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Leibniz on Form and Matter

Author(s): Daniel GarberSource: Early Science and Medicine, Vol. 2, No. 3, The Fate of Hylomorphism. "Matter" and"Form" in Early Modern Science (1997), pp. 326-352Published by: BRILL

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LEIBNIZ ON FORM AND MATTER

DANIEL GARBER

Department f Philosophy,The University f Chicago

It is widely believed that the Scientific Revolution of the seven-

teenth century definitively set aside the matter and form of the

Aristotelian schoolmen, and replaced it with a broadly geometri-cal conception of body. On this view, the new mechanical phi-

losophy, where the manifest qualities of bodies are explained interms of the size, shape, and motion of the small extended partsof bodies, was in fundamental opposition to the hylomorphic

explanations of the characteristicbehavior of bodies of different

kinds, grounded in their substantial forms. And so, for exam-

ple, the wetness of water or the heat of fire, basic and defini-

tive qualities of these substances for the Aristotelian, were explained by the seventeenth-century mechanists in terms of the shapeof water corpuscles that allowed them to slide by one another, or

the rapid motion of the particles of fire, which caused them to

penetrate the hand placed in the flame, thereby explaining the

sensations of wetness or heat.

But while the rhetoric of the age suggests a radical oppositionbetween the old and the new, between scholastic natural philos-

ophy and the new mechanist world view, the reality was consid-

erably more complex.' From the first introduction of the new

1 Typicalof the radical opposition between the Aristotelian philosophy of theschools and the new philosophy is a remark Descartes made in his letter to

Mersenne, 28 January 1641: "I tell you, between ourselves, that these six Medi-tations contain all the foundations of my physics. But one mustn't say so, if youplease, for that might make it more difficult for those who favor Aristotle to

approve them. I hope that readers will little by little accustom themselves to myprinciples, and recognize their truth, before they perceive that they destroy the

principles of Aristotle." (R. Descartes, Oeuvres, ev. ed. C. Adam and P. Tannery(Paris,1964-73), 3: 297-8.) See also the radical anti-Aristotelianismof Th. Hobbes

in Leviathan (London, 1651), esp. chapts. 46-47, and J. Glanvill, The VanityofDogmatizingLondon, 1661), chapts. 16-19.Behind the myth of the radical oppo-sition between the Aristotelian philosophy and the new mechanism of the

seventeenth century there is a second myth. The new mechanical philosophy is

? KoninklijkeBrill, Leiden, 1997 EarlyScience and Medicine 2,3

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LEIBNIZ ON FORM AND MATTER 327

mechanist philosophy early in the century, there were many whotried to show the two compatible in some way,and interpret the

new mechanist world in terms of the categories of matter and

form familiar to the schools. In this essay I would like to focus

on one such figure who is, perhaps, the most distinguished to

work in this genre, Gottfried Wilhelm Leibniz. I would like to

show how Leibniz saw his philosophy as an attempt to revive the

notions of matter and form, unjustly rejected by his mechanist

contemporaries, he thought, and show how they could find their

place within a thoroughgoing mechanistic philosophy. The story,

though, is rather complex. Leibniz lived a long time and philos-

ophized through much of his life. One can thus find a number

of different accounts of how the old philosophy of form and mat-ter can co-exist with the new mechanism. In what follows I shall

discuss a number of the more important accounts Leibniz givesof form and matter in his various writings.

Form and matter in 1669

In a letter of January 10, 1714, near the end of his life, Leib-

niz wrote the following bit of intellectual biography to Nicolas

Remond:

Besides always aking care to direct my study towardedification, I have tried

to uncover and unite the truth buried and scattered under the opinions ofall the different philosophical sects, and I believe I have added somethingof my own which takes a few steps forward.The circumstances under which

my studies proceeded from my earlier youth have given me some facilityin this. I discovered Aristotle as a lad, and even the Scholastics did not

repel me; even now I do not regret this. [...] After having finished the triv-ial schools, I fell upon the moderns, and I recall walking in a grove on the

outskirts of Leipzig called the Rosental, at the age of fifteen [i.e. 1661 or

1662] and deliberating whether to preserve substantial forms or not. Mech-anism finally prevailed and led me to apply myself to mathematics. [...] Butwhen I looked for the ultimate reasons for mechanism, and even for thelaws of motion, I was greatly surprised to see that they could not be foundin mathematics but that I should have to return to metaphysics. This led

often presented as the main opponent of the Aristotelian philosophy in the sev-

enteenthcentury.

Inreality,

mechanism wasonly

one ofmany

"new"philoso-phies. Aristotelian natural philosophy had a varietyof opponents, at least in the

first part of the century, including natural philosophies deriving from alchemi-

cal, astrological, magical, Platonistic, and Renaissance naturalisticsources. While

mechanism emerged as the principal opponent to Aristotelianism by the end of

the century, earlier in the century it wasby no means obvious that it would attain

the prominence that it came to have.





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328 DANIEL GARBER

me backto entelechies,and from the material o the formal,and at lastbrought me to understand, after many corrections and forwardsteps in mythinking, that monads or simple substances are the only true substancesand that material things are only phenomena, though well founded andwell connected.2

It is relatively straightforward to assign approximate dates to the

various parts of Leibniz's story. His early and radical mechanism

corresponds to his writings of the mid-1660s and 1670s. In works

like the Hypothesis Physica Nova (1671) and the Theoria Motus

Abstracti 1671), Leibniz presented a physics, inspired largely byHobbes, in which the explanation of phenomena in the physicalworld is grounded in geometrical bodies acting in accordance with

laws of motion. Leibniz begins to reflect on the grounds of theselaws of motion, "the ultimate reasons of mechanism", at the end

of the 1670s. The discovery of his celebrated law of the conser-

vation of vis viva (mv2) in January 1678 marks the beginning of

the second period that he notes in the above letter, the periodin which he turns back towardmetaphysics, "fromthe material to

the formal". There is much evidence of Leibniz's interest in

returning to the matter and form of Aristotle and the schoolmen

in the 1680s and 1690s, as we shall see, as part of an attempt to

ground the mechanist physics that he continues to hold onto.

According to his report to Remond, Leibniz embraced, towards

the end of his life, the philosophy of the monadology as his last

philosophical stance. There, too, we will see Leibniz's continuingcommitment to an Aristotelian conception of substance, ground-ed in the notions of matter and form.

In later sections we shall examine the status of matter and form

in his middle years and in the late philosophy of monads. But I

would like to begin by examining Leibniz's conception of his rela-

tions to Aristotelian natural philosophy in his earliest years. The

letter to Remond suggests that Leibniz thought in terms of a rad-

ical choice that one had to make: eitherone was an Aristotelian,

2 G.W.Leibniz,Diephilosophischenchriften,d. C.I. Gerhardt (Berlin, 1875-90),3: 606; trans. in G.W. Leibniz, PhilosophicalPapersand Letters,ed. L. Loemker

(Dordrecht, 1969), 654-5. Leibniz often uses the term 'entelechy' as a virtualsynonym for the substantial form in general and the soul in particular, follow-

ing Aristotle, as Leibniz understands him. See, e.g., SpecimenDynamicum 1695),in G.W. Leibniz, Mathematischechriften, d. C. I. Gerhardt (Berlin and Halle,

1849-63), 6: 236; trans. in G.W. Leibniz, Philosophical ssays,ed. R. Ariew and D.Garber (Indianapolis, IN, 1989), 119. For the term 'entelechy' in Aristotle, see,

e.g., De anima II, 412a 27, 415b 15ff.





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at which point one accepted the philosophy of matter and form,or one was a mechanist, at which point one was committed to re-

ject matter and form altogether. These, in any case, are the reflec-

tions of an old man. But when we go back to the writings of the

young Leibniz, we find an interestingly different situation.

Though a radical mechanist in this period, Leibniz clearlysaw the

new mechanical philosophy as being completely consistent with

the philosophy of Aristotle.

A central text for this program is a letter that Leibniz wrote to

his former mentor,Jakob Thomasius, on April 10/20, 1669, after

his conversion to the mechanical philosophy, a letter that Leib-

niz considered important enough to reprint with only small

changes as part of the introduction to an edition of Nizolius whichhe published in the following year. Thomasius (1622-84) taughtat the Universityof Leipzig while Leibniz was a student there and

influenced him greatly.Thomasius' thought was in many waysrep-resentative of the kind of philosophy taught at German universi-

ties in the second half of the seventeenth century. Thomasius was,first and foremost, a student of the history of philosophy, partic-

ularly the ancients; in this way he was very much connected with

the humanist temperament, still very much alive in Germany.

Though he taught standard philosophical subjects like physics,

logic, metaphysic, and rhetoric, he held that the proper way to

approach philosophical questions was through their history. Par-

ticularly important to him wasAristotle, whose philosophy he dis-

tinguished from the philosophy generally taught in the schools

under the name of Aristotelianism. In his own physics, Thoma-

sius followed Aristotle closely, and paid almost no attention to the

moderns who had reshaped the intellectual world in the earlier

part of the century.3

Earlyon in the letter, Leibniz announces his own adherence to

the mechanist philosophy. But at the same time, he makes it quiteclear that as a mechanist, he is not a follower of Descartes. After

giving a long list of Cartesians and other renovators in philoso-

phy (including Clauberg, Raey, Spinoza, Clerselier, Heerbord,

sFor more detailed accounts of Thomasius and his relation to Leibniz, see,

e.g., Max Wundt, Die deutscheSchulmetaphysikes 17. Jahrhunderts Thibingen,1939), 142ff; Christia Mercer, TheOriginsof Leibniz'sMetaphysicsnd theDevelop-mentof his Conception f Substance(Unpublished dissertation, Princeton Universi-

ty, 1988), 40ff.





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330 DANIEL GARBER

Andreae, Regius, Bacon, Gassendi, Hobbes, Digby, and van Ho-

ghelande), Leibniz declares:

As to myself I confess that I am anything but a Cartesian. I maintain therule which is common to all these renovators of philosophy, that only mag-nitude, figure, and motion are to be used in explaining corporeal proper-ties. Descartes himself, I hold, merely proposed this rule of method, forwhen it came to actual issues, he completely abandoned his strict methodand jumped abruptlyinto certain amazing hypotheses. [...] Hence I do nothesitate to say that I approve of more things in Aristotle's books than inthe meditations of Descartes; so far am I from being a Cartesian!In fact,I venture to add that the whole of Aristotle's eight books [of the Physics]can be accepted without injury to the reformed philosophy. This by itselfmeets your arguments about the irreconcilabilityof Aristotle and the mod-erns.4

In this way Leibniz declares his independence both from Des-

cartes and from his teacher.

The remainder of the letter is concerned with showing in detail

how the new mechanistic philosophy is consistent with the phi-

losophy of Aristotle, and why this mechanistic philosophy is true.

The details of Leibniz's conception of the mechanical philosophyare beyond the scope of this essay, as are his arguments in its

favor. But it is interesting to see how exactly he reconciles Aris-

totle with the moderns.

Leibniz begins by distinguishing between Aristotle and the

scholastic philosophy, a view shared my many of Leibniz's con-

temporaries.5He writes:

First about Aristotle. The scholastics have strangely perverted his meaning;no one knows this better than you, distinguished Sir, who were the first to

bring many errors of this kind to light.6

It is thus the realAristotle, and not the Aristotle of the scholas-

tics, that Leibniz will reconcile with the mechanical philosophy.Leibniz then announces how he will show the consistency of the

two:

I cannot better show the possibility of reconciling the two than by askingfor any principle of Aristotle which cannot be explained by magnitude,figure, and motion.7

4 G.W. Leibniz, Sdmtliche chrifienund Briefe(Berlin, 1923f), I.I: 15; trans. in

Phil. Papers,94.s On this theme, see Christia Mercer, "The Vitality and Importance of Early

Modem Aristotelianism," n T. Sorell, ed., TheRiseof ModernPhilosophyOxford,1993), 33-67.

6 Leibniz, Sdmtliche chriften,I.I: 16; trans. in Phil. Papers,95.

7 Leibniz, Sdmtliche chriften, I.I: 16; trans. in Phil. Papers,95.





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The reconciliation, then, will proceed by showing that properlyunderstood, Aristotle was a mechanist as well!

The first two questions that Leibniz takes up are matter and

form.8 About matter, Leibniz writes:

Primarymatter is mass itself, in which there is nothing by extension and

antitypy or impenetrability. It has extension from the space which it fills.The very nature of matter consists in its being something solid and impen-etrable and therefore mobile when something else strikes it, and it must

give away to the other. Now this continuous mass, which fills the worldwhile all its parts are at rest, is primary matter, from which all things are

produced by motion and into which they are reduced through rest.9

Thus, Leibniz argues,Aristotle'sprimarymatter isjust the extend-

ed substance of the mechanicalphilosophy.

Form isjust

aseasilyaccommodated:

Let us pass from matter to form in good order. Here too everything agreesremarkablyif we assume that form is nothing but figure. For since figureis the boundary of a body, a boundary is needed to introduce figure intobodies. [...] If mass were created discontinuous or separated by emptinessin the beginning, there would at once be certain concrete forms of mat-ter. But, if it is continuous in the beginning, forms must necessarily arise

through motion. [...] For division comes from motion, the bounding of

parts comes from division, their figures come from this bounding, andforms from figures; therefore, forms come from motion.10

In this way,the mysteriousforms of the Aristotelians are resolved

into shapes. Leibniz goes on to give similar accounts of Aris-

totelian notions like change, quality,and generation. All of these

arguments show that Aristotle's philosophy can be interpreted in

terms of the mechanical philosophy of the modems. But, in addi-

tion, Leibniz wants to show that it shouldbe so interpreted. For

this conclusion, Leibniz argues as follows:

For what does Aristotle discuss, in the eight books of the Physics,besides

figure, magnitude, motion, place, and time? If the nature of body in gen-eral can be explained in terms of these, then the nature of a particularbody must be explained in terms of a particular figure, a particular mag-nitude, etc. In fact, he himself says in the Physics,Book iii, Section 24 [202b30], that all natural science concerns magnitude (with which figure is, of

course, associated), motion, and time. He also says, repeatedly [e.g., 201a

12], that the subject of physics is movable bodies and that natural sciencedeals with matter and motion.11

8 For a more detailed discussion of Leibniz's treatment of matter and formin the Thomasius letter, see K. Moll, Derjunge Leibniz(Stuttgart-BadCannstatt,

1978-96), 2: 171f.

9 Leibniz, S&mtlichechriften, .I: 16; trans. in Phil. Papers,95.10Leibniz, Samtliche chniften, I.: 16-17; trans. in Phil. Papers,95-6.

11Leibniz, Sdmtliche chniften,I.I: 19; trans. in Phil. Papers,98.





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332 DANIEL GARBER

In this way,Leibniz claimed, Aristotle is actually the father of thenew mechanical philosophy, generally unacknowledged simplybecause he has been so badly misread for so long.

But Leibniz realized full well that he was not the only of his

contemporaries to interpret Aristotle in this way,and attemptedto reconcile his philosophy with the new mechanism. In his let-

ter to Thomasius, Leibniz mentions a number of them, including

Jean Baptiste du Hamel, Johannes de Raey,J.C. Scaliger, Kenelm

Digby, Thomas White, Abdias Trew,and Erhard Weigel. Indeed,the reconciliation of Aristotle and the moderns in roughly this

way was a genuine cottage industry among philosophers in the

seventeenth century.'2 In wanting to stand both among the

ancients and among the moderns in 1669, Leibniz was walkingwell-trod ground. As Leibniz's physics grew and matured, and as

he gave up the naive mechanism of his youth, he also gave upthis naive reconciliation between Aristotle and the moderns,

replacing it with a much more complex and sophisticated view of

their relations.

Form and matter:the Middle Years

In the letter to Remond that I quoted above, Leibniz notes: "But

when I looked for the ultimate reasons for mechanism, and even

for the laws of motion, I was greatly surprised to see that theycould not be found in mathematics but that I should have to

return to metaphysics."It is certainly wrong to suggest that Leib-

niz ever abandoned metaphysics, even in his early years. But it is

true that starting in the 1680s, he turned his attention to the meta-

physical foundations of his physics in a serious way, and arrived

at a very different conception of the physical world than he had

held in his callow youth.An important text that signals this change is the seminal Dis-

course nMetaphysicsf 1686. There, Leibniz notes that "ifmechan-

ical rules depended only on geometry without metaphysics, the

phenomena would be entirely different."'"He continues:

12For discussions of the seventeenth-century movement to reconcile the oldand the new philosophies, and Leibniz's place in it, see Mercer, Origins,chapt.2; C. Mercer, "Vitality";Th. Lennon, ed., The Battleof the Gods and Giants:the

Legaciesof Descartes nd Gassendi,1655-1715 (Princeton, 1993), 52-62.13Disc. on Met. ? 21. The French text of the Discourse an be found in Leib-





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LEIBNIZ ON FORMAND MATTER 333

For if there were nothing in bodies but extended mass and nothing inmotion but change of place and if everythingshould and could be deduced

solely from these definitions by geometrical necessity, it would follow [...]that, upon contact, the smallest body would impart its own speed to the

largest body without losing any of this speed; and we would have to accepta number of such rules which are completely contrary to the formation ofa system.14

In this way,Leibniz argues, the simple geometrical conception of

body that underlies many forms of the mechanical philosophy is

simply wrong and must be replaced by a deeper and more "meta-

physical"conception of body. And in characterizing his concep-tion of the world, he turns to the Aristotelian notions of matter

and form.

Before entering into detail on the arguments in question, Ishould say something about Leibniz's metaphysics as it emergesin this period. It is generally accepted that for Leibniz, the basic

constituents of the world are simple substances, what he comes

to call "monads"sometime in the late 1690s. These simple sub-

stances are non-extended, non-compound substances, understoodon analogy with Cartesian souls. They possess what Leibniz calls

perception and appetition, perceptions being the momentarystates of simple substances and appetition being the facultywhich

carries the substance from one perceptual state to the next. But

in addition, in this period, Leibniz also recognized corporeal sub-

stances. These complex substances, apparently extended and

made up of other smaller substances, form the subject matter of

his mechanist physics from the early 1680s to roughly the middle

of the first decade of the next century. Matter and form enter

into Leibniz's account of both.15

niz, Phil. Schrift.4: 427-63; a translation is found in Phil.Essays,35-68. Referenceswill be given to the section number alone.

14Discourse nMetaphysics, 21. For similararguments, see the Specimen ynam-icum, n Leibniz, Math. Schrift.,6: 240-42; trans. in Phil. Essays,123-4;and a short

essay devoted to this question, in Leibniz, Phil. Schrift.,7: 280-3, trans. in Phil.

Essays,245-50.

15For an overview of the notion of substance in Leibniz's philosophy, see C.Mercer and R.C. Sleigh, Jr., "Metaphysics: he early period to the Discourseon

Metaphysics",nd D. Rutherford, "Metaphysics:The late period", both in N. Jol-ley, ed., TheCambridge ompaniono Leibniz(Cambridge, 1995). The importanceof the notion of corporeal substance in Leibniz's philosophy is emphasized inD. Garber, "Leibniz and the Foundations of Physics: the Middle Years,"in K.OkruhlikandJ.R. Brown,eds., TheNaturalPhilosophy fLeibniz Dordrecht, 1985),27-130. My view was discussed at length and aspects challenged in R.C. Sleigh,Jr., Leibniz and Arnauld (New Haven, 1990), chapts. 5-6, and in R.M.





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334 DANIEL GARBER

One way in which matter and form enter is through an argu-ment designed to show that the Cartesian conception of body as

extension is incoherent or incomplete insofar as the Cartesian

bodies lack genuine unities. This argument is presented most

clearlyand forcefully in the correspondence withAntoine Arnauld

that he undertook just after composing the Discourseon Meta-

physics.He writes in a letter of 30 April, 1687:

I believe that where hereare only beingsby aggregation, herearen'tany real

beings.For every being by aggregation presupposes beings endowed withreal unity, because every being derives its reality only from the reality ofthose beings of which it is composed, so that it will not have any reality atall 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, groundswhich can never be found in this way, if we must alwayscontinue to seekfor them. I agree, Sir, that there are only machines (that are often ani-

mated) in all of corporeal nature, but I do not agree that there are onlyaggregates of substances; and if there are aggregates of substances, theremust also be true substances from which all the aggregates result. We must,then, necessarilycome down either to mathematical points, of which someauthors constitute extension, or to the atoms of Epicurus and Cordemoy(which are things you reject along with me), or else we must admit that wedo not find any reality in bodies; or finally, we must recognize some sub-

stances that have a true unity.'6

The claim is quite straightforward:the reality of an aggregate

depends on the reality of the things that compose it. And so, for

example, the reality of a flock of sheep derives from the realityof the individual

sheepthat make it

up. Ultimately,Leibniz

thinks,an aggregate must be grounded in things that are not themselves

aggregates, things that have, as he puts it, "real unity". These

things are what he calls true substances. This has an obvious appli-cation to the Cartesian conception of body. If bodies are as the

Cartesians claimed they are, the objects of geometry made real,

things that have extension and extension alone, then bodies are

divisible into arbitrarilysmall parts. In this sense they contain

Adams, Leibniz:Determinist, heist, dealist Oxford, 1994), chapts. 9-13. Myreviewsof Sleigh in Journalof Philosophy 9 (1992), 151-65, and of Adams in LeibnizSoci-

etyReview6 (1996), 89-106, contain some defense of my original view, but alsosome significant changes in my original 1985 position. The view of Leibniz that

emphasizes the importance of corporealsubstance remains

controversial, but,I

am still convinced, at heart correct. The account that follows of Leibniz's mid-dle years drawsheavily on my other writings on this theme.

16Leibniz, Phil. Schrift.,2: 96; trans. in Phil. Essays,85. The complete corre-

spondence with Arnauld is translated in H.T. Mason, TheLeibniz-Arnauld orre-

spondence Manchester, 1967). Since this translation indicates the pagination ofthe Phil. Schrift., will not give separate references to that book.





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extended parts which, in turn, contain parts smaller still but stillextended, ad infinitum.But if this is the case, then bodies as con-ceived by the Cartesians are aggregates that are composed at everylevel of further aggregates. It follows from this that they cannot

be real. And so, Leibniz argues in some notes on Arnauld from

May 1686,

Now, each extended mass can be considered as composed of two or a thou-sand others; there exists only an extension achieved through contiguity.Thus one will never find a body of which one can say that it is truly a sub-stance. It will alwaysbe an aggregate of many. Or rather, it will not be areal entity, since the parts making it up are subject to the same difficulty,and since one never arrivesat any real entity, because entities made up b

aggregation have only as much realityas exists in their constituent parts.

So, if a body is to be real, it must contain things that are genuineunities; these are what Leibniz calls corporeal substances.

What is it that gives unity to these corporeal substances? It is

not mere contiguity. Leibniz writes in a letter from 28 Novem-

ber/8 December 1686:

Suppose that there were two stones, for example, the diamond of the GreatDuke and that of the Great Mogul. One could impose the same collectivename for the two, and one could say that they constitute a pair of dia-

monds, although they are far part from one another; but one would not

say that these two diamonds constitute a substance. More and less do notmake a difference here. Even if they were brought nearer together andmade to touch, they would not be substantiallyunited to any greater extent.And if, after they had touched, one joined to them another body capable

of preventing their separation-for example, if they had been set in thesame ring-all this would make only what is called an unumper accidens.For it is as by accident that they are required to perform the same motion.

Therefore, I hold that a block of marble is not a complete single substance,

any more than the water in a pond together with all the fish it containswould be, even if all the water and all the fish were frozen, or any morethan a flock of sheep would be, even if these sheep were tied together sothat they could only walk in step and so that one could not be touchedwithout all the others crying out. There is as much difference between asubstance and such a being as there is between a man and a community,such as a people, an army, a society, or a college; these are moral beings,beings in which there is something imaginary and dependent on the fab-rication [fiction]of our mind.'8

Substantialunity, then, requires something more thanjust conti-

guity. But to answer this question, Leibniz introduces the Aris-totelian notion of a substantial form. He continues:

17Leibniz, Phil. Schrift.,2: 72.18 Leibniz, Phil. Schrift.,2: 76; trans. in Phil. Essays,79.





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336 DANIEL GARBER

A substantial unity requires a thoroughly indivisible and naturally inde-structible being, since its notion includes everything that will happen to it,

something which can be found neither in shape nor in motion (both ofwhich involve something imaginary,as I could demonstrate), but which canbe found in a soul or substantial form, on the model of what is called'me'.19

To see how the soul, the substantial form of the body, confers uni-

ty on it and makes of it a corporeal substance, it is helpful to look

at a particular example, the human being and its soul, which is

its substantial form. Leibniz writes on 9 October 1687:

[...] man [...] is an entity endowed with a genuine unity conferred on him

by his soul, notwithstanding the fact that the mass of his body is dividedinto organs, vessels, humors, spirits [...].20

It seems, here, that the human body, though made up of com-

plex parts, is unified and transformed into a corporeal substance

by virtue of the fact that it is appropriatelyconnected to an imma-

terial substance, a soul or form. But, Leibniz tells Arnauld, it is

similar in the world of non-human corporeal substances, all of

which are, like human beings, to be thought of as living things.

Returning now to the discussion of the two diamonds from 28

November/8 December 1686, Leibniz writes:

I assign substantial forms to all corporeal substances that are more than

mechanically united. But fifth, if I am asked in particularwhat I say aboutthe sun, the earthly globe, the moon, trees, and other similar bodies, andeven about beasts, I cannot be absolutely certain whether they are animat-

ed, or even whether they are substances, or, indeed, whether they are sim-

ply machines or aggregates of several substances. But at least I can say thatif there are no corporeal substances such as I claim, it follows that bodieswould only be true phenomena, like the rainbow. For the continuum is not

merely divisible to infinity, but every part of matter is actually divided intoother parts as different among themselves as the two aforementioned dia-monds. And since we can alwaysgo on in this way, we would never reach

anything about which we could say, here is truly a being, unless we foundanimated machines whose soul or substantial form produced a substantial

unity independent of the external union arising from contact. And if therewere none, it then follows that, with the exception of man, there is noth-

ing substantial in the visible world.2

And thus, for extended things in the world to be real, they must,

ultimately,be made up of corporeal substance, unities of an organ-

ic body and a substantial form. These corporeal substances, con-

'9 Leibniz, Phil. Schrift.,2: 76; trans. in Phil. Essays,79.20 Leibniz, Phil. Schrift.,2: 120.21 Leibniz, Phil. Schrift.,2: 77; trans. in Phil. Essays,80.





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ceived on the model of livings things, may, and for Leibniz will,always contain smaller parts that are themselves corporeal sub-

stances, substantial forms united with organic bodies. In this way,the chain of corporeal substances will extend downwards,big bugswhich contain smaller bugs which, in turn, contain bugs smaller

still, and so on ad infinitum.But unless bodies contain corporealsubstances at some evel, they cease to be real.

So far we have seen the Aristotelian notion of a substantialform

entering into Leibniz's discussion. But the notion of matter, the

correlate of form, enters as well into his correspondence with

Arnauld. He writes, for example, in the letter of 9 October 1687

that "as our body is the matter, and the soul is the form of our

substance, it is the same with other corporeal substances."22How-

ever, it is not entirely clear how to understand the term "matter"

for Leibniz in this context. To understand Leibniz's use of the

Aristotelian notion of matter, let me first introduce a distinction

Aristotelians often made between primary and secondary matter.

Eustachius a Sancto Paulo, a popular text-book writer from earlyin the seventeenth century, writes:

[Matter] s distinguishednto primary nd secondary.Primarymatter] ssaidto be thatwhich,beforeall else,weconceiveasentering ntothe com-

position of any natural thing, regarded as lacking all forms. ... Secondary[matter] is said to be that very primary [matter], not, however, bare, butendowed with physical actuality [i.e., forms].23

Primarymatter is, thus, the ultimate subject, that which remainswhen we consider the corporeal substance apart from all forms.

Secondary matter, though, is matter considered together with

forms, for example the bronze that constitutes the matter from

which a statue is made.

Leibniz uses this distinction to clarifyhis own use of the notion

of matter. He writes, again in the Correspondence with Arnauld,in the letter of 9 October 1687:

[E]xtended mass, considered without entelechies [i.e. substantial forms][...] is not a corporeal substance, but an entirely pure phenomenon, likethe rainbow;therefore philosophers have recognized that it is form which

gives determinate being to matter. [...] But if one considers as the matterof the

corporeal substancenot mass

without forms, but a secondmatter

which is the multiplicityof substances of which the mass is that of the total

22 Leibniz, Phil. Schrift.,2: 119.23 Eustachius a Sancto Paulo, SummaPhilosophiaeQuadripartitaCambridge,

1648), Physica,p. 119.





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338 DANIEL GARBER

body, it may be said that these substances are parts of this matter, just asthose which enter into our body form a part of it, for as our body is the

matter, and the soul is the form of our substance, it is the same with oth-er corporeal substances.24

It is relatively traightforwardo understandhow secondarymat-ter enters into Leibniz'sthought here. The organic body that,

togetherwiththe soul or substantialorm,makesup a corporealsubstance a particularivinghumanbeing,say)is secondarymat-

ter; t consistsof a multitudeof smallercorporeal ubstances, achof whichhasitsown form. Leibniz s quiteexplicit n holdingthatthe physical world contains corporeal substances within corpore-al substances, ll the waydown,and that one can never find a lev-

el at which there are not smallercorporealsubstances,each ofwhichis itselfcomposedof substantialorm and (secondary)mat-ter.And so LeibnizwritesArnauld,againon 9 October1687:

I amvery arremoved rom the belief thatanimatebodiesare onlya small

partof the others. For I believerather thateverythings full of animatebodies,and to mymindthereareincomparablymore souls thanthere areatoms for M. Cordemoy, who makes a finite number of them, whereas Imaintain that the number of souls or at least of forms is quite infinite, andthat since matter is endlessly divisible, one cannot fix on a part so smallthat there are no animate bodies within, or at least, bodies endowed witha basic entelechy or (if you permit one to use the word 'life' so generally)with a vital principle, that is to say corporeal substances, about which it maybe said in general of them all that they are living.25

But the notion of primarymatter also has a role to playin Leib-niz's thought in this period. After discussingsecondarymatterwith Arnauld in the letter of 9 October 1687, Leibniz turns to the

notion of primarymatter:

Butif one wereto understand ythe term matter' omething hat s alwaysessential o the samesubstance,one mightin the sense of certainScholas-

24 Leibniz, Phil. Schrift.,2: 119. Note that the passage beginning "But if oneconsiders..." was not actually sent to Arnauld in 1687, and probably representsan addition Leibniz later made to the text when he was considering publishingit. On this see Genevieve Rodis-Lewis,Lettresde Leibniz Arnauldd'aprisun man-uscritinidit (Paris, 1952), 1-21, and 87. Similarly,the earlier version of the first

part of this quotation has 'substantial forms' rather than 'entelechies'.

25 Leibniz, Phil.Schrift.,

2: 118. The earlier version of thispassage (inRodis-Lewis, Lettres, 5-6) reads a bit differently:"[...] one cannot fix on a part

so small that there are no animate bodies within, or at least, bodies endowedwith form, that is to say corporeal substances."GCrauldde Cordemoy was a fol-lower of Descartes who departed from the master in holding a version of atom-ism. See his Discernementu corpset de l'dme(Paris, 1666), in Cordemoy, Oeuvres

Philosophiques,d. P. Clair and F. Girbal (Paris, 1968).





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tics understand thereby the primitive passive power of a substance, and inthis sense matter would not be extended or divisible, although it would bethe principle of divisibilityor of that which amounts to it in the substance.26

In order to understand what Leibniz has in mind here, we must

make a detour into his account of force. There we will see the

scholastic notions of substantial form and matter function not

only as that which grounds the individualityof things in the world,but also as that which grounds the activity and passivityof cor-

poreal substance.

The notion of force is central to Leibniz's new science of dynam-ics, at the heart of his version of the mechanical philosophy. Leib-

niz's doctrine of force has two central pairs of distinctions, the

distinction between active and passive forces, and the distinctionbetween primitive and derivative forces. So there are four basic

kinds of force for Leibniz, primitiveactive, primitive passive,deriv-

ative active, and derivativepassive.The active forces are those that

relate to motion and its production, and include, for Leibniz,dead force (the force associated with instantaneous acceleration,

gravity, for example) and living force, associated with actual

motion. Passive forces, on Leibniz's view, involve reaction to

motion, and include resistance and impenetrability. Primitive

force is for Leibniz the actual ground of force in substance, the

substantial principle whose momentary states are particularmea-

surable degrees of force. In this way, primitive active and passiveforces are not forces in the way we now use them in physics.Rather, they are forces in the way we talk about a person beinga force to reckon with in politics, for example. On the other hand,derivative active force is a particularquantity at a given time, the

size of a body times the square of its velocity, for example, and

derivative passive force is a particular force of resistance that a

body might exert at a given time in a collision, say.27This doctrine of force is directly relevant to our discussion of

form and matter. In the SptcimenDynamicumof 1695, Leibniz

writes:

Primitive [active] force (which is nothing by the first entelechy) corre-

26Leibniz, Phil. Schrift.,2: 120. Again, this seems to be a later interpolation;see Rodis-Lewis,Lettres, 7.

27 For a surveyof Leibniz's physics that discusses these aspects of his thoughtin greater detail, see D. Garber, "Leibnizand Physics," n Jolley, ed., CambridgeCompanion.





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340 DANIEL GARBER

sponds to the soul or substantialform. [...] The primitiveorce of beingactedupon or of resistingconstitutes that which is called primarymatter n the

schools, if correctly interpreted.28

These two principles come together to form the complete (cor-

poreal) substance. Leibniz writes in an important note on the

metaphysics of force from May 1702:

Primitive active force, which Aristotle calls first entelechy and one com-

monly calls the form of a substance, is another natural principle which,

together with matter or [primitive] passive force, completes a corporealsubstance. This substance is, of course, one per se, and not a mere aggre-gate of many substances, for there is a great difference between an animal,for example, and a flock.29

Now, in discussing primary matter earlier in this section, I quot-ed Leibniz as saying that primarymatter "would not be extended

or divisible, although it would be the principle of divisibilityor

of that which amounts to it in the substance."s30erhaps we are

now in a position to understand what Leibniz might have meant

by that.

It seems evident that corporeal substances as Leibniz under-

stands them on the model of human beings and other organisms,a soul unifying a body, a substantial form connected with matter,must in some ense be extended. But extension is not a basic prop-

erty,an attribute of substance, for Leibniz; indeed, as we shall see,there is an important sense in which it is not a property at all. In

the Discourse on Metaphysics,Leibniz writes:It is even possible to demonstrate that the notions of size, shape, andmotion are not as distinct as is imagined and that they contain somethingimaginaryand relative to our perception, as do (though to a greater extent)color, heat, and other similarqualities, qualities about which one can doubtwhether they are trulyfound in the nature of things outside ourselves. Thatis why qualities of this kind cannot constitute any substance.3s

In this way,Leibniz suggests that just as the mechanists resolved

color, warmth, and sound into size, shape, and motion, he, Leib-

niz, will resolve these later notions into something more basic still.

Leibniz presses a similar theme fifteen years later in the impor-tant note of May 1702 from which I quoted earlier:

28 Leibniz, Math. Schrift.,6: 236-7; trans. in Phil. Essays,119-20. Cf. the essayDe ipsa natura (1698), ? 11, Leibniz Phil. Schrift.,4: 510-11; trans. in Phil. Essays,161-2.

29 Leibniz, Phil. Schrift.,4: 395; trans. in Phil. Essays,252.30

Leibniz, Phil. Schrift.,2: 120.

3S Leibniz, Disc. on Met. ? 12.





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I believe that the nature of body does not consist in extension alone; inunraveling the notion of extension, I noticed that it is relative to some-

thing which must be spread out [extendi],and that it signifies a diffusionor repetition of a certain nature. [...] For, since extension is a continuousand simultaneous repetition (just as duration is a successive repetition), itfollowsthatwhenever he samenature s diffused hroughmanythingsatthe same time, as, for example, malleability or specific gravityis in gold,whiteness s in milk,andresistance r impenetrabilitys generallyn body,extension is said to have place. However, it must be confessed that the con-tinuous diffusion of color, weight, malleability, and similar things that are

homogeneousonlyin appearances merelyapparent diffusion],and can-not be found in the smallest parts [of bodies]. Consequently, it is only theextension of resistance,diffused through body, that retains this designationon a strict examination.32

ForLeibniz,

one can talk about abody being extended, just

as

one can talk about a sweater being red. But just as the color of

the sweater is resolved into something more basic, the texture of

a surface that allows it to reflect light in a particular way,perhaps,so extension for Leibniz is resolved into something more basic,the diffusion of resistance. This resistance is, of course, what Leib-

niz calls primitive passiveforce, and is what he identifies with pri-

mary matter. In this way,Leibniz would say,primarymatter is not

itself extended or extension, but is that in the corporeal substance

that gives rise to extension and divisibility.So far we have been talking about form and matter as they con-

cern corporeal substances. But Leibniz also recognizes the notions

of matter and form in connection with his simple substances, theincorporeal and non-extended substances that ultimately groundthe reality of the corporeal world. As with corporeal substances,the notions of form and matter in simple substances are associ-

ated with their activityand their passivity.But activityand passiv-

ity have a special meaning for Leibniz when applied to simplesubstances. Understood on the model of the Cartesian thinkingsubstance, the momentarystates of simple substancesare only per-

ceptions. Consequently, activityand passivitymust be cashed out

in terms of perceptions alone. Leibniz writes in the Discourseon

Metaphysics:

The action of one finitesubstance n anotherconsistsonlyin the increase

of the degree of its expression together with the diminution of the expres-sion of the other, insofar as God requires them to accommodate themselvesto one another."

32 Leibniz, Phil. Schrift.,4: 393-4; trans. in Phil. Essays,251.

3S Leibniz, Disc. on Met. ? 15.





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342 DANIEL GARBER

In creating the world, at root an infinite collection of simple sub-stances, God creates them in such a way that they will be in har-

mony with one another. In this way,Leibniz suggests, what hap-

pens in one substance can have a consequence for what happensin another, even though the individual substances do not com-

municate with one another.4 And so Leibniz claims:

We ascribe to ourselves-and with reason-the phenomena that we expressmost perfectly and [...] we attribute to other substances the phenomenathat each expresses best. Thus a substance, which is of infinite extensioninsofar as it expresses everything,becomes limited in proportion to its moreor less perfect manner of expression. This, then, is how one can conceivethat substances impede or limit each other, and consequently one can saythat, in this sense, they act upon one another and are required, so to speak,

to accommodate themselves to one another. For it can happen that achange that increases the expression of one diminishes that of another.

Now, the efficacy [vertu]a particular substance has is to express well the

glory of God, and it is by doing this that it is less limited. And whenever

something exercises its efficacy or power, that is, when it acts, it improvesand extends itself insofar as it acts. Therefore, when a change takes placeby which several substances are affected (in fact every change affects all of

them), I believe one may say that the substance which immediately passesto a greater degree of perfection or to a more perfect expression exercis-

es its power and acts, and the substance which passes to a lesser degreeshows its weakness and is acted upon [pdtit].35

And so Leibniz writes in an essay dated 1683-1686, the same peri-od as the above passage:

Substances have metaphysical matter or passive power insofar as they

express something confusedly; active, insofar as they express it distinctly.36

Even though Leibniz doesn't mention form, it is not too much to

assume that form enters here, as in other texts, as the correlate

of matter, associated with activity in just the way that matter is

associated with passivity.In this way the form and matter of the schoolmen appear at

two levels in Leibniz's philosophy at that time, both in connec-

tion with corporeal substance and in connection with simple sub-

stance. But just as simple substance is supposed to underlie cor-

poreal substance, one would suppose that the form and matter of

"4Leibniz, Disc. on Met. ? 14.

s5 Leibniz, Disc. on Met. ? 15.

s6 Leibniz, Phil. Schrift.,7: 322; trans. in Phil. Papers,365. The essay is datedto 1683-86 on the basis of watermark evidence. See Leibniz, VorauseditionurRei-he VI-philosophische chriften--inderAusgabeder Akademie der Wissenschaften]erDDR [Berlin] (Miinster, 1982-91), 3: 476, 481.





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simple substances is supposed to underlie the form and matter ofcorporeal substance. Though Leibniz is not explicit about how

exactly the story goes, there is room for some informed conjec-ture and rational reconstruction.37

What binds the corporeal substance together, soul to organic

body, is pre-established harmony,Leibniz argues, the special coor-

dination between the perceptions in the soul and those in the

other corporeal substances that make up the organic body. As

Leibniz writes in the Discourse on the Metaphysics:

Everythingthat happens to the soul and to each substance follows from its

notion, and therefore the very idea or essence of the soul carries with itthe fact that all its appearances or perceptions must arise spontaneously

from its own nature and preciselyn such a waythat they correspondbythemselves to what happens in the whole universe. But they correspondmoreparticularlynd moreperfectlyo whathappens n the bodyassignedto it, because the soul expresses the state of the universe in some way andfor sometime,according o the relationotherbodieshaveto its ownbody.This also allows us to know how our body belongs to us, without, however,

being attached to our essence.38

This harmony also gives rise to causal relations between the soul

and its organic body. Insofaras the soul has clear perceptions and

the (souls of the) substances making up the organic body have

confused perceptions, the soul is acting on the substances that

make up its organic body; insofar as the soul has confused per-

ceptions and the (souls of the) substances making up the organ-

ic body have clear perceptions, the soul is acted upon by the sub-stances in its organic body. And so, the soul can be understood

as bound to (the souls of the corporeal substances making up)its organic body by relations of cause and effect, activityand pas-

sivity, by the fact that the soul and its organic body act on each

other, in the Leibnizian sense of 'act'. (This account is, of course,

repeated for each of the substances that make up the organic

body of the corporeal substance, ad infinitum.) Furthermore, as

Leibniz suggests in Discourse n Metaphysics 33, it is through the

special relation that the soul has to its body that it interacts with

everything else in the world.

Now, insofar as the soul (an incorporeal substance) has clear

perceptions, it is said to have primitive active force, which con-

37 My story here is inspired by Adams, Leibniz,393-9, though I disagree withhim on a number of important points.

38Leibniz, Disc. on Met. ? 33.





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344 DANIEL GARBER

stitutes its form; insofar as that soul (again, an incorporeal sub-stance) has confused perceptions, it is said to have primitive pas-sive force, which constitutes its primary matter. But how is this

connected with form and matter in the corporealubstance?

Again, while Leibniz is not very explicit about this, here is one

suggestion. Because of the harmony of the soul with its body,whenthe soul of the organic body has clear perceptions, it acts on its

body, and causes it to act as a whole, as a single unit, as opposedto a multitude of individual corporeal substances, each acting on

its own. In this way,the soul functions as the form of the organ-ic body, the source of its activityand the source of its unity. But

because of the same relations of harmony that bind the soul to

the organic body, when something acts on any substance in the

organic body of the corporeal substance, it thereby acts on its soul

as well. And because of the same relations of harmony,when thesoul is acted upon, this changes its relations with all of the oth-

er substances that make up the organic body. It is something of

a conjecture to saywhat exactly is going on in this circumstance,but I would suppose that what Leibniz has in mind is that by virtue

of the unity that the soul imposes on the collection of substancesin the organic body of the corporeal substance, when one sub-

stance in the organic body is acted upon (and manifests [deriva-

tive?] passive force), the others in the organic body are acted

uponas well (and thus also manifest [derivative?]

passiveforce).

In this way, by virtue of the "causal" onnections between the soul

and its organic body, primary matter or primitive passive force

thus extends itself and is diffused throughout the organic bodyof a corporeal substance-and no farther. Insofar as the connec-tions between a soul and its organic body constitute it as a gen-uine individual, one can say that that individual is really extend-

ed, by which we mean that it is a genuine thing in which passiveforce is extended. The specific magnitude of passiveforce will, of

course, depend on the magnitude of the body; but understood as

something that has magnitude, we must be talking, not about

primitive, but derivativepassive force of the corporeal substance.

However,when we think

notin terms of the

magnitudeof the

passive force, but simply in terms of the capacity a given corpo-real substance has to exhibit that force, then we are, indeed, think-

ing of "something that is always essential to the same substance."

This, properly speaking, is the primary matter of the corporeal





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substance. It is important to note here that although the prima-

ry matter of a corporeal substance understood in this way is not

identical with the primary matter (confused perceptions) of the

soul of a corporeal substance, properly speaking, it is evident that

it is grounded in those confused perceptions. It is because of the

confused perceptions of the soul that the passiveforce of any one

of the constituent substances of the organic body is diffused

throughout the whole body. Again, it is worth remarking that this

story must be repeated for each and every corporeal substance inthe organic body of a given corporeal substance, and so on ad

infinitum.In this way, Leibniz uses the Aristotelian notions of form and

matter in this middle period of his thought. His Aristotelianism

is, in a way,a central feature of his own version of the mechani-

cal philosophy. He writes in the Discourse on the Metaphysics:

It seems that the ancients, as well as many able men accustomed to deepmeditation who have taught theology and philosophy some centuries ago(some of whom are respected for their saintliness) have had some knowl-

edge of what we havejust said; this is why they introduced and maintainedthe substantial forms which are so decried today. But they are not so dis-tant from the truth nor so ridiculous as the common lot of our new philoso-phers imagines. I agree that the consideration of these forms serves no pur-pose in the details of physics and must not be used to explain particularphenomena. That is where the Scholastics failed, as did the physicians ofthe past who followed their example, believing that they could account forthe properties of bodies by talking about forms and qualities without tak-

ing the trouble to examine their manner of operation. It is as if we werecontent to say that a clock has a quality of clockness derived from its formwithout considering in what all of this consists; that would be sufficient forthe person who buys the clock, provided that he turns over its care to anoth-er. But this misunderstanding and misuse of forms must not cause us to

reject something whose knowledge is so necessary in metaphysics that, I

hold, without it one cannot properly know the first principles or elevateour minds sufficientlywell to the knowledge of incorporeal natures and thewonders of God.39

Contrary to his early position, Leibniz no longer thinks that the

Aristotelian notions of form and matter are interpretable in terms

of the basic notions of the mechanical philosophy. But, at the

same time, he argues that one can be a good mechanist and still

hang on to these notions. Indeed, he argues, in order to be agood mechanist we must do so. Form and matter don't competewith the mechanical philosophy in explaining things; Leibniz

s9 Leibniz, Disc. on Met. ? 10.





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346 DANIEL GARBER

rejects the use of forms to explain particularfeatures of the worldas much as any other mechanist does. But, he argues, thesenotions that have fallen out of the mechanist's toolbox are essen-

tial behind the scenes, properly to ground he new mechanical phi-

losophy. In particular, the notions of individuality, activity,and

passivity, necessary to ground the world of the mechanical phi-

losophy can only be explicated by returning to the schoolmen's

notions of form and matter,and by placing them in a position of

honor, not in physics proper, but at the foundations of physics.

Form and matter: the Late Years

In the previous section, we discussed the notions of matter and

form in Leibniz's middle years,when the notion of corporeal sub-

stance was central to his thought about the physical world. But

Leibniz's world changes radicallywhen the notion of a corporealsubstance is called into question. In the 1714 letter to Remond,Leibniz notes that his reflections ultimately led him to the view

that "monads or simple substances are the only true substances

and that material things are only phenomena, though well found-

ed and well connected."40Crucial to this step in Leibniz's thoughtwas a little article written by Father Ren&-Josephde Tournemine

which appeared in May1703 in thejournal he edited, the Mimoires

de Trivoux.41There Tournemine referred to the two-clock exam-ple that Leibniz liked to use to illustrate his pre-established har-

mony. He wrote:

Thiscorrespondence, armony, oesnotbringabouteither unionor essen-tial connection. Whatever esemblanceone might suppose between twoclocks,howeverustlytheirrelationsmightbe consideredperfect,one canneversay hat the clocksare united ustbecause he movements orrespondwithperfectsymmetry.42

Tournemine's rgument eemedto call into questiontheverysta-tus of corporealsubstanceand made problematicwhat Leibnizhad almosttaken for grantedin his earlierwritings, he notionthat non-extended, ndividualsubstances(or 'monads'since the

late 1690s) couldjoin togetherto form genuine complex corpo-real substances. The acceptance of Tournemine's model did not

40 Leibniz, Phil. Schrift.,3: 606; trans. in Phil. Papers,655.

41 On this, see Adams, Leibniz,295f.42 Quoted in Leibniz, Phil. Essays,196.





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change Leibniz's account of organisms or the picture of a worldof bugs within bugs, all the way down-an image, in a way, that

persisted to the end of Leibniz's life. Indeed, what remained, too,was the kind of relations between the monads making up the

organic body and the so-called dominant monad that constitutes

the soul in the corporeal substance that I outlined above. But

what was called into question, or at least made problematic in a

wayin which it wasn't before, was the claim that such organisms,

organic bodies connected with souls, were themselves genuinesubstances and thus capable of grounding the existence of the

aggregates that constitute bodies.

But Leibniz was oversimplifyingthe situation when he suggest-ed to Remond that he had completely rejected corporeal sub-stancein this last stageof his thought.For an understanding fLeibniz's inal thoughton corporealsubstance,we must turn tothe correspondence Leibniz exchanged with Bartholomaeus Des

Bosses starting in January 1706 and extending to just months

before Leibniz's death. One of the central preoccupations of their

correspondence, particularlyin the later years, is the notion of

the corporeal substance. Leibniz there recognizes clearlythat har-

mony is not enough to insure the unity of a corporeal substance.

But rather than simply abandoning the notion, he discusses with

Des Bosses what would need to be added to a collection of mon-

ads to transform it into a genuinecomplex

substance.

Throughout these years, Leibniz maintained his faith in the

mechanical philosophy. Indeed, it is in these years that he is most

eager to defend an orthodox mechanism in which everything is

explainedin termsof size, shape and motion, againstthe New-tonian heresy that would seem to introduce action at a distance.

In the essayAntibarbarus hysicus 1710?), he writes in an unchar-

acteristicallybitter tone:

It is, unfortunately, our destiny that, because of a certain aversion toward

light,people love to be returned o darkness.We see this today,wherethe

great ease for acquiring learning has brought forth contempt for the doc-trines taught, and an abundance of truths of the highest clarityhas led to

a love for difficult nonsense.43

But Leibniz seems to think that without the reality of the corpo-real substance, the reality of this mechanist world is at stake. On

43 Leibniz, Phil. Schnift., : 337; trans. in Phil. Essays,312.





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348 DANIEL GARBER

29 May 1716, only months before his death, he wrote to DesBosses:

You say that bodies can be something other than phenomena, even if theyaren't substances. I believe that unless there are corporeal substances, bod-ies disappear into phenomena. And aggregates themselves are nothing but

phenomena, since things other than the monads making them up are added

by perception alone, by virtue of the very fact that they are perceived atthe same time. Furthermore, if only monads were substances, then it wouldbe necessary either that bodies be mere phenomena, or that the continu-um arise from points, which, it is agreed, is absurd. Real continuity can

ariseonly from a substantialbond. If nothingsubstantial xisted besidemonads, that is, if composites were mere phenomena, then extension itselfwould be nothing but a phenomenon resulting from simultaneous and

mutually ordered appearances, and by virtue of that very fact, all of the

controversiesoncerning he compositionof the continuumwouldcease."There is much packed into this passage, too much to try to tease

out now. But it is clear to me that from Leibniz's point of view,the elimination of corporeal substances means the elimination of

the reality of the world of extended things. It is not entirely clear

why this should be so. In the account I gave earlier of the sense

in which corporeal substances are extended, I argued that the dif-

fusion of passive force that constitutes the extension of a corpo-real substance is grounded in the interconnection between the

substances that make up the organic body of a corporeal sub-

stance and the way they are unified by a single soul. In the mid-

dle years, Leibniz held that because of the harmony between soul

and organic body, the corporeal substance constitutes a genuinesubstance, and because of that harmony, passive force is diffused

throughout the corporeal substance as a whole. But when the real-

ity of the link between soul and organic body is called into ques-tion, Leibniz also calls into question not only the reality of the

corporeal substance, but also the reality of the extension that

results from the relations between soul and organic body. While

the reasons are obscure, Leibniz seems to hold that if the con-

nections that bind together the substances in the organic bodyare merely phenomenal, then so is the diffusion of passive force

that constitutes the extension. That is to say, the reality of exten-

sion in thephysical

worlddepends

on thereality

(i.e., substan-

tiality) of genuine individuals that are extended, or, at least, have

bodies that are extended and divisible. In his correspondence with

Des Bosses, Leibniz considers and develops the notion of a vin-

44 Leibniz, Phil. Schrift.,2: 517; trans. in Phil. Essays,203.





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culum substantiale,a substantial chain or bond, as a means toaddress the question of complex substance. His claim is that this

vinculumsubstantiale s a genuine something, distinct from the

monads, it is what we need to add to the collection of monads in

order to make of them a genuine corporeal substance. Such a

notion clearly goes beyond the metaphysics that Leibniz held ear-

lier, and outlines in others of his late works like the Monadology,insofar as it would seem to introduce something real into the

world over and above monads, their perceptions, and complexsubstances composed of monads alone.45 For that reason manycommentators have doubted that Leibniz actually adopted this

notion of a vinculum substantialeas his own.46 I agree that there

is no unequivocal evidence that Leibniz adopted this notion ashis own. But, at the same time, I think that it is clear that he saw

the problem it addresses, the unity of the corporeal substance, as

his own, and that it was something that worried him greatly at

this moment.

But be that as it may,what is interesting to me here is the wayin which Leibniz persists in linking the notion of substance that

interests him with the Aristotelian notions of matter and form. In

the appendix to a letter to Des Bosses from August 19, 1715, Leib-

niz gives a characterization of the kinds of beings that he recog-nizes. Leibniz first divides beings into genuine unities (full beings)and

aggregates.Within the

genuineunities, he

distinguishesbetween substances and modifications, and within substances, he

distinguishes between simple substances (monads), and compos-ite substances,"likeanimals or other organic beings".Such a com-

plex substance consists of "primitiveactive and passive power, or

primarymatter, i.e. the principle of resistance, and of substantial

form, i.e., the principle of impetus."47Similarlyhe writes in his

letter of 29 May 1716:

4- See, e.g., the discussion in the letter to Des Bosses, 29 May 1716, Leibniz,Phil. Schrift., : 515-6;trans. in Phil. Essays,202. For an account of Leibniz's viewson the vinculum ubstantiale, nd its place in Leibniz's thought, see B. Look, Leib-niz and theVinculum ubstantiale

(Unpublished Universityof

Chicagodissertation,

1997).

46The classic statement of thisjudgment is given in B. Russell,A CriticalExam-

inationof thePhilosophy f Leibniz(London, 1937), 151f. For a more recent argu-ment to a similar conclusion, see Adams, Leibniz,299-307.

47 Leibniz, Phil. Schrift.,2: 506. This passage is misleadingly translated in Phil.

Papers,617.





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350 DANIEL GARBER

Composite ubstancedoes not formallyconsist in monadsand their sub-ordination, or then it would be a mereaggregateor a being peraccidens.Rather, t consists n primitiveactiveand passive orce, fromwhicharisethe qualitiesand the actionsand passionsof the compositewhich are dis-coveredby the senses, f theyare assumed o be morethanphenomena.48

But Leibniz does not limit the applicability of matter and form

to the complex corporeal substance. As in his earlier thought, the

simple substance, now the monad, is also characterized in terms

of matter and form. Indeed, it is the matter and form of the mon-

ad, distinct from the matter and form of the complex corporealsubstance, that gives rise to the latter. Writing to Des Bosses on

20 September1712,Leibniznotes:

[...] If there are only monadswith their perceptions,primarymatterwillbe nothing but the passivepowerof the monads,and entelechywill betheiractivepower.Butwhenyou addcomposite ubstances, mustsaythatin addition to the activeprincipleor motive virtueone must add in thema principle of resistance.49

Similarlyhe writes on 5 February 1712:

If a corporeal substance is something real, over and above monads, just asa line is held to be somethingoverand abovepoints,then we willhave to

say that corporeal substance consists in a certain union, or better, in a real

unifying hing that Godsuperadds o the monads.Primarymatter,name-

ly, that which is required or extensionand antitypy,hatis, for diffusionand resistance, arises from the union of the passive power of the monads,and from the union of the monadicentelechiesarisessubstantial orm.50

As in his earlier doctrine, the extension of a corporeal substancearises from its matter. Leibniz writes in his letter of 29 May 1716

that "extension is a modification of primarymatter, that is, a mod-

ification of that which is formally nonextended."51The situation,

though, with respect to form is a bit more complicated. ThoughLeibniz seems to hold that a collection of monads can constitute

a genuine unity or a genuine corporeal substance only if it con-

tains a dominant monad, that is to say,a single monad that playsthe role of the soul of the organic body constituting the complexsubstance52,that dominant monad is not the substantial form of

the corporeal substance. Leibniz writes in the letter of 5 Febru-

ary 1712 that the form of a corporeal substance "will not be a

48Leibniz, Phil. Schrift.,2: 517-8; trans. in Phil. Essays,203-4.

49 Leibniz, Phil. Schrift.,2: 460; trans. in Phil. Papers,607.50 Leibniz, Phil. Schrift.,2: 435; trans. in Phil. Essays,198.

51 Leibniz, Phil. Schrift.,2: 520; trans. in Phil. Essays,206.52

Leibniz, Phil. Schrift., 2: 481-2.





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soul, which is a simple and indivisible substance", i.e., a monad.53Indeed, it cannot be. He writes in the letter of 29 May 1716 that

... the first entelechy of a composite is a constitutive part of the compositesubstance, namely its primitive active force. But it differs from a monad,since it makes phenomena real. Monads can, indeed, exist, even if bodiesare only phenomena.54

Leibniz's point here is that a collection of monads, however orga-nized, doesn't constitute a genuine corporeal substance. Conse-

quently, the dominant monad of the organism cannot be the same

as the substantial form of the corporeal substance. The form of

the corporeal substance must be something apart from the mon-

ads themselves, intimately connected with the vinculum substan-

tiale that makes the aggregate of monads into a genuine corpo-real substance. And thus he writes, earlier in the same letter:

The substantial form and primarymatter of the composite, in the Scholas-tic sense, that is, the primitive power, active and passive, are in the chain

[i.e., the vinculumsubstantiale],ust as they are in the essence of the com-

posite.55

But, nevertheless, though distinct from the dominant monad of

the composite, the substantial form of the corporeal substance

always "accompanies"the dominant monad.

As he suggests in the 1714 letter to Remond, Leibniz's thought

changes radically over the years. But even though his final doc-

trines (or better,his final

musingsin the direction of a new doc-

trine) are very different from the doctrines of his youth, at the

very end, as at the beginning, Leibniz can say with all honestythat "Idon't think that I depart from the doctrine of the schools

on corporeal substance. [...]"56In the end, as at the beginning,Leibniz remains committed to finding a place within the mecha-

nist world he is trying to create for the form and matter of the

Aristotelian tradition.

ABSTRACT

This paper discusses the Aristotelian notions of matter and form as they are

treated in the philosophy of Leibniz. The discussion is divided into three parts,



55 Leibniz, Phil. Schrift.,2: 516; trans. in Phil. Essays,202.56 Leibniz, Phil. Schrift.,2: 520; trans. in Phil. Essays,205.





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352 DANIEL GARBER

corresponding to three periods in Leibniz's development. In the earliest period,as exemplified in a 1669 letter to his former mentor Jakob Thomasius, Leibniz

argues that matter and form can be given straightforward interpretations interms of size and shape, basic categories in the new mechanical philosophy. InLeibniz's middle years, on the other hand, as exemplified in the Discourseon

Metaphysicsnd the correspondence with Arnauld, Leibniz seems to hold a moreorthodox Aristotelian view of matter and form as the constituents of the cor-

poreal substances that ground the realityof the physicalworld. In Leibniz's latest

years, as discussed in the letters with Des Bosses, matter and form enter once

again in connection with the vinculumsubstantiale, he substantial bond that is

supposed to bind monads together to form corporeal substances.

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