Active Extension and Bodily Variety in Spinoza

Active Extension and Bodily Variety in Spinoza


James Simkins

University of Pittsburgh

1. Introduction

In a series of letters written in the last two years of Spinoza's life, Ehrenfried

Walter von Tschirnhaus asks Spinoza to explain how he conceives of extensio

(extension), corpus (body) and motus (motion) in a manner that is consistent with

the existence of a variety of bodies. This is an important question for Spinoza since

several demonstrations in Ethics clearly depend on the existence of a variety of

bodies. For instance, Spinoza holds that “the human body is affected in a great many

ways by external bodies.”1 In his exchange with Tschirnhaus, Spinoza rejects the

“inert” Cartesian conception of extension as bare geometrical space.2 Instead,

Spinoza adopts the view that bodily variety is “explicated through an attribute which

expresses eternal and infinite essence.”3 These remarks are critical to interpreting the

theory of bodily individuation that Spinoza presents in Part II of Ethics.

1 Edwin Curley, trans. The Collected Works of Spinoza, Volume I (Princeton: Princeton UP, 1984), 2p14d.All references to Ethics use the following format. The first number indicates the part number. The nextletter(s) indicate a proposition [p], demonstration [d], definition [def] or axiom [a] followed by its number.The final letters and numbers indicate a scholium [s] or corollary [c]. Other elements such as introductions,appendixes, and lemmas are written out to avoid confusion. For example, 2p14d corresponds to theDemonstration of Proposition 14 of Part 2 of Ethics.

2 Samuel Shirley, trans. The Letters (Indianapolis: Hackett, 1995), Ep. 81.

3 Ibid., Ep. 83.

Ephemeris 2013 ‹58›


In this paper I work towards an interpretation of the theory of bodily

individuation that Spinoza presents in Part II of Ethics. I begin by sketching

Descartes's view of extension and his theory of bodily individuation which provided

the point of departure for Spinoza. Next I turn to Spinoza's correspondence with

Tschirnhaus in order to show that Spinoza saw what seemed to him to be an

insoluble problem with the Cartesian approach which led him to reject a passive

conception of extension. The fact that extension must be inherently active for

Spinoza suggests an interpretation of Ethics in which activities are ontologically

basic. In order to provide further support for this reading, I show that several

otherwise difficult passages in Ethics make sense under this interpretation. Finally, I

show how this interpretation can be used to solve some of the problems facing

Spinoza's theory of bodily individuation although I conclude by admitting that

significant difficulties remain.

2. Spinoza and Cartesian Extension

Before considering Spinoza's rejection of the Cartesian account of extension,

body and motion, it is necessary to sketch briefly Descartes's view on these matters

in the period when he wrote Ethics of Philosophy. According to Descartes, a body is

just “something which is extended in length, width and depth,” and all non-

geometrical properties, such as the weight, hardness or color of a body are not

fundamental but arise from the interaction of bodies with the senses.4 That bodies

have a purely geometrical nature for Descartes is made clear by his stance that

4 John Cottingham, Robert Stoothoff, and Dugald Murdoch, trans. The Philosophical Writings ofDescartes, Volume 1(Cambridge: Cambridge UP, 1985), 2a4. All citation from Principles refer to the partnumber followed by the number of the article. For example, 2a4 corresponds to Article 4 of Part 2 ofPrinciples.



“there is no real difference between space and corporeal substance.”5 This might

lead the reader to wonder what empty space could be under such a view. Since

“empty” space has length, width and depth, it has everything it needs to be a body. It

follows from this that there is no such thing as a space that is empty of bodies.

Otherwise there would have to be a “particular extension [that belongs] to nothing,”

which Descartes holds is contradictory.6 On these grounds Descartes argues for the

impossibility of a vacuum and holds that space is a plenum.

Descartes's theory of bodily individuation in Principles depends entirely upon

motion. He defines motion, in the strictest sense, as “the transfer of one piece of

matter, or one body, from the vicinity of other bodies which are in immediate

contact with it.”7 It is important to note that according to this definition motion as

transfer of a body is devoid of dynamical character.8 At the time he wrote Principles

Descartes held that motion is not an active power inherent in bodies. He held that all

motion originates with God who preserves a constant amount of it.9 This motion is

the basis for all bodily variety:

The matter existing in the universe is thus one and the same, and it is

always recognized as matter simply in virtue of its being extended. All

the properties which we clearly perceive in it are reducible to its

divisibility and consequent mobility in respect to its parts.... If the5 Ibid., 2a11.

6 Ibid., 2a16.

7 Ibid., 2a25.

8 For my account of Cartesian motion and bodily individuation, I am in debt to Wallace Anderson,“Cartesian Motion” in Motion and Time, Space and Matter, ed. Peter Machamer and Robert Turnbull(Columbus: Ohio State UP, 1976), 200-23 and Peter Machamer, “Causality and Explanation in Descartes'sNatural Philosophy,” 168-99 of the same volume.

9 Cottingham, Stoothoff, and Murdoch, The Philosophical Writings of Descartes, Volume 1, 2a36.



division into parts occurs simply in our thought, there is no resulting

change; any variation in matter or diversity in its many forms depends

on motion.10

As this passage makes clear, all variation between bodies depends on the motion of

various parts of the whole of matter. Those parts of matter that do not have different

motion from surrounding parts are divided from those “simply in our thoughts” and

are not discernible as individuals.

Returning to Spinoza, Tschirnhaus frames his inquiry into Spinoza's views on

motion, extension and bodily individuation in a Cartesian manner. In Letter 59,

Tschirnhaus writes:

[Your physical theory] is known to me from the lemmata attached to

the second part of your Ethics, which provide a ready solution to many

of the problems of physics. If time and opportunity permit, I humbly

beg you to let me have the true definition of motion, together with its

explanation. And since extension when conceived through itself is

indivisible, immutable, etc., how can we deduce a priori the many and

various forms it can assume, and consequently the existence of

figure....11

The “lemmata attached to the second part of Ethics” constitute what is commonly

referred to as the 'Physical Digression,' which is attached to the end of 2p13s. In that

section, Spinoza holds that “Bodies are distinguished from one another by motion

and rest, speed and slowness, and not by reason of substance.”12 On the surface, this

10 Ibid., 2a23.

11 Shirley, The Letters, Ep. 59.

12 Edwin Curley, trans. The Collected Works of Spinoza, Volume I, 1p13s Lemma 1.



is almost exactly the theory of bodily individuation found in Principles, but

Tschirnhaus recognizes a difference between Principles and Ethics that makes this

more problematic for Spinoza. The structure of Ethics, unlike that of Principles,

seems to require a demonstration of any position that Spinoza holds which is not a

definition or axiom. While Spinoza could make the existence of a variety of bodies

an axiom, he says nothing suggesting that in this exchange, which suggests that he

rejects this as a solution and accepts Tschirnhaus's demand for a demonstration. Yet,

as Tschirnhaus points out, the immutability of extension makes it difficult to

conceive how this demand can be met.

In his reply to Tschirnhaus Spinoza delays explaining how variety can be

deduced from extension. He responds, “Since my views ... are not yet written out on

due order, I reserve them for another occasion.”13 Luckily Tschirnhaus presses

Spinoza for an answer to his query.14 In Letter 81 Spinoza provides him with a more

satisfactory response:

Further from Extension as conceived by Descartes, to wit, an inert

mass, it is not only difficult, as you say, but quite impossible to

demonstrate the existence of bodies. For matter at rest, as far as in it

lies, will continue to be at rest, and will not be set in motion except by a

more powerful external cause. For this reason I have not hesitated on a

previous occasion to say that Descartes' principles of natural things are

of no service, not to say quite wrong.15


14 Ibid., Ep. 80.

15 Ibid., Ep. 81.



From the passage above it is clear that Spinoza rejects extension as it is conceived

by Descartes on the grounds of its inertness. It is impossible for inert matter to be set

in motion without God or some other external cause; Descartes would not object to

this premise. Since for both figures motion is the basis of bodily individuation,

bodily individuation would be impossible if, for some reason, a “more powerful

external cause” could not be invoked.

In Letter 82, Tschirnhaus asks Spinoza to explain why he refuses to invoke

God as a first mover in order to explain variety:

I should like you do to me the kindness of showing how, from

Extension as conceived in your philosophy, the variety of things can be

demonstrated a priori. For you mention Descartes's view, by which he

maintains that he cannot deduce this variety from Extension in any

other way than by supposing that this was an effect in motion started by

God. Therefore, in my opinion, it is not from inert matter that he

deduces the extension of bodies, unless you discount the supposition of

God as a mover. For you have not shown how this must necessarily

follow a priori from the essence of God, a point whose demonstration

Descartes believed surpassed human understanding.16

As Tschirnhaus points out, Descartes does not claim to deduce variety from

extension. In fact, he denies that such a thing can be done. Instead, he invokes God

as the cause of motion and, by implication, variety. Tschirnhaus challenges Spinoza

to demonstrate variety from his own conception of extension in order to show that

an alternative to Descartes's view is possible. In order to understand what it is at

16 Ibid., Ep. 82.



stake in this, it is important to realize that appealing to a source of motion that

surpasses human understanding is completely unacceptable within the framework of

Ethics. The “geometrical order” of Ethics in which propositions are each supported

by an apparently deductive demonstration from definitions, axioms and earlier

propositions does not allow inexplicable leaps. Of course Spinoza would not deny

that motion has its origins in God, but to invoke God as an incomprehensible source

of motion as Descartes does is a deus ex machina. Spinoza needs an explanation of

variety in the form of a demonstration from some attribute of God.

Fortunately, Tschirnhaus’s challenge leads Spinoza to offers a tantalizing

suggestion of his own view of extension. In Letter 83, Spinoza writes:

Descartes is wrong to define matter through Extension; it must

necessarily be explicated through an attribute which expresses eternal

and infinite essence. But perhaps if I live long enough, I shall some

time discuss this with you more clearly; for as yet I have not had the

opportunity to arrange anything in due order on this subject.17

A potentially confusing aspect of this passage must be clarified. Spinoza uses

“Extension” here to refer to Cartesian extension and not to his own revised view of

extension. The “attribute which expresses eternal and infinite essence” is Spinoza's

revised conception of extension. This is clear from that fact that matter must be

explicated through it. In order to distinguish between these two senses of extension,

I will use Cartesian, passive, or geometrical extension to indicate the former and

Spinozistic, active, or revised extension to indicate the latter.

17 Ibid., Ep. 83.



Spinoza died seven months after writing Letter 83.18 Thus, it is unlikely that

he ever got a chance to work out a detailed account of how variety can be

demonstrated from a conception of extension as “an attribute which expresses

eternal and infinite essence.” If he did work out such an account in the final months

of his life, it did not make its way into any surviving texts. The main goal of this

essay is to work out why Spinoza thought adopting an active view of extension was

a promising approach to the problem of bodily variety. This requires a careful

reading of his treatment of extension, body and motion in Ethics. While the

endeavor must be to some extent speculative, Spinoza left just enough clues that it is

possible to work out why he saw such an approach as promising

3. Active Extension in Ethics

The correspondence with Tschirnhaus reveals that Spinoza came to reject the

Cartesian conception of extension but Spinoza never explains how his own

apparently Cartesian theory of bodily individuation in the 'Physical Digression' of

Ethics survives this rejection. It would seem that the very same criticism should

apply to Spinoza's view. Once again, the text reads, “Bodies are distinguished from

one another by motion and rest, speed and slowness, and not by reason of

substance.”19 If Spinoza is to avoid his own critique of Descartes in Letter 81 then it

must be possible to demonstrate the existence of motion from extension as it is

defined in Ethics. Thus, the definition of extension in Ethics is a promising place to

start in order to understand Spinoza's theory of bodily individuation.

18 See the note on page 357 of the Shirley translation of Spinoza's correspondence (Ibid.)

19 Curley, The Collected Works of Spinoza, Volume I (Princeton: Princeton UP, 1984), 1p13s Lemma 1.



Spinoza avoids identifying extension and body with length, width and depth

in Ethics as Descartes does in Principles of Philosophy. Instead, Spinoza holds that

“extension is an attribute of God” and defines attribute as “what the intellect

perceives of a substance as constituting its essence.”20 Spinoza defines body as “a

mode that in a certain and determinate way expresses God's essence insofar as he is

an extended thing.”21 It is useful to contrast these definitions with those that Spinoza

provides in Descartes's Principles, Spinoza's commentary on Principles of

Philosophy. In that work, Spinoza defines extension as “what consists of three-

dimensions; but by extension we do not understand the act of extending or anything

distinct from quantity,” and he writes that “the nature of Body, or Matter, consists in

extension alone.”22 Spinoza, as a good commentator, is presenting Descartes's views

and not his own. While presenting his own views in Ethics, Spinoza does not use the

same Cartesian definitions. This suggests that Ethics reflects the conceptions of

extension, body and motion that Spinoza reached after rejecting Descartes. In order

to characterize his new understanding, one must interpret Spinoza's use of the

words substantiam (substance), attributum (attribute), exprimere (express) and

essentiam Dei (God's essence), which are the key concepts in Spinoza's definitions

of extension and body in Ethics and in his remark to Tschirnhaus in Letter 83.

Before providing an interpretation of these concepts, I think it helpful to

consider another problematic aspect of Spinoza's philosophical system: his theory of

conatus (striving). In 3p6 of Ethics Spinoza holds that “Each thing, as far as it can

20 Ibid., 2p2, 1def4.

21 Ibid., 2def1.

22 Ibid., I/181/10, I/187/10. All references to Spinoza's early works use the standard Gebhardt pagination.



by its own power, strives to persevere in its being.”23 Spinoza draws on 3p6 in order

to argue that “The Mind, as far as it can, strives to imagine those things which

increase or aid the body's power of acting.”24 In order for 3p6 to support this,

Spinoza must hold not only that each thing must strive to avoid its destruction but

also that each thing must constantly strive to increase its causal power. From this it

follows that it is impossible for anything to actively diminish its own causal power.

In the case of self-destruction, this is made explicit by 3p4 which reads “no thing

can be destroyed except through an external cause.”25 Spinoza writes that this “is

evident through itself.”26 Yet this view does not follow from the ordinary sense of

res, the Latin word for thing, that Spinoza uses in these passages. For instance, time

bombs and burning candles seem to cause their own destruction.27 This suggests that

Spinoza might be using res in an unusual way.

A helpful place to turn is Spinoza's definition of a singular thing at the

beginning of Part 2 of Ethics. The definition reads:

2d7: By singular things I understand things that are finite and have a

determinate existence. And if a number of Individuals so concur in one

action that together they are all the cause of one effect, I consider them

all, to that extent, as one singular thing.

The beginning of this definition is unremarkable but the second half is revealing.

The first point worth noting is that Spinoza implies that aggregates of individuals

23 Ibid., 3p6.

24 Ibid., 3p12.

25 Ibid., 3p4.

26 Ibid., 3p4d.

27 I owe these counterexamples to Michael Della Rocca, Spinoza (New York: Routledge, 2008), 138.



can be things to varying extents. It is even more significant that two individuals

which act to produce the same effect are “all, to that extent, one singular thing.”

This does not accord with the usual meaning of thing; for instance one would not

ordinarily say that whenever my roommates and I work together to produce the

effect of clean dishes we become, to that small extent, a single thing. Under what

understanding of thing would this make sense?

Under an ordinary notion of thing the activities of a thing follow from its

nature. Some of its activities may be effects, in part, of outside causes but their

influence on the activities of that thing is mediated by the thing's nature. This real

separation between the nature of a thing and the activities that thing performs allows

a thing to remain distinct from the effects it produces to the extent that two things

can both cause one effect without becoming one thing to any extent. This is clearly

what Spinoza rejects. But under what kind of view would this rejection make sense?

One possible answer, put forward by Francesca di Poppa, is that by thing Spinoza

actually means something like a causal activity or process.28 The nature of a thing

just is its activity. In other words, Spinoza abandons an object-property ontology in

which various ontologically fundamental substrates have properties that inhere in

them. Or, to put it another way, he abandons a view in which actors are fundamental

and activities follow from the nature of actors. The activities of a thing do not

merely follow from the nature of that thing; they are the thing.

An ontology based on activities seems to follow from Spinoza's causal theory

in Part 1 of Ethics. Spinoza holds that “Things could have been produced by God in

28 Francesca di Poppa, “Spinoza and Process Ontology” Southern Journal of Philosophy 48 no. 3 (2010):278-84.



no other way, and in no other order than they have been produced.”29 This

necessitarianism undermines the basis of the traditional distinction between an actor

and its activities. Under an object-property ontology, activities of actors are kept

separate from essences of actors by virtue of that fact that some potentialities are

never actualized.30 To identify me with the activity of doing dishes would not make

much sense under such a view since it is possible that I could have done some other

activity instead. So long as an actor can shed some of its activities while remaining

the same actor, then there must be some distinction between actors and activities.

Spinoza's position that “everything which can fall under that infinite intellect” must

follow “from the necessity of divine nature” collapses this distinction since all

potentialities must be realized.31 At this point there seems to be little left of the actor

except the activities. God is the primary case of this, as a being whose “power, by

which he and all things are and act, is his essence itself.”32 This also holds, as a

secondary case, for finite things by virtue of the fact that they, as Spinoza puts it in

3p6d, “express, in a certain and determinate way, the power by which God is and

acts.” This line of reasoning culminates at 3p7 where Spinoza identifies conatus

with the essence of a thing.

This new ontology elegantly addresses the common objection to 3p4. The

notion that burning candles or ticking time bombs are counterexamples to 3p4

simply reflects a confusion under this new ontology. Ordinary objects, such as

rocks, have a prevailing tendency to maintain stable internal spatial relations. Since

29 Curley, The Collected Works of Spinoza, Volume 1, 1p33.

30 This point is made in di Poppa, “Spinoza and Process Ontology,” 276.

31 Curley, The Collected Works of Spinoza, Volume 1, 1p16.

32 Ibid., 1p34d.



this is the primary effect of the things that make up the rock, the rock is a thing in

the sense that it is a bundle of activities that strive to produce one effect. It is easy to

see how one could mistakenly take stable internal spatial relations to be a

completely general criterion of whether any set of activities is a thing but each of the

apparent counterexamples to 3p4 is a case that shows stable internal spatial relations

is not a general criterion. For instance, consider a ticking time bomb. It is like a rock

in the sense that many of its constituent activities tend to maintain stable internal

spatial relations. Yet some of those activities, namely those leading to detonation,

are striving to produce a contrary effect. This tension between activities with

different effects makes the bomb a thing to a much lesser extent than the rock. It is

because the bomb is, to this extent, not a thing that it is able to destroy itself. More

broadly, any instance of apparent self-limitation can be explained as an effect of

competing causal activities within an aggregate that is only a thing to the extent that

the activities with effects contrary to the stability of the aggregate do not dominate

over those that maintain stability. Any finite thing contains some causal processes

within it that tend to cause its destruction. This would explain why, for instance,

human beings age. Yet those causal processes only exist insofar as the thing is to

some extent not a thing. The detonation of a time bomb is not the actualization of

the potentiality of its entire being. It is only the actualization of a small part of it that

is in opposition to the actualization of other potentialities. Aggregates that

completely satisfy the definition of thing -- that is, infinite things -- do not have this

kind of self-limitation. So neither 3p4 nor 3p6 is liable to these counterexamples.

It is now time to return to the question that began this digression: What does

Spinoza mean by substance, attribute, expression and God's essence? God's essence,

as I have already argued, is just God's power, which I take to mean God's causal



power. This power should not be taken to be a mere potentiality since Spinoza holds

that “everything that can fall under an infinite intellect” must be actualized.33

Instead, God's essence is actualized power, which is to say that it is activity.

Expression describes the causal relationship between two activities in which the

expressed activity is a subactivity of the expressing activity. An attribute is “what

the intellect perceives of substance as constituting its essence” which is the manner

in which the intellect perceives the infinite activity that is God.34 Substance is just

the word that Spinoza uses to denote this infinite activity when he wants to

emphasize its self-sufficiency.

Applying this new interpretation to Spinoza's definitions of extension and

body reveals that each of these terms denotes something that is inherently active.

Extension is an attribute of God, it is a way the intellect perceives the infinite

activity that is God. A body which is “a mode that in a certain and determinate way

expresses God's essence” is a finite subactivity within the infinite activity, God.35

While it is not yet clear that motion, and thereby variety, can be demonstrated from

extension conceived in this manner, it is at least not obvious, as with the inert

Cartesian view of extension, that such a demonstration is impossible. The fact that

extension is a way of perceiving an activity seems to provide promising start for

such a demonstration. This explains why Spinoza tells Tschirnhaus that “an attribute

which expresses eternal and infinite essence” can ground bodily variety whereas

“inert” Cartesian extension cannot.36 The lingering question is how one can

33 Ibid., 1p16.

34 Ibid., 1def4.

35 Ibid., 2def1.

36 Shirley, The Letters, Ep. 81, 83.



demonstrate motion and bodily variety from extension conceived in a Spinozistic

manner.

While it is relatively easy to understand extension and body by taking

activities as fundamental, understanding what Spinoza means by motion and rest is

more difficult. This is in part because Spinoza never defines motion or rest in

Ethics. The fact that a body must be understood at the most fundamental level to be

an activity and not a geometrical object suggests that motion and rest should not be

understood as merely geometrical displacement and its absence but as basic kinds of

activity. In the 'Physical Digression' in Ethics Spinoza holds that ratios of motion

and rest are what give a body its identity; for instance a body which maintains “the

same ratio of motion and rest” despite having all of its parts equally increase or

decrease in size maintains its identity.37 Spinoza never explains how this is supposed

to work in detail. He does acknowledge that his account is sketchy when he says

after the 'Physical Digression' that had his intention been “to deal expressly with

body” then he “ought to have explained and demonstrated these things more fully.”38

This remark supports the view that Spinoza leaves the task of specifying the precise

nature of motion for later work.39 It is unclear what a ratio of motion and rest is

supposed to be but it is clear that they are basic ways a body is a particular kind of

activity.

37 Curley, The Collected Works of Spinoza, Volume 1, 2p13s Lemma 5.

38 Ibid., 2p13s Lemma 7 Scholium.

39 The view that ratios of motion and rest stand as placeholders for something in a more developed accountof bodies is adopted in Jonathan Bennett, A Study of Spinoza's Ethics (Indianapolis: Hackett, 1984), 107.



4. Towards a Spinozistic Theory of Bodily Individuation

Tschirnhaus's challenge to Spinoza to show “how, from Extension as

conceived in your philosophy, the variety of things can be demonstrated a priori”

has not yet been met.40 It is to this task that I will now turn on Spinoza's behalf. That

bodies are individuated by motion and rest is clear from Spinoza's remarks but how

do we get from extension, a way of perceiving an infinite activity, to the finite

subactivities that are bodies? Spinoza gives his first hint in 1p28:

1p28: Every singular thing, or any thing which is finite and has a

determinate existence, can neither exist nor be determined to produce

an effect unless it is determined to exist and produce an effect by

another cause, which is also finite and has a determined existence; and

again, this cause also can neither exist nor be determined to produce an

effect unless it is determined to exist and produce an effect by another,

which is also finite and has a determinate existence, and so on, to

infinity.

Spinoza holds that finite things cannot exist except by being limited by other finite

things. These must be limited by other finite things and so on in an infinite regress.

But this seems to leave an obvious question unanswered. How are we to understand

this infinite regress?

Spinoza conceives of an infinite regress of finite things as an ordered whole

that is an individual in its own right. In 1p11d, Spinoza holds that the existence of




each particular body follows “from the order of the whole of corporeal nature.”41 He

provides a hint of what he means at the end of the 'Physical Digression.' About

composite individuals that are made up of other composite individuals, Spinoza

writes that “if we proceed all this way to infinity, then we shall easily conceive that

the whole of nature is one Individual, whose parts ... vary in infinite ways, without

any change of the whole individual.”42 Thus the order of nature is an infinite series

of individuals of greater and lesser magnitudes, which can be conceived as an

individual itself. The infinite causal regress that grounds the existence of each finite

thing is contained in this individual. The juxtaposition in this passage of “vary in

infinite way” and “without any change to the whole” is paradoxical, especially since

according to Spinoza no property is truly accidental to a thing. How can any part of

a thing vary under this view without changing the identity of the whole? Resolving

the paradox is essential to explaining how the immutability of extension is not

incompatible with variety as Tschirnhaus worries that it might be in letter 59.

Before resolving this paradox, it is helpful to consider another paradox facing

Spinoza in his account of finite bodies. Spinoza holds that all finite things are

limited by something else, which is a kind of imperfection. Yet he also says that

everything other than God is in God as a mode, his famous doctrine of substance

monism.43 But how can imperfections be in God? While considering this problem in

relation to imperfect ideas, Spinoza writes:

2p33: There is nothing positive in ideas on account of which they can

be called false.

41 Curley, The Collected Works of Spinoza, Volume 1, 1p11d.

42 Ibid., 2p13s Lemma 7 Scholium.

43 Ibid., 1p15.



2p33d: If you deny this, conceive (if possible) a positive mode of

thinking which constitutes the form of error or falsity. This mode of

thinking cannot be in God (by 2p32). But it also can neither be nor be

conceived outside of God (by 1p15). And so there is nothing positive in

ideas on account of which they are called false, q.e.d.

This argument concerns the imperfection of false ideas but Spinoza's Parallelism

ensures that it applies equally well to the imperfections of bodies.44 The puzzle at the

heart of the paradox is that imperfection plays a central role in his account of

finitude but lacks positive reality in some fundamental sense.

Both paradoxes can be resolved through an interpretation of activities as

fundamental. Spinoza can argue that the apparent imperfections of subactivities turn

out to be perfections when viewed in the context of the activity of which those

subactivities are a part. For instance, in the turbine of a steam engine the steam is

engaged in the activity of rising and by Spinoza's theory one could say that it strives

to displace higher, denser air. The turbine of the steam engine is connected to some

other element of the machine upon which it performs some kind of work so the

turbine's conatus resists the steam's conatus. To this extent, the steam and the

turbine limit each other and the fact that each is limited means that each has some

imperfection. However this apparent imperfection disappears if one considers the

activity of the engine, of which the turning of the turbine and rising of the steam are

subactivities; each is striving to produce the same effect of powering whatever is

connected to the engine and thus each contributes to the perfection of the whole. For

Spinoza imperfection only arises when activities are viewed out of context of some

44 By Parallelism, I mean Spinoza's thesis that “the order and connection of ideas is the same as the orderand connection of things.” Ibid., 2p7.



broader activity of which they are subactivities.

The paradox of variety and constancy can be explained in a similar manner.

The arms of turbine of a steam engine are constantly changing position as they are

turned by the rising steam. Yet whatever effect the engine strives for, such as

propelling a train at a certain speed, can remain constant. Since a thing's identity is

just the effects it produces, the identity of the engine remains constant. Spinoza can

argue that that all variety works this way.

This argument shows that Spinoza's metaphysical commitments are

compatible with bodily variety but it does not amount to a deduction of variety from

extension that would satisfy Tschirnhaus. Spinoza does not offer any such account in

Ethics so it is hard to know what he would say here. He could argue that the mere

fact that the bodily variety is not incompatible with the metaphysical system in

Ethics is sufficient to establish its existence. After all, Spinoza holds that

“everything that can fall under an infinite intellect” follows with necessity from

divine nature.45 The problem with this argument is that what makes something

possible in Spinoza's view is that it follows from God's essence. Thus, invoking

possibility in order to explain why something follows from God's essence is

viciously circular. Another option available to Spinoza is to argue that the infinite

chain of reasons that explains each finite thing cannot, by virtue of its infinitude, be

fully understood by finite creatures and thus cannot be fully accounted for in his

system. Either of these arguments could free Spinoza of the burden of providing a

detailed account of bodily variety.

45 Ibid., 1p16. Such an account would fit well with the Neoplatonic tradition that influenced Spinoza. Theidea that God actualizes every possibility is a version of the principle of plenitude by which theNeoplatonists explained diversity; see Arthur Lovejoy, The Great Chain of Being (Cambridge: Harvard UP,1936), 52.



Unfortunately, neither of these options finds much support in the texts.

Spinoza does not respond to Tschirnhaus's demand for a demonstration of bodily

variety by invoking the position that all possibles exist. Nor does he ever argue that

the demand places too heavy a burden on his metaphysics. Instead Spinoza writes

that he has not had time to work out such an account and that he will do so if he

lives long enough. This implies that such an account can be provided and echoes his

earlier admission, at the end of the 'Physical Digression,' that his account of bodies

in Ethics is not fully worked out. Perhaps a fuller account of motion and rest which

explains how ratios of motion and rest determine bodily identity might also explain

the origin of bodily variety. Whether such an account can be worked out in detail

with the help of hints from other parts of Spinoza's work is a question that I leave

for further work on this topic

5. Conclusion

An interpretation of Spinoza's ontology which takes activities and not

property-bearing objects as the basic entities allows a more satisfactory reading of

his theory of bodily individuation in Part II of Ethics. Extension, body and motion

do not have their usual geometrical meaning, instead extension is a way of

perceiving God's infinite activity, bodies are finite subactivities of this activity and

motion is a basic way of being an activity. This reading is supported by Spinoza's

remarks in letters to Tschirnhaus and by the fact that it explains away the apparent

counterexamples to Spinoza's theory of conatus. It represents significant progress

toward a Spinozistic theory of bodily individuation; in particular, it resolves the

paradoxes associated with the existence of apparently imperfect things and with an

order of nature that varies in infinite ways but remains the same. However



significant work remains to be done before a complete account of Spinoza's theory

of bodily individuation is possible.

The interpretation of Spinoza's view of extension that I have offered here is

opposed to the influential view put forward by Jonathan Bennett in A Study of

Spinoza's Ethics.46 Since this view serves as a starting point for several rival

attempts to interpret Spinoza's theory of bodily individuation, it is worthwhile to

explain why the account offered in this paper provides a more promising approach.47

Bennett adopts what he calls a field metaphysic in order to account for Spinoza's

view of extension. Under this view extension is still conceived as length, width and

depth just as in the Cartesian view; the major difference is that bodies are regions of

space with the same properties predicated upon each point of that region and

moving bodies are represented by four-dimensional “strings” of place-time points.48

Variety is explained through the different qualities that can be predicated upon these

place-times.49 Working from Bennett's theory, Don Garret argues that motion and

rest can fulfill this role if they are understood as force rather than mere translation.50

On the surface, this would seem to make sense of Spinoza's theory of bodily

individuation in the 'Physical Digression.'

46 Bennett, A Study of Spinoza's Ethics, 88-91.

47 For two interpretations which take Bennett's field metaphysic as a starting point, see Don Garrett,“Spinoza's Theory of Metaphysical Individuation,” in Individuation in Early Modern Philosophy:Descartes to Kant, ed. Kenneth Barber and Jorge Garcia (Albany: State University of New York Press,1994), 73-102 and Valtteri Viljanen, “Field Metaphysic, Power, and Individuation in Spinoza,” CanadianJournal of Philosophy 37 no. 3 (2007): 393–418.

48 Bennett, A Study of Spinoza's Ethics, 89.

49 Ibid., 108-10.

50 Garrett, “Spinoza's Theory of Metaphysical Individuation,” 80.



Unfortunately a major problem faces this approach. Extension as conceived

by Bennett is no more inherently active than it is for Descartes. Bennett would

probably contend that extension is active since moving bodies, which are active, are

just things that are predicated upon extension, which is a kind of force field.

However there is nothing about the structure of extension in Bennett's view that

rules out the possibility of a static world. It is perfectly possible that the extended

substance of the field metaphysic could always and everywhere have the same

quality predicated upon it. Calling this quality active does not improve the situation.

What makes an activity active is that it can cause some change and no change is

possible in a uniform world. to get variety one would have to impose different

qualities arbitrarily upon the uniform structure of extension.51 This is exactly the

kind of solution that Spinoza rejects when he refuses to invoke God as a first mover

as Descartes does. For Spinoza the cause of motion must already be contained in

extension prior to the existence of any moving thing. This is what is achieved by

conceiving of extension as a way of perceiving God's infinite activity and bodies as

subactivities within that activity. Only a view such as this offers any hope of

meeting Tschirnhaus's demand, the validity of which Spinoza never disputes, for a

demonstration of variety from extension as it is conceived in Spinoza's philosophy.

Acknowledgements

I would like to thank Professor Peter Machamer for the helpful andencouraging comments he provided on several drafts of this paper. Iwould also like to thank Nate Hilberg, Mike Giazonni, and the entireUniversity of Pittsburgh Brackenridge Community for providing thestimulating environment in which my ideas on Spinoza's theory ofactive extension first formed.

51 This is essentially the same point that Leibniz makes against an absolute theory of space in his third letterto Clarke. Leroy Loemker, trans. Philosophical Papers and Letters (Dordrecht: D. Reidel, 1969), 682.



References:

Anderson, Wallace. “Cartesian Motion.” In Motion and Time, Space and Matter, edited byPeter Machamer and Robert Turnbull, 200-23. Columbus: Ohio State UP, 1976.

Bennett, Jonathan. A Study of Spinoza's Ethics. Indianapolis: Hackett, 1984.Cottingham, John, Robert Stoothoff, and Dugald Murdoch, trans. The Philosophical

Writings of Descartes, Volume 1. Cambridge: Cambridge UP, 1985.Curley, Edwin, trans. The Collected Works of Spinoza, Volume I. Princeton: Princeton UP,

1984.Della Rocca, Michael. Spinoza. New York: Routledge, 2008.Garrett, Don. “Spinoza's Theory of Metaphysical Individuation.” In Individuation in Early

Modern Philosophy: Descartes to Kant, edited by Kenneth Barber and Jorge Garcia,73-102. Albany: State University of New York Press, 1994.

Loemker, Leroy, trans. Philosophical Papers and Letters. Dordrecht: D. Reidel, 1969.Lovejoy, Arthur, The Great Chain of Being. Cambridge: Harvard UP, 1936.Machamer, Peter. “Causality and Explanation in Descartes's Natural Philosophy.” In

Motion and Time, Space and Matter, edited by Peter Machamer and Robert Turnbull,168-99. Columbus: Ohio State UP, 1976.

di Poppa, Francesca. “Spinoza and Process Ontology.” Southern Journal of Philosophy 48no. 3 (2010): 278-84.

Shirley, Samuel, trans. The Letters. Indianapolis: Hackett, 1995.Viljanen, Valtteri. “Field Metaphysic, Power, and Individuation in Spinoza,” Canadian

Journal of Philosophy 37 no. 3 (2007): 393–418.


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Active Extension and Bodily Variety in Spinoza