## 1. Sources and context



While the other two great rationalists, Descartes and Leibniz, were
physical theorists and mathematicians of the first rank, who made
substantial contributions to the development of physical science, the
same cannot be said of Spinoza. Nor was Spinoza a systematic
experimentalist. Indeed, his contributions to the historical
development of physical theory are minimal. This is not because the
physical theory he presented was rejected or overlooked, but rather
because Spinoza simply never presented a physical theory as such. Most
of his writing concerning physical theory is instead in the service of
other ends: exegetical, as an expositor of Descartes' philosophy;
metaphysical, in elaborating, for example, the relationships between
God or Nature as the single substance and the finite things he treats
as "modes" thereof; or psychological, in explaining the
distinctive characteristics and possible blessedness of the human mind
as the idea of an especially complex individual body.



The main sources of evidence for Spinoza's thought concerning physical
nature are his *Principles of Cartesian Philosophy*, the first
half of his magnum opus the *Ethics,* and a number of important
letters from his correspondence. The *PCP* contains by far the
most focused and detailed of Spinoza's writing on physics proper, but
is officially billed as an exposition of Descartes. The first half of
the *Ethics* presents a physical theory only insofar as Spinoza
finds this necessary to serve his goals in that work to explicate the
nature of God and the natures and origins of the human mind and its
affects. Discussion of the physical in the correspondence, though
often illuminating, is typically directed at providing either
clarification or defense of his views in response to queries and
objections, or at discussing contemporary views and developments in
experimental and theoretical science in order to show that they are
either mistaken or consistent with his own views.


## 2. Overview of the *Ethics* as it bears on physical theory



The philosophical view that emerges from the *Ethics*, in so
far as it bears on physical theory, can be outlined as follows. God or
Nature is the unique substance (Ip14), existing essentially (Ip7),
infinite in power (Ip8), and characterized by infinite attributes,
each constituting its essence (Id4). Finite things are but
modifications of that substance, and not themselves independent beings
(Ip14); bodies in particular are modes of substance conceived under
the attribute Extension. God or Nature, as the ultimate cause of all
things, is also the cause of all the particular modifications of
extended nature (Ip18). However, substance's power is not expressed
through the operations of will and intellect; the one substance does
not act by conceiving a design in the intellect and bringing it to
existence through the will (Ip23cl, Appendix, I). Hence Nature is not
a teleological system, natural phenomena do not have purposes, and all
causation between modes is efficient, none final. Since things are
conceived through their causes, and modes are conceived always through
the attribute to which they belong, there can be no trans-attribute
causation. Bodies and their modifications cannot cause ideas, and
ideas cannot cause modifications of bodies (IIp6). All modes are
conceived through the substance in which they inhere; in this sense
God or nature is an indwelling cause of all things (Ip18). But the
particular modifications of Extension are causally necessitated
entirely by the determining operation of prior modes of the same
attribute, themselves so determined, *ad infinitum* (Ip28). The
physical domain is thus completely closed causally, impervious to
influence from modes of other attributes and to intervention of divine
will, and fully deterministic (Ip29).



Thought is another attribute through which substance is conceived
(IIp1). Since substance is unique, and the attributes simply various
essences under which it is conceived, the series of finite modal
causes in each attribute must operate strictly in parallel with one
another (IIp7). For every modification of Thought there is a
modification of Extension it mirrors, and vice versa; and the causal
order of the one is perfectly matched with that of the other. The
mind, a finite mode of Thought, is, under this parallelism, simply the
idea of the body to which it corresponds under the parallelism
(IIp13). The economy of ideas is precisely as closed, necessitated and
deterministic as that of bodies.



Bodies are individuated one from the other, not by reason of
substance, but rather by reason of motion and rest (IIp13sl1),
individual identity through time and change being a matter of the
dynamic maintenance of a distinctive ratio of motion and rest of a
body's parts (IIp13s Def.). The human body is simply a particularly
complex individual body, capable of maintaining its distinctive
structure through a wide variety of externally imposed modifications,
and capable of forming corporeal images of those bodies that affect
it. An affect that increases the body's ability to maintain its
distinctive ratio is paralleled in the mind by a modification that
increases that mind's power of thought, and the passage from lesser to
greater power is joy (IIIp11s, Affect Def. II). Modifications that
decrease the power of a body to maintain its individual ratio are
paralleled by modifications decreasing the mind's power of thought,
and such passages are sadness (IIIp11s, Affect Def. III). Further,
individuals, both minds and bodies, strive to persevere in their
existence as far as they can; that is to say, they strive to increase
the power by which they maintain their distinctive natures (IIIp6).
Bodies, then, have essences, which are powers of striving (IIIp7). The
causal interactions in which a body participates that are attributable
to the action of that body increase its power of perseverance; it is
in contrast passive with respect to those that diminish its power.
Evidently, for Spinoza, strict necessitarian determinism is consistent
with a genuine distinction between action and passion, between doing
and suffering an act.



Several fundamental and distinctive issues of interpretation
pertaining to the physical arise from this picture. How are bodies to
be conceived, if not as independent substances? How are motion and
rest to be conceived so as to make sense of the claim that bodies are
individuated by them? How are the principles of inertia and the
collision laws that follow from it to be accounted for, given that
they cannot be grounded in God's immutable will? What is the nature of
the individual striving of bodies, and how can it be reconciled with
Spinoza's deterministic dynamics of Extension? These issues cannot be
addressed independently of one another. The present discussion will
approach them as they emerge from Spinoza's engagement with Cartesian
physics, beginning with the *PCP*'s exposition of
Descartes' views.


## 3. Physical cartesianism and the consequences of metaphysical divergence


### 3.1 Areas of agreement and divergence



Spinoza agrees with the Cartesian conception of body as *res
extensa* (Latin, extended thing), i.e., things necessarily and
exhaustively conceived through
 extension.[1]
 He was, like Descartes, a plenist, rejecting the intelligibility of a
vacuum. Furthermore, we know from Spinoza's correspondence that he
accepted nearly all of Descartes' kinematic views, that is, the laws
he articulated *describing* the course of physical phenomena.
He likewise agrees with Descartes that physical nature should not be
conceived as a teleological system, and that appeals to final causes
should be banished from physical theory.



Yet Spinoza had substantial disagreements with Descartes over a wide
range of metaphysical issues that bear on physical theory. Most
obviously, he rejected Descartes' dualism of extended and mental
substances in favor of substance monism, and correspondingly rejected
Cartesian mind-body interactionism. Some of these metaphysical
disagreements penetrate right to the grounds of the physical views the
two thinkers share, revealing much of their agreement to be quite
superficial. Consider, for example, their shared rejection of appeals
to final causes in physics. Descartes held that final causal or
teleological thinking is useless in physics, not because physical
nature is not in fact teleological, but because our finite
understanding cannot hope to understand the divine will, hence cannot
grasp the purposes with which physical nature is imbued. For Spinoza,
in contrast, the problem is not epistemological but metaphysical. The
divine cause of the world has no will, and does not create things with
a plan in mind (1p32c, p33d, s2); hence nature is simply not a
teleological system at all.



Spinoza's agreement with the Cartesian laws of nature and collision
provides a telling set of further examples. Spinoza explicated and
elaborated on these at length and in detail in the *PCP*.
Interpreting this work as an expression of Spinoza's own thinking is a
delicate matter, since its explicit aim is to present and explicate
Descartes' views, not Spinoza's own. Despite this, the *PCP*
provides a number of indications of where Spinoza diverges from
Descartes on the metaphysical foundations of physics. In particular,
the demonstrations Spinoza offers of most of the basic principles of
Cartesian physics are often significantly different from or
supplementary to Descartes' own, and seem to presage important
elements of Spinoza's mature thought as expressed in the
*Ethics*.



One such supplement involves Spinoza's attempt to extend the range of
application of Descartes' collision rules. Descartes' collision rules
are limited in scope to the special case of bodies moving along a
single line. In a scholium following a corollary Spinoza adds to
Descartes' third rule, Spinoza explains that the vexed Cartesian term
"*determinatio*" (determination) signifies not just
the direction of a motion, but also a force of motion along that
direction (*PCP* IIp27s). He then attempts to demonstrate how
the Cartesian collision laws can be extended to oblique collisions, by
showing how this force can be resolved into components by the rule of
parallelograms. Spinoza's confused attempt fails, but this failure is
not of much interest on its own. Given that the oblique case is surely
more ordinary than the collinear case, and given that generality of
application is something one would surely want in collision laws, what
is interesting is why Descartes did not himself attempt to provide
rules of more general coverage, and why Spinoza felt that he had to do
so.



A plausible answer lies in a difference in their views as to the
degree and way in which physical nature forms a closed system.
Descartes held that quantity of motion, conceived as the product of
speed and bulk, is conserved in all physical
 interactions.[2]
 This view allowed him to hold that mental substances can interact
with bodies and influence their motions, so long as they influence
only their direction. But given such influence, there can be no fully
general physical laws covering collisions. The precise state of a
physical system for Descartes cannot be determined by its prior state
plus the laws of
 nature.[3]
 In this sense Descartes was not a physical determinist. Given that
the possible intrusion of extra-physical influence precludes fully
general collision laws, Descartes might not have thought it worthwhile
to puzzle too much over the formulation of laws concerning non-linear
motion, thinking it sufficient to illustrate the application of the
principles governing interaction only in the simplest cases.



Spinoza emphatically rejected Cartesian interactionism. For him,
extended nature is an entirely closed system. All the determinations
of body, including not just quantity of motion but also direction, are
wholly accounted for by the causal determination of other bodies,
combined with the nature of the body in question. Spinoza makes this
quite clear in Ip28:



> 
> 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 determinate existence
> ... and so on, to infinity.
> 



Since modes of distinct attributes cannot cause or explain one
another, and since God is the cause of modes only insofar as he is
considered to be affected by another thing under the attribute of
which they are modes (IIp6, IIp9), it follows that every determination
of an extended thing results from the exclusive determining operations
of other extended things. In this light, Spinoza should have felt more
acutely than Descartes the need for a set of collision laws of fully
general application.



Unbeknownst to him this need could only be met effectively by the
rejection of Descartes' conservation law. Spinoza nowhere calls this
law explicitly into question, and his acceptance of Descartes'
collision laws strongly suggests that he did in fact accept it. But he
cannot have accepted the metaphysical grounds Descartes offers for it.
For Descartes, substances are dependent for their existence at every
moment upon God's concurrent creative activity, and since God's will
is constant, he always recreates the whole of the extended world with
exactly the same quantity of motion as he put there in the beginning.
Each and every one of Descartes' laws of motion is for him
metaphysically grounded in the immutability of the divine will. But
Spinoza's God has no will, and the world is not a product of creation,
in the sense in which creation follows from a decision to act in
accord with a conception formed in the understanding. Spinoza's own
commitment to rationalism nonetheless demands that there be some
reason for the conservation of motion.


### 3.2 The principle of least modal mutation



This divergence over the possible metaphysical grounds for natural
laws and collision rules is important for understanding what is
fundamentally at stake in another of Spinoza's supplements to what
Descartes had himself offered in his *Principles of
Philosophy*. In a letter to Clerselier, Descartes makes clear that
of all of his rules of collision "depend on *only* a
single principle, which is that when two bodies collide, and have in
them incompatible modes, there must undoubtedly occur some mutation of
these modes to make them compatible, but this mutation is always the
least possible" (Descartes 1964-74: V, 185, emphasis
added). Following Gabbey (1996), call this the "Principle of
Least Modal Mutation" (PLMM). Despite is importance, Descartes
neither mentions the PLMM is his *Principles*, nor offers a
justification for it in the letter to Clerselier or elsewhere.



In the *PCP*, Spinoza includes the principle Descartes left
out, and offers the demonstration Descartes never attempted.
*PCP* IIp23 states: "When the modes of a body are forced
to undergo variation, that variation will always be the least that can
be." The demonstration consists of a concise and exclusive
appeal to *PCP* IIp14, Spinoza's rendering of Descartes' law of
inertia, according to which "Each single thing, insofar as it is
simple and undivided and is considered only in itself, always
perseveres in the same state, as far as it can". But just as
Descartes never explains why the PLMM is true, Spinoza never explains
why the principle of inertia supports the PLMM. Moreover, as
formulated in *PCP* IIp14, it seems *prima facie*
inadequate to do so. *PCP* IIp14 speaks of what happens to a
body *only* as it is considered in itself, simple and
undivided, whereas *PCP* IIp23 speaks of bodies undergoing
variation imposed by other bodies, and is not limited to simple and
undivided bodies. And even supposing *PCP* IIp14 relevant to
what goes on with bodies when considered as affected by other bodies,
it does not give any obvious guidance as to what then occurs. It seems
on the face of it quite possible that the least total modal variation
commanded by *PCP* IIp23 might involve a greater variation on
the part of each of the colliding bodies than would be consistent with
either body in question persevering in its state as far as it can on
its own. We are of course told they always remain in the same state
"as far as they can." But for this qualification to be of
any relevance, it will obviously have to mean "as far as they
can, in the face of the influence of external bodies"; but until
we know the content of the collision laws, we are not entitled to say
how the influence of external bodies affects a body's inertial
tendency. Yet it is just this content we need *PCP* IIp23 to
derive.



How, then, might inertia be understood so that it supports the PLMM?
In good rationalist fashion, we should expect to come to a sound
understanding of the principle of inertia by attending to the grounds
from which it follows. But just as in the case of the Cartesian
conservation law, Spinoza cannot himself have accepted the Cartesian
strategy of grounding inertia in the immutability of God's will.
Spinoza offers his own principle of inertia in the so-called
"physical interlude" of the *Ethics,* at IIp13 L3C:
"a body in motion moves until it is determined by another body
to rest; and a body at rest also remains at rest until it is
determined to motion by another". Rather than appealing to
divine will, Spinoza's demonstration of this principle seems to
proceed from causal rationalism alone.



> 
> When I suppose, for example that a body A is at rest and I give no
> consideration to other moving bodies, I can assert nothing about body
> A but that it is at rest. Now if it should thereafter happen that body
> A is in motion, this surely could not have resulted from the fact that
> it was at rest; for from that fact nothing else could have followed
> than that body A should be at rest.
> 



Since nothing in the conception of a thing as moving or at rest,
without regard to other things, could explain a change in its motion
or rest, something outside that conception is required to do so. This
demonstration cites no previous propositions or axioms of the
*Ethics*; indeed Spinoza claims his principle of inertia is
"self-evident".



But it would be unsatisfying to take inertia as primitive--to say
that bodies in fact do tend to persist in their states, though there
is no reason to be discerned in their nature why they do so. To say
this would be to take it that Spinoza accepted the Cartesian principle
as Descartes understood it, while rejecting the grounds Descartes
offered for it, and without providing any substitute for it. This is
dissonant indeed with the general tenor of Spinoza's
 rationalism.[4]
 Moreover, on this view, Spinoza would have taken the trouble to make
explicit the PLMM Descartes' rules require, only to justify it by a
direct and unelaborated appeal to a groundless principle of inertia,
which seems, on Descartes' understanding of it, quite inadequate to do
the job. Yet Spinoza evidently did think that the PLMM followed from
the principle of inertia. This suggests that he had a different
conception than did Descartes of both the nature and ground of that
principle.


### 3.3 The principle of inertia and striving



An intriguing shift in the language Spinoza uses in the *PCP*
to articulate the Cartesian laws of motion is suggestive of how
Spinozistic and Cartesian inertia may differ. In *PCP* IIp16,
Spinoza states "every body which moves in a circle, as for
example, a stone in a sling, is continuously determined to go on
moving along a tangent." The immediately succeeding proposition,
*PCP* IIp17, states, "Every body that moves in a circle
*strives* to move away from the center of the circle that it
describes" (emphasis added). Spinoza has substituted
"strives" for "is continuously determined to
do", the Latin "*conari*" for the
"*tendere*" of *PCP* IIp16, which is what
Descartes had used in expressing his own version of the law of
centrifugal motion. This substitution arguably involves a shift in
dynamical implication. *Conari* usually has the sense of the
English "exertion", "effort"
"undertaking", or "impulse"; reading
*conari* in accord with this usual sense, *PCP* IIp17
not only describes what a body moving circularly will do when it is
not compelled by an external cause, but attributes that action to the
effort or impulse of the moving body. *PCP* IIp17's invocation
of *conari*, if we read it in this active sense, signals an
ongoing effort, a continuous directedness, in this case, at
homeostasis.



One must be quite circumspect in drawing inferences from this
terminological shift on Spinoza's part. For one thing, the word for
which *conari* is substituted, *tendere*, can have
similar connotations itself, carrying the sense of a try or an
attempt. For another, "*conari"* is, as Curley
points out (Spinoza 1985, p. 280 n. 43), a perfectly good Cartesian
word, and in Descartes' usage, it is quite clear that
"*conari"* is not intended to imply anything really
active on the part of the "striving" body. In
*Principles* 3.56, Descartes tells us that the striving
(*conari*) after some motion of inanimate things "merely
means that they are positioned and pushed into motion in such a way
that they will in fact travel in that direction, unless they are
prevented by some other cause". Spinoza faithfully reiterates
this passive sense of "striving" on Descartes' behalf in
*PCP* IIId3. On the other hand, "*conari"*
is also cognate with a perfectly good Spinozistic word,
"*conatus*", which is his term in the
*Ethics* for an individual's inherent power of striving to
persevere in its being (IIp6). Spinoza identifies this power as the
essence of the individual (IIIp7), and further identifies its increase
with the individual's increased power of action, as opposed to
passion, that is, with an increase in power of self-determination as
opposed to external determination (IIIp11). This suggests that
"*conari"*, as Spinoza intends it, involves
something more than the mere passive tendency the term signifies for
Descartes. Recalling once again that the inertial tendency of bodies
described in *PCP* IIp14 cannot, for Spinoza, be accounted for
by appeal, in the manner of Descartes, to divine will, the
substitution of "*conari"* for
"*tendere"* in *PCP* IIp17 may signal the
fact that Spinoza is all along thinking of inertia as resulting from
an active principle in bodies as such.



If Spinoza's principle of inertia is to provide a ground for
*PCP* IIp17 taken as involving "*conari"* in
an active sense, then it must be taken to amount to the claim not just
that bodies will not in fact change their state unless externally
determined to do so, but also that even while external causes are
acting on a body (e.g., the sling holding the stone in circular
motion), the body's own impulse is at work actively endeavoring to
determine it to move as it would in the absence of that external
cause. And reading Spinozistic inertia this way, imputing to the body
a continuous *effort* to move so as to maintain the state it
would be in absent external determination, also suits it to ground the
PLMM. Given the symmetry of interaction, each of the bodies to an
interaction, being externally determined to change by the other, will
strive to resist change as far as it is able. Plausibly, then, the
total change of state resulting from the resolution of the opposition
of the interacting bodies will be the least total possible. This
suggests, at least tentatively, that even in the *PCP*, Spinoza
is at work attempting to shore up worries in the foundations of
Cartesian physics that stem from the unduly passive Cartesian
construal of the equation of body with extension.



### 3.4 Striving and teleology



Quite apart from the question whether Spinoza intended to impose this
more active reading of inertial dynamics on Cartesian philosophy,
either deliberately or unawares, he clearly made the striving conatus
of individual modes an important centerpiece of the mature philosophy
he presented in the *Ethics*. IIIp6, which articulates the
conatus doctrine according to which "each thing, as far as it
can by its own power, strives to persevere in its own being",
has been the subject of a great amount of interpretive puzzlement in
the literature. A main focus of this puzzlement is the extent to which
IIIp6 represents a teleological element in Spinoza's natural
philosophy. It is certainly central to Spinoza's subsequent treatment
of human psychology, according to which we strive to obtain those
things that increase our power and to avoid those that diminish it.
Spinoza takes his conatus principle to license inferences from
sentences of the form "*x* would increase
*A*'s power" to sentences of the form
"*A* does *x* so far as *A* is able";
this is genuine explanatory teleology, treating a state to be
achieved--the increase of power--as an end towards which a
thing's activity is directed, and thus as an explanatory ground for
behaviors.



One ground for reading teleology out of the conatus principle and for
regarding both teleology and that principle as fundamentally
irrelevant to Spinoza's physical theory is that the latter's first
explicit appearance in part III of the *Ethics* comes long
after Spinoza presents his accounts of extended nature and the basic
mechanics of modes thereof, indeed in a way that makes it very hard to
see how any teleology could be involved at all. Ip28 denies that any
singular thing can be determined to exist or to produce an effect
unless it has been so determined by a prior finite cause, ad
infinitum. The use made of Ip28 in IIp9 suggests that Spinoza intends
Ip28 to articulate not just a necessary condition on modal existence
and determination, but the exclusive means by which finite modes are
brought to existence and determined to have any particular effects.
This seems to allow no room for action of bodies in their own right,
no residual space for any contribution to the motions of bodies of the
active striving of the moving bodies themselves. Moreover, Spinoza
expressly denies that nature is a teleological system, and claims that
final causal/teleological explanations "turns nature completely
upside down. For what is really a cause it considers as an effect, and
conversely, what is an effect it considers as a cause"
(Appendix, I).



In this light, the problem from the standpoint of the metaphysics of
Extension -- the basis of physical theory--is to explain why
the specific configuration of a given existing mode makes any
contribution at all to the determinations that result from the
operation of external modal causes. It would be rash to read Ip28 in
such a way that the causal powers of a body owe everything to the
contributions of extrinsic causes, and nothing to the intrinsic nature
of the body itself. Spinoza says in IIp13s A1 that "all modes by
which a body is affected by another body follow both from the nature
of the body affected and at the same time the nature of the affecting
body, so that ... different bodies may be moved differently by
one and the same body." (This is a key point in Spinoza's
account of corporeal imagination, mental representation and the first
kind of knowledge, offered at IIp17-41.) So the nature of an
affected body makes a difference to the way it is affected
extrinsically. This is not surprising. But then what explains why a
body's nature makes a contribution to the way extrinsic influences
determine it? As we saw in the previous sections, some answer to this
question is required to make sense of the PLMM, and hence of all of
the collision laws. The notion, shared by the teleological reading of
conatus and the active reading of Spinozistic inertia, that it is in
the nature of bodies actively to strive of their own power, would seem
to help. But is it Spinozistic? At a minimum, any articulation of this
notion must be free from illicit teleology. Carriero (2017)
suggests a non-teleological reading of the conatus doctrine that seems
suitable. On his view, conatus should be understood as an
expression of the idea that it is constitutive of their finite
individuality that individuals maximize their being. 
"Dynamic constructions do tend to maximize their being. But
this is not because their reality is their end or good; it is an
artifact of their stability as real individuals in the plenum"
(152). But what accounts for this stability? We require a
more probing examination into Spinoza's conception of the nature of
individual bodies.


## 4. Bodies as modes of substance and as individuals.



As noted above, Spinoza accepts the basic Cartesian view that physical
things are *res extensa*--extended things. However,
whereas Descartes held that distinct bodies are distinct extended
substances, Spinoza famously holds that there is but one
substance--God or nature--and that distinct bodies are
merely modes of this one substance, considered as extended. Spinoza's
substance monism is in part motivated by inadequacies in the Cartesian
view. Descartes officially defines substance in terms of independence:
a substance is that whose existence depends upon no other thing. But
only God satisfies this definition, all other beings depending on God
for their existence. So Descartes also allows for finite
substances--minds and bodies--that are dependent only upon
God. But it is only in an equivocal sense that both God and created,
finite bodies and minds are substances. Spinoza will have none of
this. For him, independence is the *sine qua non* of substance,
and nothing that is not its own cause -- nothing whose existence
is not of its essence--is independent. Hence nothing finite and
created is substantial. Further, since everything is either in itself
or in another (Ia1), finite things like bodies are in substance, that
is, they are in some way features of the one substance.



This denial of substantiality to bodies gives rise to an important
interpretive issue. The traditional concept of a substance has at
least two important strands. One is the idea we have already seen, of
substance as independent. Spinoza clearly means his
'demotion' of bodies to modal status to be a denial that
they are substances in this sense. But another is the idea of a
substance as an ultimate subject of predication, that is, as something
of which properties or relations may be predicated, but which is
itself never predicated of anything else. Does Spinoza mean to deny to
bodies and other finite things this status as an ultimate subject as
well? That is, is talk of bodies fundamentally to be construed for
Spinoza as predicative or adjectival on substance? Or do bodies,
though they are not substances, nonetheless lie on the subject side of
the subject/predicate divide, themselves bearers of properties, but
not strictly properties of anything else? This matter is of the utmost
importance for the understanding of Spinoza's physical theory, since
deciding that Spinoza held bodies to be in fact ways substance is and
adjectival on it, in accord with the former interpretation, requires
that bodies as ordinarily conceived must be thought of as arising from
and reducible to some more fundamental qualitative variation in
spatiotemporal regions of extension. This has the consequence, to some
commentators salutary, of rendering Spinoza physical theory strongly
prescient of contemporary physical views, in which ultimately physical
nature is conceived as a field of gradient forces, bodies being not
ultimate, but rather the consequences of particular local
concentrations of certain classes of those forces, yielding certain
characteristic effects in interactions, which effects we take as
marking the presence of bodies.



In favor of the adjectival reading (promoted by Bennett 1984) is
Spinoza's use of the term "modus", or "mode",
in connection with bodies; this term regularly signifies a way
something is, or a feature it has, functioning to group what are
clearly predicates of things, and in Cartesian usage it means both
this and a dependent being. Against the adjectival reading, and in
favor of the view (promoted by Curley 1988) that Spinozistic bodies
and minds are ultimate subjects of predication, is Spinoza's
persistent references to bodies as individuals and as 
 things.[5]

The
adjectival view of bodies, unlike the subjectival, must therefore face
the difficult general question how individuals or things can be
predicated of other individuals or things. However, the question of
how bodies are individuated--the principles according to which
they are distinguished from one another and maintain identity through
time and change--presents especially interesting and thorny
difficulties for both the adjectival and subjectival views of
bodies.


## 5. Individuation of bodies and the variety in matter



While Descartes does claim (at least most of the time) that individual
bodies are distinct substances, he does not invoke this claim in his
official account of the individuation of bodies. The account he does
offer is highly problematic. Descartes holds "all the variety in
matter, and all the diversity of its forms, depends on motion"
(*Principles* 2.23). Thus the distinction between bodies is
constituted of distinctions in the motions of regions of extension. On
the other hand, Descartes defines motion "in the strict sense of
the term", as the relative change of position of a body relative
to those bodies with which it is immediate contact
(*Principles* 2.25). The circularity here is obvious, and
crippling. Diversity and variety of bodies depends on motion, but
motion depends upon a prior distinction between bodies.



That Spinoza was aware of the problem Descartes' views had accounting
for variety in extension is clear: in the late and much discussed
letter 83 to Tschirnhaus, Spinoza writes,



> 
> With regard to your question as to whether the variety of things can
> be demonstrated a priori solely from the conception of Extension, I
> believe I have already shown sufficiently clearly that this is
> impossible, and that therefore Descartes is wrong in defining matter
> through extension; it must be explicated through an attribute that
> expresses eternal and infinite essence.
> 



Spinoza goes on to express the hope that he may live long enough to
discuss these matter more clearly, since "there has been no
opportunity ... to arrange these matters in proper order."
He died before the opportunity arose.


### 5.1 The Physical Interlude



But perhaps he did present all the elements of these matters, though
in improper, hence inadequate, order. The obvious place to look for
such a presentation is in the so-called "Physical
Interlude" (hereinafter PI) following IIp13s, in which Spinoza
gives his most extended and detailed discussion of his own views about
the nature of bodies and their principles of distinction and
individuation. But the PI seems to offer little
 help.[6]
 First, at least at the time of letter 83, Spinoza thought that what
was needed to help explain variety in matter was an appeal to an
attribute that expresses infinite and eternal essence. Yet the text of
the PI makes no appeal to the infinitude, eternality or expressive
nature of extension or any other attribute. More importantly, at least
on the face of it, the account of the individuation of bodies
presented in the PI moves in much the same futile circle as that
offered by Descartes. That motion serves to individuate bodies is
quite explicit in PIDL1: "Bodies are distinguished from one
another by reason of motion and rest, speed and slowness." PID5
goes on to define "body, or Individual", in terms of
motion, and in a way that presupposes a plurality of bodies:



> 
> When a number of bodies, whether of the same or of different size, are
> so constrained by other bodies that they lie upon one another, or, if
> they so move, whether with the same degree or different degrees of
> speed, that they communicate their motions to each other in a certain
> fixed manner, we shall say that those bodies are united with one
> another and that they all together compose one body or Individual,
> which is distinguished from the others by this union of bodies.
> 



Since "body or individual" is here defined in terms of the
relations among a plurality of bodies, PID5, to the extent it is meant
to cover all bodies, is at best an inductive step of an inductive
definition of body. The obvious candidates for the base case are what
Spinoza calls "the simplest bodies", but the description
and differentiation of these is likewise in terms of their motion and
rest. Indeed, they "are distinguished from one another
*only* by motion and rest" (PIL7s, italics
added).[7]
Spinoza, then, appears to
accord with Descartes in taking bodies to be distinguished by their
respective motion and rest. But motion and rest seem in the first
instance to be determinations *of bodies*. So the motion of
bodies seems to presuppose a prior ground of their individuation.



Commentators have tried various strategies for finessing the apparent
circularity in the PI's account of the diversity in matter. Klever
(1988) urges that the key to understanding Spinoza's concept of matter
is to see that physical nature is not to be conceived as an infinite
extended expanse that somehow is put into motion, but as,
fundamentally, matter-in-motion ("*moles in
motu*"). According to Klever, "movement and rest in
extension are examples of immediate production by God, whereas the
face of the universe with its infinite variations is an example of the
mediate effects, which are a product of movement in its turn."
On this interpretation, Spinoza, rather than seeing motion as a
received quality of matter, conceives "matter as consequence of
motion" (Klever 1988, p. 171). This reading arguably answers
Spinoza's call to explain the variety in matter through an attribute
that expresses eternal and infinite essence. If God creates extended
matter, and then, in a separate act, sets it in motion, the attribute
of Extension would not suffice as an eternal expression of infinite
essence, since it requires God's additional action in its expression
of power.


### 5.2 Interpreting "motion and rest"



But if this is right, then "motion and rest" of the
physical interlude cannot simply be the ordinary motion and rest of
bodies. What then are they? Klever waxes vague and anachronistic here,
straightaway seeking to validate his claim rhetorically by citing it
as precedent of the view of contemporary physics: "in this
reversal [Spinoza] anticipates modern physics by which mass is
considered as product of energy" (ibid). (Hampshire (1987)
contains similar remarks).



Jonathan Bennett's influential reading agrees that Spinoza's physical
theory anticipates contemporary views. He also agrees that when
Spinoza talks about "motion and
 rest"[8]
 he is not invoking these terms in their ordinary senses. But rather
than simply identifying motion and rest with energy or any other trope
of contemporary physical theory, Bennett holds that the terms function
as mere placeholders for some basic physical quality, unknown to
Spinoza, but required to make sense of the *appearance* of
bodies--*ostensible* things or subjects of predication
-- in the context of a metaphysics that holds that bodies, as
modes rather than substances, are not things or subjects at all, but
rather ways that the one substance is. According to Bennett, Spinoza's
Extension is, at the fundamental metaphysical level, a four
dimensional field whose regions differ in the distribution and degree
of this basic quality. Bodies are appearances, at one or more levels
removed from this base, of the continuous path in this field
constituted by relatively consistent local patterns of distribution of
this quality. The ordinary "motion" of an ordinary
"body" is to be understood on the analogy with the way a
thaw traverses a terrain. When the snow line recedes, there is no
thing that changes its place; rather, there is a change in which
regions of the landscape have the quality of being snow-covered, and
that change describes a continuous path.



One might object to that this analogy is not clearly persuasive.
Shifts of temperature lead to a *thaw* only because
bodies--ice crystals and aggregates thereof--melt as
temperature rises, and their boundaries recede along the backdrop of a
very bodily landscape. Indeed, to thaw is just to pass from a solid to
a liquid state, and solidity is a benchmark of the bodily. If we
excise these bodily aspects of the analogy, it is unclear how much of
its explanatory force remains. But then it is unclear just how well
qualitative variations of fields can explain the appearance of bodies.
Perhaps if we knew more about this quality, the sense in which such
continuous paths of patterns of it could appear as or constitute
bodies would be clearer. Garrett (1994) adopts Bennett's field
metaphysic, and attempts to fill in the explanatory gap by providing
definite senses to the PI's uses of the terms "motion" and
"rest". Relying on Spinoza's remark, following
*PCP* IIp22, that "by force of moving bodies, we
understand a quantity of motion .... In bodies at rest, we
understand by force of resisting a quantity of rest", Garrett
claims that by "motion" and "rest" in the PI,
Spinoza means a quantity of force that moves a thing and a quantity of
force resisting such imposed movement, respectively. Furthermore,
these quantities can be ascribed, he says, to the regions of extension
themselves, rather than to bodies, thus overcoming the circularity
problem we found in Descartes. But it is unclear that Spinoza's text
can support this interpretation. *PCP* IIp22 speaks of the
force or motion "in" a body. Spinoza elaborates: "By
force in moving bodies, we understand a quantity of motion, which must
be greater, *in* bodies of equal size, as the speed of motion
is greater ... . But *in* bodies at rest we understand by
force of resisting a quantity of rest" (emphasis added). In each
mention, the force or resistance is attributed to a body. This
strongly suggests that quantity of motion and rest, as force and
resistance, are features of
 bodies.[9]
 Moreover, even supposing that it makes interpretive sense to ascribe
force and resistance directly to regions, what is being attributed to
these regions seems to be a power to move *bodies* or to slow
*bodies* down. Rather than showing how bodies could just be, or
arise from, fields of such forces, the forces themselves seem to be
characterized in ways that presuppose body; the circularity, then,
remains.



Individual bodies have an inherent stability, or robustness. They
resist destructive incursion or change in their distinctive mode of
endurance; they tend to persist in their configuration and motion in
the face of opposition to this persistence. Spinoza certainly accepts
this, as PID and IIIp6 show. If bodies either are, or are appearances
of, persistent patterns of qualitative variation of extended regions,
then it seems necessary, though hardly sufficient, that something
about such patterns would have to account for this stability. But what
might do so? In effect, this is to ask what would account for the fact
that distributions of "motion" and "rest",
conceived of as predicates of extended regions, do not vary randomly
through time. One suggestion is that nothing accounts for this
stability at all, and that the duration of a body is nothing more than
the time through which a given complex ratio of motion and rest
happens, de facto, to characterize regions of extension whose sum over
time describes what can be construed as a continuous path. There is
nothing to prevent such spatiotemporally continuous patterns from
occurring. But there is nothing in being a time slice of such a
pattern that explains why the same pattern should also characterize
any other spatiotemporal region continuous with it. There may, indeed
must, be kinematic 'laws' describing how such patterns vary (the scare
quotes cause the counterfactual supporting status of such 'laws' would
be secured only by Spinoza's necessitarianism), but nothing about any
given time slice of such patterns accounts for the fact that they are
subject to just those descriptive 'laws'. Individual time-slices of
such patterns would be wholly passive with respect to the persistence
and trajectory of the pattern as a whole.



A significant problem with this
 line[10]
 is that Spinoza uses manifestly active language to describe the
doings of individuals. For example, IIId3 defines "affect"
as "affections of the body by which the body's *power of
acting* is increased or diminished, aided or restrained, and at
the same time the idea of these affections" (emphasis added).
And in IIIp6, on which the entire psychological theory of the second
half of the *Ethics* depends, Spinoza claims that individual
things *strive* to persevere in their being; his subsequent
uses of the IIIp6 seem clearly to suggest that Spinoza intends this
striving to be understood as an a active principle rather than a mere
tendency. On the conception of individuals as ratios of motion and
rest that simply *happen* to endure, none of this would make
any sense at all.



Viljanen, who also adopts Bennett's field metaphysic, with its
implicit denial that Spinozistic "motion and rest" is to
be granted an ordinary signification, attempts to accommodate this
conception of bodies as active and potent by reading the spatial field
as a field of power, and bodies as constituted by differences in the
intensity or strength of this power (Valjanen 2007, p. 402), and
apparent motion as the redistribution in that field of various
patterns of intensification of that power (*ibid.*, p. 403). He
further interprets the "simplest bodies" of the PI --
the basic constituents of all complex individuals -- to be
distinguished as "rudimentary intensifications of spatial power,
or extended power quanta, that invariably change place" (Ibid.,
p. 408). But the question arises once again what the powers of which
these quanta are "intensifications" are powers *to
do*. They cannot, for reasons already mentioned, be powers to move
or to resist bodies. The most obvious answer, in the Spinozistic
context, would be "powers to persevere in its own being".
But to let the matter stand there would be simply to name the problem
rather than to explain it. To the questions "why does this
degree of spatial power persevere and endure in the (continuous) place
and time to the extent that it does?", the answer would seem to
be "because of the degree of power to persevere that constitutes
it". But that is just to say that it manifests the powers it
does because of the powers it has to do so -- not very
illuminating. "Motion and rest" as power appears to
provide either an incomplete or vacuous theory of indivuation.



Moreover, if a body's motion in a spatial field, including that of the
simplest bodies, is just a change of location at which a given degree
of power is instantiated, then there seems to be no means of
explaining why a particular degree of power would necessarily change
locations -- move -- continuously, as opposed to
discontinuously. But surely it is in the nature of bodies as
explananda here that they are spatiotemporally continuous.
Furthermore, if what individuates "quanta of power" are
just their degrees of intensity -- their degrees of power to
persevere -- then anywhere that degree is instantiated, that very
same body should be. But this would be consistent with the unlikely
idea of discrete, discontinuous motion of a body, and indeed with the
bi-location of bodies, that is, with the idea that a single body might
be wholly present in each of multiple regions. Assuming that Spinoza
would not accept these possibilities, the theory of "motion and
rest" as signifying spatial regions of power distinguished by
degrees of power fails to account for signal characteristics of body.
It is thus doubtful that the inadequacy of Descartes' identification
of body with extension can be overcome simply by predicating regions
of extension with different degrees of "power".



There are, then, reasons to doubt that granting Spinoza's "rest
and motion" a non-ordinary signification--energy, an
unspecified basic quality, force of motion and resistance,
intensifications of power -- can in fact give us insight into the
constitution or appearance of persisting, resistant, active bodies.
But it is worth asking whether these doubts in fact rest on an
inappropriate imaginative basis. It seems difficult imaginatively to
represent variegated fields of energy, force, or any other quality in
such a way as to make clear how bodies, with the persistent resistance
and capacities for interaction we ordinarily represent them to have,
could possible appear from or be constituted by them. But this sort of
failure of imaginative thinking cannot count against the acceptability
of a theory from a proper Spinozistic perspective. On his view, our
knowledge of body as an object of imagination is inherently
inadequate. Our imaginative ideas of bodies in their corporeality are
limited to the ideas of modifications of our own bodies. These in turn
reflect only in a confused and partial way the natures of both the
bodies with which we are affected and our own. At no time is the full
nature of any body reflected in any of the ideas we have through these
affections, hence through anything we can imagine. Hence our
imaginations cannot grasp the nature of body, and failure of the
faculty of imagination to provide insight into the link between the
fundamental basis for variety in matter and that variety itself is to
be expected. All of this is clear from IIp16-31. Any appearance
of insight into the nature of body gleaned from the imagination is as
likely to be illusion as illumination. And, as Schliesser (2017)
remarks in emphasizing Spinoza's skepticism about knowledge of the
natural world, for Spinoza, "when we locate things at a time and
place, we are always in the realm of the imagination"
(p. 175).



But if we cannot come to an imaginative grasp of how bodies or their
appearances might be constituted out of fields, then through what sort
of intellectual act might we do so? In the context of early modern
philosophy of physical nature, and in particular the Cartesian
philosophy in which Spinoza is steeped, the clarity and distinctness
of mathematical ideas provides the contrast to the incompleteness and
confusion of ideas of the imagination and sensation. And certainly the
quantifiability of properly physical qualities, and consequently their
comprehensibility within a closed system of mathematical laws, is of
the utmost importance to the credentials of the fundamental notions of
the contemporary physical theory Spinoza is alleged to have
anticipated. The scientific success of classical mechanics, relativity
theory, and, especially, quantum mechanics owes much more to the
predictive and formal success of these theories than it does to our
abilities to represent phenomena in the imagination that answer to the
basic physical elements they countenance. Point masses, gravitational
forces operating at a distance, curvatures of space time, finite but
unsurpassable velocities, and wave-packets all seem to surpass our
powers of imaginative representation. We have no real capacity to
imagine how the solid table on which my computer rests can be
identical to both a swirling cloud of particles and a warp in the very
fabric of space. On the other hand, these fundamental scientific
notions can be rendered mathematically, placed within a system of
laws, and employed to great effect in predicting and manipulating,
hence effectively representing, the same nature we represent
imaginatively.



Thus perhaps the proper criterion, or at any event *a* proper
criterion, for the success of an Spinozistic account of variety in
matter and its individuation into bodies is the quantifiability of the
basic properties in which it proceeds. Gabbey stresses this line with
admirable clarity.



> 
> To talk of bodies maintaining among themselves "the same
> proportion of motion and rest," or communicating motion to each
> other "in a certain fixed proportion" is to say nothing
> effective, unless a mathematical account is provided of those
> proportions and of the measures of motion and rest from which they are
> formed, and unless there is some account of the laws that ensure the
> claimed invariance in proportionalities. Spinoza provides no such
> laws, nor does he say how the proportions are to be mathematically
> expressed (Gabbey 1996, p. 168).
> 



Gabbey concludes that the theory of bodily individuation by ratio of
motion and rest "lacks quantitative anchoring", and is
thus "too vague to allow a assessment of what is being
claimed" (Gabbey 1996, p. 169).



That Spinoza did not himself provide the mathematicization of his
notion of motion-and-rest that would render his theory of body
non-circular and sufficiently clear to be understood (or imagined)
does not entail that this cannot be done. A number of commentators
have attempted to show that Spinoza's account of variety in matter by
appeal to "motion and rest" can be so rendered. Garrett,
whose account we have already examined, nods his head in this
direction. Recall that PId5 defines an individual as being composed of
bodies that "communicate their motions to one another in a
certain fixed manner". Later lemmas characterize this fixed
manner as a "ratio" of motion and rest. Notwithstanding
his realization that, for a number of reasons, such a ratio must be
understood as a pattern rather than a numerical proportion, Garrett's
expresses sanguine confidence that "any such pattern could be
expressed by a mathematical formula" (1994, p. 86). Matson
(1990) also places weight on the possible quantifiability of motion
and rest as a means of in rendering it a clear and distinct,
non-imaginary basis for our understanding of the individuation of
bodies, taking the idea of an atomic number as his model:



> 
> Being element No. 16 "pertains to the essence" of sulfur,
> as being yellow and smelly do not. One can in a sense
> "imagine" sulfur by its color and odor; but only by
> articulating it into the attribute, as the atomic number does, can one
> understand it.... 'Element No. 16', together with the
> comprehensive theory in which this conception is embedded, is a
> specification of 'motion and rest', indicating, in fact,
> that particular unique 'proportion of motion and rest'
> that is the necessary and sufficient condition for being sulfur.
> (Matson 1990, pp. 88-89).
> 



Matson piggybacks on to this analogy the formula for the identity of
any living thing supposedly found in its genetic code.



> 
> If it is right to think of atomic numbers as the specifications of
> motion and rest for certain stuffs, in the case of the human being (or
> any living creature) the obvious analogue is the genetic code, the
> formula for the structure of the individual's (quasi-unique) DNA
> molecule (Matson 1990, p. 89).
> 



Treating such structures as representable by formulae enhances the
impression that they are expressible in numerically quantifiable
terms.



Such attempts to interpret motion and rest as numerically expressible
quantities constitute efforts to make Spinoza's physical theory
relevant to contemporary science, by displaying how it can conform to,
and even constitute a blueprint for, its mathematical structure. They
stand, then, as responses both to Gabbey's implication that because
Spinoza does not say how his notion of motion and rest can be
expressed mathematically, his views are too vague and sterile to be of
such contemporary relevance, and to the difficulties we have seen, in
conceiving how motion and rest, as we conceive them imaginatively,
could possibly serve to individuate bodies. But at the end of the
final section of this article, we will see that, quite apart from the
vagueness, anachronism (Spinoza anticipating not just Mendeleyev, but
also Watson and Crick?) and other interpretative difficulties faced by
such attempts, there are reasons to suppose that any effort to render
basic principles of physical theory through numerical quantification
may run deeply counter to Spinoza's own attitude.


### 5.3 Individuation by essence



In the previous sub-section, we saw reasons for doubting the adequacy
of readings that treat the PI's talk of motion and rest as
constituting his entire account of 
 individuation.[11]
This section considers an
alternative interpretation of Spinoza's approach to individuation.
This account appeals to the notion of individuating essences.



In IId2 Spinoza says:



> 
> to the essence of a thing belongs that which, being given, the thing
> is necessarily posited and which, being taken away, the thing is
> necessarily taken away; or that without which the thing can neither be
> nor be conceived, and which can neither be nor be conceived without
> the thing.
> 



This does not quite offer a definition of "essence", but
rather defines what belongs to it. IId2 speaks of the essences of
"things." Individuals, or singular things, are surely
things. If what belongs to the essence of an individual is given (by
"given" Spinoza means "posited as existing"),
then so too is the individual. This suggests that the essence of an
individual is particular to that individual, since otherwise, what
belongs to it could be given without that individual being posited, so
long as some other individual with that essence were
 posited.[12]



But how are we to conceive essences, and how can they help solve the
problems we have encountered with claiming the PI, with its talk of
motion and rest, provides Spinoza's full account of individuation? In
the Preface to *Ethics* Part IV, Spinoza writes:



> 
> When I say that someone passes from a lesser to a greater perfection,
> and the opposite, I do not understand that he is changed from one
> essence, or form, to another... . Rather, we conceive that his
> power of acting, insofar as it is understood through his nature, is
> increased or diminished.
> 



Here Spinoza writes as if a body's essence and its form are one and
the same. In each of PIl4, 5 and 6, Spinoza speaks of bodily
persistence in terms of its parts keeping the same ratio of motion and
rest. If the parts do so, the body, says Spinoza "will retain
its *nature*, as before, with no change of *form"*
(emphasis added). PIl7 also speaks of a body's retaining its
"nature", despite change. These are plainly meant to state
conditions on individual persistence. These lemmas seem to equate
nature and form. So by transitivity of identity, form=nature=essence.
Moreover, Spinoza implies that so long as this form or essence is
retained, a thing is not destroyed. "Form",
"nature" and "essence" than, refer to
something in virtue of the persistence of which an individual retains
its identity.



In a series of propositions leading up to and supporting IIIp6's
articulation of the conatus doctrine, Spinoza also treats
"essence" and "nature" as synonyms, and
assigns them to things independently of the attribute under which they
are considered. IIIp4 is worthy of particular attention here. It
states: "No thing can be destroyed except through an external
cause". Garrett (2002) persuasively argues that
"external" here contrasts, not with "on the
inside", but with "inherent", where inherence is a
technical notion referring to what belongs to a thing in virtue of its
essence. This includes both the thing's essence and those properties
following from it. These are all "in" the thing. However,
a thing may also have accidental properties, which are
"in" it in the general sense in which that which is
predicated of a thing is in it, and may also be "in" it in
the sense in which one region surrounded by another is in it, but
which do not inhere in it. Such properties, in the thing in one sense
but external to it in another, may be destructive of the thing. In
IIIp4d, Spinoza writes "while we attend only *to a thing
itself*, and not to the external causes, we shall not be able to
find anything *in* it which can destroy it" (emphasis
added). Reading "in" here in the sense of
"inherent", and "external" in the sense of
"not inherent", this passage suggests that to attend to a
thing itself is just to attend to its essence--what is affirmed
in its definition--and what follows from it. To attend to what is
not inherent in it is to attend to what is external to it, to
something else. An actually existing thing, then, such as an existing
body, is its essence brought to existence. So long as a thing retains
its essence=nature=form, it retains whatever inheres in it, and
endures as the same individual.



The appeal to individuating essences accounts for the robust
persistence of bodies. In IIIp6 Spinoza says that "Each thing,
as far as it can by its own power, strives to persevere in is own
being". In arguing for this conatus doctrine, Spinoza states
that "singular things" are that "by which God's
attributes are expressed in a certain and determinate way, i.e.,
things that express, in a certain and determinate way, God's power, by
which God is and acts". "Things" here takes the
active position. Things express power; they *do* the
expressing. They are not mere expressions *of* it. Power is
expressed *by* things, rather than merely through them. Because
this is an active expression of power, the thing not only persists
through externally caused changes, but opposes those changes which
would tend to destroy it, i.e., to keep it from expressing God's power
in the way which constitutes its essence. Finally, in IIIp7, Spinoza
expressly identifies this striving with the thing's essence;
"the striving by which each thing strives to persevere in its
being is nothing but the actual essence of the thing."



Thus the form or essence of a thing, which individuates it, and whose
retention through change constitutes the persistence of an individual,
just is its inherent and individual power of striving to retain just
form, hence to resist those extrinsic determinants that would diminish
its power and destroy it. In the case of body, striving is expressed
by the active tendency of a pattern of relative motion and rest, in
their ordinary sense, of its parts to persist. The active tendency of
that pattern to persist is the essence of the individual body. That
pattern is determined in its existence transiently and externally; now
this way, and now that, now larger, now smaller, now swifter, now
slower, now with these parts, now those. Such transient, external
determination may give it accidental properties that oppose and hinder
the power of action it has in virtue of what inheres in it, and hence
limit its power of action. Another virtue of the idea that essence as
active striving is what individuates bodies is that it would provide a
basis in the nature of body for the principle of inertia, in such a
way that inertia could be taken as a ground for the PLMM we earlier
saw was needed to underwrite the collision laws.



However, this view is certainly not without its 
problems.[13]
Indeed, one of its strengths--helping to ground inertia in the
persistent activity of bodies -- is a weakness. We saw earlier
that it is not easy to square this active reading of inertia, grounded
as it is in the idea of motion pertaining to the action proper to a
body, with a good deal of what Spinoza says in the first and second
parts of the
*Ethics* about how no body can be determined to produce an
effect unless is it so determined externally. Another, related problem
for this interpretation is that it represents Spinoza as, not an
avant-garde thinker anticipating modern physics, but as a rear guard
defender, despite his official anti-scholastic stance, of the
traditional neo-Aristotelian doctrines of essence and substantial
form, open to the same charges of *ad hoc* theorizing and of
appeal to occult powers that Modernity and the Scientific Revolution
levelled against that tradition in their rise to intellectual
dominance. Indeed, the notion of the individual essence of a body
conceived as a power to maintain itself is of dubious intelligibility.
Spinoza clearly believes that an individual's power to persevere can
increase or diminish. But if this power is to constitute the thing's
essence and identity, such changes in degree cannot alter the identity
of the power. But what then constitutes the individuality and identity
of a power? In this light, the account of individuation by essence
seems unexplanatory: either it amounts to an elaborate name for the
problem of the individuation of bodies it is supposed to solve, or it
simply displaces the same sort of problem from bodies to powers.



The problem we have been addressing is to find in Spinoza a
satisfactory ground for the idea that modes of extension consititute
bodies to which dynamical laws like the laws of collision should
apply. We have characterized that problem in terms of the
"robust persistence" of bodies - their resistance to
change. Barry (2021) presents a detailed and complex treatment of
possible ways Spinoza might be thought to account for the resistence
to change bodies manifest in the dynamics of collision. He argues
that neither Spinoza's account of inertia nor the conatus doctrine can
support resistance, and that a more direct appeal to modes as
expressions of God's power or activity cannot do so either. He
suggests tentatively that, via Spinoza's parallelism (EP27), the
resistance characteristic of bodies might instead be read off of the
resistance relatively adequate ideas have to alteration in the face of
relatively less adequate ideas. This reverses the more usual
direction of reading off features of ideas from those of their modal
counterparts in extension; but, despite Spinoza's remark in letter 27
(to de Vries) that ethics is to be founded on metaphysics and physics,
turnabout here should be fair play. As Barry recognizes, however,
since not all features of modes of one attribute can be applied to the
counterparts under the other attributes, there must be something
identifiable in bodies that corresponds to the adequacy of ideas in
virtue of which they resist other ideas if the strategy is to work.
The extended counterpart of adequacy Barry fixes on is the degree to
which the collection of component bodies whose relation consitutues a
composite individual body communicate their rest and motion to one
another in a fixed manner, as discussed in the PI. One might argue
that, had Barry taked that idea seriously enough in his discussion of
inertia and the PI, the detour through Thought via the parallelism
would have been unnecessary. In any event, Barry worries here that
appreal to adequacy explains at best resistance to change i.e., the
ability of a body to retain the same ratio of motion and rest in a
collision, but not the ability to produce a change; i.e., the power of
a body to move or alter another, both of which powers Spinoza clearly
attributes to bodies.



Whether there is a sufficient Spinozistic ground for for a unified
conception of the power of modes both to resist and to bring about
changes in other modes of the the attribute under which they are
considered remains an open question. It seems likely, however,
that reading the PI, the conatus doctrine, and Spinoza's accounts and
justifications of inertia and the dynamical laws in the light of
the fact that modes each express in their own way the
infinite actvity and power of the one substance provides the
best hope for illuminating such ground. 


## 6. Spinoza and the experimental and mathematical sciences



Attempts to find anticipations of contemporary scientific physics in
Spinoza's thinking about the physical face a number of challenges
beyond simple anachronism. Contemporary physics is both resolutely
experimental and resolutely mathematical. However, there is reason to
suppose that Spinoza had dim views of both experimental method in
 science[14]
 and the prospects for an insightful mathematical description of
nature.


### 6.1 Observation



It is by now widely accepted that observation is "theory
laden", and that therefore the idea that scientific theory
proceeds through the neutral collection of data is bogus. Studies in
the logic of confirmation have likewise put an end to the
simple-minded idea that experimental method involves devising crucial
experiments whose results can, as a matter of logic, falsify a theory,
or force a choice among competing theories. Nonetheless, modern
science is still thoroughly empirical, relying heavily and essentially
on observation and experimentation in the generation, development, and
testing of theories. The truism that one can always save a theory by
rejecting auxiliary assumptions or discrediting data--reports of
observation--does not change the facts that, in practice,
observational results are taken to refute theories, and the ability to
predict and explain a wide range of observable phenomena better than
rivals remains the gold standard in scientific method.



Spinoza, however, discounted the relevance of observational data to
the discovery of truths of nature. His conception of sense experience
seems, in fact, to disqualify it from being a reliable source of
information about the world altogether. He held that sense experience,
in which the human body is affected by external bodies, can never
provide us with adequate ideas of either external bodies or our own.
He seems moreover to have denied that the method by which we discover
new truths involves either the collection of new sensory evidence or
the construction of crucial experiments. Indeed, much of the early
*Treatise on the Emendation of the Intellect* is devoted to
establishing that "the fictitious, the false, and the other
[ideas falling short of truth] have their origin in the imagination,
i.e., in certain sensations that are fortuitous, and as it were
disconnected, since they do not arise from the very power of the mind,
but from external causes, as the body (whether awake or dreaming)
receives various motions" (EMI, P84). The intellect unaided
by imagination, however construed, is the sole source of knowledge.
Observation, which involves sensory ideas derived from external
causes, has no role in the true method for acquiring adequate
knowledge.



In IIp25 Spinoza states "The idea of any affection of the human
body does not involve adequate knowledge of an external body".
Sense perception--the basis of experimental observation--is
a matter of the body's being affected by external bodies. So it would
seem that, *prima facie*, Spinoza cannot have held that
observation can be a means to an adequate knowledge of things.
Scientific knowledge--*scientia*--would, for Spinoza,
have to be adequate. Hence it seems that experimental observation
ought to be, for Spinoza, irrelevant to science. There is strong
confirmation to be found for this conclusion in Spinoza's accounts of
the kinds of knowledge.



In IIp40s2, Spinoza discusses four kinds of knowledge or modes of
cognition. These are I) knowledge from singular things; II) knowledge
from signs; III) knowledge from common notions; and IV) intuitive
knowledge. The first two are prone to falsity, as they generate
inadequate ideas. Cognition of kind (I) arises from objects
represented "through the senses in a way that is mutilated,
confused, and without order for the intellect". This is
perception from "*experientia vaga*", vague or
random experience. Knowledge of kind (II) arises from hearsay, arising
"from the fact that having heard or read certain words, we
recollect things, and form certain ideas of them ... through
which we imagine them." Spinoza groups (I) and (II) together as
knowledge of the first kind: opinion or imagination. Inadequate and
confused ideas pertain to knowledge of the first kind, and so it is
the sole cause of falsity. Both of the sorts of knowledge of the first
kind depend upon what we would ordinarily call sense experience.
Spinoza does not go so far as to assert explicitly that no true
knowledge can ever arise from sense experience. It is only when the
senses present us with representations in a way that is
"mutilated, confused and without order for the intellect"
(IIp40s2), i.e., random, that our resulting conceptions are
inadequate. But the question is whether there is any other way, on
Spinoza's views about sense perception, that the senses can represent
objects to us. Knowledge of the third kind, intuitive knowledge, does
not appear to involve the senses at all. It is knowledge proceeding
"from an adequate idea of the formal essence of certain
attributes of God to the adequate knowledge of the essence of
things" (IIp40s2). This knowledge, then, arises from the
intellectual consideration of the essence of an attribute itself,
rather than from sensuous commerce with modes of that attribute.
Knowledge of the second kind, reason, seems a more plausible candidate
for arising from experience. This is based on the so-called
"common notions". Common notions are conceptions of things
"which are common to all, and which are equally in the part as
in the whole" IIp38. Such conceptions can only be adequate, and
this would guarantee that the knowledge arising from such conceptions
is true. Spinoza also allows that if there were something common and
peculiar to the human body and external bodies by which it is
affected, and equally in the part as in the whole of each, then the
human mind will conceive that thing adequately. The problem, however,
is that given Spinoza's views about sensation is it hard to see how
such common notions could arise from sensation, and to the extent we
can make sense of this, the common notions seem limited to ideas of
extremely general features of physical objects, far too general to be
a source of any of the kinds of particular observational knowledge
required for experimental practice. The inadequacy of a conception of
a thing results from its not reflecting the entire nature of a thing's
causes. Knowledge of effects is by knowledge of causes, and while
things can interact causally only insofar as they share something in
common, there can be aspects of the causes of things not reflected in
their effects. However, if a conception is of something common to an
object and all other things, then there can be nothing in any of its
causes not reflected in the conception of it itself; whatever is
present in the cause will be present in it as well, hence reflected in
the idea of it. But what, we may ask, is even possibly shared by each
thing and equally in the part of each as in the whole? The only
obvious candidates are properties that, as Schliesser (2017, p. 15)
puts it, "reflect the peculiar modal qualities of ... a
mode": in the case of extended modes, those sorts of properties
that follow from the nature of extension: e.g., motion and rest,
taking up space, being subject to motion and to the laws of geometry,
etc.. But the sorts of observational knowledge that are crucial to
experimental method in science are hardly exhausted by the knowledge
that pertains to bodies as such. Indeed, experimental observation
depends precisely on the observational knowledge of differences,
rather than similarities.



Spinoza characterizes *experiential vaga* as experience that is
"without order for the intellect" and as "experience
that is not determined by the intellect" (*Treatise on the
Emendation of the Intellect*, P19). This experience is called
"random" because "it comes to us by chance, and
since "we have no other experiment to oppose it";
perception attained in this mode it "remains with us
unshaken". Perception from random experience can, then, be
shaken by opposing experiment, but there is nothing here that suggests
this is a matter of less random experience overruling more, rather
than multiple random experiences conflicting with one another.
Moreover, Spinoza really never tells us what it would be for
experience to be "ordered for" or "determined
by" the intellect. It is tempting to suppose that he meant,
following Bacon, from whom the term "*experientia
vaga*" is borrowed, that experience is not vague insofar as
it "proceeds by fixed law, without interruption and in regular
order". (Bacon, *Novum Organon*, Book I, Aphorism 100).
But it is unclear, given Spinoza's general denigration of sense
experience as generating only inadequate ideas of things, how the
intellect could order the collection of sense experience by law, and
it is equally unclear how the result of doing so would shore up the
inadequacy of the resulting
 observations.[15]
 Bennett, who resists the standard view that Spinoza thought
experience irrelevant to knowledge, and cites the possibility of
*experientia* non-*vaga*, i.e., experience as directed
by the intellect, as evidence for this, concedes that Spinoza is
entirely silent about *experientia* non-*vaga*, offering
no account of what it might be, other than "the experience of
someone who puts to nature questions dictated to him by Spinoza's
philosophy" (Bennett 1984, p. 24). Bennett's suggestion that a
characterization of this might have to wait until we learn more about
how the senses function seems a non-starter, though. For if we
conceive the senses as objects of empirical, experimental study, then
we cannot learn about them until we know how to order our experience,
so the question is begged; and if we conceive of them as objects for
non-experiential, non-experimental philosophical reflection, then what
more by way of the Spinozistic carrying out of this sort of work is
there to be done than Spinoza does in the
 *Ethics*?[16]


### 6.2 Experimentation



Spinoza engaged in very little experimentation of his own, but he did
show some interest in the experimental results of others. His letters
contain several discussions of experimental and theoretical dioptrics,
to be expected from a lens grinder and man of letters, as well as
discussions of recent observations of comets and whether they can be
explained on Cartesian principles, of the new microscope, and of
medical and alchemical experiments. Far and away the most famous and
significant discussion of experimentation are found in his exchanges
with Henry Oldenburg, the first Secretary of the Royal Society, who
operated largely as the mouthpiece of Robert Boyle, and in particular
those concerning Boyle's experiments on solidity, fluidity, and on
nitre. The latter of these is the most telling of Spinoza's attitude
towards the relevance of experiment to theorizing about nature. Boyle
had claimed to show that nitre (potassium nitrate) is a chemical
compound rather than a mixture, by having decomposed it into fixed and
volatile parts (potash and spirit of nitre), and then recombining them
into nitre with little or no loss of quantity. The disparate
properties of the components, he argued, showed that the nitre itself
was a compound, in which the components were altered and transformed,
rather than a mere mixture. This, in turn, suggested that the basic
constituents of the components were preserved through the interaction,
confirming the corpuscular chemical theory over the scholastic view
that chemical transformation involves the substantial form of given
matter being destroyed and replaced by some other substantial
form.



Spinoza in fact agrees with Boyle that the scholastic view is
bankrupt, but he rejects Boyle's claim that the separation of the
nitre into two parts is actually a decomposition of a distinctive
substance into two others; rather, he claims that the experiment is
consistent with the Cartesian view, itself based on reason, that
differentiations among extended substance are always owing to
different quantities of motion and rest. He claimed that the
"fixed nitre" (potash) was actually an impurity mixed into
the original sample, and that the spirit of nitre was simply the
volatile state of the pure, crystallized nitre portion of the original
mix. Thus the different chemical properties of spirit of nitre and the
original sample owe not to a difference of substantial
structure--the basic shape of the particles of each is the
same--but to a difference in their motion. In support of this
reading and against Boyle's interpretation, Spinoza claimed that, if
Boyle were actually to show what he claimed, "further experiment
seems to be required to show that Spirit of Nitre is not really Nitre,
and cannot be reduced to solid state or crystallized without the help
of salt of lye" (Letters, p. 71). Spinoza then went on at some
length to show how, in the absence of such a demonstration, it is easy
enough to explain the results of Boyle's experiments along Cartesian
lines. He further explains several experiments he himself performed
which he takes to support the Cartesian interpretation, claiming that
he "might have added further experiments which would perhaps
make the matter quite clear" (Letters, p. 76).



What matters here is not who is right in this dispute, nor whether
Spinoza's Cartesian view is in fact coherent, but Spinoza's strategy.
For it is hardly an evenhanded assessment of the experimental results.
Spinoza shows considerable ingenuity in interpreting the results of
Boyle's own experiments to be consistent with the Cartesian view, and
his own as (nearly, anyway) proof positive of it. But he shows no
inclination to pursue the question whether his own experimental
results can be interpreted along the lines of Boyle's hypothesis,
which they can be, easily enough, as Boyle's response (letter 11)
shows. Indeed, Boyle complains overall that Spinoza's interpretations
of the experimental results are wholly driven by Cartesian theory,
rather than a fair attempt to adjudicate between the two alternatives.
For example, far from proving the need for the "very fine
matter" of Cartesian physics, this conclusion has been
"assumed", by Spinoza, "simply from the hypothesis
of the impossibility of a vacuum". In other aspects of his
interpretation, claims Boyle, Spinoza 'presupposes Descartes'
theory of fire". Now Boyle's readings of the experimental data
are hardly less theory driven than are Spinoza's. But where they
differ strategically is in the fact that since the Cartesian theory
that drives Spinoza's interpretations is derived by the method of pure
rational reflection on perceptions that are *a priori* clear
and distinct, Spinoza clearly grants it a privileged standing in the
court of experimentation. On his view, to prove a conclusion that is
at odds with one dictated by reason itself, like Descartes', one has
to establish *impossibility* experimentally--which cannot,
of course, be done. So long as it is possible to interpret results as
consistent with a theory determined by rational reflection alone,
those results cannot weigh at all against the theory. Yet experimental
results that conform to rationally determined theory confirm it.



Indeed, where there are properly philosophical arguments to be had for
a thesis, experimentation is superfluous. In assessing Boyle's
experiments designed to prove that all tangible properties depend on
the mechanical features of objects, Spinoza wonders why Boyle
bothered, since this conclusion "has already been abundantly
proved by Verulam, and later Descartes". (Letter 6). Descartes
had proved this *a priori* from the fact that the sole nature
of body is extension, whose sole attributes are size, shape and
motion. Moreover, ordinary, mundane observations offer as good proof
as any that might be afforded by controlled observation. Boyle's
careful experiments could not add any weight to the evidence already
available from such ordinary phenomena as the facts that even cold
sticks will spark a fire when rubbed together, that water makes sound
when it comes to a moving boil, and that stirring and warming foul
smelling bodies make them smell yet worse. Spinoza's attitude towards
experimental observation seems to be, then, that it can have no weight
against a theory based in sound a priori philosophical intuition and
geometrical demonstration, and is easy available, though not
necessary, to confirm the results of such pure theorizing.
Experimentation can help us discover new phenomena, but it cannot help
us to prove any scientific propositions we do not already know to be
true. As Gabbey (1996) puts it, experimentation "cannot uncover
the nature of things; sensory knowledge belongs to the imagination,
the knowledge of essences and causes to the intellect alone"
(Gabbey 1996, p. 171).


### 6.3 Mathematical science



Observation and experimentation are no more central to contemporary
scientific practice than is quantification. Contemporary physical
theory, which Spinoza is said to have anticipated, is thoroughly
quantitative in character. Theories are expressed in quantitative
terms; giving an explanation of a phenomenon is typically a matter of
generating a mathematically formulated law that covers it. Unifying
theories is a matter of showing how the mathematical formulae that
comprise them can be derived from one another, how the phenomena they
concern can be commensurated. Indeed, observation itself is irrelevant
to modern physical theory unless it is expressed in quantitative
terms, since the prediction yielded by physical theories are
predictions of what the observed measures of things will be. This, in
turn, requires that the phenomena observed must be measurable.



Spinoza is, in a fairly obvious way, a champion of a mathematical
approach to understanding the physical world. But Spinoza's
mathematical model is Euclidean geometry, and this is not a domain of
mathematics that deals with quantities as measurable. And indeed,
there is strong evidence that Spinoza thought that a proper
understanding of physical nature can never be expressed in terms of
measurable quantities. For measure, both of spatial extent and
temporal duration, is a mere aid to the imagination, and not a means
of intellectually understanding. In Letter 12 to Meyer, Spinoza
distinguishes two ways of conceiving quantity. One is abstract and
superficial, as we have it is sensation and imagination; on this
conception quantities can be finite, divisible, and composed of parts.
The other is through the intellect's grasp of substance in which
"we apprehend the thing as it is in itself"; on this
conception, quantity is infinite, indivisible, and a unity. Spinoza
goes on to elaborate how measure of spatial and temporal quantity
derives from the abstract, superficial conception of quantity, and
leads to nothing but confusion in the attempt to understand physical
nature. His discussion is worth quoting at length.



> 
> From the fact that we are able to delimit Duration and Quantity as we
> please, conceiving quantity in abstraction from Substance and
> separating the efflux of duration from things eternal, there arise
> Time and Measure: Time to delimit Duration and Measure to delimit
> Quantity in such wise as enables us to imagine them easily, as far as
> possible. Again, from the fact we separate the affections of substance
> from substance itself, and arrange them in classes so that can easily
> imagine them as far as possible, there arises Number, whereby we
> delimit them. Hence it can be seen clearly that measure, Time and
> Number are nothing other than modes of thinking, or rather, modes of
> imagining. It is therefore not surprising that all who have attempted
> to understand the workings of nature by such concepts, and furthermore
> without really understanding these concepts, have tied themselves into
> such extraordinary knots that in the end they have been unable to
> extricate themselves except by breaking through everything and
> perpetrating the grossest absurdities. (Letter 12).
> 



As if to emphasize that he is speaking not just of the understanding
of nature as substance (*natura naturans*), but also of the
passive nature of the existing finite modes (*natura
naturata*), Spinoza cites the troubles one gets into as soon as
one attempts to conceive duration through the abstraction of time. The
eternity of the attributes and active nature is to be contrasted with
the duration of existing modes. Yet to attempt to understand the
duration of modes through the abstraction Time, and by implication, to
try to understand the spatial extension of modes through Measure and
Number, is to employ aids to the imagination only, and inevitably
leads not to understanding, but to
 absurdities.[17]
 We must conclude that Spinoza's views of Measure, Time and Number
confound the easy impression that he thought that the variety in
matter could be accounted for by motion and rest considered as
numerical quantities. Even if we could satisfy Gabbey's demand for a
"mathematical account of ... proportions of motion and rest
and of the measures of motion and rest from which they are
formed", that would not meet Spinoza's own demands for the
intellectual understanding of the nature and existence of bodies.



Relying largely on Spinoza's denial of the divisibility or
measurability of extension as it is properly conceived (as opposed to
imagined), Alison Peterman (Peterman 2012, 2015) has advanced the bold
thesis that Spinoza's extension is not spatial or dimensional at all,
and that, accordingly, Spinoza's bodies do not occupy space. On this
view, Spinoza means something quite different by
"extension" than Descartes or anyone else has meant. For
Peterman, it is not just the apparent divisibility and measurability
of extension that is an illusion of the imagination, but its very
spatiality. Peterman argues that spatial extent would necessarily be,
at least potentially, divisible, and that since Spinoza denies that
extension is even potentially divisible, he must not understand
extension as spatial (Peterman 2012, 
p. 50).[18]
She further supports this
view by noting that, while Spinoza explicitly characterizes extension
in spatial terms in his exposition of Descartes' view in the
*PCP*, he does not so define extension in expounding his own
views in the *Ethics*, but rather says that extension is
"conceived through itself" .



Peterman's view has the benefit of helping Spinoza avoid the
difficulties of making clear how something genuinely spatial cannot be
divided or measured. But this benefit comes at substantial costs. For
one thing, Spinoza is hardly shy in the *Ethics* about making
his heterodox views explicit. If he thought that the wildly heterodox
claims that extension is not dimensional and that bodies do not occupy
space followed from the indivisibility of extension, and endorsed
those claims, one would expect him to have made the inference
explicit, rather than leaving it for the reader to draw. Second, the
view renders Spinoza's philosophy oddly irrelevant to the physical,
which certainly concerns nature as a spatiotemporal domain, and which
is a preoccupation of everyone with whom Spinoza is in intellectual
commerce. Third, and relatedly, even conceding, as one must, that no
imaginative grasp of extension or bodies can constitute an adequate
conception of them, if extension is not dimensional and bodies do not
occupy space, the question arises why we so much as imagine them that
way, that is, why the ideas of the affections of our bodies are
*images* at all. Leibniz, in the more idealistic phases in
which he denies the ultimate reality of space and time, feels acutely
the obligation to explain why spatiotemporal phenomena are
well-grounded in what is ultimately real. And Kant, who denies the
spatiotemporality of things in themselves, goes to great lengths to
explain why the phenomenal appearances of these things must be in
space and time, and conform to the categories as well. Even if Kant's
claim that space and time are the forms of intuition looks like a
label for the problem rather than a genuine explanation, it least it
is a recognition of the problem. But Spinoza, on Peterman's view,
equally rejects the reality of space and its apparent occupants, but
seems to have nothing at all to say about why the appearances are as
they are, i.e., imagined. Finally, it is obvious that, on Peterman's
view, "motion and rest", which Spinoza invokes as an
infinite mode of extension and in the individuation of bodies, cannot
have their ordinary signification of local motion and rest. So she,
like others who deny that "motion and rest" have their
ordinary sense for Spinoza (see section 5.2 above) owes an account of
what they are. But the burden seems even greater for her view, since
it is quite unclear just what extension might properly be conceived to
be, if not dimensional. The only characterizations available seem
purely negative: not finite, not measurably, not spatial. But what,
then? Peterman argues that it is not surprising that the attribute of
extension should be undefined, since it is "conceived through
itself". But to say that something is conceived through itself
is surely not to say that it is conceived only negatively or in no way
at all.



For these reasons, it seems preferable to take the interpretive path
Peterman considers and rejects, of holding that Spinoza's extension is
indeed dimensional and his bodies occupants of space, but that
extension is not really, but only imaginatively, divisible and
measurable. To reconcile the indivisibility of extension and the
immeasurability of bodies with the extension's spatiality, we can
simply say that one way of conceiving substance is as spatially
expended, but that so conceived, it is not divisible, in the sense
that it cannot be divided into multiple substances; and we can say
that bodies take up space, but cannot be measured, because there is no
sense to be made of the idea that there is some definite portion of
the infinite extension any part thereof occupies, as there would be if
extension were finite. To conceive extension through itself
would just be to conceive spatiality; this secures the relevance of
Spinoza's extension to the physical, and likewise provides a ground
for the spatiality of appearances in imagination. This preferable
path, however, takes us no closer to a reconciliation of Spinoza's
thinking about the physical with the observational, experimental, and
mathematical character of modern and contemporary physical science.
Indeed, it seems that, as Schiesser (2017, p. 186) remarks, "it
is ... a mistake to understand Spinoza as a fellow traveler of
the scientific revolution."



We saw earlier that there are grounds, though hardly conclusive, for
supposing that Spinoza held a fundamental metaphysical view of
physical nature that is akin to the contemporary view of the physical
world as composed of fields of force, with bodies in some sense being
constituted by relatively stable patterns, relative to our own, of
force. However, Spinoza's hostility to observation as a source of
knowledge, his view that experimentation can at best provide examples
of what we know through reason, and his rejection of the idea that
physical nature is to be known through number and measurable
quantities, suggest that his convergence with contemporary physical
science goes no farther than this possible anticipation of the theory
of fields as fundamental.


## 7. Conclusion



It is far from clear that any thorough and consistent account of
Spinoza's physical theory can be found. He says too little that is
focused and direct, and the various partial and indirect discussions
of such fundamental topics as inertia and the individuation of bodies
are individually underdeveloped and problematic, as well as in
*prima facie* tension with one another. A few general
interpretive strategies present themselves. We might take both his
claim that all determinations of extended modes of substance are
extrinsically caused by other finite modes and his talk of essence and
conatus seriously. On such a reading, Spinoza tried to develop an
ecumenical account of bodies that both conformed to the mechanical
principles of the Cartesian view and preserved the sense that bodies
are centers of real activity; but his entitlement to that sense is
hard to square with mechanism and only dubiously earned through the
appeal to essences. We might, on the other hand, focus on either of
the two aspects of Spinoza's thinking about the physical, downplaying
the other. Focusing on conatus and essence might enable us to take the
latter, properly ethical and psychological half of the *Ethics*
at face value, but only at the cost of being debarred from seeing how
it fits with the mechanical view of the physical world, and those
field metaphysical refinements of it that form the basis of modern
physics. Focusing on the idea of wholly extrinsic modal determinism,
we will see Spinoza as a visionary thinker whose physical theory both
anticipates and provides a metaphysical basis for contemporary
physical views, albeit without their central experimental and perhaps
quantitative dimensions; but then the ethical and psychological half
of Spinoza's thought, depending as it does on the idea that
individuals, including bodies, are centers of active striving, proper
to themselves, is cut adrift. Or we might take each aspect seriously
for what they are worth in their own domains, seeing Spinoza as both a
visionary thinker about the physical and a subtle and original
theorist of the psychological, but one whose doctrines cannot be
squared with each other, or with the sort of naturalism that sees the
acting subject as fitting seamlessly into physical nature. But in any
of these cases, we lose the unity of Spinoza's thought, which was
clearly of vital importance to him.



In retrospect, Spinoza's view of physical nature appears as an
unstable hybrid, perhaps even incoherent. But it of great interest as
a testimony to the striking originality of its author and to the
unsettled state of play in the open field that was mid-17th
century natural philosophy.