(p. 67) 6. Universals (Avicenna and Abelard)
There is a core question about universals, which perplexed ancient and medieval thinkers, and still exercises philosophers today; they have even borrowed the medieval nomenclature for the main positions taken. Some things in the world are the same, not by being numerically identical (as John Marenbon is numerically identical with the author of this book), but by being the same in some respect: this saucer, that coin, and that mirror are all the same, for instance, in being round; all the animals in that field are the same in being horses. Is it enough simply to suppose that there are these many particular things which are the same in these respects, or is there some additional entity, besides the particular things—a universal—in respect of which they are the same? Those who believe there are such entities—universal things—are called ‘realists’; those who consider that real universals are unnecessary are ‘nominalists’ (from the Latin nomen = name): they accept that there are universals in language (such as the words ‘round’ and ‘horse’), but deny that there are universal things.
There is at least one striking difference between medieval and contemporary ways of posing the ‘problem of universals’. It is partly, but not wholly, a matter of terminology. In the Categories, Aristotle divides things into substances and nine sorts of accident (see Chapter 4). A primary substance is a particular belonging to a natural kind, not the result of human artifice: a man or woman, a (p. 68) flower or a stone (but not a table or a house). The accidents are properties which attach to substances, and can come and go. So, for example, ‘Fat red-faced John, Arthur’s son, is sitting, wearing a jacket, in the kitchen this morning, eating and hearing the music’ describes a primary substance, John, and his accidents in each of the categories. John also has properties, known as differentiae, which are not accidents because he cannot be without them: they include rationality, a defining feature of all humans, and having sense perception, a defining feature of all animals, human and non-human. In the Middle Ages, the problem of universals was usually posed about substances.
Medieval thinkers asked whether, in addition to the primary substances, there are universal secondary substances: species (such as Man), and genera (such as Animal or Living Thing) which bring together different species. Philosophers today not only use a different terminology; they also usually discuss universal properties, such as roundness or redness, rather than substances. One reason for the difference is a gap between medieval and contemporary science. Following Aristotle, most medieval thinkers thought of natural kinds as fixed and determinate, whereas we consider them to be continuously evolving and to have fuzzy boundaries. This difference is not, however, as wide as it first appears. Medieval writers did also discuss universal properties (accidents and differentiae, in their terms), and many contemporary philosophers accept that there are some determinate, fixed natural kinds, such as water, and these do indeed figure in some contemporary discussions about universals.
The problem of universals in antiquity
Notoriously, Plato held that there are really existent independent Ideas or Forms which alone truly exist and are the objects of knowledge. These Ideas filled the role of universals, although Plato conceived them rather as particulars which served as (p. 69) paradigms for all other particulars. Aristotle rejected Platonic Ideas, but, according to most interpretations, he was a realist who denied that universals exist independently of or outside the particulars which instantiate them, except in the mind. Alexander of Aphrodisias, the greatest of the ancient followers of Aristotle, who died early in the 3rd century AD, developed Aristotle’s position by tackling a serious problem it faces. Alexander argues that an Aristotelian universal must in some way be in its particulars. But universals are not divided out between particulars as parts, in the way we might share a cake—as if this horse had part of the universal Horse and that horse another part. Every horse is wholly a horse: the universal is entire within each of its many particulars. But, Alexander points out, no thing can be wholly in many numerically different particulars. Suppose that the whole universal Horse were in Black Beauty, then it could not be in any other thing, and so the only horse would be Black Beauty. Universals, therefore, cannot be things, and so they must just be mental conceptions. If so, however, they must be empty, misleading conceptions, since it has just been admitted that nothing in reality corresponds to them.
Alexander answers the objection by turning to the idea of abstraction. In geometry, for instance, we conceive figures, such as squares and triangles, apart from matter, although they can exist only in matter. But we do not regard these conceptions as empty or misleading. Alexander applied the same reasoning to universals. But the path he suggests is not straightforward. If the solution is to remain a realist one, it has to explain how there is a basis in reality for the universal concept abstracted in the mind, and yet avoid making that basis into a thing wholly within many numerically different particulars.
Avicenna on universals
One of the most sophisticated and influential ways of dealing with this problem was proposed by Avicenna, probably basing himself (p. 70) on some of Alexander’s ideas. Consider an act of abstraction. Suppose we want to think about horses, abstracting from all the accidental features of this or that horse, such as its white or chestnut colour, and just considering what it is in virtue of which they are horses: what Avicenna calls, apparently interchangeably, ‘horse in as much as it is horse’ or ‘horseness in as much as it is horseness’.
According to our usual way of thinking about abstraction, we would distinguish two elements: the real horses, such as Black Beauty and Bucephalus, which are particular things, and our abstracted mental conception of Horse or horseness, which is a universal, since it relates to every particular horse. Avicenna, however, understands that abstraction can be seen not just in terms of its result—a mental conception—but in terms of what it picks out in reality, as the basis for the mental conception. When I am abstracting, then I am regarding Black Beauty simply in as much it is a horse: I am picking out what Avicenna sometimes calls a ‘nature’—in this case, horse(ness)—and basing my mental conception on it. And so there are in fact three elements: horse(ness) in as much as it is horse(ness)—the nature; the particular thing—Black Beauty; and the mental conception of horse(ness). The nature, horse(ness), Avicenna insists is in itself absolutely nothing except horse(ness). By contrast, the particular thing consists, not just of horse(ness), but also of all the accidents that characterize Black Beauty. The mental conception of horseness adds universality to the nature on which it is based, which in itself is neither universal nor particular.
Avicenna’s position, it might at first sight seem, could be summarized as being that there are natures, particular real things, and universal concepts. Natures themselves are neither particular nor universal, but become particular real things when accidents are added to them, and, when conceived in the mind, have universality added to them and become universal concepts.
(p. 71) Avicenna’s view was, indeed, taken in this way by some of his medieval Latin readers, but he would have rejected this way of treating natures as some special sort of thing. The immediate question, Avicenna realizes, which a critic will put to him about his notion of nature is whether the horse(ness) in Black Beauty is different from the horse(ness) in Bucephalus. If he says ‘Yes’, then how will he maintain that they are both horses? If he denies it, then it will follow that numerically one horse(ness) is in both, and so numerically the same thing is wholly in numerically different particulars.
Avicenna takes the only way out: he denies both that the horse(ness) in Black Beauty is different from the horse(ness) in Bucephalus and that the two horse(nesse)s are numerically one. Since he accepts that to be different is simply not to be numerically one, he seems to be denying the principle of the excluded middle (that for any x and any F, x either is F or is not F). But Avicenna avoids doing so by insisting that we should refuse to answer the question ‘Is horse(ness) in as much as it is horse(ness) one or not one?’ It is a malformed question, because it takes horse(ness) in as much as it is horse(ness) as if it were some sort of thing, a nature, which is a subject for predication (that is to say, something about which we can say ‘It is one’, ‘It is not one’, as we say that this page is white).
The horseness in Black Beauty is neither different from that in Bucephalus, nor the same in number as it. When we consider horseness in as much as it is horseness, Avicenna holds, we are simply understanding Black Beauty or Bucephalus in a special way, which disregards many features which no particular horse can be without. Horseness in as much as it is horseness is not another thing, over and beyond the particular horses, about which problems concerning whether it is one or many can arise, but it does provide a basis in reality for the universal concept of horse we can form in our minds.
(p. 72) Early medieval realism
Alexander of Aphrodisias’ argument against the existence of universals was made known to philosophers in the Latin tradition by Boethius. Boethius also proposed a version of Alexander’s abstractionist response, but in a rather unclear way which left room for philosophers in the schools of the early 12th century to propose various, conflicting Boethian answers to the problem of universals. The abstracted universal concepts in the mind were unproblematic, but the 12th-century thinkers struggled to explain how they were based on real universals in particulars: what did Boethius mean by saying that the same likeness (for example, the likeness of horse) is both something that can be perceived by the senses in particulars and yet is grasped by the intellect alone as a universal?
One interpretation, ‘material essence realism’ (MER), was popular in the early 1100s and reflects an approach that was common before thinkers began to study Boethius’ solution closely. According to MER, universals underlie particulars as their material. Black Beauty is, then, the universal, Horse, which is individuated—that is to say, made into this particular horse—by its accidents, such as his black colour, his size, weight, and position in place and time; Bucephalus is exactly the same universal, Horse, but with different individuating accidents.
MER has, then, a strongly realist conception of universals. According to it, Aristotle’s primary substances are simply the one secondary substance together with individuating accidents. Other interpreters of Boethius avoided holding that there are underlying, material-like universal substances. Instead, they proposed that Black Beauty and Bucephalus are simply ‘not different’ from each other in respect of being horses, and the universal Horse has its basis in the collection of all horses, and also—some held—in the individual horses in so far as they are horses. Some of these theorists would, therefore, claim that (p. 73) everything is a particular. But they remained realists, since they held that universals exist too, as collections of particulars or even as the particulars themselves.
Abelard on universals
Abelard argued powerfully against all these versions of realism. He pointed out that it was incoherent to hold, as MER does, that accidents individuate substances. Accidents are dependent on their substances: if there were no Black Beauty, his blackness would not exist. But if Black Beauty is individuated by his accidents, then his blackness and other accidents need to exist in order for Black Beauty to exist. Moreover, Abelard claims that, since according to MER it is the same universal animal which exists in John Marenbon and Black Beauty, it will have to be at once both rational and irrational, which is impossible. Against the collection theory he objected that collections are unlike universals because they are not in all their members as a whole, and they come after and consist of their members.
Abelard’s most striking contribution to the history of the problem of universals lies, however, not in these arguments against realist theories but in the conclusion he drew from them. Unlike any of his predecessors, he did not try to devise a more subtle realist position, or openly invoke the idea of common natures, but insisted that universals are just words. He was the first to defend this nominalist position (and, indeed, the word ‘nominalist’ was first coined to describe him and his followers).
True, one of his teachers, Roscelin of Compiègne, anticipated Abelard’s position in some respects. In the early 1090s, Anselm attacked Roscelin for holding that universals are nothing more than the breath emitted when a word is uttered. Roscelin and a few of his contemporaries apparently believed that logic is concerned exclusively with language, and that the various special (p. 74) terms used by logicians—not just ‘universals’, but also ‘differentiae’ and ‘accidents’—therefore signify other words, not things. But none of them tried to provide, as Abelard would do, the central element of a nominalist theory of universals: an account of how we can talk about the world using universal words (as we do when we say ‘Black Beauty is a horse’ or ‘Horses are animals’), if there are no universal things.
Abelard sees language as related to the world in two main ways. Words ‘nominate’, that is to say refer to, things in the world, and they also ‘signify’ things, by producing a concept of them in the hearer’s mind. Abelard recognizes that there are problems about both sorts of semantic relationship, if he wants to hold that there no real universals. But he believes they can be overcome. Universal words cannot nominate universal things, because there are no universal things, but they can nominate all the particulars which fall under them: so ‘man’ nominates John, Joan, Jan, and every other human. Abelard recognizes, however, that a universal word like ‘man’ does not nominate John in the same way that ‘John’ does. ‘John’ nominates John as a discrete individual. ‘Man’ nominates John according to how he comes together with other humans, to his nature as a human being.
It is this coming together which, according to Abelard, is the ‘common cause of imposition’ of the universal word ‘man’. And, of course, Abelard strenuously denies that being a man (or, as he also calls it, the status of man) is a thing of any sort. Particular men, he says, ‘come together in this, that they are men’. And he then adds: ‘I do not say “in man”—since nothing is man other than a discrete thing—but in being a man. Being a man is neither man nor any thing, if we consider it carefully.’
The most difficult problem for interpreters of Abelard’s theory is to know precisely what position he is taking here. On one view, he is like a 21st-century austere nominalist, who simply declares that things fall into various groups by being similar to each other in a (p. 75) certain respect and that such similarity needs no further explanation. On another view, although Abelard is able to say that status are not things because they are not substances or accidents, the only two sorts of thing his Aristotle-based ontology admits, they do in fact play the role of things—they are close to Avicennian natures—and allow him to give a realistic twist to his theory, despite his claims to have rejected realism.
Abelard’s problem about the other semantic relationship, the signification of thoughts, is that, if there are no universal things, then there is no object of which a universal word can produce a thought. This objection gains its force from his way of answering the first one: if ‘man’ is imposed from a common cause, then this community of cause prevents it from producing the thought of any one human being. Abelard replies by explaining how we can create all sorts of conceptions or images in our mind, among them conceptions which are not of one particular but are common to many particulars of the same sort. So, for instance, I can create an image of something which is neither John, Joan, nor Jan, but just an image of a human being: it is this ‘common conception’ which is the object of thought when I hear the word ‘man’.
Duns Scotus: transforming Avicenna’s solution
Although Abelard had many followers in the second half of the 12th century, with the arrival of new Aristotelian and Arabic sources his nominalism was forgotten. Avicenna’s treatment of universals was very influential, but interpreted in various ways. Duns Scotus took over Avicenna’s idea that the nature of something can be considered just in itself, but he adapted it. The central problem for Avicenna’s theory is to explain how horse(ness) in as much it is horse(ness) is neither numerically one (because in that case one thing would be wholly present in many) nor diverse in number (because in that case it would not explain how both Black Beauty and Bucephalus are horses). Avicenna (p. 76) himself argues that it is numerically neither one nor diverse, because it is nothing except horseness, and so it is not some sort of thing to which being one or not being one can be attributed. Scotus proposes, rather, that horseness is numerically neither one nor diverse because it is one, but not numerically one. Unlike Avicenna, then, Scotus is willing to treat a common nature as a thing, but it is a sort of thing which, he says, has, not numerical unity, but ‘less-than-numerical unity’.
There are for Scotus, therefore, two sorts of unity: numerical unity or singularity, by which Black Beauty is one thing and Bucephalus another; and the less-than-numerical unity which their common nature, horseness, has in virtue of its being the same horseness, though in many numerically diverse horses. Precisely because horseness is less-than-numerically unified, it can be wholly in many numerically different things while still being (in some way) one.
But why accept that anything can be unified in this less-than-numerical way? Scotus contends that, unless there really are common natures which are less-than-numerically one, then the similarities and differences we observe in nature will simply be mind-dependent. If there is no real common nature of horseness shared by Black Beauty and Bucephalus (and, because shared, less-than-numerically one), then Black Beauty and Bucephalus are alike just because that is how they appear to us.
Scotus produces some powerful arguments to support his view. For instance, he asks us to consider what is really the opposite of a black thing. It must be white, and it must be a real thing too (if it is really opposite), and, since everything real is one—a maxim everyone accepted—it must be one. But it is not numerically one, since it is not as if there were only one white thing really opposite to this black thing: any white thing is its opposite. It is true that Scotus’ justification for less-than-numerical unity supposes that no other form of realism is tenable, but Scotus does give detailed arguments against the other existing theories.
(p. 77) Scotus has also to explain what makes Black Beauty and Bucephalus, who share the common nature horseness, into individual horses. He argues against seeing accidents, matter, or something merely negative as the principle of individuation, and is left with the view that each individual is indeed individuated by an individuator (sometimes called, especially after Scotus’ time, a ‘haecceity’—that is, a thisness), which ‘contracts’ the common nature into an individual. But the two entities within the individual, the common nature and the individuator, are not, he says, distinguished as thing and thing, but merely, as he describes it, ‘formally’. There is just one thing, Black Beauty, for example, which has two formally distinct realities: the common nature of horseness, and an individuator.
Ockham: nominalism again
William of Ockham rejected Scotus’ baroque apparatus of individuators and formal distinctions. Two items, he insisted, can be distinguished only as thing and thing, concept and concept, or thing and concept. Scotus’ theory depends on being able to hold both that Black Beauty’s nature is different from what individuates him, and that this nature and the individuator are not different things from one another, nor therefore from Black Beauty himself.
By rejecting the distinctions on which Scotus’ position rests, Ockham can find many arguments against it. For example, from Ockham’s perspective, Scotus must hold that Black Beauty is not different from his nature, horseness, because they are not different things. But Black Beauty is a different thing from Bucephalus (which is also not different from its nature). Black Beauty’s nature is therefore a different thing from Bucephalus’ nature. So every horse will have to have its own nature (and, says Ockham, its own species)—an absurd conclusion.
Ockham rejected not just Scotus’ but every variety of realism. Universals, he argued (like Abelard, whose works he did not (p. 78) know), are not things in the world. Rather, they are unreal mental objects or, as he came to think later, they are identical to our acts of thinking them. Ockham sees no need to introduce anything like Abelard’s status: it is enough for these mental universals to refer to all the particulars which fall under them. He conceives them as terms in a mental language, which are naturally linked to the things for which they stand. Whereas the word ‘horse’ in English applies to horses merely by convention, the mentalese term HORSE is somehow fitted (by similarity and through causality, he suggests) to stand for all and only horses.
Ockham’s nominalism (and the somewhat different, nominalist theory developed a little later by John Buridan in Paris) did not settle the problem. Universals were the subject of lively controversy in the late 14th and 15th centuries, and perhaps the most sophisticated and complex solution to the problems they raise was given at the very end of the 16th century by Suárez. Suárez drew especially on Ockham and Scotus, but he was joining in an intellectual conversation the terms of which went back much further, certainly as far as Alexander of Aphrodisias and, through him, to Aristotle.