Abelard’s philosophy is the first example in the Western tradition of the cast of mind that is now called nominalism. Although his view that universals are mere words (nomina) is typically thought to justify the label, Abelard’s nominalism – or better, his irrealism – is in fact the hallmark of his metaphysics. He is an irrealist not only about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. Instead, Abelard holds that the concrete individual, in all its richness and variety, is more than enough to populate the world. He preferred reductive, atomist, and material explanations when he could get them; he devoted a great deal of effort to pouring cold water on the metaphysical excesses of his predecessors and contemporaries. Yet unlike modern philosophers, Abelard did not conceive of metaphysics as a distinct branch of philosophy. Following Boethius, he distinguishes philosophy into three branches: logic, concerned with devising and assessing argumentation, an activity also known as dialectic; physics, concerned with speculation on the natures of things and their causes; and ethics, concerned with the upright way of life.1 Metaphysics falls under Abelard’s account of “physics” as the second branch of philosophy, which is sufficiently broad to allow for traditional metaphysical concerns as well as issues proper to natural philosophy.2 Determining his metaphysical commitments is a matter of teasing them out of his discussions in philosophy of language and natural philosophy.
I’ll begin with Abelard’s antirealism about universals (§I), since it is the key to his irrealism. It provides the foundation for his conviction that only individuals exist, a thesis that calls for further analysis of the nature of individuals (§II). Most individuals are a kind of integral whole, namely, a hylomorphic compound of form and matter, belonging to natural kinds. Abelard clarifies how the elements of such complex individuals are related to one another with his theory of identity (§III), and he develops a theory of how individuals interact to make up the world, using far less by way of ontological resources than other philosophers (§IV). The result is a subtle and sophisticated irrealist metaphysics, one of the most interesting and original in the history of philosophy.3
Abelard is notorious for his claim that universals are nothing but words, a thesis he defends by arguing at length that ontological realism about universals is incoherent. More exactly, Abelard holds that there cannot be any real object in the world that satisfies Boethius’s criteria for the universal: being present as a whole in many at once so as to constitute their substance (i.e. to make the individual in which it is present what it is).4 In his discussion of universals, Abelard echoes Boethius’s own dialectical strategy by first attacking the view that the universal is a real constituent of each individual thing (§I.1), and thereafter the view that the universal is the collection of things (§I.2); to this Abelard adds further arguments against a family of views that identify the universal with the individual thing in some fashion (§I.3).5 In each case Abelard tries to show that realism about universals leads to absurd consequences. I’ll only review some of his objections against each position; he has much to say, not all of it of equal merit.
Material essence realism, the position of Abelard’s teacher William of Champeaux, is a sophisticated version of the realism that was prevalent among philosophers at the beginning of the twelfth century. It can be summarized in three theses.6 First, it holds that the material essence – that is, the genus with regard to its subordinate species, or the species with regard to its subordinate individuals – is a Boethian universal, since it is simultaneously present as a whole in distinct items, making them what they are as the “material” of their essential being: the material essence animal is present in the species man and ass, the material essence man is present in Socrates and Plato. Second, it holds that the material essence is “contracted” (made metaphysically less general) by the addition of forms accidental to it; since it is essentially the same in distinct items, whatever differentiates those items cannot be essential to it, and hence must be accidental. For individuals, this reduces to the claim that accidents individuate substances.7 Third, it holds that individuals are metaphysically composed of the material essence in combination with the forms that serve to individuate them. Hence Socrates is composed of the material essence man plus his particular height, weight, and so on; likewise for Plato.
Abelard offers two powerful objections to material essence realism, “a view completely incompatible with physics” (LI Isag. 11.10–11; Spade 1994, 28), that is, with metaphysics. The first runs as follows (LI Isag. 11.11–24; Spade 1994, 29; and LNPS 517.25–29).8 Consider the material essence animal, wholly present in the species man and ass. In the former species it is informed by rationality, and in the latter by irrationality. Yet it is by definition the selfsame material essence that is wholly in each; indeed, that is what entitles the view to be called a form of realism. Hence contraries are simultaneously present in the (generic) material essence, which is impossible.
The defender of material essence realism might counter that contraries are not actually present in the material essence, but are merely potentially present, and thus there is no conflict. But Abelard insists that this reply doesn’t work. Each species is actually informed by a contrary, and the material essence is actually present in each as a whole; hence the material essence is actually informed by one contrary in one species and by the other in the other; since it is wholly one and the same in each, it is therefore actually informed by contraries, and the contradiction results.
Abelard takes up another rejoinder, namely, that there is only a contradiction if contraries are present in the same individual, not just in the species or genus (LI Isag. 11.25–28; Spade 1994, 30). He replies with a new reductio-argument, as follows (LI Isag. 11.28–12.4; Spade 1994, 31–32). Assume that individuals are to be identified with their material essences. Thus Socrates can be identified with animal, as likewise can Brunellus the Ass; but then by transitivity Socrates is Brunellus, and hence he is both rational (as Socrates) and irrational (as Brunellus); thus contraries are present in the same individual.
The real work in Abelard’s reply is done by his identification of individuals with their material essences, which the defender of material essence realism is not likely to grant, insisting instead that the individual is the material essence only in combination with individuating forms (as described in the third thesis above). Yet Abelard argues that material essence realism is in fact committed to the view that the individual really is just its material essence. He argues for this claim by elimination, as follows (LI Isag. 12.4–14; Spade 1994, 33).9 According to material essence realism, the individual consists in its material essence plus its advening forms. Clearly the individual cannot be identified with its accidents, since then they would not be accidents but substance. But why not think the individual is its advening forms in combination with its material essence? Abelard’s background reasoning runs as follows. Such advening forms include the specific differentia for the kind of thing the individual is, e.g. rationality in the case of Socrates. The differentia cannot be merely accidental to the material essence, or it would not be a part of making the thing what it is; rationality makes Socrates human, and is not just an accidental feature. Nor is the differentia merely “co-present” in the individual: Socrates would be no more than an accidental union of a material essence and some form(s), really two things rather than one.10 Yet the differentia cannot simply inhere in the material essence: it either produces something essentially different, contrary to the basic tenets of material essence realism, or, by Abelard’s main argument, contraries will simultaneously inhere in the same thing. The only option remaining is to hold that the differentia is not a separate quality at all but already informs the material essence – not rationality but rational animal.11 Abelard explicitly states the consequence of this last option. Since the individual is composed of the material essence and advening forms, including the differentia, then Socrates must be composed of his material essence and differentia, i.e. his material essence in combination with his informed material essence, which is absurd.12 By elimination, then, individuals must be identified with their material essences, and Abelard’s reductio ad absurdum of material essence realism in the case of individuals holds.
Abelard’s second objection to material essence realism attacks its second and third tenets, that “individuals are made by their accidents”: for, as Abelard says, “if individuals draw their being from accidents, then surely accidents are naturally prior to them, just as differentiae are to the species they lead forth into being” (LI Isag. 13.5–15).13 However, it is impossible for accidents to be prior to substance, and so material essence realism leads to another absurdity.
Abelard’s second objection is not a mere terminological point. Accidents are features of something, characterizing their subjects in one way or another. And, precisely because they are accidental, their subjects are what they are independent of whatever accidents they possess. Yet if Socrates’s individuality derives from accidents, then what it is to be Socrates depends on the accident(s) individuating him – which is just to say that they aren’t accidental but essential to Socrates, contrary to hypothesis. The individuality of an individual cannot be due to some feature that depends upon or is derived from the individual itself; features of an individual cannot ground its individuality without being a constitutive part of that individual.14 In fact, no medieval philosopher argued seriously for accidental individuation after Abelard proposed his objection.15 Instead, they drew the moral that the principle of individuation had to be an essential constituent of the individual.
Abelard’s attack on the most sophisticated form of realism in the twelfth century was taken to be decisive. Even William of Champeaux, when faced with these and other objections from Abelard, gave up material essence realism and switched to what I’ll call an indifference theory (as detailed in §I.3 below). Yet before turning to this latter sort of theory, we need to look at Abelard’s objections to another form of realism.
Collective realism takes the universal to be, roughly, the collection of its instances: all men collected together are the species man, all animals taken together are the genus animal, and so on.16 Such a view seems sensible and natural when applied to natural kinds, which consist distributively in their present members; this is the sense in which there are “endangered species,” for instance. Whether it can be extended to provide an account of universals, by identifying the real collection of instances as the universal, is another question. Abelard offers three reasons to think it cannot.
First, Abelard charges that collective realism is an ignoratio elenchi: collections are integral wholes, not universal wholes, and thereby fail to satisfy Boethius’s criteria for the universal – they are common to their members as parts of the whole, not as a whole that is present in each (LI Isag. 14.32–40; Spade 1994, 48),17 as witnessed by the grammatical fact that we say that something belongs to an integral whole rather than saying it is the whole, which would be appropriate for universals (Dial. 547.31–34; cf. also LI Isag. 15.18–21; Spade 1994, 55).18 Abelard has no objection to the existence of integral wholes, as we shall see in §III below, for they do not involve any metaphysically objectionable “shared presence” (as universal wholes do). By the same token, they aren’t relevant to the problem of universals.19
Second, Abelard maintains that since collections are defined extensionally, “any group of many men, taken together, would properly be called a universal” (LI Isag. 15.1–4; Spade 1994, 50). Extensional definition is inadequate; if all brute animals were destroyed, the Collective Realist would have no way to distinguish the species man from its genus animal.20 Furthermore, the collective realist hasn’t given any reason why the collections that are universals have to be complete. A partial collection of humans is as much a collection of humans as a complete collection; why shouldn’t it count as a species?21 Even setting that difficulty aside, it isn’t clear what “complete” means: all presently existing humans? Past, present, and future humans? All possible humans? No answer seems satisfactory.
Third, Abelard objects that whereas universals are prior to their instances, integral wholes are posterior to their members (LI Isag. 15.5–18; Spade 1994, 53–54).22 Consequently, wholes are destroyed whenever any part is destroyed, though a given whole may be destroyed while a part continues to exist (though of course not qua part).23 Thus if Plato should die, the collection comprising the species man is destroyed, and thus its parts (such as Socrates) are no longer men – an absurd result. Even if we grant that the species now consists of all the remaining men, Socrates qua member of the collection has changed essentially, since the collection “constitutes his substance” (as required by Boethius’s criteria) and has itself changed, an equally absurd result.
Abelard’s attack on collective realism, like his attack on material essence realism, seems to have been decisive. No subsequent philosophers in the Middle Ages tried to identify universals with collections of things.
Faced with Abelard’s devastating criticism, William of Champeaux “corrected his theory so that thereafter he said that things were the same not essentially but indifferently” (HC 89–91; Radice 1974, 60). Such “indifference theories” granted that only individuals exist, and explained specific and generic sameness among distinct individuals not by recourse to a shared entity but rather by saying that such individuals are “indifferently” the same.24 The universal is then identified with the real individual thing, which, in its indifferent guise, satisfies Boethius’s criteria for the universal: Socrates is the species man in that he is indifferently the same as other men, the genus animal in that he is indifferently the same as other animals. William of Champeaux adopted a negative criterion, saying that distinct individuals are indifferently the same when there is nothing in which they differ; Walter of Mortagne a positive criterion, saying that distinct things are indifferently the same when there is some real thing, a status, in which they agree.25 Their theories are realist in virtue of their claim that some real thing, namely, the individual, is a universal.
Abelard’s main objection to indifference theories runs as follows. If Socrates is the species man, then it is Socrates who is predicated of many, and hence he is universal; conversely, if the species is identified with Socrates, then the species is not predicated of many, and hence is individual (LI Isag. 15.26–35; Spade 1994, 57; and LNPS 518.37–519.2).26 No matter how indifference is explained, the identification of Socrates as the species leads to the absurd result that there is no difference between the individual and the universal.
The obvious response to Abelard’s criticism is to insist that Socrates is indifferently the same as many only qua species, and that in himself he is completely individual.27 Yet this solves nothing, Abelard points out, since the phrase “Socrates qua species” refers to no thing at all, or at least to nothing but Socrates, and so cannot avoid the absurd result (LNPS 519.27–520.6). Nor does it help to multiply contexts by suggesting that Socrates qua species is is indifferently the same as many but qua individual is not the same as many; Abelard can press the same question about what locutions such as “Socrates qua . . .” refer to (as well as noting that “something is not attributed to the genus in the same sense in which it is removed from the individual”).28 From a metaphysical point of view, Abelard maintains, indifference theories merely serve to obscure the fact that the only real things are individuals: “If Socrates were to agree with Plato in a thing that is man, still the only thing that would be man is Socrates himself, or some other man; hence Socrates must agree with Plato either in himself or in another man,” and both alternatives are unacceptable (LI Isag. 16.5–9; Spade 1994, 59). An indifference theory holding that agreement takes place “in a thing,” as Walter’s positive account does, will encounter these difficulties.29
William of Champeaux’s negative criterion for sameness, where two things are indifferently the same when they do not differ in something, might seem to avoid this charge and so be an improvement: Socrates and Plato do not differ in man, since each is a man, and so they are indifferently the same. Abelard tartly dismisses this move: “It could also be said in this fashion that Socrates doesn’t differ from Plato in stone, since neither is a stone, and so no greater agreement is indicated in them in man than it is in stone” (LI Isag. 16.9–13; Spade 1994, 60–61). This refutation, too, was decisive. Abelard recalls that when William was compelled to give up this view, his second to be refuted by Abelard, William’s “lectures went completely to pieces, so that they could scarcely be recognized to be about dialectic at all” (HC 96–98; Radice 1974, 60).
From his antirealist arguments, Abelard concludes that there are no (non-semantic) real objects in the world that satisfy Boethius’s criteria for the universal, whether as things in their own right or as real constituents of or in things. Instead, everything that exists is individual, or, as Abelard sometimes puts it, “personally distinct.”30 He explains the individuality of the individual as follows (LI Isag. 64.20–24):
Thus we say that individuals consist only in their personal distinctness, namely, in that the individual is in itself one thing, distinct from all others; even putting all its accidents aside, it would always remain in itself personally one – a man would neither be made something else nor be any the less a this if his accidents were taken away from him, e.g. if he were not bald or snubnosed.
To understand this passage properly we have to consider several topics. First, the distinctive feature of individuals is their individuality, which, as Abelard maintains here, is ontologically primitive (§II.1). Nearly all individuals, it turns out, are also form-matter composites, the exceptions being God, angels, and human beings; matter is basic and primary, whereas most forms are reducible to and supervenient upon their material components (§II.2). Hylomorphic individuals are also one type within a wide variety of integral wholes present in the world, wherein the form is the organizing principle of the parts of the whole composite (§II.3). Individuals have natures, and thereby belong to natural kinds (§II.4); their natures also set the limits of what is possible (§II.5).
Abelard countenances two criteria of individuality in the passage quoted above: (a) being one in itself; (b) being distinct from all others. As for (a), whatever is one in itself does not have the source of its unity located in some principle or cause extrinsic to it. Individuality must therefore be intrinsic to the individual. Primary substances such as Socrates satisfy (a), despite their including a good deal of complexity: Socrates is a composite of form and matter: with respect to form, Socrates is composed of essence, attributes (propria), and accidents; with respect to matter, Socrates is composed of his physical parts, and is related to them as an integral whole. The unity possessed by these elements is provided by Socrates himself; they constitute the unified and organized concrete individual that is Socrates, each in its own way. Nothing other than Socrates needs to be brought forth to explain why the parts or constituent elements of Socrates are what they are; what it is to be a hand depends on what it is to be an arm, and indeed on what it is to be a human being in the first place. As for (b), Abelard insists that individuals are distinct in all their features: Socrates differs from Plato in form as well as in matter.31 Such primary substances are “distinct from all else” (Dial. 51.11–13).
Abelard denies that individuality is a formal feature of things. There is no “individual differentia” that belongs essentially to an individual, making it individual. The specific differentia is the last such distinguishing element that enters into the constitution of an individual (Dial. 546.28–547.26).32 In the absence of an individual differentia, the individual cannot have a proper definition (Dial. 584.26–29). Furthermore, there is no attribute belonging to Socrates that doesn’t also characterize the species man, and nothing belonging to the species that doesn’t belong to some or to many men (LI Isag. 63.16–18 and LNPS 555.33–35). This claim establishes a fortiori that no formal feature can be responsible for the individuality of the individual. Abelard also offers several independent arguments against taking any accidental form or collection of accidental forms to be the ground of individuality: as we have seen, such accidental forms would thereby be prior to the substances in which they are to be founded; they cannot be present per accidens in the subjects that they render individual; if the entire collection of accidents belonging to an individual is taken to be the ground of individuality, the individual will change with every accidental change; there will be an infinite regress of accidental individuating forms; terms such as “Socrates” will be mere adjectives rather than substantives.33 Even if there is a description that uniquely picks out Socrates, it does so in virtue of accidental properties that Socrates possesses contingently, presupposing rather than grounding his individuality (LI Isag. 63.4–18 and LNPS 556.1–10; cf. also Dial. 569.1–18). Therefore, individuality is not a formal feature of individuals.
Nor did Abelard consider individuality to be a material feature of individuals, since there are immaterial individuals, e.g. human souls, angels, God; the fact that matter does not explain individuality is compatible with material differences being grounded in the distinctness of the material individuals, of course.
Thus Abelard holds that there is no principle or cause which accounts for the individuality of the individual, or at least that there is no principle or cause other than the very individual itself, and thus there is no “metaphysical” problem of individuation at all. For Abelard, individuality, unlike generality (which is purely linguistic), is primitive and needs no explanation. Yet this does not entail that individuals themselves must be simple or incapable of further analysis. They are paradigmatically concrete individuals, such as Socrates and Fido, and almost always hylomorphic compounds.34
Abelard holds that in the mundane world, i.e. everything apart from God and angels (including fallen angels), everything is made of form and matter.35 Strictly speaking, the “matter” of something is that (a) out of which it is made, and (b) in which it remains as a part (LI Isag. 79.5–9; LNPS 509.23–26 and 564.14–15; Dial. 415.5–6 and 575.18–36; TC 4.51 288.769). Flour, when made into bread, no longer retains its form as flour, and hence is not the matter of bread in the strict sense. Even so, Abelard countenances things that satisfy (a) as the “matter” of something in a loose sense, whether they satisfy (b) or not. The strict sense allows Abelard to talk about the multiplicity and variety of material parts, from bricks in houses to apples in apple pie; the loose sense allows him to speak generally of material ingredients, such as flour in bread, as well as to endorse the reductive claim that there are really only four elements: earth, air, fire, and water. These four elements are literally the building blocks, and hence the matter (in a loose sense), of the rest of the world. Abelard highlights their importance with his theory of primary and secondary creation.36
In primary creation, God created ex nihilo the four elements as the primordial matter for all other bodies. Initially the elements are thoroughly intermingled in a fluid chaotic mass; each element is then differentiated from the mass by the pairing of its distinctive qualities: air with moistness and lightness, fire with lightness and dryness, water with moistness and softness, earth with heaviness and hardness.37 These elements are indestructible and sempiternal, out of which all else comes to be (Dial. 418.36–37 and 550.34–35; TC 3.141 and 4.40).38 In secondary creation, God does not create any new matter but instead creates substantial forms that inform existing matter, differentiating it into natural kinds, perhaps by literally adding successive substantial forms: to a material body he adds life, then the power of sensation, and finally rationality, thereby producing a human being.39 This process can be analyzed logically as a descent down the Porphyrean Tree, moving from general to specific features: from substance to physical substance, to living physical substance, to rational living physical substances. But ontologically it always remains at the level of concrete individuals, from a thing to a body to an animal to a human; at no point is there an animal that isn’t a fully determinate kind of animal. (Genera and species exist only in and through primary substances.) Now in order to exist a concrete individual needs a full complement of accidental forms, since Socrates must have some definite height, eye color, and the like; but these are features of the particular matter of which Socrates is made.
Abelard exploits this last insight in thinking about form-matter composition. He holds that matter and form are principles of mundane objects, and that they always exist mixed together; neither can exist without the other, although they may be conceived independently (LI Isag. 25.1–4 and 25.32–33; LNPS 565.3–5; and TI 72–74).40 He gives a surprisingly modern twist to this Aristotelian claim. The form of a physical object is just a particular configuration of its matter: “We strictly call ‘form’ what comes from the composition of the parts” (LI Isag. 79.9–10; cf. also LNPS 565.16). The form of a statue is its shape, which is no more than the arrangement of its matter – the curve of the nose, the size of the eyes, and so on. Thus forms are supervenient on matter, and have no ontological standing independent of it (a claim to be made more precise after examining Abelard’s theory of identity in §III below). This is not to deny that forms exist, but to provide a particular explanation of what it is for a form to inhere in a given subject, namely, for that subject to have its matter configured in a certain way. For example, the inherence of shape in the statue just is the way in which its bronze is arranged. The supervenience of form on matter in form-matter composites explains why Abelard holds that mundane things are identical with what they are made of (Dial. 415.26–33). With one exception.
The human soul is unlike all other souls, which are merely material.41 Abelard carefully states his position in glossing Genesis 2:7 (the text in capitals is the biblical citation Abelard is commenting on):
THE LORD GOD FASHIONED MAN FROM CLAY, i.e. from moist earth, as though it were tightly packed together rather than loose; and He thus infused the soul into a body that was already created. This passage suggests that the human soul is dissimilar from all other living beings in the very manner of its creation. For in the creation of all other living beings, God was said to have produced “the heavens and the earth” along with body and soul together – which suggests that their souls are made of those very elements.
(Hex. 102.21–103.3)
The human soul, by contrast, is not made from the four elements (Hex. 104.8: non de aliquo materiali primordio). Abelard holds that the human soul is incorporeal, and, despite not having access to Aristotle’s discussion of the soul in De anima 3.5, he holds that it is incorporeal for essentially the same reason as Aristotle: the understanding doesn’t need a body in order to think, whether as an instrument or an object (LI Cat. 212.30–31; LI De in. 3.1.24, G 313.33–35; and TI 5).42 He also believes that it is capable of existence apart from the body, and hence must be numerically different from the body and from the composite. Nevertheless, when combined with the body the result is a unified individual human being. Abelard argues that the traditional division of Substance into the corporeal and the incorporeal must be inadequate, since humans, comprising both body and soul, are strictly neither, although they are one by nature (LI Isag. 48.10–49.11 and LNPS 547.12–549.3).43 And since the human soul is not supervenient on the body, Abelard concludes that the human soul is not, strictly speaking, a form at all.44 Yet the human soul acts as a substantial form while it is joined to the body; if not a form, it is closely analogous to one. Abelard takes this to be the explanation of Porphyry’s remark that all things come to be either from form and matter or from the likeness of form and matter (Isag. 4 18.9–11): human beings are only analogous to ordinary form-matter composites, whereas all other physical objects are straightforward form-matter composites (LI Isag. 79.19–30, and LNPS 564.25–565.2).45 Abelard therefore endorses hylomorphism for mundane objects, setting humans aside as a special case.
Abelard, following Boethius (De div. 12.17–20, 879B), holds that there are two fundamental types of substantial wholes: (a) universal wholes, which distribute a common essence; (b) integral wholes, which embrace quantity (IP 6 166.6–28; Dial. 339.30–32 and 546.21–27).46 Now (a) and (b) are distinct, as noted in §I.2 above; they correspond roughly to the modern distinction between distributive and collective classes. Abelard has argued at length that there cannot be any non-semantic objects satisfying (a) in the world. However, there are wholes that satisfy (b), namely, integral wholes; they meet most of Boethius’s conditions on commonness, failing only in that the whole is not present in each of its parts as the universal whole is said to be.47 Abelard countenances many types of integral wholes: collections, no matter how their members are selected; structured composites, whether naturally unified (such as Socrates and his limbs) or artificially unified (such as the walls, floor, and roof of a house); continuous quantities that are homogeneous material “substances,” namely, stuffs, such as water or gold; geometrical objects, such as lines, defined by the relative position of their parts; temporal wholes, such as a day and the hours that make it up. Yet despite their variety, integral wholes are organized around a relatively simple taxonomy, as we shall see.
Substantial integral wholes, like quantities in general, are divided into continuous and discrete (LI Cat. 169.4–5 and Dial. 71.16–18, following Aristotle, Cat. 6 4b20). Abelard endorses Aristotle’s view that continuous wholes have parts that are connected by a shared boundary, but thinks that they should be strictly defined as wholes “whose parts are situated without any intervals” so that “there are no gaps among them,” and discrete otherwise.48 Abelard doesn’t subdivide the category of continuous wholes any further. His examples are spatial and temporal wholes on the one hand, and three-dimensional solids on the other; the latter, consisting in lines, planes, and surfaces, are generated by points and are the real constituents of which all bodies are composed. Abelard therefore identifies homogeneous material “stuffs” (described in §II.2 above) as the paradigmatic cases of continuous wholes.49 They possess no well-defined parts, but are individuated by their amounts or measures: a cup of water, a block of marble, a pound of flesh.
Abelard gives most of his attention to discrete integral wholes, that is, wholes whose parts permit separation. There are three nested types: collections, which involve only a plurality of parts; aggregations, which require some proximity among the plurality of parts; and composites, which require the aggregated parts to be combined and structured in a definite way.50 Each type has distinctive features. Collections, whose parts are the members of the collection, are the simplest kind of discrete integral whole; extensionally defined and unordered, they are as close as medieval philosophers ever came to set theory: any three cats make a collection, as do a finger and a particular whiteness.51 Since the members of the collection are linked only in belonging to the collection (Dial. 548.13–15), their individual natures are irrelevant, a fact Abelard takes into account by typically discussing them in terms of their cardinality – a pair, a triple, a nonet.52 Since collections exist only in and through their members, they are merely supervenient and add nothing to Abelard’s ontology. So too for aggregations, which are collections whose members are located in close proximity, e.g. a crowd is a collection of people assembled in one place, a heap a collection of pebbles one on top of another. Such aggregations are no more than their members in a given spatial location, and thus add nothing to the world.
Composite wholes differ from collections and aggregations in requiring their parts to have some fixed structure relative to one another (LI Cat. 171.9–17 and Dial. 575.37–576.7). A house, for example, is a composite whole in which the walls must stand on the floor and in turn support the roof; a mere collection of house-parts, even a heap of house-parts, does not constitute a house (LI Cat. 171.15–17). In this instance the structure is artificial, but it need not be; Socrates is a composite whole with regard to his bodily limbs. All form-matter composites are therefore composite integral wholes, taking the “structure” in question to be given by the substantial form that organizes the material parts of the whole in the proper way.53 Whether these composite wholes add anything to the ontology depends on what we have to say about the ontological standing of their organizing forms.
Abelard’s theory of substantial integral wholes is not a pure mereology in the modern sense, since he holds that there are privileged divisions: just as a genus is properly divided into not just any species but its proximate species, so too the division of a whole must be into its principal parts (Dial. 548.29–31). Intuitively, some wholes have a “natural division” that takes precedence over others; a sentence, for example, is divided into words, syllables, and letters, in precisely that order (Dial. 67.17–22 and 548.31–36). Yet alternate divisions, perhaps yielding alternate parts, are available. There seems to be no easy way to determine what the principal parts of a given whole are, that is, which of the many possible divisions should be privileged. According to Abelard, there were two schools of thought on the question. The maximalists held that parts are principal when they are maximal, i.e. belong only to the whole, not to another part; the destructivists held that parts are principal when the whole would be destroyed by their destruction (Dial. 549.4–20; cf. also Sent. 15 and 34–36).54 Abelard finds neither position satisfactory.
Maximalism presents an easy target. Take some composite integral whole, such as a house. Its principal parts, intuitively, are the floor, walls, and roof; none of these is a part of any of the others (e.g. the floor is not part of the roof), and taken together they constitute the whole house, so the maximalist criterion seems plausible in this case. Abelard makes short work of it nonetheless. Initially divide the house into two parts, the floor on the one hand and the roof-and-walls on the other; then the roof will not be a principal part (since it is part of the roof-and-walls) and neither will the walls. Clearly, any part can be made principal or secondary by proper choice of division, and so maximalism fails (Dial. 549.21–34).
Destructivism faces a different challenge, namely, that by its lights every part of a given integral whole must be a principal part. Abelard reasons as follows. Take any random part of a house, say a pebble in the wall. Since wholes are defined through their parts, if the whole exists then any part of the whole must also exist (Dial. 343.34–35 and 550.9–13).55 This is logically equivalent to its contrapositive, namely, that if any part of the whole fails to exist, the whole also fails to exist (Dial. 346.31–34 and 550.15–16). Thus if the pebble no longer exists, the house no longer exists. More precisely, the whole H1, which is that very house with all its parts, including the pebble, no longer exists once the pebble no longer exists, although the distinct whole H2 (all of the parts of that very house other than the pebble) has now come into being – H2 formerly was part of H1 (Dial. 550.24–33).56 Thus any random part of a whole is a principal part of that whole, according to the destructivist criterion, and this result is unacceptable.
In contrast to both maximalists and destructivists, Abelard proposes that the principal parts of a whole are those whose conjunction immediately results in the complete whole (Dial. 552.38–553.7). His intent seems to be that the nature of the composition (if any) that defines the integral whole also spells out its principal parts. A house consists of floor, walls, and roof put together in the right way; this says nothing about the constituent sub-parts of the floor or the walls or the roof, in particular leaving it open whether each requires all of its sub-parts to be the principal part it is. Abelard’s criterion therefore improves on destructivism, since the existence of the whole entails the existence of its principal parts but not necessarily any of their sub-parts. It also improves on maximalism, since it derives the principal parts from the compositional structure of the whole. Where such structure is lacking, the principal parts are just the parts as ordinarily identified. The principal parts of a collection, for example, are just each of the members of the collection, whatever may be the case with any given member’s sub-parts; the principal parts of an aggregation are the members located in proximity to one another.
According to Abelard, individuals have natures, and in virtue of their natures they belong to determinate natural kinds. But an individual’s nature is not something really shared with or common to other individuals; Abelard’s refutation of realism has shown that this is impossible.57 Nor is the nature anything in addition to the substantial form and attributes of the individual: Socrates does not have a human nature as well as his substantial form and the attributes consequent on having that form (including material properties). Instead, he belongs to a given natural kind in virtue of having a specific or generic substantial form, one completely individual to him.
Like most medieval philosophers, Abelard held that we are largely ignorant of the natures of things, by which he meant the full array of features that being a certain kind of thing may involve. We do not even know why risibility is an attribute of human beings, much less why some plants are poisonous, what makes volcanoes erupt, or how to tell dogs from foxes. It is the business of “physics” to investigate the natures of things and their causes (as noted at the beginning of this chapter). In this connection, Abelard often uses the word “nature” loosely to cover more than the individual’s substantial form, instead capturing the typical material organization, behavior patterns, way of life, and so on: “Sleeping after a meal is part of the lion’s nature.” Presumably this kind of talk will be cashed out in the end by talk of substantial and accidental forms different kinds of things have, and Abelard’s intent is usually clear from context.
But what of the precise meaning of “nature”? Abelard interprets Porphyry’s remark that “the species collects many into a single nature” (Isag. 3 12.15–17) linguistically, explaining that the name of the species refers to the things it does “due to their natural creation” (ex creatione naturae) (LNPS 553.29–32; cf. the parallel passage at LI Isag. 57.27–30). He glosses this last phrase by citing Boethius’s definition of “nature,” which he further explains as follows:58
Boethius says that nature is “the likeness of things that come into being,” as though to say explicitly that the same things are of one nature that are similar to one another by natural activity. Accordingly, we call the name “man” a nature, which is naturally common to many things in virtue of its single imposition, due to the fact that they are naturally similar to one another in that each of them is a rational mortal animal.
(Secundum mag. Petrum 17)
By “naturally similar” Abelard means that the similarity between Socrates and Plato is not conventional, but rather a fact about the world that follows from each being human, which is itself a function of their biological history. In short, Abelard takes a natural kind to be a well-defined collection of things that have the same features, broadly speaking, that make them what they are. Why a given thing has some features rather than others is explained by how it got that way – the natural processes that created it result in its having the features it does, i.e. being the kind of thing it is; similar processes lead to similar results. On this reading, it is clear that natural kinds have no special status; they are no more than discrete integral wholes whose principle of membership is similarity, merely reflecting the fact that the world is divided into discrete similarity-classes of objects. Furthermore, such real relations of similarity are nothing themselves above and beyond the things that are similar (see §IV.1 below). In his positive account of universals, Abelard notoriously argues that there is no thing in which different items of the same sort agree; instead, each simply is what it is, which constitutes their agreement (LI Isag. 19.29–20.6; Spade 1994, 90–91).59 He sometimes refers to each thing’s being as it is as its “condition” (status), but this shorthand carries no metaphysical baggage. Socrates and Plato are objectively more similar in what they are (namely, human) than are Socrates and Brunellus (although the latter are similar in being animals), but in itself this adds nothing to Abelard’s ontology.
The division into natural kinds is, presumably, a “shallow fact” about the world: matters could have been otherwise had God ordained them differently; fire might be cold, heavy bodies fall upwards, frogs reason. As noted in §II.2 above, in secondary creation God sorts things into natural kinds by creating inherent substantial forms. This is part of a more general process whereby God establishes “natural power” (vis naturae) in things to take the place of the direct exercise of His efficacious will during the six days of Creation, i.e. where the causal powers of things are implanted via their substantial forms.60 (This is what allows Abelard to pass from a thing’s individual nature to the interacting system of all such things as “Nature.”) If these causal powers were different, then natural kinds might be different as well, or might not have been as sharply differentiated as they are now. Given how matters stand, natural kinds carve the world at its joints, but they are God’s chosen joints.
The upshot is that what it is to be a certain kind of thing is deeply tied in with what things of that sort are able to do. (A human being lacking rationality would not be human at all.) Abelard puts this insight to good use in accounting for real modalities.
Abelard recognizes that “possible” and cognate modal terms are systematically ambiguous between referring to possible states of affairs (possibilities) and the grounds for an agent’s possible acts (powers) (LI De in. 3.13.57, MP 181 79.9–11). The distinction between them, roughly, is that possibilities are relative to natural kinds and powers are relative to individuals. Most of Abelard’s discussion centers on the former, though he suggests that the latter may be the more basic, as we shall see.61 To begin, however, let us consider each in turn.
Following a line of thought found in Boethius, Abelard analyzes possibility in terms of natures.62 He presents the outlines of his account as follows:
“Possible” and “contingent” mean the same thing. For we do not here take “contingent” for what actually happens, but for what can happen, even if it should never happen, so long as the nature of the thing is not incompatible with its happening but instead permits it to happen (dummodo natura rei non repugnaret ad hoc ut contingat, sed patiatur contingere). For example, when we say “It is possible for Socrates to be a bishop,” this is true even though he never is one, since his nature is not incompatible with it.
(Dial. 193.31–36)63
The nature of something determines what is and isn’t possible for it. More exactly, simple modal claims are analyzed into relations of compatibility that obtain among properties and natures. These compatibility-relations are objective rather than linguistic or conventional; Abelard follows the Aristotelian tradition in identifying real forms of opposition as features of the world.64 Like other relations, of course, these forms of opposition merely supervene on things that are opposed. We derive our knowledge of such possibilities from observation. We know that Socrates’s nature is compatible with bishophood, for instance, because we observe that there are some men who are bishops; Abelard reasons that whatever holds for one must hold as possible for all, “for otherwise things that differ only in their accidents would differ in kind” (Dial. 193.36–194.5), a claim underwritten by Abelard’s view that the species is the individual’s nature.65 Abelard’s extended analysis of real opposition, while glossing Cat. 10–11 and explaining the topic from opposites, gives content to his otherwise abstract analysis of modality.
As with possibilities, so too with necessities: something is necessary if a thing’s nature requires it. The necessary is thus inevitable, since it proceeds from natural requirements.66 By the same token it might be thought that the possible is what can be avoided – what might be or might not be – but this straightforward equation is complicated by different senses in which something may be fixed in advance (and thereby unavoidable), or, in Abelard’s preferred terminology, “determinate.”67 Now determinateness is not strictly a modal notion. It is grounded in epistemic facts about what is knowable or “certain” ex natura rei (Dial. 211.5–7) or ex se ipsis (212.15). Roughly, the nature of something spells out what it can or will do, as described above; if further epistemic conditions are met – if we can somehow know now what will take place – the event will be determinate, and if not, not.
In addition to the simple modal statements already canvassed, Abelard applies his nature-based analysis to modal sentences that have an appended condition: “It is possible that S is φ while ψ” where the subordinating conjunction might be while, whenever, if, as long as, and so on, and in particular φ may be ψ.68 Here the ascription of possibility is only relative to the condition. Abelard tells us in LI De in. (309.91, G 430.5–9) that these sentences have two readings: (i) the nature of the S that is φ permits it to ψ; (ii) the nature of S permits it to φ and ψ together. Relative modality, like simple modality, is explained in terms of natures.
In keeping with the Aristotelian tradition, Abelard sharply distinguishes “It is possible that S is φ” from “S can be φ”: the latter, but not the former, ascribes a real power (potentia or potestas) to S. For the latter to be true a further constraint in addition to its possibility must be satisfied, namely, that nothing precludes S from becoming69 φ (whether S ever becomes φ or not).70 Given that human beings walk, then Abelard’s account of power is, intuitively, that Socrates can walk if he is not now tied to a chair, dead, legless, locked in the closet, or the like. The presence or absence of such causal factors is a matter of how the world actually is. The nature determines the bounds of possibility, the world determines the possession of power.
Abelard’s account of powers is little more than a sketch, but he returns to them in one of his few remarks to address directly the ontology of the possible. In TSch 3.95, he points out that even philosophers who have made a point of investigating the natures of things have concerned themselves almost exclusively with the natures of creatures in their ordinary experience, not with God’s divine power that is in command of all created natures; indeed, strictly speaking, the nature of something must comply with God’s will. As a result, “when they say that something is possible or impossible, i.e. to be compatible or incompatible with a nature, they take the measure of this according to the capacities of creatures only, not the strength of the divine power.” Absolute possibilities may be relative to the natures of (created) things, but such natures are themselves subject to God’s power; in the final analysis, then, possibilities depend on powers, though Abelard says no more about how this is to be understood.71
Abelard endorses the traditional account of identity, derived from Boethius, which holds that things may be either generically, specifically, or numerically the same or different (LNPS 535.34–41).72 Yet the distinctions represented in the traditional account are not sufficiently fine-grained for Abelard’s philosophical purposes. He elaborates an original theory of identity, apparently developed in the first instance for theological problems surrounding the Trinity, but of general application.73 Four kinds of identity are at the heart of Abelard’s new theory: essential sameness and difference, closely tied to numerical sameness and difference (§III.1); sameness and difference in definition (§III.2); sameness and difference in property (in proprietate) (§III.3).74 Roughly, Abelard’s account of essential and numerical sameness is intended to improve upon the identity-conditions for things in the world given by the traditional account; his account of sameness in definition is meant to supply identity-conditions for the features of things; and his account of sameness in property opens up the possibility of there being different identity-conditions for a single thing having several distinct features.
Abelard’s account of essential sameness and difference is based on the twelfth-century reading of essentia as meaning “concrete thing”, and has nothing to do with the technical notion of essence (i.e. the set of properties that make something to be what it is). He holds that x is essentially the same as y when x is numerically the same concrete thing (essentia) as y. Otherwise, x and y are essentially different, which happens when they are “at variance” (dissident) with one another.75 Coreferential terms pick out essentially the same thing. For Abelard, the Morning Star is essentially the same as the Evening Star. Each of Socrates’s individualized substantial forms is numerically the same concrete thing, namely, Socrates himself; hence they are essentially the same as one another and essentially the same as Socrates, though such forms are not numerically the same as each other. More generally, the formal elements that constitute a concrete thing are essentially the same as one another and essentially the same as the concrete thing of which they are the formal constituents. This conclusion fits well with traditional philosophical usage, at least in the case of substantial forms, since it is customary to say that Socrates is his essence (Socrates is what it is to be Socrates). The corresponding general thesis does not hold for parts, however. Abelard maintains that the part is essentially different from the integral whole of which it is a part,76 reasoning that a given part is completely contained, along with other parts, in the whole, and so is less than the quantity of the whole (TC 4.12).77 Essential sameness, then, is fundamentally an ontological notion. In later medieval terminology, such things are really the same, the same res.
Numerical difference does not map precisely onto essential difference. Roughly speaking, numerical difference is a function of there being discrete “units” that can serve as sortals for enumeration, as in the case of distinct forms; it also happens when things have no part in common: they are “distinct in respect of the quantity characterizing the concrete thing in question” (TC 3.150: adeo tota essentiae suae quantitate ab invicem discreta sunt). This opens up the possibility that there are things neither numerically the same nor numerically different from one another (TC 3.153), as follows. The failure of numerical sameness, as characterized by Abelard, may be due to one of two causes. First, objects are not numerically the same when one has a part that the other does not have, in which case the objects are essentially different as well. Second, objects are numerically different when neither has a part belonging to the other. Numerical difference entails the failure of numerical sameness, but not conversely: a part is not numerically the same as its whole, but it is not numerically different from its whole. Thus x is essentially different from y when either (a) x and y have only a part in common, in which case they are not numerically the same; or (b) x and y do not have any parts in common, in which case they are numerically different as well as not numerically the same.
Abelard’s account of numerical sameness and difference has surprising consequences for metaphysics. Since things may be neither numerically the same nor numerically different, the question “How many things are there?” is ill-formed as it stands and must be made more precise.78 Furthermore, the ontological standing of forms can be clarified in terms of Abelard’s theory of essential and numerical identity. Putting the human soul aside as a special case, a mundane individual’s substantial forms are essentially the same as the individual, as noted above; they are also numerically the same as that individual, since neither can be destroyed without the destruction of the other, a consequence of Abelard’s definition. They are neither numerically the same as nor numerically different from one another, though, since one may involve the other as a constituent, as e.g. animality involves corporeality. Accidental forms are essentially the same as the individual they inform but, unlike substantial forms, they are not numerically the same as the individual; they can be created or destroyed without affecting the being of the individual. Yet accidental forms do not differ numerically from the individual they inform, since at least each has the individual’s substance as its subject of inherence, and in that sense is a metaphysical “part.” Indeed, forms in general are configurations or arrangements of parts of the individual, as noted in §II.2 above, and so merely supervene on the individual (or the individual’s matter) while being neither numerically the same as it nor numerically different from it. Finally, like essential properties, accidental properties are numerically different from one another. Now Abelard only countenances concrete individual substances. But that is not quite to say that the forms of something cannot be distinguished from it and from one another, and Abelard’s theory of essential and numerical identity allows us to explain this precisely.79
Essential and numerical sameness and difference apply directly to things in the world; they are extensional forms of identity. By contrast, sameness and difference in definition is intensional, roughly analogous to modern theories of the identity of properties.80 Abelard holds that x is the same in definition as y when (a) what it is to be x requires x to be y, and (b) what it is to be y requires y to be x; otherwise, x and y are different in definition.81 This is a deliberately extended use of “definition,” since it applies to items that lack a strict Aristotelian definition by genus and differentia: individuals, artifacts, and the like.82 It is a matter not only of one thing being the other, or even necessarily being the other, but rather being such that “insofar as it is the one it requires only that it be the other, and conversely”; this connection is stronger than coextension. Abelard takes it to be even stronger than necessary coextension, for he says that colored substance and corporeal substance are necessarily coextensive but different in definition: they are necessarily coextensive since in order for anything colored to exist it must be a body, and conversely, but the one isn’t part of what it is to be the other, any more than having spatiotemporal location is part of what it is to be colored, although this too is a necessary feature for anything colored to actually exist (TC 3.143). Hence the formulation “what it is to be x requires x to be y” in the definition above.
Abelard says that this mode of identity applies strictly to the case of a single concrete thing, in which case items that are the same in definition are ipso facto essentially the same. The converse does not hold. A single concrete thing, such as a block of marble, can be both white and hard, but whiteness and hardness differ in definition; indeed, as Abelard sees it, things generally have diverse properties.83 Although identity in definition strictly applies only to the case of a single concrete thing, we can loosely speak of two white things as being the same in definition as a straightforward extension of this mode of identity. Abelard himself relaxes the requirement that the items in question be concrete things when considering how Porphyry (Isag. 4 16.20–17.10) can hold that a differentia is both divisive (dividing the genus) and constitutive (constituting the species); he concludes that there is nothing about division that inherently requires constitution, nor conversely, and hence divisive and constitutive differ in definition (TC 3.156, TSB 2.4.98, and LNPS 559.26–29). Yet a differentia is not a concrete thing (essentia), which suggests that we should follow Abelard and relax the strict requirement, as in the general formulation given above.
It might seem that the three modes of identity already discussed would be sufficient for Abelard’s philosophical purposes: two extensional modes for analyzing relations among real things in the world, one intensional mode for the features possessed by real things. Yet in TC 3.140–141 Abelard introduces a fourth mode of identity: sameness and difference in property. It is appropriate when something has a degree of internal complexity, particularly when it has a multiplicity of features that do or do not characterize one another. He offers a pair of examples.
First, consider a cube of marble, which exemplifies both whiteness and hardness. In this case, what is white is essentially the same as what is hard, since they are numerically the same concrete thing, namely, the marble cube. It is also clear that the whiteness and the hardness in the marble cube differ in definition. Even so, what is white is characterized by hardness (the white thing is hard), and conversely what is hard is characterized by whiteness (the hard thing is white).84 The properties of whiteness and hardness are “mixed” since, despite their being different in definition, each applies to the selfsame concrete thing (namely, the marble cube) as such and also as it is characterized by the other.
The interesting case is where something has properties that “remain so completely unmixed” that the items they characterize can be called different in property. Abelard presents an extended analysis of one example: a waxen image, such as the shape of an eagle impressed on wax by a signet ring, whose matter is the wax and form is the geometric pattern. However, since his remarks make it clear that he is presenting a purely general case of a (form-matter) composite in relation to its matter, this is how I’ll describe it.85
The matter out of which a form-matter composite is made is essentially the same as the composite, since each is the entire material composite itself. Yet despite their essential sameness, they are not identical; the matter is not the composite, nor conversely. The matter is not the composite, for the composite comes to be out of the matter, but the matter does not come to be out of itself. The composite is not the matter, since “nothing is in any way a constitutive part of or naturally prior to itself.” More precisely, the matter is prior to the composite, i.e. has the property priority with respect to the composite, whereas the composite is posterior to its matter, i.e. has the property posteriority with respect to its matter. Now despite being essentially the same, the matter is not characterized by posteriority, unlike the composite, and the composite is not characterized by priority, unlike the matter. Hence the matter and composite are different in property; the properties priority and posteriority are unmixed.86
The matter is of course what is posterior, that is, the thing that is posterior, namely, the composite; the composite is what is prior, that is, the thing that is prior, namely, the matter – two instances of Abelard’s special “what is x” locution – but the matter is not posterior, and the composite is not prior (the unvarnished “is x” locution). In keeping with the distinction mentioned in the preceding paragraph, these “what is” identities don’t “mix” the respective properties.
Abelard’s analysis makes no assumptions about whether these property-bearers have any ontological standing. In his first example, the marble cube is a concrete thing, and hence is an individual. In his second example, the composite is a concrete thing, but the matter has no independent ontological standing while part of the composite – or at least no other standing than being not numerically the same as the composite (since the composite can pass away while the matter remains). Abelard offers no general guidance; presumably each case is to be decided on its own merits.87 The merit of this new mode of identity is that it calls attention to cases where something has a degree of internal complexity, whatever the standing of the items said to be different may amount to. A look at two applications, one from theology and the other from philosophy of language, should testify to the subtlety and power of Abelard’s account.
First, Abelard notoriously uses his theory of identity to shed light on the Trinity. The three Persons are essentially the same as one another, since they are all the same concrete thing (namely, God); they differ from one another in definition, since what it is to be the Father is not the same as what it is to be the Son or what it is to be the Holy Spirit. The three Persons are numerically different from one another, for otherwise they would not be three, but they are not numerically different from God: if they were there would be three gods, not one. Moreover, each Person has properties that uniquely apply to it – unbegotten to the Father, begotten to the Son, and proceeding to the Holy Spirit – as well as properties that are distinctive of it, e.g. power for the Father, wisdom for the Son, and goodness for the Holy Spirit. The unique properties are unmixed in Abelard’s technical sense, for the Persons differ from one another in their unique properties, and such properties do not apply to God; the distinctive properties are mixed, though, in that God is characterized by each (the powerful God is the wise God is the good God).88 Further than that, Abelard holds, human reason cannot go. His account is at best an analogy (similitudo), but one that illuminates matters while preserving the essential Mystery of the Trinity.89
Second, Abelard draws a distinction between words construed solely as physical objects (voces) and words construed as bearers of semantic meaning (sermones).90 As a physical object, a word is no more than a particular non-repeatable set of vibrations in the air.91 As a bearer of semantic meaning, it has a role in a norm-governed system of linguistic practices (institutiones). In short, we have an instance of a physical item playing a functional role, a kind of “composite” analogous to a form-matter composite.92 The properties of each are unmixed; physical and semantic properties do not characterize the same subjects. The word “animal,” for example, as a meaningful unit of language has the semantic property predicability of many, but as an utterance-token has the property unrepeatability – but the physical object is not predicable of many, and the word is by its nature repeatable.93 Abelard’s theory of identity allows us to tease apart the differences between the utterance and the linguistic item, keeping their properties unmixed and freeing us from confusion.
Abelard takes Aristotle’s categories to be a guide to the fine-grained metaphysical structure of substances and accidents, although each category has to be investigated in its own terms (§IV.1); the concrete world is spatiotemporal, though what exactly this amounts to has to be worked out (§IV.2). There are causes, but strictly speaking there are neither events (§IV.3), nor propositions or “the things that are said by sentences,” namely, dicta (§IV.4).
Boethius held that Aristotle’s aim in the Categories is to talk about the primary words signifying the primary kinds of things there are qua signifying them.94 Abelard distinguishes signification strictly speaking, i.e. generating an understanding, from reference; he then interprets Boethius as holding that Aristotle’s aim is to talk about the most general and simple words that refer to the natures of things.95 There are ten such words, according to Aristotle and Boethius: “substance,” “quantity,” “quality,” “relation,” “time,” “place,” “action,” “passion,” “position,” and “possession.” Abelard emphasizes that this list is not metaphysically privileged. As far as the natures of things are concerned, there could easily have been more or fewer categories; the rationale behind the traditional list is semantic rather than ontological.96 Yet nothing Abelard says suggests that he thinks Aristotle’s tenfold division of the categories is mistaken or misdirected. Indeed, he carefully follows it as a guide to the categorical structure of the world in all his writings. Given his practice, Abelard’s comments about the natures of things and the number of categories merit a less radical reading, common to all medieval nominalists: we cannot simply read off ontology from Aristotle’s categories – it is not, nor was it meant to be, a catalogue of the kinds of real things there are; the nature of each categorial item has to be investigated on its own terms, which is what Abelard proceeds to do in LI Cat. and the first part of the Dialectica.
Abelard accepts the traditional identification of concrete individuals with primary substances, although strictly speaking the distinction between primary and secondary substances is really a linguistic distinction between proper and common nouns (LI Cat. 140.19–24).97 In fact, much of what Aristotle has to say about substances Abelard explains linguistically, noting that Aristotle talks about language rather than things here, since the nature of substance is more familiar than the natures of the other categories (LI Cat. 139.31–37). For instance, Aristotle’s claim in Cat. 5 2b7–8 that species are “more substance” than genera turns out, in Abelard’s hands, to be a remark about how specific terms have more determinate reference than generic terms (LI Cat. 148.7–12). Still, when applied to things, the best description of substance is “what can exist on its own” (per se subsistit: LI Cat. 140.10–11).98 Unfortunately, Abelard doesn’t elaborate on this claim. Primary substances, as concrete individuals, exemplify all of the traits described in §II above; Abelard adds little new in glossing Aristotle’s discussion.
Abelard accepts Aristotle’s division of Quantity into discrete and continuous, but unlike Aristotle he is a committed indivisibilist with regard to continuous quantities.99 Abelard reaches his position by aligning continuous quantities with Aristotle’s distinction between simple and compound quantities. Continuous quantities, since continuity is defined by connections among parts, must thereby be compound, and hence made up of simple quantities: atoms for bodies, instants for times, phonetic elements for utterances (LI Cat. 168.31–169.2). The clearest example is the case of bodies. According to Abelard, lines, planes, and solids are generated by and made up of points, “although no authority says so” (LI Cat. 179.27–29). More precisely, a “point” is a quantitative unit that is indivisible in itself, having no extension in any dimension, that adjoins an equally indivisible subject, namely, a physical particle (an atom).100 These indivisible units are far too small to be perceived, and hence too small to be the actual units of measure we employ, but they are the foundation of all measure in the category of Quantity, and are the constituent elements of bodies (LI Cat. 168.5–8 and 183.1–3; Dial. 56.23–24, 56.31–33, and 57.15–20). Abelard does not say, but presumably these minuscule bodies are the indivisible atomic units of the four elements established in first creation.
Abelard offers two arguments to establish that lines consist in points. The first argument is suggested by Boethius (In Cat. 204C-D): if a line is cut into parts, then points appear at each cut, which are understood to have existed prior to the cut; but a line can be cut anywhere; hence a line consists of points everywhere (LI Cat. 179.41–180.3 and Dial. 59.6–13, ascribed by Abelard in the latter to one of his teachers).101 Now it could be objected that this argument only shows that points are distributed throughout a line, not that they belong to its essence. Abelard replies that if they do not then there is no sense to be made of the claim that the line is continuous. What else would be its parts? The points of a line would have no more relevance to the line and its continuity than particles of whiteness inserted throughout the line, which is unacceptable. Thus a line must consist in points. In the second argument, Abelard reasons that if lines are made up of line-segments and not of points, then each line-segment must itself be made up of line-segments, and so to infinity; hence the length of a line would be ill-defined (LI Cat. 181.5–7 and Dial. 58.13–15).102 Thus lines must consist in points. Both arguments can be generalized to establish that planes consist in lines and solids in planes.
Even if these two arguments establish that lines consist in points, they do not in themselves show that points make up lines, i.e. that an aggregate of points has length.103 Abelard is aware of the difficulty. He mentions as an objection a passage in which Boethius claims that putting one point on top of another has no effect, like piling nothing on nothing (De inst. arith. 87.16–88.1). He also knew that the claim that points are dimensionless makes it hard to see how any aggregate of them could produce length. In the Dialectica Abelard tries to duck the question, pleading mathematical ignorance,104 but in LI Cat. he suggests that if superposition does not make a real compound, then neither would putting one point right in front of the other (LI Cat.181.3–4). Abelard holds that points can be next to one another, and indeed that a line can even be constituted by two points; with this in mind he proposes that Boethius’s claim that superposition “has no effect” should be interpreted as the points being stacked on top of one another “without any interval” (LI Cat.181.36–38); hence Boethius is not really objecting to the composition of lines out of points, but merely noting that points with the same location do not have any length. Therefore, Abelard concludes, lines are made up of points as well as consist in them.105 As for lines, so too for planes, and solids in their turn. Hence bodies consist in and are ultimately made up of atoms. Of course, this claim involves a certain amount of idealization, as Abelard recognizes; the human body, for example, has pores, and so is at best a “perforated solid”; marble and the purest gold, by contrast, seem to have no interstices at all (LI Cat. 183.41–184.12). But these are just refinements of Abelard’s atomist account of the world.
According to Aristotle, the category of Quality includes (a) habits and dispositions; (b) passible qualities or passions; (c) natural capacities or incapacities; (d) geometrical forms and shapes. Abelard, following Boethius, raises the question whether (a) to (d) are genera or species of Quality; he argues at length, contra Boethius (In Cat. 244D–245A), that they are not (LI Cat. 225.21–227.2 and Dial. 101.5–103.18).106 Abelard goes so far as to call this a mistake on Boethius’s part (Dial. 103.5–6), and he asserts that taking them as genera or species “is repugnant to reason in every way” (LI Cat. 226.3). Furthermore, he asserts, Boethius knew better, since he himself laid down the axiom that a genus is always to be divided into two proximate species.107 In the Dialectica Abelard leaves it that (a) to (d) is just a listing of various qualities. His view in LI Cat. is more detailed. There he argues that (a) and (c) differ not by opposites, as a division into species would require, but can even include the same things: natural talents that are developed by training, for example. Likewise, habits and dispositions cannot themselves be species (or subspecies) of Quality, since the only difference between them is how deeply implanted they are. Nor is (b) a species, but a grab-bag of effects that might be engendered in a recipient. By contrast, (c) and (d), taken on their own, might properly be called species, in which case “the division of Quality will be irregular, partially by species and partially by accidents, and should really be called a list rather than a division” (LI Cat. 226.25–27).
Abelard agrees with Aristotle (Cat. 8 11a16–17) that the single common feature that applies to all and only qualities, even if the category is not well organized, is that they are like and unlike, much as all quantities are equal or unequal (LI Cat. 248.38–40 and Dial. 105.9–10). Yet sorting out Aristotle’s maxim takes some work, Abelard holds. First, he is explicit (as Aristotle is not) that it is the subjects possessing the qualities that are properly alike or not: a given body, in virtue of its particular whiteness, is similar to another white body (which is white in virtue of its particular whiteness); the qualities are responsible for the bodies’ being as they are, and hence for why they are like one another, despite having nothing in common (LI Cat. 249.11–18). Second, likeness or unlikeness seem to be qualities themselves, and so to belong to the category of Quality; many philosophers, even one of Abelard’s teachers, have thought so (LI Cat. 249.19–23 and Dial. 105.14–17).108 But there is a conclusive argument to think otherwise. If likeness were a quality, then it too would inhere in each of two white bodies, since they are like one another in respect of their whiteness; but then each body also possesses the quality likeness, and hence is like the other body in that respect, and so there must be another likeness inhering in each; and so to infinity (Dial. 105.18–19). The correct conclusion to draw, of course, is that likeness is not a quality but a relation (LI Cat. 249.23–25). When two subjects are alike, a particular likeness will be present in each. This particular likeness is not entirely the same as the quality that grounds their likeness, since “it is possible for whiteness to exist in a subject while everything else is destroyed, in which case it isn’t called ‘like’ anything else since it doesn’t retain the likeness” (Dial. 106.8–10). The regress can’t get a foothold since relations don’t engender likeness among the relata. In the end, Abelard thinks that likeness isn’t really different from the things that are alike, as his theory of relations holds.
Abelard follows Boethius (In Cat. 217B–C) in thinking that when Aristotle gives the first definition of the relative in Cat. 7 6a36–37 he is reporting Plato’s view, and that the second definition in 8a31–32 is his own, correcting what Aristotle suggests are the deficiencies in Plato’s account.109 Roughly, Abelard holds that in their respective definitions Plato was concerned with words whereas Aristotle followed the natures of things (LI Cat. 217.10–13 and Dial. 86.14–16),110 and consequently they didn’t differ in their views but only in how to take “relation”: Plato took it to include all permissible grammatical correlatives, Aristotle only real relations (LI Cat. 217.15–21; cf. also Dial. 91.34–92.10). Abelard’s exposition and analysis of Aristotle’s discussion of relatives is complicated – he has to take into account Aristotle’s gradual development of his own view out of his criticism of Plato’s definition – but the main lines of Abelard’s own reductive account of relations are presented in his explication of Aristotle’s definition.111 Socrates is the son of Sophroniscus; suppose that he is taller than his father. Whether fatherhood or tallness is at issue, the items related to one another are the grounds or subjects (fundamenta vel subiecta) of the relations: Socrates and Sophroniscus. The relation itself, fatherhood, and its converse relation sonship, strictly belong to Relation, as whiteness does to Quality; and just as the inherence of a particular whiteness in Sophroniscus is what it is for him to be white, so too the inherence of a particular fatherhood in Sophroniscus is what it is for him to be a father (which requires the simultaneous inherence of a particular sonship in Socrates). Again, just as a particular quality is a quale, Abelard calls a particular relation a “respect” (respectus), since it is that in virtue of which one thing is taken with respect to another, i.e. is relative to the other. Finally, in addition to the subjects and the respects in which they are related, there are the features due to which the relation obtains: the particular heights of Socrates and Sophroniscus, for instance.
Abelard seems to countenance sheer ontological extravagance when he raises the question whether there are distinct particular fatherhoods in a man who has several sons (LI Cat. 218.32–219.20 and Dial. 89.20–31). He argues that each time a man has a son, a new respect is made that wasn’t there previously, since now the man is a father in virtue of his particular relationship to that son; even were all the other sons to die, he would continue to be a father, since he is the father of this son. There are thus as many particular fatherhoods as there are sons (and sonships). Since this line of argument is perfectly general, it follows that there is always a particular respect in virtue of which subjects are related, when they are related. When Socrates is taller than Sophroniscus, there is a particular respect, namely, the particular case of taller than Sophroniscus that Socrates has, in virtue of which they are related; this respect no longer exists when Sophroniscus grows taller or no longer exists, although everything else about Socrates, including his height, could remain unchanged. Yet it is one matter to recognize that things are multiply related by distinct instances of the same kind of relation, another to think that some multiplication of entities is taking place. Abelard never calls respects “things” (res), though he does so term their subjects. Furthermore, something must have certain respects if other conditions are met. Given the particular heights of Sophroniscus and Socrates, Socrates will be taller with respect to Sophroniscus, and Sophroniscus shorter with respect to Socrates. But then these two relations supervene on Socrates, Sophroniscus, and their heights, and are not independent of them. (Indeed, Socrates is not really distinct from his height, as we have seen in §II.2 above.) Abelard reminds us that in speaking of relations “things don’t differ the way names do” (Dial. 88.19–20). The respect in which Socrates is taller than Sophroniscus is essentially the same as Socrates, but neither numerically the same as nor numerically different from him; we can identify it ontologically as his height, which sometimes is a respect in which he is taller than Sophroniscus, and sometimes not, as when Sophroniscus no longer exists. Distinct respects are different in definition, which does not necessarily entail ontological multiplicity.
Abelard complains that Aristotle only described the first four categories in any detail, namely, Substance, Quantity, Quality, and Relation; as a result, less is known about the remaining six categories. In fact, Abelard’s treatment of the final four categories, namely, Action, Passion, Position, and Possession, is as perfunctory as Aristotle’s (Dial. 80.30–81.6; cf. also LI Cat. 251.27–38 and 256.8–11). Abelard excuses himself on the grounds that Aristotle himself asserted that these last categories were obvious (Cat. 9 11b10–11), at best a weak excuse (LI Cat. 256.8–11). But whatever his reason, Abelard declines the opportunity to explore fertile ground left untouched by Aristotle, with an important exception: space and time. These categories hold a privileged place in Abelard’s scheme of things. Following Boethius, Abelard holds that in addition to the four Aristotelian causes, which are strictly principles of things, there are two principles per accidens, namely, space and time, “in that everything that comes to be or exists is in space or in time” (LI Isag. 33.26–30; cf. also the reference in LI Cat. 290.14–16).112 Thus space and time have a privileged position in metaphysics and demand a closer look.
Strictly speaking, Aristotle does not have a category for either space or time. Instead, he treats them initially as types of continuous quantities, and then again in the categories of Where and When, although these categories refer not to space or time precisely but to location in each. Yet in each case space and time are accidents, that is, dependent entities characterizing the items that have them: Socrates has his own space (think of him as “taking up” room) and his own time (think of his age), a view sharply different from modern Newtonian conceptions of space and time as absolute or substantival entities that function as containers for things and events. Aristotle’s full theories of space and time are developed in the Physics, of which Abelard knew next to nothing; with only the sketchy material in the Categories, however, Abelard develops his own account of space – more precisely, of place – and time.
Abelard distinguishes two conceptions of place, which he calls “quantitative” and “substantial” place (Dial. 79.3–6), corresponding to the difference between space conceived as a quantitative feature of a body on the one hand, and as a feature relating that body to its surroundings on the other (roughly the place it is in). The former is defined as “the quantity strictly surrounding a quantitative body or some part of it” (LI Cat. 189.5–6), where by “strictly” Abelard seems to mean “most closely.”113 A solid body has its place surrounding and circumscribing it; likewise its constituent elements – surfaces, planes, lines, and points – each has its own place, and, just as bodies are built up from the atoms corresponding to indivisible points, so too are places built up from the “atomic places” of each atom; the resulting compound places are therefore continuous wholes.114 A compound quantitative place is closely linked to the solid body it characterizes; it is, roughly, the boundary layer immediately next to the outermost surface of the body. In short, Abelard has a volumetric conception of the place of a body.
Substantial place, by contrast, is a relational feature of something that explains where it is: Rome, the theater, home (Dial. 79.4–6); perhaps even outside (LI Cat. 257.25–30). It is clearly not the same as quantitative place, since that remains the same even after moving from one city to another (Dial. 79.14–15). Presumably each of these “locations” has been defined by quantitative place, or a generalization of quantitative place, as e.g. a city includes everything inside its boundaries, a theater or house everything inside its walls. A substantial place, then, is defined quantitatively and then as an aggregate whole. The real cash-value in Abelard’s introduction of substantial place isn’t a new kind of “place” (contrary to his own suggestion), but the relational fact of one thing being “in” another, each of which is defined quantitatively.115
Abelard therefore has the two fundamental components of a relational theory of space, namely, (a) place defined in terms of things, and (b) spatial relations between things. Now Abelard has only a limited version of (b), since his account doesn’t make use of all spatial relations (such as to the left of) but only one, namely, containment; he clearly takes this single relation to be sufficient, however, since he is careful to point out exactly how far it can be applied: the firmament is not contained within any larger place, and hence the question of spatial location makes no sense for the world as a whole (Dial. 79.27–28).116 Containment is also a one-many relation in that a given substantial place can have many things in it. If we permit Abelard to define arbitrary regions around things, then he has a complete relational theory of space.117
Time is altogether more problematic than space. Abelard is a temporal indivisibilist, holding that “compound times” such as hours, days, months, or years consist in and are composed of instants (LI Cat. 184.34–38 and Dial. 62.12–15). But he rejects the view that time is something independent of things “timed,” so to speak; it is rather “a given quantity according to whose duration (permanentia) the existence of anything whatsoever is measured out,” as for example when we say that something was alive for a year (LI Cat. 184.30–34). Much as quantitative place is (intuitively) the amount of space something takes up, so too “time” as a quantity is the amount of time something takes up or lasts – think of “age” or “duration”: an age is clearly the age of something, an accidental adjunct of the thing it characterizes, like Abelard’s (and Aristotle’s) “time.” The time (age) of something is clearly accidental to it, since what something is differs from how old it is. Time is accidental in a stronger sense, too, for things that are currently temporal need not always be in time. Just as space is a finite artifact, created by God, so too is time: Abelard holds that time began when the world was created, and will end once God transfers everything to eternity, where things exist without temporal attributes (LI Cat. 189.1–2).
In the Dialectica Abelard holds that everything has within itself its own times by which it is measured. The parallel with age is again helpful: Socrates has an age that is suitable to him, Plato his own suitable to him; an instant is a personal “atom of age” for a given individual out of which compound times, such as days, are made for each thing. These “personal days” are then coordinated and synchronized by reference to sidereal time, the movement of the sun across the heavens (Dial. 62.17–31).118 But in LI Cat. 185.6–19 Abelard rejects this view, reasoning that while individuals may have individual times, these individual times need not be personal in the sense described; they can each have the standard unit-measure of (say) a day, so that the age of any given thing is constructed from common units. (Common in the sense that they are the same units for all, not that they are literally shared.) Socrates and Plato have different ages, but each has the age he has by having the duration he has, measured out in common units; ages are personal while days are common. Now some philosophers saw a difficulty in taking an instant to be indivisible if it were present to the whole world at once, and indeed in many different individuals simultaneously (LI Cat. 186.15–17). Abelard replies that the simplicity of an instant refers to its not having parts, in particular successive parts, and so its distribution in many individuals need not compromise its indivisibility; just as a human is a unity despite having multiple limbs, so too an instant can be a unity despite having multiple individual subjects (LI Cat. 186.20–26). This sidesteps the difficulties facing coordination and synchronization of separate individual times, although it threatens to make time quasi-substantival by treating a “day” as a compound largely independently of Socrates’s day-long duration. Abelard seems to sense this threat, suggesting that perhaps time-bound individuals have some temporal aspects but that time is an extrinsic measure, the way height is (LI Cat. 185.19–186.14 and 186.18–20). He nevertheless insists on the link to sidereal rotation as a way to preserve the relational aspect of time, just as the link to the firmament preserves the relational aspect of space.119
Time is therefore a compound whole assembled from individual instants that are the same for all. More exactly, any temporal stretch will be such a compound whole. Abelard maintains further that temporal wholes are continuous: the present instant is the shared boundary between the past and the future, and the successive instants of the present follow on one another “like flowing water” without gaps.120 (He asserts but does not try to prove this.) The three terms of McTaggart’s A-series, “past,” “present,” and “future,” are the fundamental relational properties that hold for things: they locate something in time, describing when it occurs, providing a categorical “substantial when” as a counterpart to the quantitative time described above. So too for more determinate terms like “yesterday” or “next month,” which are the types of time when something occurs (LI Cat. 256.26–32; cf. also Dial. 78.3–18).121
Abelard stresses that temporal wholes are radically different from ordinary integral wholes.122 For an ordinary integral whole, the existence of the whole entails the existence of its (principal) parts, as described in §II.3 above. But this seems false for temporal wholes. For example, a day consists of twenty-four hours; if the first hour exists, then the day is said to exist, although none of its other parts do – in fact, all its other parts must fail to exist when any given part exists, since if the day exists then exactly one part of it exists. Now each hour of the day is on an equal footing with any other hour, and hence either all or none of the hours must be a principal part; no matter which of the competing criteria we adopt (maximalist, destructivist, or Abelard’s), the hours of a day will all qualify as principal parts. Worse yet, strictly speaking only an instant of a given hour exists, so the first hour of the day itself is a temporal whole made up of largely non-existent parts. But we cannot speak of a whole most of whose parts are non-existent. Abelard concludes: “The truth of the matter is that we can never truly and strictly say that a day exists, or that it is a whole, or a quantity, or even anything at all” (LI Cat. 187.40–188.1). Such temporal constructs are perhaps like wholes: they are “quasi-wholes” (Dial. 554.35), or mere “fictitious substances” to which we attribute “fictitious properties” (LI Cat. 176.4–5). Likewise, “‘past’ and ‘future’ are names of things that do not exist” (Dial. 63.22–23), and strictly speaking “past time” or “future time” is as oxymoronic as “dead man” (Dial. 63.30–32). In short, Abelard is a “presentist”: only the present exists, although past times did exist (they just exist no longer) and that future times will exist (but they do not yet exist). Abelard is not rejecting the reality of time so much as calling attention to the fact that existence is tied to the present instant alone.
Abelard knows little more than the bare outlines of Aristotle’s doctrine of the four causes.123 The material cause and the formal cause were discussed in §II.2 above, and Abelard devotes only a brief paragraph to the final cause, identifying it as the reason something is done, e.g. a war is fought for the sake of victory. He gives most of his attention to efficient causality, loosely described as whatever “acts or works where something, namely, the effect, is brought forth” (Dial. 414.23–24). Abelard’s main concern is to clear up what he regards as a common and unfortunate error about efficient causality, the view that we can bring (natural) substances into being. For substantial generation is strictly God’s province, and indeed is better described as “creation”; human beings can only rearrange existing materials, as in manufacturing, or initiate processes that continue through natural or Divine means, such as childbirth or growing crops (Dial. 416.31–417.37 and 418.21–23; LI Cat. 298.28–299.5; and Hex. 10.22–11.8). (Given God’s role in creating Nature, natural means are, in some sense, Divine means.) Even complex technical processes, such as making glass or smelting metals, do no more than manipulate materials and exploit natural processes. But this claim is not symmetric. Humans beings cannot create substances, but they can destroy them; we can burn a tree to ashes, kill living creatures, and, in general, make things worse off than they are (Dial. 418.23: “corruption seems to be left up to us”).
Causes are not identifiable as any particular kind of thing; indeed, they may not be things at all, as Abelard is at pains to argue. Someone might be whipped for not wanting to go to the market, hanged for a past theft or go to war for future glory, die from not eating, be damned for not doing what he ought; the absence, present nonexistence, lack, and privation identified as the respective cause of each outcome are not real things (LI Isag. 20.11–12, Spade 1994, 92; LI Cat. 293.21–35; LI De in. 3.04.36–37, G 368.40–369.11).124 This seems correct, at least as far as ordinary usage goes. What Abelard does not provide is a theory of causation. He was perhaps skeptical that there could be such a theory, given our ignorance of the natures of things and the diversity of what might count as a cause, but he does not argue for that position either. Yet even in the absence of a theory of causation, Abelard’s examples suggest that causes need be nothing over and above the items involved in causal interaction. In particular, nothing Abelard says about causation requires us to postulate events, states of affairs, or facts.
A standard reason for postulating events is the claim that things in the world are linked together in various ways: Socrates’s throwing the ball, an event, is the cause of Plato’s jumping aside, another event. Socrates is not the cause but rather his throwing the ball is, though we may (misleadingly) identify him as such, e.g. when we say that Socrates, due to his throwing the ball, was the cause of all that followed. But Socrates’s throwing the ball is not a thing in the world the way Socrates is, though it somehow includes Socrates as a constituent. It is instead another kind of entity altogether, an event. We can generalize this notion to include relationships that may be non-causal in nature, such as Socrates’s being taller than Plato; these are states of affairs. Even if we reject any real causal connections in the world, states of affairs seem to exist. Furthermore, states of affairs may obtain or not. Socrates may be taller than Plato, or he may be shorter; each seems equally a (possible) state of affairs. Let us say that states of affairs that obtain are facts. It might then seem that the world consists of facts, not things, although things are “constituents” of facts.
Abelard rejects this line of reasoning. An event such as Socrates’s throwing the ball is no more than a particular accident from the category of Action, namely, throwing the ball, inhering in him at a given time. There is no need to postulate anything over and above Socrates and his accidental features, whatever ontological status they may have. So too for states of affairs: Socrates’s being taller than Plato is just Socrates and Plato and their respective heights, as noted in the discussion of Relation in §IV.1. We can talk as though there are events or states of affairs, but they are nothing apart from the concrete individuals that make up Abelard’s world.
That said, it should be noted that Abelard does use the term eventus in his discussion of future contingents.125 But there are reasons not to translate this as “event,” with its accompanying philosophical baggage. Abelard typically speaks not simply of an eventus but instead of the eventus rei or eventus rerum, such as a sea-battle.126 But not tomorrow’s sea-battle, or yesterday’s: he is talking about the present sea-battle, the sea-battle as it takes place. Thus the eventus of the sea-battle does not refer to the event of which the sea-battle is a part, but to the occurrence (or “obtaining”) of the sea-battle. But the occurrence of the sea-battle is nothing other than the sea-battle, just as Socrates’s existence is nothing more than Socrates: neither the occurence nor his existence outlasts or is outlasted by its subject. And the sea-battle itself is nothing but the ships and sailors and their doings.127 Hence Abelard’s use of the term eventus doesn’t commit him to the existence of events, or anything beyond concrete individuals.
Abelard argues that sentences (propositiones) must signify more than just the understandings of their constituent parts. First, a sentence such as “Socrates runs” somehow deals with Socrates and with running, not with anyone’s understandings. We talk about the world, not merely someone’s understanding of the world. Second, “consequential sentences” (consequentiae) like “If there is a man, there is an animal” are false if taken to be about understandings, for someone could entertain the concept man without entertaining the concept animal, and so the antecedent would obtain without the consequent. Third, understandings are evanescent particulars, mere mental tokenings of concepts. But at least some consequential sentences are necessary, and necessity can’t be grounded on things that are transitory, and so not on understandings.128 Sentences must therefore signify something else in addition to understandings, something that can do what mere understandings cannot. Abelard describes this as signifying what the sentence says, calling what is said by the sentence its dictum (plural dicta).129
Intuitively there is much to recommend Abelard’s move. Sentences are typically used to say things about the world, not about people’s thoughts (except insofar as their thoughts are part of the world), and what is said doesn’t seem to be as transient as the saying of it. Furthermore, sentences aren’t true or false as such, but only true or false in virtue of saying what they say: “Socrates is running” is true because what it says, namely, that Socrates is running, is so in reality (LI De in. 100, G 327.20–21; LI Top. 225.25–29 and 226.28–29; and Dial. 156.22–33). So too for why sentences are judged necessary or possible, or opposed to one another (LI De in. 3.04.26, G 367.13–20). We can even explain the truth-conditions for (say) consequential sentences in terms of what their constituent parts say, so that a consequential sentence is true when it cannot be as the antecedent says unless it is as the consequent says (LI De in. 3.04.25, G 367.2–5; and Dial. 155.25–38). Finally, what sentences say can be the same even though the sentences differ syntactically. To the modern philosophical ear, Abelard’s dicta sound very like propositions, abstract entities that are the timeless bearers of truth and falsity, possibility and necessity. Is this what Abelard has in mind by the dictum of a sentence?
Abelard declares repeatedly and emphatically that dicta, despite being more than and different from the sentences that express them, have no ontological standing whatsoever. In the short space of a single paragraph he says that they are “no real things at all” and twice calls them “absolutely nothing.”130 In a way they underlie sentences, but they aren’t real things: quasi res propositionum, cum tamen nullae penitus essentiae sint (LI De in. 3.04.26, G 367.12–13). For although a sentence says something, there is not some thing that it says (Dial. 160.33–34).131 In modern terms, Abelard denies the existence of propositions; he refuses to reify what sentences say. A dictum can be the cause of a sentence’s truth without being a thing, since causes can literally be nothing at all (as noted in §IV.3 above). Even if dicta are about the world in some fashion, things in the world are not parts or constituents of dicta, which gain no ontological foothold through them.
Abelard argues for his irrealist view by showing that to think of what a sentence says as a “real thing,” abstract or concrete, involves a serious confusion about the semantic properties of sentences. This is clear, he reasons, especially in the case of consequential and negative sentences, since they may be true even if the concrete things they seem to concern have been destroyed: “Socrates is not in the house” can be true even if Socrates doesn’t exist, and “If there is a rose, there is a flower” is true whether there are any roses or not (LI De in. 3.04.21–22, G 366.16–30). But the semantic confusion is there even if we focus on simple affirmative categorical sentences like “Socrates is a man.” Such sentences seem to be directly about Socrates. Yet Abelard maintains that they too do not require us to bring in any object or entity to explain how they function and why they hold, for the simple reason that sentences are not names:
Now “Socrates” signifies him because he is Socrates, but it still doesn’t say that he is Socrates, as “Socrates is Socrates” does; accordingly, a sentence’s dictum differs from a name in this regard, namely, that the sentence says “Socrates is Socrates” (which isn’t any real thing), whereas “Socrates” doesn’t say this even though it refers to Socrates (because he is Socrates).
(LI De in. 3.04.23, G 366.35–40)132
The semantic job of sentences is to say something, which is not to be confused with naming or denoting some thing. It is instead a matter of “proposing” how things are, so long as this is not given a realist reading:
Furthermore, it’s clear that the things sentences say aren’t real things, since their predication can’t be applied to any real thing – of what things can it be said that they are “Socrates is a stone” or “Socrates is not a stone”? If sentences were to denote or put forward real things, then surely they would have to be names. But sentences differ from all words precisely in this regard, namely, that they propose something to be (or not to be) something else. Yet “being (or not being) some real thing” is not any real thing at all. Thus sentences do not simply denote any real things, the way names do, but instead propose how they stand towards one another, namely, whether they are suitable to one another or not. Then they are true when it is so in reality as they state, and false when it is not so in reality. And surely it is so in reality as a true sentence says, but there isn’t any real thing that it says. Accordingly, a sort of “way things stand” is expressed by sentences; they don’t denote any real things.
(Dial. 160.23–36)133
Sentences say things, and they even say things about things – better: sentences say how things stand – but they do not refer to or denote things, whether ordinary things like Socrates or extraordinary entities like propositions (which then “correspond” to things), despite the fact that we can and do refer to dicta. Abelard is even hesitant in speaking of a “way things stand,” immediately hedging this “way” (modus) with “sort of” (quasi) to take away any ontological bite it might have. There is no more need for a realm of special entities, propositions, to account for the fact that sentences say things than there is for a realm of promises that are embodied when somebody makes one, or timeless platonic resolutions waiting for a committee to pass them.
Instead, Abelard reasons, semantics should tell us what a given sentence says, not metaphysics. It is properly the business of “logic” to look into the meaning of words, and of “physics” to investigate whether the world is in agreement with the statement; each enterprise is necessary to the other (Dial. 286.31–35). Abelard only gestures at the compositional nature of semantics, which begins with single words and combines them into expressions whose sense is a function of their constituent parts (Dial. 287.1–4), but he wrote hundreds of pages on the precise logical behavior of words, phrases, quantifiers, and so on, all of which is used in determining what it is a given sentence says. The most we can say in general is that sentences express how things are.
Real things do have an impact on sentences, not as what they say but determining whether what they say is true or false. A sentence is true if it is in reality as it says it to be; concrete individuals are truthmakers for sentences, and nothing is required beyond them.134 Simple affirmative sentences are true when things are as the way the sentence says they are, or, roughly, in virtue of the existence of things that are as the sentence says, and relational sentences likewise; consequential or necessary sentences are true in virtue not of the mere existence of things but how their natures are, so that e.g. “If there is a rose, there is a flower” is true depending on the natures of roses and flowers.135 Whatever difficulties there may be in spelling out the truth-conditions for a given sentence or type of sentence, they are not, in the end, metaphysical difficulties. Sentences, and what they say, are made true or false by the ways things are, which is no more than the things themselves. From a metaphysical point of view, there are no dicta.136
1. Boethius, In Isag. maior 1.3 140.18–141.19, following an old Stoic tradition (Diogenes Laertius 7.39–41); see also In Cat. 161B–C (by implication), De top. diff. 1.5.50 15.3–5, In Cic. Top. 1044C–1045B, and the rather diffuse discussion in In Isag. minor 1.3 8.1–9.12. The same tradition is reported by Augustine in De civ. Dei 8.10. Abelard’s remarks are found in LI Isag. 1.7–11; LI Top. 289.40–290.2 and 316.1–14; LNPS 506.18–23; and TC 2.31; he distinguishes logic from physics in Dial. 65.18–19 and 286.31–287.5.
2. Abelard’s account is reminiscent of Aristotle’s claim that metaphysics is generally the knowledge of the causes or principles of things (Metaph. A.1 981b27–28). Abelard knew “metaphysics” only as the name of a work by Aristotle in which he discussed the categories more deeply: LI Cat. 251.30–32 and Dial. 81.2–4. His knowledge derives from Boethius’s asides at In Cat. 252B–C (cited in LI Cat. 239.33–240.6) and 262A.
3. Abelard’s positive account of universals as words and his account of linguistic modalities – properly parts of “logic” rather than “physics” – are dealt with elsewhere in this volume, in the chapter on his philosophy of language (chapter 4 below).
4. Boethius, In Isag. maior 1.10 161.16–22 and 162.16–163.3, an account parallel to In Cat. 164C–D (taken from Porphyry’s In Cat. 62.19–33). Abelard’s solution to the problem of universals depends on what he calls “transference”: the literal presence of a universal in each object exemplifying it is “transferred” to the semantic properties of certain words, namely their predicability, so that e.g. common nouns refer to each of their subjects as a whole. See Jacobi’s discussion in chapter 4 of this volume.
5. See LI Isag. 10.15–16, 31.23–31; Spade 1994, 22, 171–172; and LNPS 528.28–529.21 for Abelard’s understanding of Boethius’s strategy in the latter’s In Isag. maior 1.10 161.15–163.5. These views are “realist” in virtue of identifying the universal with some real thing or things said to satisfy Boethius’s criteria.
6. Abelard describes Material Essence Realism in HC 85–89 (Radice 1974, 60), LI Isag. 10.17–11.9 (Spade 1994, 60), and LNPS 515.14–31; see also Pseudo-Joscelin De generibus ac speciebus 33 and Walter of Mortagne, Tractatus “quoniam de generali,” 2–3.
7. This second thesis derives from Boethius, De Trin. 1 168.56–63 and 2 169.83–89; it was widely accepted in the early Middle Ages. Abelard ascribes it to William of Champeaux in Dial. 541.24–37 (the only clear reference to William in that work).
8. See also Pseudo-Joscelin De generibus ac speciebus 39; Walter of Mortagne, Tractatus “quoniam de generali” 17.
9. Geyer’s text and apparatus are faulty here; the manuscript is as follows: “Quod verum sit autem id quod supra assumpsimus, scilicet quicquid est in Burnello aliud a formis Burnelli est Burnellus, inde manifestum est, quia neque formae Burnelli sunt Burnellus, cum iam accidentia essent substantia, neque materia simul et formae Burnelli sunt Burnellus, cum iam corpus et iam corpus esse corpus necesse esset confiteri” (MS Milan Biblioteca Ambrosiana M63sup fol.2va47–51).
10. See LI Isag. 80.22–81.5 and LNPS 566.7–27 for Abelard’s arguments against the mere co-presence of the differentia.
11. Abelard tells us that William of Champeaux held that “when the name of the differentia is put for the species in the division of a genus, it isn’t taken from the differentia but instead is put as a substantive name for the species” (Dial. 541.34–36), with the result that “rational is equivalent to rational animal” (541.29–30).
12. Socrates is a rational animal, that is, a rational animate body; hence he is essentially a body. But the differentia “rational,” by the argument given above, is not the name of a quality such as rationality but rather the name of the species, rational animate body. Since Socrates is his material essence plus his differentia, he is therefore body (his material essence animate body) and something already body (his differentia rational animate body) – an impossibility: see the text in n. 9 above.
13. Aristotle raises a similar objection in Metaph. Z.13 1038b23–27; see also LI Isag. 64.7–65.5 for a fuller attack on accidental individuation. Abelard takes the sense of “naturally prior” used in his objection from Cat. 12 14a29–30: x is prior to y if y depends on x for its being, but not conversely; this is Aristotle’s second mode of priority, which he calls “the prior by nature” at 14b15. Abelard’s gloss of this later passage in LI Cat. 288.4–5 explicitly recognizes that such dependence doesn’t require the preceding existence in time of what is prior, which sidesteps the difficulty that no ordinary substance can exist without accidents.
14. Abelard’s objection can be applied, for example, to the modern identification of individuals with chunks of space-time. Abelard would hold that the path traced in the four-dimensional space-time continuum either itself constitutes an individual (in which case any path arbitrarily selected would do), or, if not, illegitimately relies on the individuality of the individual who is tracing out the given path: we look to see what places Socrates occupies at distinct times, thereby appealing to his individuality; and this we cannot do.
15. Abelard’s objection says nothing against the epistemic claim that we discern or distinguish individuals through their accidental features, which most medieval philosophers, including Abelard, continued to endorse.
16. Collective realism is expounded and defended in the De generibus ac speciebus of Pseudo-Joscelin. Abelard describes it in LI Isag. 14.7–17 (Spade 1994, 41–62); see also the brief remarks in John of Salisbury, Metalogicon 2.17.27; Compendium logicae 3.29 50.41–52; Ars Meliduna 219ra40–42. Some inspiration may have been derived from Porphyry, Isag. 3 14.7–11, and Boethius’s In Isag. maior 3.12 236.16–237.23. Collective realism is not a form of twelfth-century set theory or mereology: such collections exist in and through their members and do not include their parts (the parts of animals do not belong as such to the collection of animals).
17. There is a similar objection in Ars Meliduna 219rb2–4. The distinction between integral wholes and universal wholes is well-entrenched in twelfth-century philosophy, deriving from Boethius, De div. 12.17–14.20 (879B–880A). Pseudo-Joscelin rejects Boethius’s criteria for the universal in De generibus ac speciebus 134–135, claiming that Boethius put them forward “where he proves that genera and species do not exist, which can only be proved by sophistry” (134).
18. Abelard develops the point from Boethius, De div. 14.12–15 (879D).
19. Pseudo-Joscelin argues that the collection is “in” the individual in the same manner in which we say that Socrates is touching a wall although only his fingertips are literally in contact with it (De generibus ac speciebus 89–93), and the collection is thereby wholly present in each member. Abelard counters that Socrates would be said of his parts in the same way, making him a universal too (LI Isag. 14.40–15.15.1; Spade 1994, 49)!
20. Pseudo-Joscelin avoids this objection by defining his collections intensionally, made up not of individuals but of their individualized forms: the species man is the collection containing the individualized form of humanity that Socrates has, the (distinct) individualized form of humanity Plato possesses, and so on; the genus animal the distinct individualized form of animality each animal possesses (De generibus ac speciebus 85).
21. This objection points to a deeper problem, namely whether an individual (Socrates) is what it is (human) before being part of a collection. If so, then belonging to the collection has no part in making the individual what it is, and hence the collection cannot be a Boethian universal. If not, then one collection is as good as another, it seems, and there is no reason to prefer complete to incomplete collections, or indeed to arbitrary collections.
22. Abelard takes the claim from Boethius, De div. 12.24–25 (879B). Abelard’s third objection, like the first, turns on the fact that universals and integral wholes have incompatible features.
23. See Abelard’s gloss on Boethius’s remark in Dial. 575.5–14; compare Boethius, De div. 14.1–3 (879C). Similar objections are reported in Pseudo-Joscelin, De generibus ac speciebus 112, and Ars Meliduna 219ra43–47.
24. Abelard describes indifference theories generally in LI Isag. 13.18–14.6 (Spade 1994, 41–44) and LNPS 518.9–24; see also Pseudo-Joscelin, De generibus ac speciebus 50; and Walter of Mortagne, Tractatus “quoniam de generali” 26. The terminology of “indifference” derives from Boethius’s account of sameness among the Persons of the Trinity: De Trin. 1 167.41–168.55 and 3 173.168–170.
25. For William of Champeaux see his Sententiae q.1 25.1–9 and Abelard’s summary in LI Isag. 16.9–10 (Spade 1994, 60). For Walter of Mortagne see his Tractatus “quoniam de generali” 29–31; the same position is described by Abelard in LNPS 518.24–27, Pseudo-Joscelin in De generibus ac speciebus 50, and retrospectively by John of Salisbury in Metalogicon 2.17.14–15 and Policraticus 7.12.2.
26. See also the concise summary of the objection in LI Isag. 37.3–17. Walter of Mortagne recounts Abelard’s objection in Tractatus “quoniam de generali” 42.
27. Walter of Mortagne, Tractatus “quoniam de generali” 43.
28. LNPS 519.11–26; Walter of Mortagne, Tractatus “quoniam de generali” 48.
29. Abelard’s criticism of Walter’s account depends precisely on the latter’s insistence that Socrates’s status as an individual is some sort of thing. In his own account of universals, Abelard adopts some of the same terminology but rejects that claim: see LI Isag. 19.29–33 (Spade 1994, 90), which refers to his argument here.
30. The following remark is typical: “There is no thing that is not distinct” (LI Cat. 157.8). Abelard will qualify this conclusion in light of his theory of identity and the existence of integral wholes and collections, as described in §II.3 and §III below.
31. Abelard holds that x is distinct from all else when none of x belongs to anything not all of which belongs to x, which is (roughly) how he explains numerical diversity: see §III.1 below.
32. Abelard takes the point from Plato by way of Porphyry: see Isag. 3 12.9–13.
33. See Abelard’s second objection to material essence realism, discussed in §I.1 above; LI Isag. 64.7–65.5; and LNPS 520.6–14.
34. We first have to determine the ontological standing of concrete individuals relative to their forms, matter, and constituent parts to state this claim with more exactness, a project that will occupy the rest of §II and the analysis of identity in §III. At a first approximation, Abelard holds that individuals are concrete entities such as Socrates and Fido, as well as some of their forms; other forms, their matter, and their physical parts are only “individual” in a derivative sense.
35. See Hex. 10.9–11: “Since angels are incorporeal they are not included among mundane creatures the way humans are.” In In Isag. maior 1.10 160.23–161.7, Boethius distinguishes two classes of incorporeals in explaining Porphyry’s questions about universals: those that are necessarily conjoined with bodies, such as points and line, and those that need not be, such as God and the (human) soul. Abelard thinks that elements of the first class are actually corporeal; see the discussion in §IV.1 below. The human soul is exceptional among mundane objects, as we shall see.
36. Abelard describes primary and secondary creation while examining substantial generation and corruption in LI Cat. 297.41–298.20 (there called “the earlier and later creations”) and Dial. 419.1–420.6, and again while glossing Genesis 1:1–2 in Hex. 9.7–17.19.
37. This description draws on Dial. 419.5–12 and Hex. 9.7–14.3. The chaotic mass has the features of the biblical creation of “heaven” (the qualities associated with air and fire) and “earth” (the qualities associated with water and earth) on the first day (Genesis 1:1); the Holy Spirit then organized this undifferentiated mass (Genesis 1:2: Spiritus Dei ferebatur super aquas). Abelard sidesteps the question whether at first there were only the distinctive qualities paired to make the four elements, or whether there were indivisible form-matter compounds where the quality-pairs are form to some underlying prime matter; even Dial. 418.33–34 doesn’t resolve the issue.
38. See the discussion of Abelard’s atomism in §IV.1 below.
39. Secondary creation is modeled on God’s creation of man from clay in Genesis 2:7: Dial. 419.13–15 and 419.25–27; Hex. 10.22–11.8 and 102.12–20. In his description of secondary creation and elsewhere – e.g. LI Cat. 149.38–150.1 or TI 38–39 – Abelard presupposes rather than argues for the plurality of substantial forms. He tells us, for instance, that God “initially fashioned man’s body from clay and thereafter (deinde) infused his soul” (Hex. 102.14–15), a process that involves the form of corporeity as well as the human soul.
40. In the passages from TI we are also told that the process of conceiving forms free from matter is “abstraction” and of the underlying matter without forms “substraction.”
41. Abelard draws the consequences for material souls explicitly in LI Cat. 298.25–26: “When a brute animal dies, its soul is corrupted along with it, while it is hauled into non-being.”
42. Abelard makes the same point in explaining Aristotle’s remark at Cat. 7 7b38–39 that the senses operate in and through bodily instruments, in contradistinction to the understanding: LI De in 3.01.23 (G 313.20–30), Dial. 556.23–36. Nevertheless the soul, like the senses, can be a subject for accidents (namely individual mental acts), even though it is incorporeal: LI Isag. 94.37–39.
43. Abelard never tells us how to divide Substance properly.
44. See LI Isag. 79.17–18 (appearing practically verbatim at LNPS 564.24–25): “Rationality is not strictly called ‘form,’ since it doesn’t arise in the subject from the arrangement of its parts”; he offers independent arguments for this conclusion in LI Cat. 212.37–213.5. (Abelard follows common practice in referring to the human soul by its constitutive feature, viz. rationality.) While Abelard does not explain how a non-form (the soul) and the body can be united to make something naturally one, but this is presumably due to divine agency: God creates each human soul as needed and infuses it into the body, creating a composite that is “naturally one” by supernatural action.
45. Abelard’s account differs radically from Boethius’s gloss of this passage in the latter’s In Isag. maior 4.11 268.10–12.
46. Abelard also discusses “formal wholes,” such as the division of the soul into its constituent powers (Dial. 555.20–559.37), and “wholes according to substance and form,” such as the combination of a substantial form with its differentia (Dial. 559.38–561.23), but only integral wholes are discussed here. The broader division also derives from Boethius, De div. 38.17–27 (887D–888A). Recognizing universal wholes doesn’t commit Abelard to thinking that there are any in the world, of course. He also takes up accidental wholes, which we’ll ignore here; see the discussion of quantitative wholes in §IV.1 below.
47. This might not seem to be so in homogenous continuous quantities, where every part is of the same kind as its whole, e.g. every line-segment is itself a line. Abelard argues that in such cases the parts are clearly less in quantity than the whole, and so they are not really the same as it: Dial. 547.34–548.10 and 576.12–22. Note that Abelard uses “part” only for proper parts (Dial. 554.15–17).
48. For Aristotle see Cat. 6 4b35–36, which Abelard follows at LI Cat 169.12–13 and Dial. 71.25–26. Abelard’s preferred definition is given in LI Cat. 169.23–28 and Dial. 73.19–27.
49. For geometrical solids see LI Cat. 179.26–184.12, Dial. 57.14–60.38, and the discussion in §IV.1 below.
50. See Dial. 431.23–432.5, Dial. 548.11–21 (only collections and composites), and LI Cat. 170.34–171.17 for the following discussion.
51. In Secundum mag. Petrum 31 Abelard rejects the proposal in 13 that the members of a collection together with the collection make a new collection (the unrestricted “upward” axiom).
52. Abelard allows there to be overlapping subcollections within a given collection, so that e.g. a triple contains three distinct pairs: Secundum mag. Petrum 32–33. In general, any collection of units (i.e. an n-tuple) is a species of number, as Abelard argues in LI Cat. 169.33–170.33 and Dial. 64.11–65.19.
53. The converse thesis, namely that all composite integral wholes are hylomorphic compounds, also holds if we take “form” broadly.
54. Destructivism is extensively discussed in the contemporary De generibus ac speciebus 1–31 (with the destructivist criterion announced in 7).
55. Strictly speaking only collections are defined through their parts; aggregations and composites have additional requirements, but a fortiori must also consist in their parts, and so Abelard’s argument is perfectly general.
56. Abelard’s line of reasoning here is an application of his general thesis that quantitative change is literally impossible: an integral whole cannot have more or fewer parts, since then it would be a different integral whole. Apparent cases of quantitative change are really cases of replacement, as described. See LI Cat. 299.11–300.26 and Dial. 421.32–424.5 for Abelard’s defense of the general thesis (sometimes known as the “paradox of increase”).
57. See TI 75–76: “There is no nature that subsists indifferently; any given thing, wherever it exists, is personally distinct and found to be numerically one . . . What else is human nature in this man, i.e. in Socrates, but Socrates himself? Surely it is nothing other than exactly the same in essence.” (The proviso “exactly the same in essence” is a technical phrase explained in §III.1 below.) Abelard expresses the same sentiment in many other passages, for instance LI Isag. 24.17–20; Spade 1994, 122.
58. Abelard cites Boethius as claiming that nature is similitudo rerum nascentium here and in LI Cat. 278.16–20 and LI De in. 3.01.35 (G 315.21–22); Boethius says ipsa nimirum similitudo nascentium (In Cat. 166A), though rerum for nimirum would be an easy mistake to make. Note that Abelard passes over in silence Boethius’s four “official” definitions of “nature” given in Contra Eutychen 1, which are not as susceptible to his reductive interpretation.
59. There is a remarkably similar passage in William of Ockham, Ordinatio I d.2 q.6 (see Spade 1994, 181–182, §§162–163) that reaches what is recognizably the same solution.
60. See Hex. 38.3–39.3, summarized neatly in 45.5–11: “In the works of those six days, God’s will took the place of natural power while Nature itself was created – that is, a certain power was bestowed upon those things which then came to be, whereby they were afterwards able to reproduce themselves or bring about whatever effects were to proceed from or be engendered by them.” (See also Hex. 55.8–13.) Abelard refers to this process in describing the origins of substantial change: LI Cat. 298.11–12 and Dial. 419.17–23. God’s ability to do otherwise than he does is relative only to God’s omnipotence; as Abelard notoriously argues in TC 4, God’s intrinsic goodness constrains him to do only what is best. In later medieval terminology, such claims are relative to God’s absolute rather than his ordained power.
61. Modern logicians try to reduce de re to de dicto modality, while Abelard embraced the opposite reduction of de dicto (or, as Abelard called it, de sensu) to de re modality because of problems about quantifying into and over de dicto modal propositions and the consequent unwelcome ontological commitments. The modal logic of his time, as of our time, is not equipped to deal with these difficulties: standard logical operations on simple categorical sentences do not carry over to de dicto sentences, whereas they do carry over to de re sentences.
62. Boethius holds that possibilities are rooted in the individual’s matter and nature: In De in. maior 3.9 238.8–239.14; cf. In De in. maior 3.9 233.26–28 and 5.13 416.21–22. Boethius also describes the Peripatetic view of possibility as depending on “the nature of the thing” (In De in. maior 3.9 197.18–23). There are echoes of the view, applied to necessity, in In Cic. Top. 1154A–B and Cons. 5.6.29.
63. See also Abelard’s explanation of modal opposition in Dial. 200.22–32. Abelard mentions his analysis of possibility frequently, e.g. in 35 and 53 of the excursus to LI 3.12; Dial. 98.16–18; TC 5.58; TSch 3.51. Note that Abelard is proposing an analysis of modality, not a reductive elimination of it; “compatibility” is itself a modal notion.
64. Analogous to the Tarski biconditional for simple categorical sentences “‘S is φ’ is true ⇔ S is φ” Abelard endorses “‘S is φ’ is possible ⇔ the nature of S is compatible with φ” (Dial. 205.24–35).
65. See §II.1 above. Abelard’s claim is less plausible if we take “nature” loosely, including (say) typical behavior, for then it seems that there are informative claims to be made at the level of individuals: “Socrates always gets sleepy in the middle of the afternoon; that’s just his nature.” Abelard will try to assimilate such cases to ascription of powers rather than possibilities, but it’s not clear that this is anything more than regimentation on his part. His restriction to the level of the species does explain how we can assess modal statements about nonexistents, since their nature is the same as that found in existing members of the same kind: see LI De in. 3.13.74 (MP 197 84.20–23).
66. Abelard glosses necessity as the inevitable in LI Isag. 4.22–24, 3.9.143 (G 437.37–38) and 3.9.188 (G 446.32–33), and 35 of the excursus in LI 3.12; LNPS 510.25–27; Dial. 194.7–9 and 272.11–12; TSch 3.101 and 3.107.
67. Abelard emphasizes that necessity and determinateness differ: LI De In. 3.09.143 (G 438.11–17). He even proposes dividing up the species of the possible into the determinate possible and the indeterminate possible: LI De in. 3.13.55 (MP 179 78.20–23). Abelard tries at length to sort out the conceptual connections among necessity, determinateness, and avoidability in addressing the problem of future contingents raised by Aristotle in De in. 9, but his concerns have more to do with human freedom than with explicating modality.
68. See 67–106 of the excursus to LI 3.12, as well as Dial. 206.13–210.18, for Abelard’s discussion of relative modals. The notion is an extrapolation from Aristotle’s claim in De in. 9 19a23–24 that anything that is must necessarily be while it is: LI De in. 3.09.166–169 (G 442.4–30).
69. Abelard emphasizes “becoming” here because he has in mind cases in which S cannot actually be φ but could become φ, e.g. “Socrates can die” (Socrates cannot literally be dead since “Socrates” is necessarily the name of a living creature): Dial. 197.2–12. This criterion faces complications arising from Aristotle’s distinction between rational and irrational powers (De in. 13 22b36–23a4), where S has an irrational power if S can φ or not-φ, but we can put those aside for now.
70. There seems an obvious flaw: if Socrates has never had medical training but nothing precludes his performing open-heart surgery on a patient, then Abelard’s account entails that Socrates can perform open-heart surgery. But this is to confuse the sense in which Socrates can try to do something with its more idiomatic “success” use – to confuse the capacity with the capability, we might say. Abelard is here concerned with the former, not the latter; see LI Cat. 229.15–231.32 and Dial. 96.18–99.24.
71. Abelard has to revise his account of powers, which refer to possibilities, to make this line of thought coherent. Notoriously, he holds that God can be necessitated by His nature (which is why God cannot do other than He does), which suggests that there may yet be a place in the theory of modality for natures, at least divine natures.
72. See Boethius, In Isag. maior 2.6 191.21–192.19 and De Trin. 1 167.48–168.56 (the locus classicus). Numerical sameness is the medieval version of the modern conception of identity as a relation a thing has to itself.
73. There is no systematic exposition of a theory of identity in IP, LI, or Dial. In LNPS 558.11–560.15 (found almost verbatim in the anonymous student compilation Glossae “secundum vocales,” 178–179), Abelard describes the modes of sameness and difference in essence, number, definition, likeness, change, and function. In TSB 2.4.82–102 he treats the same modes but in greater depth; much of his exposition is repeated in TC 3.138–164 with the additional mode of sameness and difference in property. The account in TSch 2.95–100 is deliberately simplified, treating only essence, number, “property or definition” (an amalgam of each), and likeness.
74. Technically these modes involve not difference but “diversity,” since difference requires a differentia, but I’ll ignore that refinement in what follows.
75. For essential and numerical sameness and difference, see TC 3.139 (same) and 3.148–153 (different), TSB 2.4.83 (same) and 2.4.90–95 (different), TSch 2.95, LNPS 558.15–17. The formulation here is taken from TC 3.139, which is derived nearly verbatim from TSB 2.4.83. Now in TC 3.139 Abelard sorts out the details of numerical sameness and difference, and hence included the proviso that they must be numerically the same concrete thing. His account presupposes and does not try to explain what being “numerically the same concrete thing” consists in. More exactly, it presupposes an account of concrete things (individuals) and their identity-conditions, presumably of the type sketched in §II.1 above.
76. See TC 3.148 and 3.151; TSB 2.4.90; TSch 2.97; LNPS 558.24–25; Secundum mag. Petrum 33.
77. This line of thought is absent from TSB 3.2.7 because of his unclarity over numerical identity in that work (see n. 75 above). Abelard takes his reasoning to explain Boethius’s axiom that the part is not the same as the whole, De div. 14.14 (879D). As noted in §II.3 above, Abelard uses “part” only for proper parts (Dial. 554.15–17).
78. Abelard is committed to this result for theological reasons, since in the case of the Trinity the answer differs depending on whether we are counting gods (one) or persons (three): see e.g. the end of TC 4.9. His application of the theory of identity to the world at large just reiterates this ontological indeterminacy.
79. These conclusions fit well with an anonymous report of Abelard’s views on the ontological standing of forms, given immediately after the text of the Tractatus de intellectibus in the single exemplar of that work: MS Avranches Bibliothèque Municipale 232 F. 68v–71v. The report, partially transcribed in Cousin and Jourdain 1859, vol. ii.754–755, concludes that Abelard and his followers “assert that no form is a real thing (essentiam) for which any of the following hold: (i) the subject suffices for its being; (ii) the arrangement of parts with respect to one another or along with another; (iii) that it be present due to something extrinsic; (iv) for whose departure it is necessary that a substance be added” (755). That is, only positive non-relational real accidents might be “things” in a loose sense, i.e. not numerically the same as their subjects.
80. This is not to be confused with Abelard’s notion of identity “in property” discussed in §III.3 below.
81. For sameness and difference in definition, see TC 3.142–144 (same) and 3.154–157 (different), TSB 2.4.84–85 (same) and 2.4.96–98 (different), TSch 2.95–99, LNPS 559.5–29.
82. Why then does Abelard use the term “definition” at all? The answer may be that Aristotelian definition was the only known (quasi-formal) way to specify the feature or features that are peculiarly or especially appropriate to something in virtue of what it is. This seems to be the intent of Abelard’s stipulation in TC 3.143, TSB 2.4.85, and LNPS 559.11–12 that by “definition” here he intends something that “fully expresses the meaning” of a term and what is suitable to it, neither exceeding nor exceeded by it.
83. Abelard suggests in TC 4.1 that the same concrete individual may be characterized in indefinitely many ways; see also LI Isag. 25.6–8; Spade 1994, 127.
84. Abelard is careful to distinguish “x is φ” from “x is what is φ”: the former describes how a subject is characterized, whereas the latter is an identity-statement, identifying a subject with something characterized in a certain way. See Abelard, LNPS 522.10–32 and 523.11–36 (which should be compared to LNPS 539.24–44), although Geyer’s text is unreliable in several places.
85. Abelard describes the wax-example in detail in TC 3.140–141, and returns to it in TC 4.85–92 with brief mentions in TC 4.102 and 4.106. (He describes the same example in TSB 3.2.59, though of course not presenting it as an instance of difference in property, a conception absent from the latter work.) To follow Abelard’s analysis it should be recognized that while the terms materiatum and formatum have a dual use – they refer to either (a) that which comes to be out of the matter or form, respectively, in which case each term picks out the whole composite; or (b) that which is enmattered, namely the form, or that which is informed, namely the matter – Abelard consistently uses only (a).
86. Abelard offers a second example in an aside in TC 3.141: Socrates is some thing, namely a body, that is characterized by everlastingness, since the material elements that make up his body never cease to exist, although it is not true that Socrates himself is everlasting. (See also TC 4.40.)
87. Abelard faces the challenge of explaining how what is really the same thing, the composite, can fail to be characterized by the properties priority and posteriority without granting independent ontological standing to each of the property-bearers, and in particular to the matter. Otherwise he faces the objection that such contradictory properties really do characterize one and the same thing, namely the concrete individual.
88. See especially TC 4.85–92 for Abelard’s detailed comparison of the properties of each Person to sameness and difference in property.
90. The distinction is present, though inchoate, in LI Isag. 37.34–39.3 (where it appears as a distinction between taking voces ut res and voces ut voces), alluded to again in LI Cat. 292.38–40. He regiments his terminology in LNPS, most famously in contrasting the possibilty that universals are voces with his own view that they are sermones: LNPS 522.10–13.
91. In LI De in. 3.02.6–8 (G 335.1–25) Abelard cites with approval Boethius’s definition of the vox as what we would call an utterance-token produced in a certain way (In De in. maior 4.18–20).
92. In LNPS 522.22–25 Abelard likens a word to a statue (composite) made out of stone (matter), exactly analogous to the waxen image and the wax in TC 3.141; here the unmixed properties are being made by the sculptor, which only applies to the statue (see §IV.3 below) and is analogous to semantic properties, and being made by God, which only applies to the stone and is analogous to physical properties.
93. See LNPS 523.37–524.2, where Abelard explains that the proposition “The concrete thing that is the utterance is predicable of many” is false because once an utterance-token “has been spoken” it “cannot be taken hold of again”: dictum est enim et non potest amplius sumi, meant to echo Aristotle, Cat. 6 5a33–35, which underlines the transience of the utterance: Sed dictum est et non potest amplius hoc sumi (ed. comp. 56.13–14; see Dial. 54.11).
94. Boethius, In Cat. 161A: Ut igitur concludenda sit intentio, dicendum est in hoc libro de primis uocibus, prima rerum genera significantibus in eo quod significantes sunt, dispositum esse tractatum. This view was designed to resolve a dispute in antiquity over the subject-matter of the Categories, namely whether it was mainly about words (and hence a work of logic) or about things (and hence a work of metaphysics). Abelard endorses Boethius’s dictum in LI 2.00 111.18–112.1 and 113.26–33.
95. Abelard presents the distinction between signification and reference ex professo in LI Cat. 112.31–113.2 and LI De in. 3.00.6–11 (G 307.26–309.25). The Categories and the De interpretatione are therefore works of logic, since they are about words, but the former studies them with regard to reference whereas the latter does so with regard to signification: LI Cat. 113.29–33 and LI De in. 3.00.11 (G 309.14–25).
96. Abelard is explicit and unambiguous: LI Isag. 54.32–55.3 and LI Cat. 116.35–117.7. One proposal for a lesser list is the fourfold division Aristotle presents in Cat. 2 (LI Cat. 126.27–36): items that are respectively either present in a subject or not, and said of a subject or not. (Abelard gives this division a semantic interpretation in LI Cat. 131.10–37.) From some of his remarks, it seems that another candidate for Abelard would be a division of items depending on their degree of ontological standing or independence.
97. Abelard explains in LI Cat. 157.23–28 that primary and secondary substances, as words, differ “in their manner of reference” since the former refer to individuals “as personally distinct and different from all others” whereas the latter “appellate them as agreeing.”
98. Abelard finds fault with Aristotle’s preferred criterion for substance, namely that while being one and the same it is susceptible to contraries (Cat. 5 4a10–12), since this equally applies to (say) whiteness, which, while remaining whiteness, can be either dull or lustrous; Abelard proposes to correct Aristotle by stipulating that “susceptible” must be taken with regard to sustaining contraries as their foundation, not merely being informed by them: LI Cat. 160.25–161.17 and Dial. 52.27–53.10.
99. For Abelard’s account of continuous quantity and of (some) discrete quantities, see §II.3 above.
100. Abelard makes the point most clearly in Dial. 57.14–16; see also LI Cat. 179.29–33. Strictly speaking, a body is made up of atoms, which are indivisible point-amounts of bodies; Abelard sometimes loosely speaks of bodies as composed of points.
101. Abelard gives a physical reading to this argument in LI Cat. 182.16–28 and Dial. 60.25–35 when he puzzles over how a blade could cut through a line: it can’t slice through a point, since points are indivisible; nor can it pass through the distance between two points, since there is none. Abelard finally concludes that the blade must spread apart two adjoining points and thereby pass between them.
102. Abelard seems not to know Aristotle’s claim that only actual infinities, not potential infinities such as those involved in (infinite) divisibility, are unacceptable.
103. Mathematically, the difference is between a set of elements, such as the points belonging to a line, and a measure-function defined over those elements producing a nonzero result.
104. See Dial. 59.4–6: “Although I have heard many solutions given by mathematicians to this objection, I judge that I shouldn’t put any forward, since I fully recognize my ignorance of that art.”
105. Abelard argues elsewhere that we can explain the intensity of qualities by real superposition, so that something becomes whiter, for instance, by having more particles of whiteness on top of each other: Dial. 428.35–429.20.
106. Abelard neutrally calls (a)–(d) “types” (maneriae) of Quality in most of his discussion.
107. Boethius, De div. 28.26–27 (884C); Abelard, Dial. 103.11–12.
108. In the second passage, Abelard ascribes the view to “my former teacher V.” (William of Champeaux? Ulger of Angiers?). Aristotle seems to have put the cat among the pigeons with his remark that Quality can include many relative terms: Cat. 8 11a21–22.
109. In Boethius’s translation, the first or “Platonic” definition is: “Things are said to be relatives when they are called what they are of another, or in any other way relative” (ed. comp. 58.23–25). The second definition is: “Relatives are those things for which their very being is to stand as relative in some fashion” (ed. comp. 62.17–18).
110. Note how the Platonic definition describes how things are called what they are, whereas the Aristotelian definition talks about their very being.
111. See LI Cat. 216.35–217.8 and Dial. 83.24–32 and 86.22–27, the sources for the ensuing discussion. I have regimented Abelard’s somewhat fluid terminology. Note that in using fundamenta and subiecta interchangeably Abelard is at variance with later medieval terminology, which sharply differentiates them.
112. For Boethius, see In Isag. maior 2.3 174.14–175.4, and also De top. diff. 2.7.22–24 35.2–17, In Cic. Top. 1145D–1147D.
113. See LI Cat. 189.28–30: “Surely for a place to surround a point is nothing but to circumscribe it, that is, to delimit it in such a way that it is its place, and for this purpose it doesn’t have to be greater”; cf. also Dial. 60.21–23.
114. Abelard takes this last argument from Aristotle, Cat. 6 5a9–13 (ed. comp. 55.16–21): see LI Cat. 189.13–19 and Dial. 59.29–60.4.
115. Abelard begins his discussion by running through Boethius’s nine senses in which one thing is said to be “in” another: Dial. 78.25–79.2 (referring to Boethius, In Cat. 172B–C).
116. The firmament was the outermost sphere of the heavens, created on the Second Day, in which the fixed stars are located (Genesis 1:17); Abelard examines its physical composition in Hex. 37.6–40.18.
117. To account for putatively “empty” places Abelard should therefore maintain that the world is actually a plenum, where something such as air is actually present, and thus reject the existence of a vacuum – which is precisely what he does in the prologue to the Sic et non (96.169–171) while discussing the interpretation of texts.
118. This account is described, and labeled the “common view,” in LI Cat. 184.38–185.6. The real difficulty here is the “coordination problem” but Abelard does address the question why we construct temporal wholes out of the successive instants in a given thing rather than taking (coordinated) instants across distinct things; see also LI Cat. 186.23–31.
119. Abelard draws the connection clearly in LI Cat. 186.9–12: “Thus when we say that an action takes a year we don’t have to postulate a year in it, or many years or many days that exist simultaneously, but only a single year that adjoins the world simultaneously as a whole, namely the firmament along with all the substances it includes.” See also Dial. 554.8–13. This is as close as Abelard comes to Aristotle’s conception of time as the measure of motion.
120. Abelard is following Aristotle, Cat. 6 5a7–8: IP Cat. 67.3–7, LI Cat. 186.26–34, Dial. 62.13–22.
121. Abelard notices the indexical character of these terms but doesn’t say much about it. He says nothing about the B-series “earlier” and “later.”
122. Abelard discusses the oddities of temporal wholes in LI Cat. 186.39–188.22 as well as Dial. 62.32–64.6 and 553.8–554.36; I draw on all of these in what follows.
123. His knowledge derives from Boethius: see n. 112. He discusses the four causes in Dial. 414.21–417.37.
124. In the last passage Abelard appeals to Augustine, citing his doctrine that sin is a privation in support of his claim that causes need not be things.
125. Abelard discusses future contingents in LI 3.09 and Dial. 210.21–222.25; he does not often speak of an eventus outside this context; he uses the term in glossing Cat. 12, discussing the truth of sentences, and occasionally elsewhere.
126. In this expression the rei/rerum is a subjective genitive, so that Abelard is speaking of the thing’s (or the things’) coming-about, the “coming-about” that belongs to the thing or things. What is more, Abelard uses the expression eventus rerum interchangeably with res eveniunt, which clearly ascribes an activity or property to the res (see for example Dial. 218.16–219.24).
127. In LI De in. 3.09.44–47 (G 422.41–423.27), Abelard asks how philosophers who hold that all past and present events, but no future events, are determinate should interpret the res of the eventus rerum: are they concrete things, or are they dicta? He puts forward puzzles for each alternative, but doesn’t address the question on his own terms. However, it is noteworthy that he does not consider the suggestion that the res are anything like states of affairs.
128. Abelard’s arguments are presented in LI De in. 3.04.17–19 (G 365.39–366.12) and Dial. 154.20–155.24.
129. Abelard also calls it the existentia rei/rerum in Dial. 154.10, 155.35, 156.29, 156.34, 157.14–15; TI 81–82; and TC 4.156. He seems to use this expression interchangeably with essentia rerum in Dial. 155.26 and 155.34. Abelard uses the term dictum only in his LI (apart from a single occurrence in Coll. 202), but for consistency and convenience I’ll use it throughout.
130. See LI De in. 3.04.16; nullae omnino essentiae (G 365.37) and nil est omnino (G 365.33 and 365.1).
131. At one point Abelard even refuses to say anything positive about dicta, to avoid any grounds for granting them ontological standing: LI De in. 3.04.41 (G 369.37–39). This dodge won’t work, but it shows how committed he is to not granting them any metaphysical status.
132. The Latin text runs as follows: “Quippe ‘Socrates’ ipsum significat in eo quod Socrates est. Nec tamen dicit ipsum esse Socratem, sicut ‘Socrates est Socrates’ dicit. Unde in dicto propositionis differentiam habet ipsa a nomine, quod videlicet propositio dicit ‘Socrates est Socrates,’ quod non est aliqua essentia, ‘Socrates’ vero id non dicit, licet Socratem nominet secundum hoc quod est Socrates.”
133. Again, the Latin text runs as follows: “Patet insuper ea quae propositiones dicunt nullas res esse, cum videlicet nulli rei praedicatio earum [reading earum for de Rijk’s eorum] aptari possit; de quibus enim dici potest quod ipsa sint ‘Socrates est lapis’ vel ‘Socrates non est lapis’? Iam enim profecto nomina oporteret esse, si res designarent ipsas ac ponerent propositiones, quae quidem ab omnibus in hoc dictionibus differunt quod aliquid esse vel non esse aliud proponunt. Esse autem rem aliquam vel non esse nulla est omnino rerum essentia. Non itaque propositiones res aliquas designant simpliciter, quemadmodum nomina, immo qualiter sese ad invicem habent, utrum scilicet sibi conveniant annon, proponunt; ac tunc quidem verae sunt, cum ita est in re sicut enuntiant, tunc autem falsae, cum non est in re ita. Et est profecto ita in re, sicut dicit vera propositio, sed non est res aliqua quod dicit. Unde quasi quidam rerum modus habendi se per propositiones exprimitur, non res aliquae designantur.” Abelard uses the same line of argument in LI De in. 3.04.22–23 (G 366.30–35).
134. Abelard tartly remarks that we should no more confuse truth or “being in reality” (esse in re) with metaphysics or “being a real thing” (esse rem) than we should confuse being in a house with being a house: LI Top. 226.7–8.
135. Abelard holds that true consequential sentences are true from eternity, by which he means that their truth depends solely on the natures of things involved, which God has timelessly established to be as they are: Dial. 264.38–265.1, 282.25–29, 283.12–15.
136. Although Abelard’s metaphysics takes irrealism as its inspiration, making it congenial to our contemporary philosophical temperament, it has received comparatively little attention from scholars. Few of his important texts are available in translation, and Abelard’s philosophy of logic and language has generally taken pride of place in philosophical studies. Yet there are works on several aspects of Abelard’s metaphysics that can be consulted for further reading, in addition, of course, to the texts of Abelard himself.
Marenbon 1997a is a general survey of Abelard’s philosophy, including discussions of many metaphysical topics. Detailed discussions of Abelard’s arguments against realist theories of universals can be found in Boler 1963, Tweedale 1976, King 1982, and Bertonelli 1987, with a general overview in de Libera 1987; collective realism comes in for extended treatment in Freddoso 1978 and Henry 1984. The metaphysical side of Abelard’s solution to the problem of universals, in particular whether the status is some kind of thing or a special non-thing, is discussed at length in Tweedale 1976, Maloney 1982, Blackwell 1988, and Marenbon 1997a; the impact of Abelard’s semantical views on his metaphysics is explored in de Rijk 1980 and 1985.
Abelard’s theory of individuality is treated in Wade 1963 and extensively in Gracia 1984. Marenbon 1997a dissects Abelard’s views on matter and form; Henry 1985 takes up Abelard’s account of matter and integral wholes, building on his previous analyses in Henry 1972 and Henry 1984. Natures are discussed in Marenbon 1997a, and Abelard’s account of real modality in Marenbon 1991.
Brower 1998 takes up Abelard’s theory of relations, one of the few studies of Abelard’s account of the Aristotelian categories. King 1982 and Perler 1994 take Abelard to propose an ontology of facts. The fundamental study of Abelard’s account of dicta was Nuchelmans 1973, placed in a wider context by de Libera 1981, who allies it with philosophical issues about states of affairs, facts, and events; the question has since been taken up in de Rijk 1982, Jacobi 1983, Pinzani 1995, and Guilfoy 1999.