Gyula Klima
1. Introduction: the subject matter of logic and the problem of universals
It might seem that the problem of universals should have little to do with the issue of the subject matter of logic. After all, in (formal) logic we deal with the deductive validity of arguments based on their formal structure, whereas the problem of universals, at least in one of its possible formula- tions, is the question of what corresponds to the universal terms of our language, which constitute precisely the “material” part of arguments, the part we disregard or abstract from in formal logic. However, upon a closer look, there is a certain connection. On the semantic conception of validity (which is also the intuitive motivation for syntactic rules of inference in deductive systems), a formally valid argument has to be truth-preserving, i.e., the truth of the premises has to guarantee the truth of the conclusion. In a formal semantic system, this notion of “truth-preservation” is spelled out in terms of the idea of compositionality, namely, the idea that the semantic values of complex expressions are a function of the semantic values of their components. Given this idea of compositionality and the range of all possible evaluations of the components of the propositions constituting an argument, the semantic notion of validity can be spelled out by saying that an argument is valid just in case there is no possible evaluation of the primitive components of its propositions that would, based on the composition of these components, render the premises true and the conclusion false. Obviously, this notion of validity presupposes that we have a pretty clear idea of what the range of all possible semantic values of the primitive components in question are and how those deter- mine the truth and falsity of propositions based on their compositional structure. But then, when we deal with predicate logic, some of those possible semantic values are precisely the correlates of our universal terms, the bone of contention in the problem of universals.
So, in the end, the semantic notions of truth and logical validity in predicate logic, being dependent on what the correlates of our universal terms are, demand at least a certain semantic clarification of the issue of universals. Contemporary conventional wisdom that we can glean from ordinary logic textbooks would tell us that those correlates are sets, the “extensions” or “denotations” of common terms. (See, e.g., Hurley 2008: 82–84) And if we press the issue of what sets are, then we are told that they are possibly completely arbitrary collections of just any sorts of things, yet somehow they are “abstract entities”. Clearly, ordinary logic text books can just stop there. After all, they are not supposed to go into the metaphysical problems of “abstract entities”: qua logic texts, they are just supposed to provide some validity-checking machinery, and need not worry about the possible ontological qualms of metaphysicians these machineries involve, just like elementary math texts, as such, need not worry about the ontological status of “mathematical entities” when they concern them- selves only with providing reliable methods of calculation or construction. This sort of attitude of the logician toward the metaphysical issues raised by his subject is almost as old as the subject itself, as is testified by Porphyry’s famously raising the fundamental questions concerning univer- sals just in order to set them aside as pertaining to “deeper enquiries”, but not to logic. (Spade 1994: 1) And of course it is one of the famous ironies of the history of ideas that it was precisely on account of these questions that medieval logicians got so much involved in these “deeper enquiries” that John of Salisbury in hisMetalogicon (John of Salisbury 2009: 111–116) had to complain about how his contemporaries’ endless debates over these issues confuse, rather than instruct, their students of introductory logic. But despite the pedagogical validity of John’s objection to this practice, one cannot really blame those logicians who get involved in these issues; after all, as we shall see, the answers to Porphyry’s questions determine to a large extent the construction of logical semantics in general, and thus the understanding of the relationship between the subject matters of logic and metaphysics in particular.
2. Realism, nominalism, conceptualism
Apparently, the primary issue concerning universals is ontological: are there universal entities? After all, nobody in their right mind would doubt whether we have universal words, i.e., words that on account of their meaning apply to a multitude, indeed, to a potential infinity of entities. However, the question then is: how come we can have such universal
terms at all? Plato’s “realist” answer, namely, that the difference between universal and singular terms hinges on the ontological difference between the kinds of entities these terms primarily name, rests on a relatively simplistic understanding of the semantic relations of these terms: i.e. the notion that their meaning consists in naming these different kinds of entities in the same way. In fact, generalizing on this idea we might say that on a realist conception semantic differences are accounted for in terms of the ontological differences of the semantic values of syntactical items of different categories, and not in terms of the differences in the semantic functions of these items themselves: on this approach, in realism we can have semantic uniformity at the expense of ontological diversity.
By contrast, those medieval thinkers who were convinced by Aristotle’s and Boethius’s arguments against platonic universals (by John of Salis- bury’s time practically everybody (Klima 2013a: n. 27)) would account for the semantic diversity of singular and common terms not on the basis of the ontological differences of the kinds of entities these terms denote, but rather in terms of how they denote the same kind of entities, namely, individuals, the only kind of real entities there are. Thus, on this under- standing of the Aristotelian view,we can have ontological uniformity on the basis of semantic diversity. As we shall see, the two formulae just italicized can be regarded as the two extremes of a whole range of possible positions concerning the relationship between semantics and metaphysics, ranging from extreme realism to thoroughgoing nominalism. Indeed, let me call the theoretical extreme of extreme realism the position that holds that all semantic differences are ontological differences: different items in seman- tically different syntactical categories differ in what kinds of entities their semantic values are and not in what kinds of semantic functions relate them to their semantic values. By contrast, on the other theoretical extreme we have the position of extreme nominalism, which would hold that all different items in semantically different syntactical categories differ only in the kinds of semantic functions that relate them to their semantic values, but all those semantic values are ontologically of the same kind, the same, single kind of entities (or just the one single entity) there is. But in order to see how actual historical positions can be arranged on this theoretical scale, we should get into some further details concerning each extreme.
On the platonic view, as we could see, the semantic relation between common and singular terms and their semantic values would be of the same kind: namely, denoting a single entity. What would make the difference would be just the further ontological relation of the entity
denoted by the common term, the universal, to its singulars as their exemplar. It is only on account of this ontological relation that we can use these terms to denote secondarily the singulars imitating or participat- ing in their exemplar, but what the terms truly and primarily denote is the exemplar itself. So, on this platonic understanding, thesemantic function of universal terms would be the same as that of singular terms, namely, denoting a single entity, just like the representative function of a portrait is to represent a single individual. However, just as the portrait of a monarch can stand for a whole nation and thus can identify someone as a member of that nation (say, in a passport), so the name of the universal can stand for a whole kind and thus identify any individual participating in it as a member of that kind.
On the Aristotelian view, on the other hand, universal terms are universal precisely because they apply to a multitude of singular entities, the same singular entities we can denote by their proper names, but differently, namely, in a universal fashion, in abstraction from their individ- ual differences. So, on this conception, what accounts for universality is abstraction, a mental activity, the activity of the Aristotelian agent intellect (nous poietikos, intellectus agens), which by this activity produces the first universal representations, the so-calledintelligible species out of the singular representations of sensible singulars stored in sensory memory, the so- called phantasms. The intelligible species, however, although they are universally representing mental acts, generally were not regarded as the universals Porphyry meant to consider in his work. An intelligible species on this conception is rather an acquired disposition enabling the receptive intellect (nous pathetikos, intellectus possibilis) to form a universal concept in actual use. For example, once I acquire the intelligible species of circles, that enables me to form actual thoughts about circles in general, but that does not mean that I am thinking of circles all the time. Thus, in possession of the intelligible species my mind still needs to form time and again another mental act, the so-called formal concept, to form an actual thought, as when I actually think that all circles touch a straight line in one point. However, this mental act is still not the universal. It is a universally representing singular act of a singular human mind; so, my universal concept of circles is not the same item as your universal concept of circles, even if those concepts are exactly alike in their representational content, just like my dance moves I perform with my body are not the same items you perform with yours, even if we are making exactly the same kinds of moves, say, in a chorus line. Whatis the universal in the intended sense is the common representational content of both your concept and
mine, on account of which we can be said to have the same concept, despite the individual differences of the mental acts whereby we have it, just like we can be said to make the same dance moves, despite the individual differences of our bodies whereby we make them. Therefore, this commonly intended object, the universal representational content of both of our individual mental acts, was rightly called by later scholastic thinkers the objective concept or intention, both because it is the universal representation of the ultimately intended objects, namely,all singulars of the same kind fromsome of which the intelligible species giving rise to this concept was abstracted in the first place, and because it is the common objective content of the formal concepts of all those individual human minds that are capable of thinking this objective concept at all.
Now, even if this notion of a universal (as the objective representational content of individual mental acts representing a natural kind of singulars in an abstract fashion) may seem to be rather contrived from a contemporary perspective, it should be clear that the conception that treats universals as objective concepts, the universality of which is the result of the intellectual activity of abstraction, does not allow in its “core ontology” the sort of “abstract objects” Plato entertained. On this view, the intellect can form universal objects of thought, but those objects of thought are not objects or things absolutely speaking. Since they are the results of a mental activity, they are ontologically posterior to that activity. (Although Scotus and his followers would insist that among individuals of a certain kind there is a certain less-than-numerical unity that is ontologically prior even to this activity, and even Aquinas would admit a certain formal unity among individuals of the same kind prior to any activity of the intellect (Klima 2013a: n. 39)). As Averroes was often quoted by medieval authors:intellec- tus facit universalitatem in rebus – it is the understanding that generates universality among things.
3. Scholastic “conceptualisms”
To see this issue in a little more detail, we should see exactly how the pieces of the theory presented so far fit together in this tradition of medieval logic, which I like to call “via antiqua semantics”, in contrast to a radically different medieval logical tradition that emerged from the works of Wil- liam Ockham, John Buridan, and their fellow nominalists, which I refer to as “via moderna logic” (Klima 2011a, 2013a). As we shall see, both of these approaches to logical semantics are basically variations on what may still be called conceptualism; however, they are based on radically different
conceptions of what concepts are and how they are related to their objects, and accordingly give rise to very different constructions of logical semantics.
The easiest way to make this contrast is through the analysis of an example. Take one of the staples of scholastic lore: “Every man is an animal”. This is an affirmative, universal categorical proposition (in the medieval sense of ‘proposition’, meaning sentence-token), both terms of which are common or universal terms, joined by a copula and determined by a universal sign of quantity (a universal quantifier, as we would say). On the commonvia antiqua analysis, the subject and predicate terms of this proposition, its categorematic terms, have their semantic property of signifying human and animal natures, respectively, on account of being subordinated to the respective concepts our minds abstracted from their individuating conditions in the humans and animals we have been exposed to. Thus, although whatever it is on account of which I am a man (i.e., a human being, regardless of gender) is a numerically distinct item from whatever it is on account of which you are a man, the concept we abstracted from humans we have been exposed to in forming our concept of man abstracts from any individual differences (“individuating condi- tions”). This is precisely the reason why this concept will represent not only the humans we have been exposed to, but any past, present, future and merely possible humans, that is to say, whatever it is that did, does, will or can satisfy the condition of being human, whatever this condition is, and whatever means we have (or don’t have) for verifying the satisfac- tion of this condition (which would be a question of epistemology and not of semantics). Accordingly, the corresponding term (‘man’ in English or ‘homo’ in Latin) can stand for any of these individuals in a proposition. Indeed, this is what it does in this proposition: it stands or (to use the Anglicized form of the scholastic technical term commonly used in the secondary literature) supposits for all human beings that presently exist. (For an overview of scholastic theories of “properties of terms”, including supposition, see Read 2011) The reason why this term supposits only for presently existing humans is the present tense of the copula, which restricts the supposition (reference) of the term to present individuals that actually satisfy the condition of its signification, namely, those individuals that actually have human nature signified in general by this term. By contrast, with different tenses or modalities, or when construed with verbs and their derivatives that signify acts of the cognitive soul (i.e., sensitive or intellect- ive, as opposed to the purely vegetative, soul) that are capable of targeting objects beyond the presently existing ones (such as memory, imagination,
anticipation, abstract thought, etc.), the supposition of this term would be extended, orampliated, to use the Anglicized form of the scholastic term, to past, future, or merely possible humans. (Klima 2001a, 2014) Since medieval philosophers did not equate ontological commitment with quan- tificationà la Quine, they did not find any special ontological difficulty in talking about “non-existent objects”, that is, objects of our cognitive faculties beyond the objects directly perceived in our present environment. In fact, even the ontologically most squeamish nominalists would not hesitate to quantify over mere possibilia, simply because the flexibility of their theory of quantification and reference, namely, the theory ofsuppos- ition coupled with the theory of ampliation, allowed them to contend that these mere objects of thought (and of other cognitive acts) are simply nothing, and so to inquire into their nature and ontology would be just a wild goose chase, amounting to nothing. (Cf. Klima 2014, 2009: c. 10.)
The nominalists, however, did have a bone (or two) to pick with via antiqua semanticists on other aspects of their theory. In the first place, and perhaps most fundamentally, the medieval “realists” (practically any- body before Ockham), even if they did not buy into Plato’s “stratified ontology” of universals vs. singulars, and had a much more sophisticated semantic theory than the uniform naming relation between different kinds of words and correspondingly different kinds of things, they did preserve some sort of semantic uniformity at the expense of some sort of ontological diversity.
As we have seen, the signification of common terms, based on the idea of words being subordinated to concepts to inherit their natural semantic features, coupled with the Aristotelian theory of abstraction, led to a peculiar theory of predication within this framework, often referred to in the literature as the inherence theory of predication. The theory is simple enough: the predication ‘x is F’ is true, just in case the F-ness of x actually exists, or equivalently, just in case F-ness, the form or property signified by the predicate F in the individual x actually inheres in x. The problems start when we consider all sorts of substitution instances of F. For then we start realizing that, apparently, by the lights of via antiqua semantics, as Ockham put it “a column is to the right by to-the-rightness, God is creating by creation, is good by goodness, just by justice, mighty by might, an accident inheres by inherence, a subject is subjected by subjection, the apt is apt by aptitude, a chimera is nothing by nothingness, someone blind is blind by blindness, a body is mobile by mobility, and so on for other, innumerable cases” (Ockham 1974: I, 51). In short, to the nominalists, starting with Ockham, it appeared that their realist opponents (in the case
of Ockham, especially John Duns Scotus and Walter Burleigh) generate metaphysical problems where there shouldn’t be any, simply on account of a misconception of semantics, because their conception would “multiply beings according to the multiplicity of terms” (Ockham 1974: I, 51).
To be sure, the “realists” did make a number of metaphysical distinc-