the men are spatially discontinuous objects and cannot be the subject of numerically one entity.

To the claim that a third entity is required to tie the related individuals together Ockham responds with an argument that in some ways reminds us of Bradeley's argument against relations. If we are told that two objects can be relationally tied together only by the mediation of some third entity, we must ask, Ockham claims, how that entity is related to the original two entities. Is it related to them immediately—without the mediation of additional entities? If it is then objects can be related immediately so that there was no need to postulate such an entity in the first place. If it is not then additional entities must be introduced into the analysis; and, of course, the same question will arise with respect to these entities. Now, either we will at some point arrive at a relating entity that is immediately related to the objects it relates or we will not. If we do it is possible that there be immediately relatable objects. But in that case it seems that relations in general are unnecessary, for, as we have said, we could have construed our original objects as immediately relatable. If, on the other hand, we do not arrive at immediately relatable objects, we are faced with an infinite regress in which case relating entities are powerless to do the job assigned them.²¹

Not only does he reject the notion of relations, but Ockham finds it dangerous to speak of the individuals signified₂ by relative terms as related or relatives. It can lead us to think that there is something in the being of those objects that is merely relative, and that Ockham thinks is absurd. It is better, he suggests, to reserve the term 'relative' for the various concrete terms in the category. This amounts to the proposal to treat the term 'relative' as a term of second intention, as a term predicable exclusively of linguistic objects.²² As regards the abstract counterparts of relatives, Ockham again follows the general procedure introduced in the case of substance. The expressions are mere facons de parler; they provide us with shorthand ways of saying things that could be said exclusively with the use of the less problematic concrete forms.

Ockham's treatment of the remaining six categories is relatively brief. The same general pattern is exhibited throughout. In each case Ockham rejects the "natural" interpretation outlined earlier. On his view, the concrete forms from the various categories are to be construed as connotative terms signifying₁ only substances and qualities while signifying₂ the truth of contingent propositions which state that the conditions required for the applicability of the relevant predicates have been met. The abstract forms do not, of course, introduce any new entities, and this tempts us to say that there are synonymous with their concrete counterparts. But while Ockham sometimes says this, his considered view is that they are not terms at all but incomplete symbols to be parsed along the lines suggested above.

But if we think back to Ockham's account of the categories, we see that his analysis alters his original conception of the classification. The categories were first presented as a classification of categorematic terms according to the mode in which they signify¹ substances, and at that point all abstract terms seemed to cast doubt on Ockham's account. The subsequent analysis, however, has shown that most abstract terms are eliminable so that their inclusion in the categories is not really problematic at all. Although they cannot serve to answer the various category-generating questions, they are analyzable in terms of expressions that can.

But while most abstract terms are eliminable those that purport to signify¹ sensible and dispositional qualities are absolute and, therefore, essential to the significative power of language. But it turns out to be a mistake to construe the categories as a classification of terms according to the mode in which they signify¹ substances. For one thing abstract qualitative terms do not signify¹ substances at all; for another the various concrete terms from the adjectival categories can, as Ockham's analysis of those categories indicates, signify qualities as well as substances, Patches of color, for example, can be round or square; can be of such and such a length; can be in this or that place; etc.

Thus, we must broaden our conception of the categories and construe them as a classification of terms according to the mode in which they signify₁ objects (where 'object' is neutral as between substances and qualities). But, then, although Ockham himself never makes the move, there would be good reason for subsuming the various non-eliminable abstract terms from the category of quality under the category of substance. Such terms do not signify₁ anything at all in the mode of quality, so that they do not belong in that category; and although they do not signify₁ substance, they agree with terms like 'man' in signifying₁ their significata₁ in the mode of essence or substance—by telling us what those significata₁ are. Given the broadened conception of the categories to which Ockham's analysis has driven us, this entails that abstract terms like 'whiteness' and 'courage' belong in the category of substance.²³

But this is not to say that substances and qualities are not very different sorts of things. Ockham is clear on this point. Whereas substances are independent entities which can exist of and by themselves, qualities can only exist in another. But while Ockham wants to preserve the distinction between substances and qualities, he stands opposed to a view that dominates the traditional interpretation of Aristotle's categories. On that view transcendental terms—universally predicable expressions like 'object', 'entity', and 'thing'—are not univocally predicable of everything. They have different meanings when they are predicated of things as different as substances and qualities. Ockham pays lip service to this view—doubtless because it is a view that Aristotle is fairly explicit about defending;²⁴ nevertheless, his considered opinion is that the view is wrong.

Ockham's account of ambiguity or, as he calls it, equivocality, takes as its background the theme that spoken language is an extension of mental language. He tells us that a term is univocal if it is subordinated to or an extension of just one mental word; whereas, expressions that serve as extensions of different mental words are equivocal. 'Bat', for instance, plays in different contexts the roles of two quite different natural signs and consequently is equivocal. Now Ockham tells us that there is at least one transcendental expression which is, in its application to all objects, subordinated to just one mental word. That in effect is to say that at least one transcendental term is univocally predicable of all things.

Ockham's most detailed defense of this claim is found in that section of the Summa Logicae that immediately precedes his analysis of the categories. At first glance it appears that he is presenting us with an argument here, but if we look closer it becomes clear tht he is merely stipulating that there is one mental word that is predicable of all objects. Given the context, however, we need not construe Ockham's stipulation as arbitrary; we can, on the contrary, construe him as stating a presupposition for the ensuing analysis of the categories. That analysis is an ontological investigation; it is an attempt to determine what there is. Ockham can be interpreted as saying that unless some one expression is univocally predicable of all things, we can make no sense of that investigation. Ontology has maximal generality of scope; there is nothing that is not incorporated in its subject matter, for the task of the ontologist is to determine what objects, entities, or things there are. But notice that unless there is some one expression that is univocally predicable of all things, we cannot say this. To specify the subject matter of ontology we need some term like 'entity', 'object', or 'thing' that can in one sense be applied to everything. As I interpret him Ockham is telling us that there must be one universally predicable mental word to which at least one conventional transcendental is subordinated. Without this the analysis that follows makes no sense.

Notes

¹ Although Ockham defines the term 'syncategorematic' more narrowly than this in chapter 4, his subsequent use of the term converges with mine. See, for example, chapter 69.

² To be accurate here we would have to employ the distinction between primary and secondary signification that I outline later. Employing that distinction we would have to say that a proposition of this sort is true just in case the subject is numbered among the primary significata of the predicate; otherwise it is false. This issue of truth conditions is pursued in the second paper, "Ockham on Generality."

³ Of course it may be that other entities are involved, but Ockham wants to claim that if this is so the analysis of predication will never reveal it. The pressure to postulate additional entities must come from other quarters. As it turns out, additional entities (albeit individuals) are involved in the use of some predicates from the category of quality; but as the second part of this paper shows, it is the analysis of abstract terms and not predication that establishes this fact.

⁴ There is, of course, one sense of 'particular' in which 'particular' designates real, i.e. non-linguistic entities, but in that sense it is not opposed to 'universal'. See chapters 14 and 19 for an account of this sense of the term.

⁵ This account is likely to remind the reader of Wilfrid Sellars' account of intentionality. Sellars himself admits his debt to medieval philosophy in general in "Being and Being Known" in Science, Perception, and Reality (New York: Humanities Press, 1963), 41-59 and to Ockham, in particular, in "Towards a Theory of Categories" in Experience and Theory, Lawrence Foster and J. W. Swanson, eds. (Amherst: University of Massachusetts Press, 1970), 55-78.

⁶ Ockham himself introduces this dichotomy as a distinction among names, a grammatical category incorporating both nouns and adjectives. Nonetheless, this same sort of phenomenon is at work in the case of other parts of speech, e.g., verbs and their gerund-forms ('run' and 'running'). Fastening on this fact I speak not of concrete and abstract names but of concrete and abstract terms.

⁷ Again, Ockham presents this dichotomy as a distinction among names; but here he clearly is tempted to extend the distinction beyond that grammatical category. Thus, he speaks of verbs, adverbs, etc. as connoting this or that about substance and quality. Following out these hints, I speak of absolute and connotative terms rather than names.

⁸ 'Signify₀' is neutral as between the four senses of 'signify' outlined in chapter 33. In place of this sense of 'signify', Ockham frequently employs the term 'importare'. Literally this means "to carry into" and conveys clearly the notion of introducing into discourse.

⁹ 'Signify₁' is roughly equivalent to the first sense of 'signify' discussed in chapter 33; and one could easily expand my account in such a way that the term could also fit the second sense of 'signify' found in that chapter. In the interests of brevity, I do not engage in the relevant expansion here.

¹⁰ 'Signify₂' covers both the third and fourth senses of 'signify' found in chapter 33.

¹¹ Ockham tells us that this account of the categories originates with Averroes. Readers will find a very similar explication of Aristotle's categories in Gilbert Ryle's classic paper "Categories," reprinted in Flew, A. G. N., Logic and Language, 2nd series (Oxford: Basil Blackwell, 1953), 65-81.

¹² See in particular chapters 7 and 16.

¹³ In dealing with the category Ockham does not consider the case of concrete terms like 'unicorn' that have no significata₁. It seems, however, that he would want to construe them as connotative terms signifying₂ the truth of some proposition.

¹⁴ Ockham does not provide much commentary here. He seems to think that our natural linguistic intuitions will substantiate his claim. See, for example, chapter 8.

¹⁵ The account presented here is clearly Ockham's. The difficulty, as I suggest, is that Ockham sometimes says things that are inconsistent with this analysis. My own inclination is to emphasize the revolutionary rather than the reactionary side of Ockham's account.

¹⁶ If it is to be construed as anything more than a general way of pointing to the contents of the category of quality, this technique for dividing the category is inadequate. Thus, there are terms like 'light' that do not naturally fit any of these divisions. Actually, the only division that Ockham finds crucial is that between terms expressive of figure and form, on the one hand, and all the remaining terms in the category, on the other.

¹⁷ This premise is never stated as explicitly as I suggest here. It is rather implied as it is, for example, in chapter 44.

¹⁸ My account deviates from Ockham in order of presentation. He deals with the category of quality after he deals with the categories of quantity and relation. His analysis of figure and form, then, is far briefer than my account would suggest. He merely applies the results of his analysis of these two categories to abstract terms expressive of figure and form and concludes with little commentary that these terms are not absolute. Since I want to bring to the fore the real existents (substances and qualities) in terms of which Ockham analyzes quantity and relation, I introduce Ockham's reductionism in terms of figure and form. What I have done is expand his own treatment of this species of quality in terms of his analysis of quantity and relation.

¹⁹ This argument is found in Ockham's Commentary on the Categories which exists only in early editions.

²⁰ This account holds only in the case of natural signs or intentions. Both Ockham and Aristotle want to claim that given the poverty of conventional languages, a term, 'T₁', can be a relative even though there is no term, 'T₂,', such that 'T₂' is the relative of 'T₁'. My account requires expansion, then, to handle this case. In the interests of brevity I omit the expansion here.

²¹ Since this argument is found in chapter 51, it is not from Ockham's own hand; nonetheless, it is sufficiently like other arguments found in authentic sections of the text to warrant the label "Ockhamistic."

²² My use of the term 'second intention' deviates from my analysis of that term in the first part of this paper. There I define second intentions as a sub-class of intentions of the soul. Although Ockham construes this as the proper meaning of the term, he extends his use of the term as I do here, to cover conventional signs as well.

²³ Of course, if we make this modification in the Ockhamistic theory of categories, the term 'substance' hardly does justice to the richness of this category. A new term would have to be introduced to capture the ontological force of the expanded category.

²⁴ See Ockham's Commentary on Porphyry, chapter 3, Ernest Moody, ed. (St. Bonaventure, New York: Franciscan Institute Publications, 1965), 44-45. Ockham refers to this passage in chapter 38 of the Summa.