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Substantial simplicity in Leibniz: form, predication, & truthmakers.


ACCORDING TO LEIBNIZ, (1) there are constraints on what counts as a genuine individual substance. (2) Four such constraints are derivative from the Aristotelian and scholastic traditions: substances are (1) independent; (3) (2) essentially active; (4) (3) persistent through change; (5) and (4) ultimate subjects of predication, that is, never themselves predicated of other things. (6) And yet, there is at least one further constraint on an entity's counting as a genuine substance, exclusive to Leibniz's philosophy: substances are (5) simple, per se unities. (7) In his correspondence with Arnauld, Leibniz says:
 I believe that where there are only beings by aggregation, there
 aren't any real beings. For every being by aggregation presupposes
 beings endowed with real unity, because every being derives its
 reality only from the reality of those beings of which it is
 composed, so that it will not have any reality at all if each being
 of which it is composed is itself a being by aggregation, a being
 for which we must still seek further grounds for its reality,
 grounds which can never be found in this way, if we must always
 continue to seek for them. (8)

Individual substances are simples, lacking proper parts. Any purported being that does possess proper parts--that is, entities "by aggregation"--will not suffice as a genuine Leibnizian substance. In light of this requirement, an accurate interpretation of Leibniz ought to avoid at all costs attributing to him a component ontology, that is, a view according to which individual substances are the very individuals that they are--and are numerically distinct from other individuals--in virtue of their component parts. (9)

For the interpreter of Leibniz, it is quite the difficult task to remain faithful to his emphasis on substantial simplicity without at the same time running afoul of the other primary traits. Independence may be the sole exception here. For instance, the traditional theistic doctrine of divine simplicity has generally operated under the presumption that God is entirely a se or "from himself." In fact, most scholastic theologians believed that God's simplicity requires aseity, such that all dependence relations are absent in God. (10) An authentic simple would be dependent on nothing other than itself, including any mereological parts of which it may be composed. The general point being, that while simplicity and independence are mutually accommodating, they are less straightforwardly combined with the other primary characteristics; in fact, the former may jointly bring about difficulties for the latter. Reflect for a moment on a substance's essential activity.

Substances, Leibniz declares, are active entities, possessing appetitive and perceptual capacities that enable them to immanently bring about their states. Such capacities are often modeled on God's attributes or perfections--power, knowledge, and will (or goodness) serving as the primary examples utilized by Leibniz. Consider [section]48 of the Monadology: God has power, which is the source of everything, knowledge, which contains the
 diversity of ideas, and finally will, which brings about changes or
 products in accordance with the principle of the best ... And these
 correspond to what, in created monads, is the subject or the basis,
 the perceptive faculty and the appetitive faculty ... (11)

Earlier in Leibniz's career he expresses similar sentiments, detailing the resemblance
 between God and creature as manifest in accord with the divine
 perfections: It can even be said that every substance bears in some
 way the character of God's infinite wisdom and omnipotence and
 imitates him as much as it is capable. For it expresses, however
 confusedly, everything that happens in the universe, whether past,
 present, or future--this has some resemblance to an infinite
 perception or knowledge. And since all other substances in turn
 express this substance and accommodate themselves to it, one can
 say that it extends its power over all the others, in imitation of
 the creator's omnipotence. (12)

Substances act spontaneously via such capacities or causal powers. (13) Yet, provided that Leibniz does recognize as constitutive of a substance some quantity of causal power, one might be suspicious that Leibniz has run afoul of the simplicity requirement on substances. That is, what are causal powers such as knowledge, power, and will, if not authentic parts of a substance? Consider Leibniz's response in an exchange between himself and DeVolder in 1703:
 You doubt, esteemed Sir, whether a thing that is one and simple is
 liable to change. But since only simple things are true things,
 what remain are only entities by aggregation; to that extent they
 are phenomena, and, as Democritus put it, exist by convention and
 not by nature. So it is obvious that unless there were change in
 simple things, there would be no change in things at all. Indeed,
 not even change can come from without, since, on the contrary, an
 internal tendency to change is essential to finite substance, and
 change could not arise naturally in monads in any other way. (14)

De Volder's worry seems to be this: if all real beings are simple (as Leibniz attests), then change at the level of metaphysical reality is impossible. The very concept of change, on De Volder's reckoning, presupposes inner-working parts of the entity that changes and, hence, complexity; yet individual substances, on Leibniz's view being entirely simple, lack such parts and, hence, complexity. To the contrary, Leibniz asserts that monads are both simple, and operative immanent change is internal to them.

I wish to emphasize a worry similar to that broached by De Volder. Rather than the problem of change, however, I have in mind another difficulty with which Leibniz is confronted: how can Leibniz preserve the simplicity of an individual substance (singular) on the one hand, while retaining the view that causal powers (plural) are constitutive of substances on the other? It is this question that I address in the present essay. I shall argue that causal powers are not to be understood as veritable parts of a substance in a manner that renders substances as complex entities; to make this entirely evident we shall concern ourselves with ([section]II) Leibniz's revival of the scholastic notion of substantial form, ([section]III) his theory of accidents, and ([section]IV) his account of metaphysical predication, respectively. (15)

To reiterate, our primary question is the following: how does one make sense of the relation of causal powers to the substantial subject without attributing a component metaphysic to Leibniz? With that in mind, here is a familiar story from the history of early modern philosophy. Descartes, in hopes of grounding the new mechanistic science of the 17th Century, rid the philosophical landscape of many tired and ill-conceived contrivances that had been fashionable during the preceding centuries. One such contrivance is the notion of a substantial form. In his Sixth Replies Descartes describes the difficulty with these "occult" devices:
 But what makes it especially clear that my idea of gravity was
 taken largely from the idea I had of the mind is the fact that I
 thought that gravity carried bodies toward the centre of the earth
 as if it had some knowledge of the centre within itself. (16)

Substantial forms are supposed to be like "little minds" or internal forces in objects, but such suppositions are mistaken. Descartes explains,
 But later on I made the observations which led me to make a careful
 distinction between the idea of the mind and the ideas of body and
 corporeal motion; and I found that all those other ideas of ...
 'substantial forms' which I had previously held were ones which I
 had put together or constructed from those basic ideas. (17)

Positing substantial forms in material objects, Descartes believes, is the result of a confusion; particularly, a confusion whereby mental qualities--which reside in the mind alone--are relocated into inert bodies. As distinct kinds of substances, body and mind possess different properties or features, and the two ought not be confounded on pain of objectionable metaphysical consequences.

Against the progressive sentiment of the day which was (largely) sympathetic with the Cartesian view, Leibniz sought to revive the scholastic notion of substantial form, to make it respectable as a metaphysical instrument of explanation. Again, this is all familiar to the reader, and I shall not rehearse its details further. Instead, what I shall do in this section is explore the connection between Leibniz's renewal of substantial forms in philosophy, his account of causal powers, and his ardent emphasis on the simplicity of individual substances. While it may appear that Leibniz is leading us to identify a veritable one (an authentically simple substance) with an ostensible many (a plurality of causal powers), I shall demonstrate how such a reading of Leibniz is misguided given an appropriate understanding of the notion of substantial form. This will be made all the more evident by first appealing to the scholastics themselves, and appreciating the fact that it is the substantial form that serves as the ground for all the causal powers in substantial things.

II.1. In the scholastic tradition, causal powers were subsumed under the substantial or accidental form of a thing, whether that thing be material or immaterial in nature. In material objects, the substantial form serves as the explanatorily basic component which distinguishes the objects in terms of natural kinds. (18) Since form is so intimately tied to natural kinds, form is often thought to approximate a principle of organization, such that matter organized in a horse-wise fashion is so in virtue of the equine substantial form that informs it. Organizational capacity, however, does not exhaust the function of substantial form. Any fully-articulated conception of substantial form must also take into consideration the fact that the causal capabilities of a thing determine the kind to which it belongs. (19) Hence, the substantial form indicates the natural kind of the thing in virtue not only of the organization of the matter of which the thing is composed, but also in virtue of the causal capacities that the thing exemplifies. So, a material thing's having the propensity to rational thought (rather than, say, to seek out nutrients through its roots) is due to its having the substantial form of humanity.

St. Thomas Aquinas, for instance, conceived the substantial form as the internal causal principle of a complete substance. In Summa Contra Gentiles he asserts that "all accidents are certain forms added onto the substance, caused by the principles of the substance," (20) where by "principles" he has in mind the dual notions substantial form and matter which collectively make up the substantial composite. Of course, Aquinas did not think that every accident of a singular substance was really due to the internal workings of the substance itself, since clearly some accidents of material substances are explained by external sources. In De Ente et Essentia he clarifies, noting: "everything that holds true of something is either caused by the principles of its nature, as is a human being's capacity for laughter, or comes to it from an external principle, as light in the air comes from the sun's influence." (21)

Following Aquinas, Francisco Suarez often likens the substantial form to an active principle which serves as a "principle of operation" in substances, (22) the genuine causal "source of the entire esse and of all the properties." (23) Commenting on this causal role, Robert Pasnau recommends that it is not limited to so-called formal causality but also to efficient causality as well: "the substantial form can be viewed as playing something very much like the role of an internal efficient cause, sustaining and regulating the existence of that which the efficient cause originally produced." (24)

I think Pasnau's analysis is on target. Still, though it is perfectly acceptable to construe the substantial form as approximating the internal efficient cause of a substance, more precision in its characterization would be beneficial. Some scholars suggest that a substantial form is little more than a collection or bundle of causal powers--a genuine many as opposed to a one. (25) Call this the "bundle-view." Alternatively, other scholars represent the substantial form as the ground for the causal powers of a substance, the (single) entity in virtue of which a substance has the causal powers it does. Call this the "grounding view."

On my reading, the latter view is to be preferred over the former. Scott MacDonald aptly describes the grounding view, saying,
 According to Aquinas, a species of natural substances is indicated
 by their performing a particular kind of activity. Substances of
 species S are members of S by virtue of having the capacity for
 performing the activity characteristic of Ss. A particular
 substance's substantial form is the ontological ground of that
 capacity; Aquinas calls this ontological ground the substance's
 first actuality. Thus, in virtue of its substantial form a
 substance has a specific set of powers and potentialities which
 constitute its capacity for performing its characteristic activity.
 For a substance to exercise its specific powers and actualize its
 specific potentialities is for it to perform its characteristic
 activity. Aquinas calls the state in which a substance has
 actualized its specific potentialities the substance's second or
 final actuality. (26)

Rather than a mere collection of capacities, the substantial form is that from which causal powers arise. It seems to me that one should not confuse Leibniz--or the scholastics--with anyone positing a bundle-view of causal powers. After all, "individuals" and "collections" are different ontological categories altogether. Consider the following example. (27)

Suppose that having the substantial form "caninity" entails having causal powers [C.sub.1], [C.sub.2], and [C.sub.3], while having the form "humanity" entails having causal powers [C.sub.1], [C.sub.2], [C.sub.3], and the additional causal power [C.sub.4]. If the substantial form is reckoned a mere collection or bundle of powers, then the explanatory resources for determining why a given bundle contains the powers it does are paltry at best; what is more, there is apparently nothing in virtue of which the powers are united in the bundle. In short, we are left with little explanation for why the dog possesses the causal powers it does instead of the causal powers possessed by the human being. If, on the other hand, the substantial form is understood as the ground for the causal powers of a thing, our explanation runs deeper: the substantial form is that which gives rise to the bundles in a kind, and also serves as a unifier of the bundle. Accordingly, there is an explanation for why a substance has the powers it does and an explanation for what unifies the causal powers--the substantial form. By itself, it provides the explanatory resources for making sense of all the varying causal contributions of one single thing. (28)

Assume now that the preferred interpretation is one according to which the scholastics endorsed the grounding view. Recall from above that Aquinas had, perhaps carelessly, urged that the substance itself causes or brings about its own states or accidents. Such a characterization, at least from the pen of Aquinas, is a bit off the mark; certainly his claim was far too strong, since he elsewhere acknowledges that external causes too bring about change--as when light in the air is a result of the sun's causal influence. Leibniz, however, denies substantial interaction amongst finite substances, and thus, the possibility of external causes originating from any entity other than God. He, unlike his scholastic predecessors, thinks that all finite change comes about internally. Any external action on a substance can be performed by God alone; and, in the absence of occasionalism, (29) all natural changes in finite subjects must be brought about by the internal workings of the substances themselves.

II.2. In his correspondence with Arnauld, Leibniz is keen to argue for the utter simplicity of substances by way of an argument from composition. Supposing we have two things, the only way to guarantee that there is some one thing over and above the two things is to posit a relation between the two givens. Yet, there is no relation strong enough to guarantee that one thing arises from two things, excepting the identity relation. Aggregative beings are second-rate entities at best, and not to be counted as genuine substances. Real beings or individual substances are simple and unified, closely akin to what traditional scholastic philosophers had described under the heading "substantial form": "Substantial unity requires a complete, indivisible and naturally indestructible entity, since its concept embraces everything that is to happen to it ... [which can be found in] a soul or substantial form." (30)

Leibniz clearly hopes to revive the notion of substantial form in serious metaphysical theorizing, contra the claims of Descartes and others. (31) However, one ought to wonder in what vein he means to revive it? After all, the scholastics had one and all taken substantial form to be the indicator of the natural kind, while there is a strong sense in which Leibniz is unconcerned with natural kinds in the material world. That is, on a strict reading of his system, at the metaphysical ground floor there are only monads, simple substances differing from one another as individuals. But it is here, precisely, that Leibniz's appeal to substantial form ought to be appreciated. Certain scholastics understood some substantial forms to actuate matter into a certain species, such that there is one and only one substantial form per individual substance, marking it off as a member of some species, making it what it is. (32) In a way, Leibniz agrees. Substantial form makes a thing the thing that it is, but at the level of individual and not species. Or, more plainly, each individual substance belongs to a species all its own in virtue of its form.

Leibniz describes individual substances in a manner resembling Aquinas' account of immaterial substances: particularly, angels. Characterizing the nature of angels, Aquinas says:

"If therefore the angels be not composed of matter and form, as was said above ... it follows that it is impossible for two angels to be of one species; just as it would be impossible for there to be several whitenesses apart ... since whitenesses are not several, except in so far as they are in several substances." (33)

An angel, unlike a human being, is substantial form alone, and not a form-matter composite. In a letter to the Landgrave Ernst von Hessen-Rheinfels, Leibniz draws an analogy between his own view of finite substance and Aquinas' description of angels:
 [I]f St. Thomas was able to maintain that every individual
 intelligence [that is, angel] specifically differs from every
 other, what harm will there be in saying as much of every person
 and of conceiving individuals as infimae species, provided that
 species be taken not in a physical but in a metaphysical or
 mathematical sense.? (34)

Not only are Leibnizian substances like Thomistic angels in terms of belonging to individual species, but also like angels, monads are nothing over and above their substantial forms:
 But spirit is to be understood ... as a soul or as a form analogous
 to a soul, not as a simple modification, but as something
 constitutive, substantial, enduring, what I usually call a monad,
 in which there is something like perception and appetite. (35)

Found in or arising from the substantial form are "something like" perception and appetite, which I gloss as the causal powers of substantial things. Leibniz's rehabilitation of substantial forms, traditionally conceived as that in virtue of which a thing has the powers it does, parallels his insistence on the internal causal forces found in substances. "Each substance is the true and real cause of its immanent actions, and has a force of acting ... [and] it is impossible for it to behave merely passively." (36)

From this an important consequence follows: just as the ontological correlate of the complete concept--that is, the haecceity--is identical with the nature of the substance, and the nature of the substance is identical with the law-of-the-series, so too the law-of-the-series is identical with the substantial form. The substantial form of a substance just is the whole substance itself. In De Ipsa Natura, Leibniz explains,
 But if, indeed, the law God laid down left some trace of itself
 impressed on things, if by his command things were formed in such a
 way that they were rendered appropriate for fulfilling the will of
 the command then already we must admit that a certain efficacy has
 been placed in things, a form or a force, something like what we
 usually call by the name 'nature,' something from which the series
 of phenomena follow in accordance with the prescript of the first
 command. (37)

States arise or follow from the substantial form, which is just to say that the law-of-the-series directs the progression of states of an individual substance.

To this point I have attempted to show that Leibniz's gloss on substantial form makes possible a reading of substances as metaphysical simples--beings lacking proper parts or components that function as that which grounds causal powers. Still, two problems remain evident. The first difficulty arises in light of our reckoning of substantial forms: an appropriate account of substantial forms, I urged, is one according to which they unify a bundle of powers in a given kind. If this is right and causal powers are a genuine many--albeit internal to the singular substance--then substances are complex and simplicity is (again) undermined. This problem will receive attention in [section] IV below, where an appeal to Leibniz's theory of metaphysical predication will be of some use.

Requiring our immediate attention, however, is the second difficulty. Recall that simplicity and independence come together as a conceptual package. Simplicity demands independence from other created beings, such that, if the independence of a substance is threatened, so also is its simplicity. Now, the difficulty for Leibniz arises insofar as he often insists that there are modes or accidents that are at once produced by the substance and distinct from the substance. Yet, if substances have distinct accidents, and indeed, as Leibniz often declares, cannot exist without them, then substances appear dependent upon their accidents in a manner detrimental to substantial independence. (38) This problem will concern us below in [section] III where I will attend to Leibniz's understanding of modes or accidents; in particular, the ways in which they are thought to inhere in individual monads.


Leibniz is often catalogued as a substance-accident realist. Accordingly, there are (in the robust sense of there are) substances, and these substances have or possess certain features--the accidents, properties, modes, or states (39) that are causally and immanently produced by the substantial form (which, recall, just is the substance itself). Now, accidents all by themselves need not compromise substantial simplicity. After all, Aquinas and other Medieval philosophers had maintained that immaterial substances--for example, angels--were singular entities which, nonetheless, had accidents. Whenever some accident inheres in an angel, the angel's simplicity is not corrupted; instead, the simple substance is said to enter into a larger substantial composite of which it and the accident are constituent parts. So, Leibniz need not fear that a monad's possession of some mode or state affects its simplicity per se.

What should concern Leibniz, however, is the fact that the possession of accidents is problematic in respect to independence. After all, substances are, according to Leibniz, independent of every entity except God, and the having of really distinct accidents appears to saddle substances with a dependence on their accidents. If substances have accidents, and these accidents are entities whose reality is additional to the reality of the substance in which they inhere, then the dependence relation between the two may threaten a substance's independence from other created entities.

III.1. Should the objection be pressed that the postulation by Leibniz of a metaphysic of substances cure accidents all by itself serves as an admission on his part that his ontology of substance lacks the necessary features for independence, then one might think that little more could be said on Leibniz's behalf. Yet such a prima facie evaluation of his substance-accident realism would be overly hasty at best, unfair at worst. One need not think that to be a per se, independent, metaphysically simple unity, a thing must be characterized as some sort of bare particular, stripped of all qualitative features. (40) Recall the Monadology passage wherein Leibniz draws a correlation between God's power, knowledge, and will on the one hand, and on the other the perceptive and appetitive faculties of created things, noting that "in God these attributes are absolutely infinite or perfect, while in the created monads or in entelechies... they are only imitations of [God]." (41) In whatever way these attributes or causal powers are characterized, they are not to be understood as distinct parts or components of a substance, but instead as that bit of divine reality transferred to the creature at the initial moment of creation. (42) In virtue of his creative act, God produces the substance and, eo ipso, its causal powers. Might the accidents of a monad be characterized in a similar vein?

At the outset, one issue is certain: Leibniz never entertains the notion that accidents are proper parts of substances. The part-whole relation would recommend that a substance (the whole) is dependent in at least this sense: it is dependent upon the parts of which it is composed. Even his scholastic predecessors, many of them substance-accident realists, had shied away from such an understanding of accidents; instead they earmarked certain accidents as flowing from the very essence of the substance in virtue of the natural kind it exemplified. (43) Such accidents are the realized potentialities inherent in the nature of the substance, and are distinct from nonessential accidents or properties that substances may or may not exemplify (that is, that Socrates exemplifies risibility is essential to him in virtue of his natural kind, while his being pale is accidental only). In any event, the scholastic story of substance-accident relations is part and parcel of the more general relations between matter and form, (44) act and potency, essence and existence. (45) What it is important to recognize is that no Medieval understood accidents as parts of a substance. (46)

Like the scholastics, Leibniz's sympathies are Aristotelian enough to consider a substance as a "this-such," an individual thing. (47) The sense in which a predicate or an accident is "in a subject" (in-esse) is nonmereological in nature: as Aristotle declares, "By 'in a subject' I mean what is in something, not as a part, and cannot exist separately from what it is in." (48) Both Aristotle and Leibniz accept the separate ontological classes of substance and accident while shying away from a mereological understanding of their relation to one another. (49) Leibniz expresses the sentiment on more than one occasion that, "[n]o entity that is truly one is composed of parts. Every substance is indivisible and whatever has parts is not an entity, but is only a phenomenon." (50) Still, even if Leibnizian accidents are not to be reckoned proper parts of a substance in a compositional sense, the mature Leibniz often indicates that they are distinct from the substances that have them. Though a dependence via parthood relations are not a concern here, a real distinction of substance and accident may nonetheless be thought to have dire consequences for substantial independence (and, hence, simplicity). After all, a substance depends upon its properties in at least one way: it depends upon accidents in order to exemplify them.

Leibniz is drawn toward distinguishing between substances and accidents in hopes of avoiding the unsavory theological consequences that ensue upon its denial. In Theodicy, directing his comments toward Bayle and the occasionalists, he says:
 If the accidents are not distinct from the substances ... why shall
 one not say, with Spinoza, that God is the only substance, and that
 creatures are only accidents or modifications? Hitherto it has been
 supposed that the substance remains, and that the accidents
 change; and I think one ought still to abide by this ancient
 doctrine. (51)

Denial of distinctness between substances and accidents leads to the metaphysical difficulty of distinguishing between (a) possible worlds wherein a plurality of substances exist and (b) possible worlds wherein there is only one substance--God--and the remaining entities are merely accidents of the one substance. (52) God cannot, Leibniz thinks, be the sole causal-explanatory base of the accidental modifications of finite substances, since one would then be at a loss explaining the difference between the being of God and the being of the created world. The question at issue, then, is whether this division between substantial particulars and accidents constitutes an inconsistency in Leibniz's views on the utter independence of monads.

Throughout his career Leibniz appears to endorse two positions on accidents, both consistent with his nominalism: (53) (1) at times he argues that accidents simply point toward the ways a substance is, and so are mental abstractions from the particular substance itself. Call this the Abstract-Accidents View (AA). (2) At other times, accidents do assume an entitative status as concrete particulars that are really distinct from the substances having them. (54) Call this the Concrete-Accidents View (CA). According to both AA and CA, accidents remain categorized as perceptual states of a monad at a given moment. Still, CA renders his independence requirement that much more difficult to sustain, since in such an instance an accident is some thing in addition to the being of the substance. In the next subsection, I lay out both AA and CA as I understand them to occur in Leibniz's texts. A note of warning: I do not mean to suggest that the two views are ultimately reconcilable. Instead, I hope to point toward some reasons that Leibniz might have had to adopt a firm distinction between substance and accident, as (CA) alleges, even though such a position is at odds with other tenets of his metaphysics. Later, in [section] IV, I will argue that his theory of metaphysical predication reflects certain of his intuitions, according to which a thoroughgoing endorsement of (AA) is in order.

III.2. If Leibniz sanctions a version of nominalism according to which accidents are nothing over and above the substance itself, then substantial independence can be reckoned less problematic. Such a view of the reality of accidents--what I refer to as (AA)--occurs in writings throughout his career. In one of his earliest pieces, "A Preface to an Edition of Nizolius" (1670), Leibniz recommends a preference for the concrete over the abstract, lumping modes or states in the latter category rather than the former: "For concretes are really things; abstractions are not things but modes of things. But modes are nothing but the relations of a thing to the understanding, or phenomenal capacities." (55) Here, accidents or modes are denied entitative status full-stop. This view follows on the heels of scholastic precedent, as Francisco Suarez had paid due homage to his own nominalist scruples by assuming a similar stance:
 Accordingly there are in created entities certain modes affecting
 these entities, and their nature seems to consist in this, that
 they do not themselves suffice to constitute being or entity in the
 real order of things, but are intrinsically directed to the actual
 modification of some entity without which they are quite incapable
 of existing. (56)

Closely following the writing of his Discourse on Metaphysics, Leibniz reiterates this view in his "On the Reality of Accidents" (1688); here he catalogues different ways of understanding the relationship between substances and accidents, ultimately finding fault with all of those assuming the reality of the latter. It is enough, he thinks, to align oneself with the position according to which abstract terms such as "white" do not pick out real beings in the world. Instead,
 I will say that substance does change, that is that it has
 different attributes at different times; this cannot be doubted.
 Whether some reality perishes and arises with change, however; or
 whether there are different realities within a substance, that are
 the foundations for different predicates: all this need not be
 asked, and ff it is, it is not easy to determine. But it is enough
 to take substances as things and to tell truths about them. (57)

Finally, nearing the end of Leibniz's life, he and Des Bosses discuss the reality of accidents in their correspondence (20 September 1712). I shall quote Leibniz's response to his correspondent at length:
 Let us come now to the real accidents which are in this unifying
 thing as their subject. You will agree, I believe, that some of
 them are only its modifications, which disappear when it is
 removed. But you ask whether there are not certain accidents which
 are more than modifications. Such accidents seem, however, to be
 entirely superfluous, and whatever is in such a substance other
 than a modification seems to pertain to the substantial thing
 itself. I do not see how we can distinguish an abstraction from the
 concrete, or from the subject in which it is. (58)

Leibniz again rejects any view according to which accidents are real things. They are no more than abstractions from the concrete individual substance, and as such, add nothing new to the being of the substance itself. Again to Des Bosses (20 September 1712), Leibniz says, "every accident is a kind of abstraction; in truth, substance alone is concrete." (59)

While consistent with the independence of finite substances from all other created entities, AA renders difficult his other statements to the effect that substances and their accidents are actually distinct. After all, how might a mental abstraction be thought of as really distinct from a substance? To be really distinct is to be separable, at least by God's power. (60) The second theory Leibniz tended to endorse--CA--better fits the distinctness thesis. (61) Accidents, according to this second model, are themselves actual entities distinct from their substances; they are concrete particulars closely approximating our contemporary use of property-instances or tropes. (62)

General properties (for example, heat) are generated via the mental process of abstraction, and thus are entirely conceptual; singular properties (for example, this heat), however, are concrete individuals requiring a substance in which to inhere. (63) Leibniz says, "If someone maintains that the same wisdom in number or the same heat in number is in two subjects at once, the fact that one says that the wisdom of the one fails, whereas the wisdom of the other still subsists, can refute this." (64)

If accidents possess an entitative status on their own, then it stands to reason that they are distinct or separable from the substances in which they inhere. If accidents are individuals attaching themselves to substances, then no longer are substances entirely independent beings, since they are dependent upon the concrete accidents that they exemplify. In the next subsection, I will address the incongruity between AA and CA; in doing so, I will point toward reasons why Leibniz felt pressure to recognize a genuine distinction between substances and accidents, and hence, to grant accidents the status of individual particulars. The pressure develops generally as a result of his wish to distinguish the created world from God, particularly as a result of his account of creaturely versus divine causation. However, as I shall argue, Leibniz had within his system the means to distinguish substances from accidents without at the same time designating the latter as individual (concrete) particulars.

III.3. Independent of either AA or CA, Leibniz always affirms the following two principles in relation to accidents: (i) accidents arise causally from within the substance itself, and (ii) accidents are nontransferable between distinct finite substances. Regarding (i) Leibniz stipulates that it is the finite substance itself--rather than God--that serves as the explanatory (that is to say, causal) foundation for accidents. To Arnauld he declares,
 [E]ach of these substances contains in its nature the law by which
 the series of its operations continues, and all that has happened
 and will happen to it. That is, all its actions come from its own
 depths, except for dependence on God. (65)

According to (ii) the nontransferability of accidents, Leibniz means that they are essentially tied to the substances possessing them. He says, "Accidents cannot be detached, nor can they go about outside of substances, as the sensible species of the Scholastics once did. Thus, neither substance nor accident can enter a monad from without." (66) Even were accidents detachable, there can be no satisfactory causal account of how they might be transferred: commenting on this influxus physicus causal model, Leibniz asserts, "But since it is impossible to conceive of material particles or of species or immaterial qualities which can pass from one of these substances into the other, this view must rejected." (67) In fact, for any accident at all, that accident could not have existed without the substance whose accident it is. "An accident ... needs not only some substance in general but that very one in which it inheres, so that it cannot change it." (68) Inherence then denotes a relation of essential dependence, that is, the accident is essentially dependent upon the subject whose accident it is.

These two principles deserve further exploration. The operative notions implicit in them are "cause" and "inhere." I shall argue that the former, when restricted to immanent causation in a finite substance, is coextensive with the latter (for Leibniz). Consider the idiom,

(1) An accident F inheres in substance a. (69)

Substances are the (immanent) causal sources of all their accidents, and these accidents are just momentary, dependent (perceptual) states arising from within the substance itself. (70) Admittedly, Leibniz's concept of inherence is difficult to parse in anything but a coarse-grained sort of way. From his "On the Abstract and Concrete" (ca. 1688), he says: "It seems that something inheres in a subject, if and only if, its reality belongs to the reality of this subject." (71) Whatever reality an accident has is dependent upon the reality of the subject whose accident it is. Since, as Leibniz maintains, all accidental states arise from within the substance itself, a (noninitial) (72) state's inhering in a substance just is its having been caused by that substance. As such, I suggest that inherence is to be explained causally, where the relevant sort of causation is cashed out in terms of efficient causal production. (73) As Leibniz says to Bayle, "God produces substances from nothing, and the substances produce accidents by the changes of their limits." (74) Our idiom then reduces to,

(2) An accident F is caused by substance a.

Or, perhaps better,

(3) If accident F inheres in substance a, then substance a causes accident F.

As it turns out, Leibniz's claim is even stronger than (3), since finite substances cause nothing other than their accidents, precluded as they are from causal interaction amongst themselves and causal action on the infinite substance, God. So, for any noninitial, nonrelational accident at all, if it is caused by the substance, then it inheres in the substance. (75) This amounts to a new reading:

(4) An accident F inheres in substance a if, and only if, substance a causes accident F. (76)

Unfortunately, associating inherence and causation in this way is consistent with the worry that Leibniz wished to avoid--an account wherein the being of God is distinguished from the being of the world only as one of a substance to its accidents, that is, Spinozism. God, as cause of the world of monads, would be the only substance, while finite substances would inhere in the infinite substance, God. It is just this worry, I think, that persuades Leibniz to posit a separability between substance and accidents.

Nevertheless Leibniz has the resources to curtail the Spinozist ramifications of causal inherence, particularly, his distinction between types of causal relation. Recall that Leibniz often remarks that God is the only operative transeunt cause and that creatures, precluded from causal interaction amongst themselves, act immanently. (77) God brings about a world separate from himself, while creatures bring about their own internal accidents. (78) Since (4) above is consistent with the Spinozist view that all creatures are mere modes of God, it must be restricted in order to discriminate between God's causal activity and creaturely causal activity:

(4*) An accident F inheres in substance a if, and only if, substance a immanently causes accident F.

Inherence, on this analysis, is tied not to causation broadly construed, but to immanent causation alone.
 leaving aside the dependence that we have on [God] ... I say, in
 order to speak only of secondary causes or of the ordinary course
 of nature, I hold that, without needing any new operations from
 God, in order to explain things we can be satisfied with what God
 gave to them from the start. Thus in my view, every substance
 produces by itself in an orderly way everything that will ever
 happen to it internally. (79)

Leibniz denies that finite substances inhere in the divine nature even though the divine nature causes (that is, creates) finite substances. Hence, he can restrict inherence to the causal relation between a finite substance and its accidents in the hope of avoiding the possibility of Spinozism. (80) In this way we are able to take Leibniz seriously when he warns of "confusing substances with accidents. (81)

What Leibniz provides us, I suggest, is a parallel model of causal-explanatory dependence: of finite substance on infinite substance, and of accident on finite substance. In both cases dependence relations obtain, but the relations themselves are of different sorts: (a) there is a genuine separability between God and creation due to the transeunt nature of God's action, while (b) there need not be the same separability between created substances and their modes due to the immanent nature of the creature's action. (82) This is quite significant, since monadic independence can be salvaged on such a model. After all, in order to maintain consistency within the whole of his metaphysics Leibniz should disavow the very possibility of distinctness or separability between a finite substance and its inhering state. Why? Because if some substance a had a different state than that which was written into its complete concept, then it would not in fact be substance a but some numerically different substance, substance a*.

At this point the question may be posed as to whether God, by his infinite power, could separate substance a (at time [t.sub.1]) from its corresponding state (at time [t.sub.1])? If so, there may be room for positing a separability between substance a and its state. Given the modal strictness of his essentialist metaphysics, however, even this move would be impossible insofar as Leibniz endorses a genuine one-one correspondence between the (metaphysical) nature of a substance and its complete concept. The strength of such a correspondence guarantees that even the miraculous states of a substance are contained within its individual concept. (83) If the state of substance a in any way departed from the corresponding predicate contained within its complete concept, then no longer are we considering substance a but instead (a very similar though still numerically different) substance a*. Of course, this foray into Leibniz's modal metaphysics is a controversial matter, and much more space would be necessary in order to fill in the relevant details. (84) Suffice to say that, on my view, the immanent state of a substance is not separable from the substance in which it inheres in the same way that God is separable from the created universe. In fact, we may say that the former is not separable at all.

In sum, Leibniz separates God from created world by way of one causal process--transeunt causation. And yet the causal relation between a substance and its accidents--immanent causation--need not entail a real separability. Though Leibniz is often compelled to refer to substance and accident as distinct entities, the pressure to do so does not mitigate the fact that they are not really distinct in the traditional sense (that is, separable one from the other).

To this point, I have not suggested that Leibniz's views on accidents--AA and CA--are ultimately reconcilable; I fear that they are not. (85) According to CA, accidents are counted as genuine entities, while in AA they are merely abstractions. I have simply tried to demonstrate that Leibniz tended to waffle between the apparently opposing views. In what follows, however, we shall see further evidence that the better alternative for Leibniz would be to avow AA, the view according to which modifications or accidents of substances are abstractions from the ways a substance is at a moment. I shall return to this point in [section] IV.2 below, where I argue that Leibniz can consistently maintain the functional complexity of a substance without inferring from this a variety of metaphysical complexity--that is, a genuine compositional relation between substance and accident. First, however, we return to a consideration of the causal powers of a substance; I argue that the preservation of substantial simplicity can succeed by way of Leibniz's theory of metaphysical predication.


Suppose that the foregoing sections have elicited a kernel of truth: a Leibnizian individual substance is entirely simple and independent of any other created entity. Indeed, it just is a substantial form. If understanding Leibnizian substances in this vein is found to be nonobjectionable, then my proposal for articulating monadic simplicity is this: let predication be our manner of articulating the structure of a simple substance. Or, perhaps better, let predication suffice for the structure that a metaphysically simple substance lacks. No doubt, such a proposal is beset with problems, not the least of which is Leibniz's fully spelled-out account of predication and truth. (86) Abstracting from the cumbersome details, consider for the moment Leibniz's advice in [section] 8 of the Discourse:

We must therefore consider what it is to be attributed truly to a certain subject.
 Now it is evident that all true predication has some basis in the
 nature of things and that, when a proposition is not an identity,
 that is, when the predicate is not explicitly contained in the
 subject, it must be contained in it virtually. (87)

In the context of this passage, Leibniz perspicuously moves from the material mode to the formal mode, first talking about the (metaphysical) "nature of things" and then to the (semantic) containment relation between the predicate and subject of a proposition. My interest here being primarily his metaphysics of substance, I propose to take seriously his reference to the material mode and the metaphysical account of predication it seems to presuppose. (88)

Any account of Leibnizian predication must take into consideration the fact that all individual substances are instantiations of complete concepts. As such, a few comments on the complete concept doctrine are in order. Clearly we cannot, on Leibniz's behalf, identify actual substances with complete concepts. After all, concepts are ideas, while actual substances are not. Concepts have always existed in the divine mind, while actual substances have not always existed. Concepts do not undergo change, while actual substances do. So they are obviously not identical. Represented functionally, the complete individual concept is the concept God cognitively grasps when thinking about substance a, allowing him, as it were, to correctly pick out a and not some other distinct substance b.

But what is included in the complete concept? Too often commentators assume that the complete concept of a substance is exhausted by some sort of conjunctive list of predicates designating the properties of a substance. If this were correct, then God's instantiation (read: creation) of such a concept would render the resulting actual substance no more than a mere bundle of properties. (89) Such a reading fails to accurately capture the robustness of the content inscribed in the complete concept. Jan Cover and John

O'Leary-Hawthorne recognize this, noting that,
 individual concepts must be acknowledged as having a dual aspect,
 of both singularity and generality ... A complete individual
 concept, one might say, has some content over and above the
 general properties that can (at least by God) be extracted from it.
 To say what this extra content is would be to express something
 that corresponds to the roles Rayed by individuals or bare
 haecceities in singular propositions (90)

The idea seems to be this: let the complete concept "contain" all the intrinsic, nonrelational truths that a substance instantiates in the same way that the concept red "contains" the further concept colored. What, after all, would have to be added to the latter concept in order to get the former? Whatever it might be, the containment relation cannot be designated on the model of a mere list of predicates.

Now, suppose we render Leibniz's Discourse statement in the following fashion, taking "a" as a constant designating some individual substance and "F" as a predicate picking out some feature or aspect of a. Let's call this "Leibnizian Truth" (LT):
 LT: "a is F' is true if, and only if, there exists a complete
 concept of a--call it c--F is a member of c, and there is a
 numerically distinct thing y, where y falls under c, and a = y.

Each individual substance has a complete concept, and inclusive within this concept is the predicate denoting some feature or aspect of the individual substance. On the semantic or formal-mode side, if the complete concept of substance a contains a certain predicate F then the predication "a is F" is true. Otherwise the predication is false. This is Leibniz's famous conceptual containment, predicate-in-subject doctrine of truth. My interest, as I said, is with metaphysical predication. The individual substance itself, falling under or instantiating the complete concept, just is the nature or haecceity. So, on the metaphysical or material-mode side: if the instantiation of that complete concept--the nature or haecceity--possesses (91) the property or feature designated by the predicate F, then the predication "a is F" is true. Otherwise, the predication is false.

What we have here is a model of predication wherein the contemporary notion of truthmaking can be of service. Generally, the truthmaking apparatus can be articulated in a number of different ways, though the core doctrine has it that for every propositional truth P, there is a truthmaker for P, where the truthmaker is something whose very existence entails or necessitates (92) the truth of P. In the case of a true predication, there will always exist some being whose very existence is that in virtue of which the predication is true. (93) As Leibniz says, there must be a foundation "in the nature" of some entity for true predications; extrapolating from this clue, we can say that there must be something in or about the entity itself that makes some predication true. (94)

Stepping back from Leibniz for the moment, let us consider the method of truthmaking. One of the more interesting aspects of truthmaker theory is that the truthmaker itself is meant to be metaphysically impartial or ontologically neutral. As Jeffrey Brower puts it,
 [t]o characterize an entity as a truthmaker ... is to characterize
 it in terms of a certain metaphysical function or role it
 plays--that of necessitating (in a certain way) the truth of the
 predications it makes true. But such a 'functional'
 characterization places no restriction on the specific nature or
 ontological category to which a truthmaker can belong. (95)

Truthmakers may belong to such divergent metaphysical categories as properties, events, constituents of individual substances, and even the whole individual substances themselves. Take, for instance, some contingent claim like "Dixie the cat is fmicky." In order to ground the truth of the predication one needs to go beyond the mere existence of Dixie the cat, since Dixie the cat may have existed without being finicky. (96) Instead of appealing to the whole individual substance (that is, Dixie herself) as the truthmaker, one may alternatively appeal to facts (for example, the truthmaker for the claim is the fact that Dixie the cat is fmicky, (97) where if such a fact exists, then the predication is true) or perhaps to properties (for example, the truthmaker for the claim is the trope Dixie-the-cat's-fmickyness, (98) where if such a trope exists, then the predication is true). As regards intrinsic or essential predications, however, it often makes sense to designate the whole individual substance itself as the truthmaker. For instance, consider the predication "Dixie the cat is an animal": for such essential predications, it makes sense to say that Dixie herself is the truthmaker for the claim, just in virtue of being the individual substance that she is. Consequently, in any possible world wherein Dixie the cat exists, the claim "Dixie the cat is an animal" will be true. In sum the concept of a truthmaker is neutral as regards the ontological status of the entity serving as the truthmaker for predications.

IV. 1. Our target, again, is the structure of a metaphysically simple monad, and we are attempting to make clear such a structure without imparting to Leibniz any variety of a component ontology. My proposal is that sense can be made of one strand of Leibniz's metaphysical picture by application of the truthmaker theory. Recall LT, where the truth of some predication depends upon the nature of an individual substance as designated by the complete concept of that substance. If anything lacks simplicity, it is surely a complete concept, a genuine complex of predicates, both singular and general in nature. However, the ontological correlate of the complete concept--the nature or haecceity or substantial form--is simple, and to articulate how this is possible in relation to the causal powers of an individual substance, truthmaker theory will be of some help.

In a piece of recent scholarship on the doctrine of divine simplicity, Jeffrey Brower utilizes truthmaker theory to defend the doctrine against claims of incoherence. He takes as central to divine simplicity the following requirement on intrinsic predication, which he refers to as "Divine Simplicity" (DS):

DS: If an intrinsic predication of the form "God is F" is true, then God's F-ness exists and is identical with God. (99)

The charge of incoherence against the doctrine of divine simplicity, Brower argues, has largely focused on the presumption that "God's F-ness"--for example, God's will or goodness, God's power, and so forth--designates a genuine property or attribute of God, and then identifies God with that property. Such a result is absurd, however, since (among other worries) properties are by their nature exemplifiables, whereas God is not an exemplifiable. There cannot, then, be a straightforward identity between God and one of his properties. Against the charge of incoherence, Brower recommends a Truthmaker Account (TA, this as opposed to a property account) of predication in order to clarify the doctrine:

TA: ff an intrinsic predication of the form "a is F" is true, then a's F-ness exists, such that this entity is understood as the truthmaker for "a is F." (100)

As we saw above, truthmakers are ontologically impartial, and so to say that God is identical with the truthmaker for essential predications true of him does not commit the proponent of divine simplicity to the ridiculous conclusion that God is identical with a property. Instead,
 if God is divine, he is identical with that which makes him divine;
 if he is good, he is identical with that which makes him good; and
 so on in every other such case. On this interpretation, therefore,
 divine simplicity just amounts to the claim that God is the
 truthmaker for each of his true intrinsic predications. (101)

God's metaphysically simple structure is henceforth maintained, while charges of incoherence go by the board. I wish to suggest a similar reading of intrinsic essential predications in relation to Leibnizian substances. Particularly, my focus will be on the so-called perfections or causal powers of an individual monad, and the sense in which predications of them to the individual substance need not render its nature complex, since in point of fact, they constitute the very nature of the substance.

As we have noticed, causal powers are essential to the substances which possess them. Now, to predicate a causal power of an individual substance is to say that the substance has some causal power among a range of possible causal powers. And, to have some causal power from a relevant range is to have a particular one (this one or that one). This just means that for God to grant some causal power--say, will--to substance a is to give it a's will. That particular power could not have been given to b or c or any other, entailing that causal powers are essentially tied to the nature of the substance that exercises them--such capacities just are included in what it is to be the individual substance that one is. In the Discourse, while differentiating miraculous powers from powers natural to a substance, Leibniz remarks,
 That is why, if we include in our nature everything that it
 expresses, nothing is supernatural to it, for our nature extends
 everywhere, since an effect always expresses its cause and God is
 the true cause of substances. But what our nature expresses more
 perfectly belongs to it in a particular way, since it is in this
 that its power consists. But since it is limited, as I have just
 explained, there are many things that surpass the powers of our
 nature and even surpass the powers of all limited natures. (102)

The substantial nature expresses more perfectly, belonging to it "in a particular way," what amounts to its causal power; as such, the connection between an individual's nature and its causal power is quite intimate. But, again, what to make of the structure of the monadic nature, including as it does its causal powers? For us, what amounts to the same question is: how are we to spell out the metaphysics of intrinsic predication for, say, the proposition "Substance a is powerful" while maintaining the simplicity of substance a?

It being as thorough a model as any, I shall take Brower's TA as the standard-bearer for my truthmaker theory. With this formulation in hand, we take as an instance the following:
 (P) If an intrinsic essential predication of the form "Substance a
 is powerful" is true, then a's powerfulness exists, such that this
 entity is understood as the truthmaker for "Substance a is

One is warranted in asking: What is this entity that serves as the truthmaker? To answer this question we shall have to tweak Brower's DS somewhat, concerned as we are with individual substances of a Leibnizian stripe rather than with the divine nature; call it Monadic Simplicity (MS):

MS: If an intrinsic essential predication of the form "Substance s is F" is true, then s's F-ness exists and is identical with substance s.

Since causal powers are so strongly connected with the nature of the substance, the proposition "Substance a is powerful" is an intrinsic essential predication. And, given our MS formulation, monadic simplicity entails that any Leibnizian individual substance is identical with the truthmaker for the essential predications true of that substance. So, filling in MS on the model of our current intrinsic predication:
 (P*) If an intrinsic essential predication of the form "Substance a
 is powerful" is true, then a's powerfulness exists and is identical
 with substance a.

That is, if substance a has power, then substance a is identical with that which makes it powerful. And, so for any other intrinsic predication about substance a in reference to its causal powers, that is, substance a's knowledge or substance a's will or goodness. For any Leibnizian substance, that substance just is identical with its causal power, which is just to say, that's just what it is to be that particular Leibnizian substance: to have this power, that knowledge, and this will or goodness. In order to articulate true predications about some individual substance, appeal to properties or constituents of the substance is unnecessary; we need only appeal to truthmakers.

Clearly, this makes sense of Leibniz's emphasis on the simplicity of individual substances. The structure of such a substance--taking heed, if there is sense to be made of a simple thing having a structure at all--is difficult to discern from a purely ontological point of view. However, given a story told from the perspective of the metaphysics of predication, we can attribute to Leibnizian substances perfections in the guise of causal powers without doing injustice to monadic simplicity, that is, we fall short of attributing to Leibniz a component ontology.

This, it seems to me, is a perfectly acceptable way of construing Leibniz's simplicity doctrine. It also has the additional benefit of being consistent with the close reading of Leibniz's appeal to the substantial form, detailed above ([section] II). The substantial form, I argued, serves as that in virtue of which a substance has the causal powers it has, and there was a concern that the substantial form was identifiable with a genuine collection. Yet, provided the account of metaphysical predication presented, the purported bundle of causal powers is going to be reduced to one member anyway. The substantial form, understood as a metaphysical simple, remains intact since to designate the causal powers just is to designate the substantial form of the substance.

We have so far discussed only intrinsic essential predication. There remains to consider the issue of contingent predication, and the extent to which--if any--it poses problems for monadic simplicity. I shall argue that it does not, and furthermore, that a Leibnizian account of predication may resolve the tension in his theory of accidents.

IV.2. As was emphasized above ([section] III) Leibnizian substances have accidents, often characterized as modes or states. Moreover, the predications wherein such modes are taken into account are intrinsic rather than extrinsic, though they are understood by Leibniz to be intrinsic, contingent predications. Now, having presented a truthmaker account of Leibnizian intrinsic essential predication, it would be nice to have a unified story to tell about intrinsic predications that are contingent; that is my concern here. Before proceeding, however, I should clarify the dichotomy between predications concerning powers on the one hand and predications concerning modes or accidents on the other. On what basis might Leibniz draw such a distinction? That is, why should the predicates corresponding to the causal powers of a substance be predicated differently than the predicates corresponding to the modal accidents of a substance?

Causal powers are essential to an individual substance in a way that modes are not, that is, the modal connection between a substance and its powers is more robust than the connection between a substance and its states. In order to demonstrate this, appeal will be made to a heretofore unmentioned feature of causal powers that ought to be catalogued, if only briefly. Causal powers are always compatible one with another, while modes or states are not always so. Robert M. Adams, discussing Leibniz's ontological argument for God's existence, suggests understanding "compatibility" as a modal term, and in illustration on Leibniz's behalf, offers the following as definitive: "'A and B are incompatible' means the same as 'It is necessary that A and B are not in the same subject.'" (103) Adams, it seems to me, is correct. Though he does not offer this analysis as a strategy for clarifying the distinction between perfections and causal powers on the one hand, modes and states on the other, I think such a strategy is attractive for our purposes. Of states in particular Leibniz says, "A state of a thing exists if there is any true contingent proposition whose subject is the thing. Change is the aggregate of contradictory states." (104) I take it then that substance a's having perceptual experience E at time [t.sub.1] is incompatible with substance a's also having perceptual experience J at time [t.sub.1]. States are incompatible in the same way that my weighing 370 pounds (a mode of me) at time t, is incompatible with my being 2 feet tall (a distinct mode of me) at time [t.sub.1].

Causal powers, on the other hand, are always compatible with one another, and Leibniz uses his analysis of this fact to serve as the basis for his ontological argument for God's existence. (105) In order for the traditional ontological argument to be successful, Leibniz thought, it has to be shown first that God is a possible being, that is, that he is a being whose attributes are mutually consistent. Given that perfections or causal powers are all affirmative, positive attributes of God, Leibniz invites us to consider two perfections A and B:
 If they are incompatible, then the proposition 'Quality A and
 quality B cannot be in the same subject' ... cannot be an identical
 proposition; for then 'Where A is, B cannot be' would be the same
 as 'A is A' or 'A is B,' and so the one would express the exclusion
 of the other, and so one of them would be the negative of the
 other. But this is contrary to the hypothesis, for we have assumed
 that all attributes [that is, perfections] are affirmative. (106)

God's having knowledge is always compatible with God's having power and God's having will or goodness. Similarly, substance a's having the causal power, will, or goodness to degree x is always compatible with its having the perfection knowledge to degree y. (107) Given any such causal power, it is always compatible with any other. And so, prima facie, compatibility serves as a difference-making feature between causal powers and modes. The latter are contingent (or maybe, "contingent") (108) features of substances, while the former are not so.

With this dichotomy in hand, we shall turn back to true predications of modes. Insofar as the predications involving accidents are intrinsic to the simple substance, the substance itself must serve as the truthmaker. And yet, since the predications are also contingent, a problem arises: truthmaking is a form of broadly logical necessitation, which means that should some particular simple substance exist and hence serve as the truthmaker for all its intrinsic predications (as monadic simplicity seems to require), then the very existence of that particular substance will make that predication true. Contingency seems to go by the board.

In order to make the problem more salient, consider it from a different angle. Finite creatures are all simple beings. Given the proposed commitment to the thesis that for any truth at all, that truth will have a truthmaker, we have attributed to Leibniz a variety of truthmaker necessitarianism. (109) Accordingly, since for Leibniz all true, genuinely intrinsic predications are made true by the creature itself, all such predications are necessary. So far as I can see, at this point there are two possible avenues to take as regards contingent intrinsic predication, once both simplicity and truthmaker necessitarianism are countenanced: (a) maintain that apparently intrinsic, contingently true predications are actually extrinsic, or (b) maintain the intrinsicality of contingently true predications while denying that this poses a problem for the contingency of certain predications. Now, in virtue of the fact that option (a) presumes that the truth of certain predications is relational in nature, I think the best option to pursue on Leibniz's behalf is (b). That is, given the Leibnizian thesis that all relations are reducible to monadic properties and, hence, grounded intrinsically, it would be difficult to cash out predications about the modal state of a particular substance by appeal to yet further entities. (110)

With this in mind, take the following proposition as exemplary of an intrinsic predication of some accident: "Substance a has perceptual experience F." This singular proposition predicates an accidental mode of some individual substance. Consider now the truthmaker formulation.

TA: If an intrinsic predication of the form "a is F" is true, then a's F-ness exists, such that this entity is understood as the truthmaker for "a is F."

The truthmaker may be either the accident--a's having perceptual experience F--or the substance itself--substance a. On the face of it, one might suspect that substance a could have existed and yet lacked this perceptual experience; perhaps it might have had perceptual experience J in the place of F. If so, the accident is the truthmaker for the proposition, and hence, it is contingent. While one would be correct that the proposition is contingent for Leibniz, it is so for a very different reason than our intuitions might suggest. (111)

Is it really the case that a Leibnizian substance could have lacked an intrinsic accident that it in fact possesses? It seems that a negative answer is in order, since Leibniz's strong essentialism entails that, for example, an Arnauld who in possible world [beta] is blue-eyed would not be numerically identical with the Arnauld in the actual world a who is instead green-eyed. In such a case, the complete concepts of Arnauld in each world would differ, entailing distinct individuals. (112) Leibniz's essentialism about property possession makes it difficult to specify how any truth about a substance is contingent at all (Or, at least, how any proposition is contingent in the way that present-day philosophers tend to think of contingency). (113)

Leibniz believes that he has a way to curtail such worries. As it stands, his solution is not consonant with a purely metaphysical predication story, and we shall have to revert to his intensional account, appealing to the conceptual realm of truths rather than the ontological realm of things. For Leibniz, the very nature of what it is to be an individual substance--what a substance is in the narrow sense--is spelled out in terms of predications that are robustly necessary; the necessity is worn on its sleeve openly, so to speak. On the other hand, the way a substance is at a given time, that is, predicates corresponding to its states, is necessary in a slightly different sense. That is, the sense in which a substance possesses its accidental clothing is not a fact about its narrowly-construed nature. So, for Leibniz, this less-than-robust sort of necessity just is his version of contingency. Such Leibnizian contingency is intertwined with what is often referred to as his infinite-analysis account of contingency, involving scrutiny at the conceptual level.

In identities this connection--between subject and predicate--is self evident; in
 other propositions it must appear through the analysis of terms ...
 For in necessary propositions, when the analysis is continued
 indefinitely, it arrives at an equation that is an identity.... But
 in contingent propositions one continues the analysis to infinity
 through reasons for reasons, so that one never has a complete
 demonstration ... but the reason is understood completely only by
 God, who alone traverses the infinite series in one stroke of the
 mind. (114)

The general Leibnizian line on distinguishing contingent from necessary truth involves discriminating between propositions requiring an infinite analysis or proof to reach an identity of subject and predicate (such truths are contingent) from propositions requiring only a finite analysis or proof (such truths are necessary). Robustly necessary truths--such as "Substance a is powerful"--involve strict identities that are purportedly provable in a finite manner, concerned as they are with the narrowly construed nature of the substance. Less robustly necessary truths--such as "Substance a has perceptual experience F"--involve identities that are provable only given an infinite series. For Leibniz, the latter are contingent, concerned as they are with the accidental clothing of the substance. (115)

So the predicate F, while essential to substance a, is contingent on the assumption that an infinite analysis would be required to demonstrate the analyticity of the claim. Generally speaking, this is just to say that the ways in which a predicate is contained in a subject is open to different sorts of explanatory relations. The explanatory relation in which causal-power predicates are contained in substance-subjects is one of strict identity which is, in some sense, finitely provable. Alternatively, the explanatory relation in which accident or state predicates are contained in substance-subjects is distinct from identity in the previous sense--less strict and provable only by an infinite analysis. So, there is a sense in which Leibnizian contingency really is a matter of intensions, broadly conceptual at its roots.

If this is correct, then I suggest that a univocal account of predication will suffice even for intrinsic contingent predication, insofar as it is the subject itself that makes true the claims about it, that is, the substance itself does serve as the truthmaker even for intrinsic contingent truths. This sort of story is hinted at by Leibniz in his "On the Reality of Accidents" (ca. 1688), which was discussed above in [section] III.2. Recall that Leibniz asserts that substances can be understood to have different accidents at different times, although
 [w]hether some reality perishes and arises with change, however; or
 whether there are different realities within a substance ... it is
 not easy to determine. But it is enough to take substances as
 things and to tell truths about them. (116)

Appealing as I have in this section to broadly conceptual facts, to be consistent we ought to include in our account of monadic simplicity these intensional markers, specified by Leibniz. Reformulating MS from above to indicate necessity of the robust stripe, we can call the following Monadic Simplicity for Necessary Truths (MSN).

MSN: If an intrinsic essential predication of the form "Substance s is F" is true, then (1) s's F-ness exists and is identical with substance s, and (2) this identity is, at the conceptual level, finitely provable.

For necessity that is less straightforward--for Leibniz, indeed, it is contingent--we can formulate a statement of Monadic Simplicity for Contingent Truths (MSC).

MSC: If an intrinsic accidental predication of the form "Substance s is F" is true, then (1) s's F-ness exists and is identical with substance s, and (2) this identity is, at the conceptual level, provable only in an infinite number of steps.

Consider that in the very substance itself we have been given the full story via the complete concept doctrine--for any nourelational, noninitial state of a thing--for why this thing is the way that it is. This would seem to suggest that the substance just is the truthmaker for any claim to be made about the substance--necessary or contingent. In order to get a handle on contingent predication, however, appeal to the conceptual sphere is required, as I have shown. If an analysis of the subject and predicate reveals an identity in a finite proof, the proposition is necessary. If not, and the proof unfolds infinitely, then we have a case of intrinsic contingent predication. Either way, the substance serves as the truthmaker for any predication about it.

IV.3. Provided the story as I have related it is true, it seems that Leibniz's considered theory of accidents ought to align itself with AA as detailed above in [section] III.2. That is, accidents are merely the ways a substance is at a time, nothing ontologically additional to the substance itself. (117) Substances then are independent of other created entities. After all, if the substance itself is the truthmaker for all predications, one need not infer ontological additions to reality. I should mention that there are those who would deny the picture as I have presented it--at least as regards Leibniz's theory of accidents, and hence, his account of contingent predication. For instance, there are certain scholars, such as Jan Cover and John O'Leary-Hawthorne, who maintain the following picture of the substance-accident relation:

"The whole entity, we suggest, is what one gets when one strips away the accidental accouterments of the individual--trappings understood by all to be other than genuinely internal to the ultimate subject of predication underlying the accidents." (118)

In such a case, the accidents--not being internal to a substance--would be the truthmakers for contingent claims.

There is a sense in which I understand the intuitive pull toward interpreting Leibniz in this way. It is, after all, consonant with the distinction he draws between substances and accidents. On the contrary, however, I cannot understand how, on such a picture, Leibniz is able to maintain the independence of a substance. That is, granting the simplicity of the substance on the one hand and the inherence of an individual accident on the other hand, there appears to be a relevant sense in which the substance is dependent upon some other created entity.

It may be further argued against the position I attribute to Leibniz that it is no version of substance-accident realism. After all, according to my interpretation accidents are nothing ontologically additional to substances. Against this objection, however, I should note that metaphysical realism comes in many different flavors. According to the view that I endorse on Leibniz's behalf, there genuinely are accidents in the same way that there are smiles or sunburns. Jan's smiling or Jan's having a sunburn is, again, nothing over and above Jan's being a certain way. Similarly, for Leibniz, it just turns out that accidents are nothing over and above the substances in which they inhere. (119)

University of South Alabama

Correspondence to: T. Allan Hillman, Department of Philosophy, HUMB 124, University of South Alabama, Mobile, AL 36688.

(1) The following standard abbreviations are used in citations from Leibniz (cited by page, unless otherwise noted): A = Samtliche Schriften und Briefe (Darmstadt and Berlin: Berlin Academy, 1923); cited by series, volume and page. AG = G. W. Leibniz: Philosophical Essays, ed. and trans. R. Ariew and D. Garber (Indianapolis: Hackett Publishing Company, 1989). C = Opuscules et fragments inedits de Leibniz, ed. Louis Couturat (Paris: Felix Alcan, 1903; reprinted Hildesheim: Georg Olms, 1966). DSR = De Summa Return: Metaphysical Papers, 1675-1676, ed. and trans. G. H. R. Parkinson (New Haven: Yale University Press, 1992). G = Die philosophischen Schriften von Gottfried Wilhelm Leibniz, ed. C. I. Gerhardt (Berlin: Weidman, 1875-90; Reprinted Hildesheim: Georg Olms, 1965); cited by volume and page. GM = Leibnizens Mathematische Schriften, ed. C. I. Gerhardt (Halle, 1849-63; Reprinted Hildesheim: Georg Olms, 1971); cited by volume and page. Grua = Textes inedits, ed. Gaston Grua (Paris: Presses Universitaires de France, 1948). H = Theodicy, ed. Austin Farrer and trans. E.M. Huggard (La Salle, Illinois: Open Court, 1985). L = Gottfried Wilhelm Leibniz: Philosophical Papers & Letters, ed. and trans. L. E. Loemker, 2nd ed. (Dordrecht: Reidel, 1969). LA = The Leibniz-Arnauld Correspondence, ed. and trans. H. T. Mason (Manchester University Press, 1967). LR = The Leibniz-Des Bosses Correspondence, ed. and trans. Brandon Look and Donald Rutherford (New Haven: Yale University Press, 2007). LS = Leibniz: The Shorter Leibniz Texts, ed. and trans. Lloyd Stricldand (New York: Continuum, 2006). NE = Nouveaux essays sur l'entendement humain, cited by book, chapter, and section as in A 6.4; translated in RB. PM = Leibniz: Philosophical Writings, ed. G. H. R. Parkinson, trans. M. Morris and G. H. R. Parkinson (Totowa: Rowman & Littlefield, 1975). RA = The Labyrinth of the Continuum, ed. and trans. Richard Arthur (Yale University Press, 2001). RB = New Essays on Human Understanding, ed. and trans. Peter Remnant and Jonathan Bennett (Cambridge University Press, 1996). Schmidt = Fragmente zur Logik, ed. and trans. Franz Schmidt (Berlin: Akademie Verlag, 1960). SS = Leibniz: Monadology and Other Philosophical Essays, eds. and trans. Paul Schrecker and Anne Schrecker (Indianapolis: Bobbs-Merrill Publishing, 1965). T = Essais De Theodicee, cited by section number as in G 6.21-471, translated in H.

(2) Some allege that Leibniz never articulated a fully developed theory of substance. For example, see Paul Bartha, "Substantial Form and the Nature of Individual Substances," Studia Leibnitiana 25.1 (1993): 43-54. I agree, however, with Donald Rutherford, who argues that "during different parts of his career Leibniz takes different features of substance as starting points for his deliberations, and that consequently different members [of the list of the primary features of substance] at times receive greater prominence than others." See his Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995), 134.

(3) See for example G 4.439-40: L 312; G 2.495-6: L 611; and G 2.97: LA 121.

(4) See for example G 4.509: L 502; G 4.168-9: L 516; and A 6.3.326.

(5) See for example G 4.517-18: L 493; G 2.251-2: L 530; G 2.264-5: L, 535; and A 6.3.326.

(6) See for example, G 4.43233: L 307. Donald Rutherford adds to the list of requirements on a Leibnizian substance the following: "For any substance, there is a principle of individuation sufficient to distinguish it from every other actual or possible substance." Leibniz and the Rational Order, 134. As regards Leibniz's principle of individuation, I agree with Jan Cover and John O'Leary-Hawthorne that such a principle is (a) internal to the substance and (b) amounts to the whole substance itself. See their Substance & Individuation in Leibniz (New York: Cambridge University Press, 1999).

(7) I should note that it is a particular sense of simplicity that makes it "exclusive" to Leibniz's metaphysics of substance. That is, Aristotelians and certain scholastics would certainly agree that substances are per se unities, and hence, not aggregative. However, Leibniz's sense of simplicity denies complexity full-stop, as shall be made clear below, and it is in this sense that the simplicity criterion is unique to him.

(8) G 2.96: AG 85, original italics. See also G 2.252: AG 177; NE 2.12.6: RB 146; G 2.76: LA 94; and G 2.118: LA 151.

(9) I take the nomenclature of "component ontology" from Jan Cover and John O'Leary Hawthorne. See their Substance & Individuation, 40-55. For their denial of a reading of Leibniz according to which the latter's metaphysics exhibits a type of component ontology, see Chapter 6 in particular.

(10) God is dependent upon no other being at all, full-stop. Hence, God's aseity--and mutatis mutandis his simplicity--demands that God have no accidents on which his substance might be thought to depend. For more on this, see Jeffrey Brower, "Simplicity and Aseity," in The Oxford Handbook of Philosophical Theology, eds. Michael Rea and Thomas Flint (Oxford: Oxford University Press, 2009), chap. 5. As may be obvious at this point, Leibnizian independence is qualified, such that no substance is dependent upon another created thing.

(11) G 4.615: AG 219, original italics.

(12) G 4.438: AG 42. See also G 6.602: AG 210; G 2.125: LA 159-60; G 6.616: AG 220; GM 7.239: LS 38; A 1.15.560: LS 39; and Grua 425. For more on Leibniz's very strong imago dei doctrine, see my "Leibniz on the Imago Dei" in Oxford Studies in Early Modern Philosophy, vol. 5, eds. Daniel Garber and Steven Nadler (Oxford University Press, forthcoming).

(13) There is a relevant sense in which I am here identifying causal powers with the aforementioned capacities. I take it that capacities and causal powers alike manifest themselves such that they may be had by a thing even though they are not exercised. So my having the causal power (capacity) to [PHI] does not entail that I [PHI], but only that I have the ability to [PHI] if the relevant circumstances obtain. Rather than causal power per se, it is a substance's spontaneity that renders the capacity an actuality. For more on spontaneity, see Donald Rutherford, "Leibniz on Spontaneity," in Leibniz: Nature & Freedom, eds. Jan Cover and Donald Rutheford (Oxford: Oxford University Press, 2007), 156-80. For the most part I shall prefer the term "causal powers" to either "capacities," "perfections" or "(divine) attributes." Though in [section]IV.2 we shall have reason to use the terms interchangeably.

(14) G 2.252: AG 177.

(15) Before proceeding, one further consideration ought to be addressed: aside from causal powers, Leibniz also attributes to an individual substance such purported elements as a nature, a haecceity, and what he often refers to as the law-of-the-series. I take it as well-established, following the recent scholarship of Jan Cover and John O'Leary-Hawthorue (Substance & Individuation, chap. 6), that the nature of any individual substance is identical with its haecceity--that is, the ontological correlate of the complete concept--which is in turn identical with its law-of-the-series--that is, the inherent law of progression that determines the states of the substance and the order in which such states are produced. As Cover and O'Leary-Hawthorne persuasively argue, the nature, haecceity, and law-of-the-series are not to be understood as distinct components of a substance, but just as the substance itself.

(16) The Philosophical Writings of Descartes, vol. 2, eds. and trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch (Cambridge: Cambridge University Press, 1984), 298.

(17) Ibid.

(18) For example, see Francisco Suarez, On the Formal Cause of Substance: Metaphysical Disputation 15, trans. John Kronen (Marquette University Press, 2000), disp. 15, sec. 11, a. 3-4, pp. 178-80. (All cited passages from the work of Suarez will indicate disputation, section, article, and page number from the relevant translated text). This is not to say that matter plays no role whatsoever; it does distinguish material from immaterial objects.

(19) For instance, here is Francisco Suarez: "For in human beings there are perhaps more accidental faculties and forms, and more perfect ones, than in other natural things, and yet these do not suffice for the constitution of any complete natural being. In addition to these accidental forms there is required a form to nile, as it were, over all those faculties and accidents and to be the source of all actions and natural changes of the human being and the subject in which the whole variety of powers and accidents is rooted and unified in a certain way." Formal Cause, 15.1.7, p. 21. For further discussion of this aspect of substantial form, see Eleonore Stump, Aquinas (New York: Routledge, 2003), chap. 6.

(20) Summa Contra Gentiles, trans. English Dominican Fathers (New York: Benziger Brothers, 1924), bk. 4, chap. 14. Consider also his Summa Theologiae: "Wherefore, since power ... is of two kinds, namely, power in reference to being, and power in reference to act; the perfection of each of these is called virtue. But power in reference to being is on the part of matter, which is potential being, whereas power in reference to act, is on the part of the form, which is the principle of action, since everything acts in so far as it is in act." Second and Revised Edition, trans. Fathers of the English Dominican Province (Online Edition:, I-II, q. 55, a. 2, my italics. (Hereafter cited as ST followed by part, question, and article.)

(21) From St. Thomas Aquinas, St. Thomae Aquinatis Doctoris Angelici Opera Omnia, vol. 43 (Rome: Commisio Leonina, 1882), 4.127-30 (my italics), trans, and cited by Robert Pasnau in his "Form, Substance, and Mechanism," Philosophical Review 113.1 (2004): 37.

(22) Suarez, Formal Cause, 15.11.4, p. 179.

(23) Francisco Suarez, On Efficient Causality: Metaphysical Disputations 17, 18 and 19, ed. and trans. Alfred Freddoso (New Haven: Yale University Press 1994), 18.2.3, p. 53. See also 18.5.1, p. 121; also see note 19 above.

(24) Robert Pasnau, "Form, Substance and Mechanism," 35.

(25) For instance, see Eleonore Stump and Norman Kretzmann, "Being and Goodness," in Being and Goodness, ed. Scott MacDonald (Ithaca: Cornell University Press, 1991): 98-128. While they do not explicitly refer to form as a collection of powers, they do refer to it as a "set of characteristics" and liken it to the view of contemporary philosopher Sidney Shoemaker's causal powers view of properties at p. 102, n. 17.

(26) Scott MacDonald, "Egoistic Rationalism: Aquinas's Basis for Christian Morality," in Christian Theism and the Problems of Philosophy, ed. Michael Beaty (University of Notre Dame Press, 1990), 329-30 (footnotes omitted).

(27) Thanks to Jeffrey Brower for his help in fashioning the example.

(28) There is ample support for reading the scholastics as proponents of the grounding view. Keeping in mind that for Aquinas the soul is the substantial form of the human body, consider this observation from his Summa Theologiae: "For the soul by its very essence is an act.... So the soul itself, as a subject of its power, is called the first act, with a further relation to the second act" (I, q. 77, a. 1, my italics). See also STI, q. 5, a. 1; I, q. 76, a. 1; I, q. 77, a. 1; and I-II, q. 3, a. 2, all cited by MacDonald ("Egoistic Rationalism," 329). Suarez agrees: "For, just as from the same cause many effects can arise, so also from the same form many powers can arise.... For at times many powers are found together in the same thing, not only according to the same physical form, but even according to the same specific difference, as in the human being intellect, will, and risibility arise from rationality. But at times these powers arise from the same form according to various grades of it, which are often distinguished by us by their order to powers or actions, even though in reality the grades themselves are not distinct in substantial forms." Formal Cause, 15.10.6, 129-30, my italics.

(29) For Leibniz's denial of occasionalism, see G 2.45-8: LA 33-5; G 4.47981: L 457-8; and G 4.504-16: L 499-508.

(30) G 2.76: LA 94. See also G 4.478-81: L 454-56. For a contemporary discussion of composition and the relations whereby two objects might be said to compose some further object, see Peter van Inwagen's excellent discussion in his "When Are Objects Parts?" in Philosophical Perspectives (1): 1987, 21-47.

(31) For example, see Discourse on Metaphysics (especially [section][section] 9-11) G 4.433-5: AG 41-3.

(32) At least Aquinas, perhaps in the minority, thought there was only one substantial form per individual substance. Duns Scotus and Ockham, on the other hand, thought multiple substantial forms could be found in a single substance, even though the latter still thought the forms jointly determined the kind to which the substance belongs.

(33) STI, q. 50, a. 4. For commentary, see Stump, Aquinas, 44.

(34) G 2.131-2: LA 73-4, footnote omitted. See also G 4.433-4: AG 41.

(35) G 4.510-11: AG 162, original italics.

(36) A 4.1621(L2): RA 311 nL2, original italics. Two further likenesses between Leibniz's monads and Thomistic angels: (1) in both, substantial form serves as the individuator of the entity. For further discussion of individuation in Aquinas and Leibniz, see Cover and O'Leary-Hawthorne, Substance & Individuation, 196-7, 250. (2) Just as Leibniz pronounces the indestructibility of monads (for example, C 523: AG 34 and G 4.443: AG 42), so too does Aquinas infer the incorruptibility of angels due to their being entirely constituted by form (sans matter). For the latter's discussion, see ST I, q. 50, a. 5.

(37) G 4.507: AG 158-9, my italics.

(38) Leibnizian substances, after all, depend upon nothing other than God. To be dependent upon God, I take it, would be a nonobjectionable sort of dependence; since the sort of independence that Leibniz has in mind is one according to which created substances depend upon no other created thing. Really distinct accidents, on the other hand, may be thought to threaten even the latter sort of independence, since substances would depend upon accidents (at least) for exemplification. In his critical discussion of Descartes' Principles Leibniz remarks: "since substance and accident depend upon each other, other marks are necessary for distinguishing a substance from an accident. Among them may be this one: That a substance needs some accident but does not need a determinate one but is content, when this accident is removed, with the substitution of another. An accident, however, needs not only some substance in general but that very one in which it inheres, so that it cannot change it" (G 4.392: L 389-90). See also note 40 below.

(39) For the most part, I use these terms interchangeably (as does Leibniz).

(40) From New Essays: "If you distinguish two things in a substance the attributes or predicates, and their common subject--it is no wonder that you cannot conceive anything special in this subject. That is inevitable, because you have already set aside all the attributes through which details could be conceived. Thus, to require of this 'pure subject in general' anything beyond what is needed for the conception of 'the same thing' ... is to demand the impossible" (NE 2.23.2: RB 218).

(41) G 6.615: AG 219, original italics.

(42) In [section] 16 of De Ipsa Natura, Leibniz asserts of his opponent Johann Christian Sturm that the latter "has admitted to me that a certain particle of divine power can, and indeed must, be understood in a sense as belonging to and attributed to things. (In my opinion such a particle must be an expression, an imitation, a proximate effect of the divine power, for this power itself cannot be cut up into parts in any case.)" (G 4.507: L 507, original italics)

(43) For instance, Aquinas has a tendency--at times--to speak of intellect and will as though they are accidents. Indeed, they are propria, and, and in this sense at least, accidental. See, for example, ST I, q. 77, a. 5-6. Such accidents as intellect and will, one might suppose, could only be separated from the rational substance in which they inhere by the power of God. Even still, supposing that God were to separate the intellect from some human being, then at the very least that human being remains apt to the having of that accident. This aptness for possessing intellect, we might say, is essential to the very existence of a human being in a way that having an actual intellect is not. For more on intellect and will in Aquinas' philosophy, see Thomas Pasnau, Thomas Aquinas on Human Nature (Cambridge: Cambridge University Press, 2002), 151-160.

(44) On my reading, Leibniz does not recognize such a distinction--at least, no distinction according to which matter turns out to be real. Inasmuch as it is divisible to infinity, matter is always merely phenomenal according to Leibnlz. See, for example, G 2.76-8: LA 93-6; G 2.90-102: LA 113-29; G 4.47882: AG 139-42. Such a reading of Leibniz--as endorsing a metaphysic of simple, immaterial substances from his mature period forward--may appear to some as naive. Admittedly, I leave to one side Leibniz's flirtation with corporeal substance. My reading of Leibniz's references to corporeal substance is of a piece with what Robert Adams calls "a qualified one substance" account wherein corporeal substances are not bona fide composites (though I acknowledge that some of Leibniz's texts do not fare well on such a reading). See Adams's Leibniz: Determinist, Theist, Idealist (New York: Oxford University Press, 1994), 265-9, 292-4. Much of Adams's discussion serves as a response to Daniel Garber, who offers a reading of Leibniz's middle years according to which corporeal substances are somehow basic. See his "Leibniz and the Foundations of Physics: The Middle Years" in The Natural Philosophy ofLeibniz, eds. Kathleen Okruhlik and James Brown (Dordrecht: Reidel Publishing, 1978), 27-130. For his reply to Adams's criticisms, see Garber's book review of Adams's work in Leibniz Review 6 (December 1996): 89-106. More recently, Garber has weakened his position. See his "Leibniz and Fardella: Body, Substance, and Idealism" in Leibniz and his Correspondents, ed. Paul Lodge (Cambridge University Press, 2004): 123-40; as well, see his "Leibniz and Idealism" in Leibniz: Nature & Freedom, eds. Cover and Rutherford, 95-107. For further rumination on this debate, see Paul Lodge, "Garber's Interpretations of Leibniz on Corporeal Substance in the 'Middle Years,'" Leibniz Review 15 (2005): 1-26.

(45) I take the scholastic act-potency distinction to come as a package with the form-matter and essence-existence distinctions. At bottom, Leibniz denies the real existence of matter, and hence cannot accept that there is any part of a substance that is in potency. Neither does he believe that essences and existences are separable. See the preceding note.

(46) Though one might consider William of Champeaux's reflection on the possibility of accidents serving as the individuators for substances to be closely akin to understanding them as parts. For a discussion of Champeaux and Peter Abelard's criticisms, see Peter King's "Metaphysics" in A Cambridge Companion to Peter Abelard, eds. J. Brower and K. Guilfoy (Cambridge: Cambridge University Press, 2004), 65-125.

(47) As Leibniz says to Bayle, God creates an individual substance rather than "a [mere] universal of logic" (T, [section] 390: H, 358)

(48) Categories, 2.1 a24-25 in The Complete Works of Aristotle, vol. 1, trans. J. L. Akrill, ed. Jonathan Barnes (Princeton University Press, 1995), 3.

(49) Granted, for Aristotle, this is limited to certain cases, as in other circumstances he recognizes the parthood relation as playing a central role in the substance-accident dichotomy. Still, the question may be asked, "Is the in-esse relation really nonmereological?" After all, by itself the "in a subject" relation is open to a mereological understanding. That is, an accident's "being in a subject not as a part" does not rule out the possibility that the substance

and its accidents are related as distinct parts of a further whole. This sort of whole-building apparatus is prima facie unproblematic, though Leibniz does often deny that there are any genuinely aggregative beings at all. See the distinction below that follows.

(50) Schmidt 481. Translated and cited by Robert C. Sleigh in his Leibniz & Arnauld: A Commentary on Their Correspondence (New Haven: Yale University Press, 1990), 124. See also G, 2.270: L 537 and G 4.436: AG 44.

(51) [section] 393: H, 359-60. See also G 4.363-5: L 389-90 and T [section] 32: H 142.

(52) For more on this, see my "The Early Russell on the Metaphysics of Leibniz & Bradley," Synthese 163.2 (2008): 245-61. Also see Cover and O'Leary-Hawthorne, Substance & Individuation, especially chap. 7.

(53) In general, I take Leibniz's nominalism to amount to the claim that, strictly speaking, there are no universals, that is, entities that can be instantiated in multiple locations at the same temporal moment. For more on this, see Benson Mates, The Philosophy of Leibniz: Metaphysics & Language (New York: Oxford University Press, 1986), chaps. 10 and 14.

(54) These accidental particulars are still understood to be dependent upon the substances in which they inhere and to have a nonmereological relation to their substantial subject.

(55) 4.147: L 126.

(56) Francisco Suarez, On the Various Kinds of Distinctions, trans. Cyril Vollert (Milwaukee: Marquette University Press, 1947), book 7, chap. 1, sec. 18, pp. 29-30. I do not mean to imply that this amounts to Suarez's complete view of accidents, but only that, such a construal of accidents was not original to Leibniz.

(57) TA 6.4.996, my italics. Trans. Stefano Di Bella, The Science of the Individual: Leibniz's Ontology of Individual Substance, (Dordrecht: Springer Publishing, 2005), 259. For commentary on Leibniz's "On the Reality of Accidents," see Massimo Mugnai, "Leibniz on Substance and Changing Properties," Dialectica 59. 4: 503-16. For my commentary, see [section] IV below.

(58) 2.457-8: L 606.

(59) G 2.458: LR 269.

(60) For a discussion of how separability is implied by distinctness in Descartes, see Paul Hoffman, "Descartes's Theory of Distinction," Philosophy & Phenomenological Research 64.1 (2002): 57-78. Leibniz's treatment of distinctness is, to my mind, relevantly similar.

(61) There is some precedent for the view according to which accidents are particulars, distinct from the simple substance in which they inhere. Descartes endorsed such a theory, maintaining that substantial minds are entirely simple, even though such minds possess ideas that are things distinct from the substance itself. On the simplicity of mental substance, he says in the Sixth Meditation: "the mind is utterly indivisible ... when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any parts within myself ... As for the faculties of willing, of understanding, of sensory perception and so on, these cannot be termed parts of the mind, since it is one and the same mind that wills, and understands and has sensory perceptions." The Philosophical Writings of Descartes, vol. 2, p. 59. On the individuality of certain modes of substance, see his Principles of Philosophy, found in The Philosophical Writings of Descartes, vol. 1, eds. and trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch (Cambridge: Cambridge University Press, 1984), 213-4.

(62) See D. C. Williams, "The Elements of Being," Review of Metaphysics 7 (1953): 3-18; and Keith Campbell, Abstract Particulars (Oxford: Blackwell, 1990). For further commentary on trope theory, see David Armstrong, Universals: An Opinionated Introduction (Boulder: Westview Press, 1989), 16-18.

(63) For a description, see Leibniz's De Cogitationum Analysi (1679) at A 6.4.2767-74. See also T [section] 32: H 142.

(64) A 6.4.991. Trans. Massimo Mugnai, "Substance and Changing Properties," 512. See also A, 6.4.997-1000. There is, of course, historical precedent for this kind of property-instance view of accidents. St. Thomas, for instance, maintained of the quality whiteness that "this whiteness ... is singular and particular and individual" (Quodlibetal Questions 9, q. 2, a. 2). The latter quotation is translated by Brian Leftow in his "Aquinas on Attributes," Medieval Philosophy & Theology 11 (2003): 2-3. For an excellent commentary on Aquinas's "trope" theory of accidents, see the whole work 1-41. Stefano Di Bella interprets Leibniz as holding something like a trope theory of accidents. See his The Science of the Individual, 23-33.

(65) G 2.136: LA 170, my italics. See also G 2.57-58: LA 64-5 and G 4.439- 40: L 312.

(66) G 6.605-6: AG 214. See also G 7.398-9: AG 337.

(67) G 4.499: L 460. See also G 6.607: AG 213 and G 7.398-9: AG 337. For commentary on Leibniz's criticisms of this model, see Eileen O'Neill, "Influxus Physicus," in Causation in Early Modern Philosophy, ed. Steven Nadler (University Park, Pennsylvania: Penn State University Press, 1993), 27-56.

(68) 4.364: L 390. See also G 2.516-17: AG 203.

(69) The manner in which I tie together the inherence and causation idioms in what follows is very similar to the way in which Jorge Secada explains the same notions at work in the metaphysics of Descartes. See his Cartesian Metaphysics (Cambridge University Press, 2000), 194-204, 298, n. 50.

(70) For example, see G, 4.521-2: L, 495-6: "the present [accidental] state of each substance is a natural result of its preceding state." See also G 2.124-6: 159-61; G 2.135-6: LA 170 and T [section] [section] 290-1: H 303-4.

(71) A 6.4.990. Translated by Stefano Di Bella, Science of the Individual, 255.

(72) I say "noninitial states" are caused by a finite substance since, presumably, at creation God outfits a substance with its original accidents. At this first moment, then, the finite substance is not the cause of its initial accidents. See also note 75 below.

(73) To Gerhard Molanus (2/12 October 1698) Leibniz explains that, "a substance consists in productive power, [and] its existence in general will certainly consist in the immediate application of power to work" (Grua 425, my italics)

(74) T [section] 395: H 360.

(75) I say "nonrelational" because I take it that, just as relations are not real in the Leibnizian universe, so too the complete concept does not explicitly contain relational predicates; instead, any relation can be said to exist only in the sense that it supervenes on monadic states, and as a result, all relational predicates are reducible to one-place predicates. I say "noninitial" because God's creation of bona fide individuals indicates that substances are not created bare---that is, without their accidental clothing. For more on Leibniz's metaphysic of relations, see Cover and O'Leary-Hawthorne, Substance & Individuation, chap. 2.

(76) Again, this is so for all noninitial accidents.

(77) Strictly speaking, transeunt causation is a variety of causation wherein that which is causally produced is external to the agent. Immanent causation is such that the effect causally produced is internal to the agent. Both are species of one primitive dependence relation: efficient causation. It just turns out that efficient causation has two aspects: one according to which the very existence of some thing is granted, and the other according to which there is some change in an already-existing thing. For instance, one might think that no efficient cause could (immanently) bring about the existence of itself, though it could (transeuntly) bring about the existence of another thing (for example, as when God transeuntly produces individuals via creation). Yet efficient causation as a sort of change is such that it may be either transeunt (for example, God's concurring with the activity of creatures) or immanent (for example, monadic changes in perceptual states). I attempt to give a reading of Leibniz that fits with this dichotomy.

(78) This is not to say unequivocally that God cannot produce accidents in creatures. Instead, I simply mean to nile out the possibility of a creature's transeuntly bringing about some effect. That is, there is no creaturely transeunt causation at all.

(79) A 3.6.451, my italics. Translated by Lloyd Strickland on his website entitled Leibniz Translations (2003-08) at http://www.leibniz-translations .com/hospital1.htm. Also, "Each substance is the true and real cause of its immanent actions, and has a force of acting ... [and] it is impossible for it to behave merely passively" (A 4.1621(L2): RA 313 nL2, original italics). See as well T [section] 395: H 360.

(80) For further commentary, see Sleigh, Leibniz & Arnauld, 134.

(81) T [section] 393: H 359.

(82) See Francisco Suarez, who endorses the view according to which finite substances are causally distinct though not separable from their accidents or modes. He says, "it is not part of the notion of an efficient cause as such that the principles of acting and being acted upon should be really distinct in either their subject or their whole being." On Efficient Causality: Metaphysical Disputations 17, 18 and 19, ed. and trans. Alfred Freddoso (New Haven: Yale University Press, 1994), disputation 18, chap. 7, sec. 54, p. 173. Also, discussing the relation of mode-to-substance in the philosophy of Descartes, Anthony Kenny explains: "the way in which modes depend on substance is not the same as that in which finite substances depend upon the infinite substance. Modes are logically dependent on substance; they 'inhere in it as a subject'.... Created substances are not logically, but causally, dependent upon God. They do not inhere in God as subject, but are effects of God as creator." Descartes: A Study of His Philosophy (New York: Random House, 1968), 134.

(83) A word of caution here. There are two kinds of miracles, according to Leibniz. Those of "the First Rank," such as creation and Incarnation (see T [section] 249: H, 280), and those of an "inferior" sort (G 7.377). Regarding the first kind, God may be said truly to perform them alone. The latter, however, are in some sense a cooperative endeavor (say I). In perhaps his most lucid discussion of divine concurrence, Leibniz can be seen to leave room for concurrence even in miraculous cases; that is, he distinguishes properly between God's ordinary concurrence and God's extraordinary concurrence: in [section] 11 of Causa Dei Leibniz says, "God's concurrence (even the ordinary, nonmiraculous, concurrence) is at the same time immediate and special" (G, 6.440: SS, 115). For an account of how Leibniz's metaphysics can accommodate such a distinction, consult Robert Adams, "Predication, Truth and Transworld Identity in Leibniz" in How Things Are, eds. James Bogan and James McGuire (D. Reidel Publishing: 1985), 223-83 and Sleigh, Leibniz & Arnauld, especially 134. However, see also the following note.

(84) For a denial of my reading see Mark Kulstad, "Two Interpretations of Pre-Established Harmony in the Philosophy of Leibniz," Synthese 96.3 (1993): 477-504. According to Kulstad there is no one-one correspondence between the nature of a substance and its complete concept. For a reading of Leibniz which more closely approximates my own, see Robert Adams, "Predication, Truth, and Transworld Identity," 223-84. Marc Bobro and Kenneth Clatterbaugh, in their "Unpacking the Monad: Leibniz's Theory of Causality," Monist 79.3 (1996): 408-25 also criticize the sort of view that I advocate, inasmuch as they believe that all miraculous states are brought about by God alone. Against this sort of view, however, I agree with Sleigh that substances persist (and must persist) via their own causal activity, and as a result, numerically the same substance could not survive a miraculous state that was not at least partially a causal product of its own nature. For a reading of Leibnizian states according to which this is an unproblematic view for Leibniz, see especially Sleigh, Leibniz & Arnauld, 134.

(85) Commenting on Leibniz's theory of accidents in the later works, Massimo Mugnai too finds perplexing such diverging views, often found side-by-side. He concludes, "It seems very difficult to determine how this claim [of a real distinction between accident and substance] fits with his general doctrine of the substance and of its [non-distinct] modification." "Substance and Changing Properties," 516.

(86) Leibniz's account of truth and predication is, admittedly, much more complex than I here make it out to be. Truth and falsity are generally taken to depend on the intensions or concepts of the terms involved in some proposition, such that it makes sense to say that the predicate term or concept is contained in the subject term or concept. So, given the logical structure of the propositions or concepts, truth or falsity can be ascertained. For instance, in correspondence with Arnauld Leibniz says: "[S]ince there must always be some basis for the connection between the terms of a proposition, and it is to be found in their concepts" (G 2.56: LA 63-4, original italics). For a precise account of Leibniz's theories of truth and predication, see Adams, "Predication, Truth and Transworld Identity," especially 241-58; and all of Robert C. Sleigh, "Truth and Sufficient Reason in the Philosophy of Leibniz," in Leibniz: Critical and Interpretive Essays, ed. Michael Hooker (Minneapolis: University of Minnesota Press, 1982), 209-42. See also note 88 below.

(87) G 4.432-3: AG 40-1, my italics.

(88) On my view, we have from Leibniz a genuine correlation established between the formal and material mode, such that in the formal mode a predicate is related to the complete concept in the same way that in the material mode an accident is related to a substance, and that enough of a metaphysical story can be gleaned from the latter to give an honest assessment of his account of metaphysical predication. My intention in what follows is not to provide a Leibnizian basis for truth or predication, but is instead (a) meant as an earnest reckoning of Leibniz's statement in the Discourse that true predication is founded in the nature of things, and (b) meant to show that an account of the metaphysical structure of a monad may fall out of our analysis.

(89) For more on the bundle theory of substance and its relation to Bertrand Russell and Leibniz, see my "The Early Russell on the Metaphysics of Leibniz & Bradley," 245-61. For further discussion of this topic, see also Cover and O'Leary-Hawthorne, Substance & Individuation, 171-5. Some may think it pertinent to cash out the instantiation of the complete concept in the following way: the conjunction of predicates in a complete concept also includes a subject to which all of the predicates can be applied. To my mind, such a position would be preferable to a whole-hearted bundle view, even though it fails to capture--to my reckoning--Leibniz's considered views on haecceitas.

(90) Substance & Individuation, 171.

(91) I take it as unproblematic for some complex concept to contain further less complex concepts as constituents or members. However, the relation of possession between a substance and its feature is less straightforward. See [section] III above.

(92) Truthmaking is often understood as a species of entailment. See John Fox, "Truthmaker," Australasian Journal of Philosophy 65.2 (1987): 188-207. For criticism of this position, see Gonzalo Rodriguez-Pereyra, "Truthmaking, Entailment, and the Conjunction Thesis," Mind 115, no. 460 (October 2006): 957-82. Elsewhere, Rodriguez-Pereyra alleges that truthmakers are instead to be understood as a primitive form of explanation. See his Resemblance Nominalism: A Solution to the Problem of Universals (Oxford: Oxford University Press, 2002), 34.

(93) Of course, one might insist that the "that in virtue of which" be spelled out in more detail for any purportedly complete theory of truthmaking. On the other hand Gonzalo Rodriguez-Pereyra maintains, and I agree, that it is a sui generis variety of explanation, and that perhaps the best we can do in making this more plain is simply to provide examples. See his Resemblance Nominalism, especially chaps. 1 and 2.

(94) According to many contemporary philosophers, every truth has a truthmaker (though I take it as controversial as to whether every truth has a unique truthmaker--see in particular John Fox, "Truthmaker," especially 189-90). But if every truth has a truthmaker, then the question arises: what about true predications about possibles? So far, I have concentrated only on actual objects, things or substances that have bona fide natures (that is, actualized, created substances). One might be able to tell a story according to which counterfactual truthmakers come to bear, such that if some entity existed, then it would suffice as the truthmaker for some predication. And, perhaps that is the appropriate story, though I think that for Leibniz it would be best to say that God's essence or nature serves as the truthmaker for predications about possibles. See Monadology [section] 44 (G 6.614: AG 218), where he declares that God serves as the ground for the eternal truths as well as all possibles.

(95) Jeffrey Brower, "Simplicity and Aseity," 111. Brower also rightly recommends that one should not take the notion of truthmaking as in itself a causal notion, but as instead an explanatory one. As he says, "[i]t would, perhaps, be better to speak of truth-explainers rather than truth-makers" (125, n. 16, original italics)

(96) Such predications are extrinsic. Extrinsic predications characterize entities in light of their relations to other distinct entities, while intrinsic predications are those understood as characterizing entities in light of how those very entities are themselves. See Jeff Brower, "Simplicity and Aseity," 124, n. 1; see also David Lewis, On the Plurality of Worlds (Oxford: Blackwell Publishers, 1986), 61.

(97) See David Armstrong, A World of States of Affairs (Cambridge University Press, 1997).

(98) See Kevin Mulligan, Peter Simons, and Barry Smith, "Truthmakers," Philosophy and Phenomenological Research 44 (1984): 287-321.

(99) Jeffrey Brower, "Simplicity and Aseity," 108.

(100) Ibid., 112.

(101) Ibid., 112 (footnote omitted).

(102) G 4.441: AG 49, my italics.

(103) Robert Adams, Leibniz: Determinist, Theist, Idealist, 143.

(104) A 6.4.569. Trans. and quoted in Rutherford, "Leibniz on Spontaneity," 161.

(105) Perhaps the best commentary on Leibniz's version of the ontological argument is to be found in Robert M. Adams, Leibniz, 135-56.

(106) A 6.3.572: DSR 93.

(107) It should be remarked here that the perfections or causal powers had by God are not identical with those had by creatures. God's powers, as it were, are always maxed out, whereas creaturely powers are had in a lesser degree due to a creature's "limitation." For example, see Discourse [section] 1 (G 4.425: AG 35) and the correspondence with Arnauld (G 2.125: LA 159-60).

(108) say "contingent" because it is unclear to what extent our contemporary notion of contingency is applicable to Leibniz. See the following paragraphs for further clarification.

(109) Broadly defined, truthmaker necessitarianism is the view according to which the very existence of a truthmaker is enough to necessitate that truth which it makes true. So, if there exists some entity e that makes true some proposition P, then at no possible world can e exist and P fail to be true. See D. M. Armstrong, A World of States of Affairs, especially chap. 8. Also see his Truth & Truthmakers (Cambridge University Press, 2004), 5-8.

(110) Leibniz's reducibility thesis amounts to something like the following: semantically, all polyadic or two-place predicates are ultimately reducible to monadic or one-place predicates. Ontologically, any relational fact about a thing is reducible to some property or accident intrinsic to the thing. So, the metaphysical ground for any relation that substance a has with substance b is internal to substance a. I should add that there is some scholarly controversy surrounding the ascription of such a reducibility thesis to Leibniz. Cover and O'Leary-Hawthorne (Substance & Individuation, chap. 2) agree that Leibniz explicitly affirmed a reducibility thesis, and they argue that Leibniz's strategy is ultimately successful. A view of Leibniz contrary to the above is provided by Dennis Plaisted, Leibniz on Purely Extrinsic Denominations (Rochester University Press, 2002) who denies that Leibniz ever maintained such a reducibility thesis.

(111) "Accidents of every individual substance, if predicated of it, make a continent proposition" (C 20: PM 100).

(112) Strictly speaking, one cannot get the denial of counterfactual or transworld identity merely from the complete concept theory by itself. More is required. See Adams, "Predication, Truth and Transworld Identity." For a detailed reading of Leibniz as advocating the world-boundedness of individuals (and hence, superessentialism), see Fabrizio Mondadori, "Leibniz and the Doctrine of Inter-World Identity," Studia Leibnitiana 7 (1975): 22-57. According to my reading of Leibniz, he was no superessentialist. See the next note.

(113) Leibnizian essentialism actually maintains only that a given individual substance could not have had a different complete concept than the one it has, leaving open the possibility of it existing in other worlds. Hence, the complete concept does not by itself commit Leibniz to world-bound individuals. If Leibniz is no reductionist about relational properties, then they too are contained in a substance's complete concept. If so, then Leibniz would appear to be committed to world-bound individuals. For a reading of Leibniz wherein such relational properties are not so contained, see Cover and O'Leary-Hawthorne, Substance & Individuation, chaps. 2 and 3. For a contrary reading, see Plaisted, Extrinsic Denominations.

(114) Grua 302: AG 28. See also L 264f.

(115) It should be stressed that truthmaker theory, all by itself, does not suffice to salvage contingent truths even about God. Contingent predications regarding the divine is a controversial topic. In his study, Jeff Brower argues that contingent truths about God--for example, "God creates d"--are only apparently intrinsic. In fact, he argues, such contingent truths are actually extrinsic. See Brower's "Simplicity and Aseity," especially 117-23; also see his "Making Sense of Divine Simplicity," Faith & Philosophy 25.1 (2008), especially 19-20. As I mentioned above, I do not think such an account is open to Leibniz, given his reducibility thesis concerning extrinsic truths.

(116) A 6.4.996, my italics. Trans. Stefano Di Bella, Science of the Individual, 259.

(117) Again, whether or not this view is ultimately reconcilable with view CA above--that is, accidents as individual particulars distinct from the substance--I leave for another time.

(118) Cover and O'Leary-Hawthorne, Substance & Individuation, 40.

(119) would like to express gratitude to Jan Cover, Michael Jacovides, and Jeffrey Brower for their comments and suggestions on previous drafts of this essay. The latter, especially, was most helpful in regard to his attention to my treatment of the Medievals. Any errors are, of course, my own.
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Title Annotation:Gottfried Wilhelm Leibniz
Author:Hillman, T. Allan
Publication:The Review of Metaphysics
Article Type:Report
Geographic Code:1USA
Date:Sep 1, 2009
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