Spinoza’s Three Kinds of Cognition: Imagination, Understanding, and

Definition and Essence in the Treatise on the Emendation of the Intellect

Spinoza distinguishes three kinds of human cognition, let’s say, imagination,

reason, and intuition. Although I think his handling of the trichotomy is stable across

his writings, I want to focus on the TdIE presentation because certain things

concerning definition and essence come out especially clearly there.1

What Spinoza has his eye on is what we might think of as the quality of

human cognition. More specifically, his classification has to do with how cognition

or thought is ordered. In particular, the trichotomy concerns the difference between

its being superficially ordered and its reflecting the world’s deep structure. He does

think that certainty accompanies such well-ordered cognition: when I understand

and see why something is the way it is, Spinoza holds I am certain and I know I

cannot be mistaken. But that is not his focus. His focus is on understanding itself.

Here’s how Spinoza introduces the bottom level of cognition. (By the way,

although the TdIE lists four headings, I am, following the Ethics (2p40s2), going to

collapse the first two headings into a single bottom level):

1. There is the perception we have from hearsay, or from some sign

conventionally agreed upon.

Spinoza gives as examples my knowledge of the date of my birth and of who my

parents are.

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2. There is the perception that we have from casual experience; that is,

experience that is not determined by the intellect, but is so called because it

chances thus to occur [casu sic occurrit], and we have experienced nothing

else that contradicts it, so that it remains in our minds unchanged.

Spinoza gives as examples my knowledge that I shall die, my knowledge that oil

feeds fire and water extinguishes fire, and my knowledge that a dog is barking

animal and man is a rational animal.

Spinoza describes the second kind of cognition as follows:

3. There is the perception we have when the essence of a thing is inferred

from another thing, but not adequately. This happens either when we infer a

cause from some effect or when an inference is made from some universal

which is always accompanied by some property.

I’m going to key on the idea that this cognition involves essence. More specifically,

this cognition involves an inference from some feature of a thing to its essence, so it

corresponds to a posteriori cognition, in the pre-Kantian sense of a posteriori. It is

“outside in” cognition, cognition from the surface to an underlying causal structure.

That is, the cognition involves the movement from property, effect, or consequence

to essence, cause, or ground.

Spinoza gives several examples of this (in §21). One that I think is especially

helpful is this:

When we clearly perceive that we sense such-and-such a body and no other,

then from this, I say, we clearly infer that the soul is united to the body, a

union which is the cause of such-and-such a sensation. But from this we

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cannot positively understand [non absolute inde possumus intelligere] what is

that sensation and union.

Spinoza thinks that fact of sensation shows that I am united to a body. He may even

think that it tells me a little bit about what the soul is: namely, whatever the soul is

—that is whatever its essence turns out to be—it must be such that it grounds its

union with the body. This alone, however, would make for a quite blank and

abstract characterization of the mind’s nature, as Spinoza emphasizes. In footnote g,

he explains:

For by this union we understand nothing beyond the sensation itself; that is,

the effect from which we inferred a cause of which we have no

understanding.

And in footnote h, Spinoza warns that although such conclusions are certain, they

must be treated with “great caution,” because:

When things are conceived in this abstract [abstracte] way and not through

their true essence, they are at once confused by the imagination. For to the

things that they conceive abstractly [abstracte], separately, and confusedly,

men apply terms which they use to signify other more familiar things.

Spinoza holds that while this kind of cognition does provide understanding, the

understanding it provides is limited. Because the understanding of what the soul is

left mostly blank—because we do not conceive the soul through its “true essence”—

it will be very easy to make the mistake of associating with it all sorts of things that

do not belong to it.

And here’s how Spinoza characterizes the third kind of cognition:

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4. Finally, there is the perception we have when a thing is perceived through

its essence alone, or through knowledge of its proximate cause.

This kind of cognition is “inside out,” in that it goes from underlying basis to

outward feature. It is a priori cognition, again in the old sense, that is, from essence,

cause, or ground to property, effect, or consequence. He gives a few examples. The

one I find most helpful is this: “from the fact that I know the essence of the soul, I

know that it is united to the body.” If I know, for example, that what the (human)

mind is is the idea of the (human) body within the infinite idea of God, then I’ll see

that the mind must be united to the body and how it is united (i.e., as an idea to its

object).

The distinction between the first kind of cognition, on the one hand, and the second

and third kinds, on the other, is, roughly, the distinction between imagination and

understanding. In the Ethics, Spinoza tells us that the lower form of cognition

follows the “the order and linking of affections of the human body” and the second

two forms of cognition follow “the order of the intellect” (2p18s). The first kind of

cognition is ordered imagination-wise; the second two kinds are ordered

understanding-wise. I want to begin by taking up the contrast between imagination

and understanding.

Part 1 Imagination versus Understanding

In the TdIE (§51), Spinoza warns the reader the he will “not here be giving

the essence of every perception, explaining it through its proximate cause, for this

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belongs to Philosophy.” This is in contrast to the Ethics, where Spinoza tells us quite

a bit about what imaginative cognition is. I’m going to draw on the Ethics account,

because it helps to fill out Spinoza’s picture.

My body exists in the plenum, along with other bodies. When other bodies

bump into my body, they sometimes leave a dent in my brain. When this occurs,

there is an idea of the brain dent in my mind. This follows from Spinoza’s account of

what the mind is, a difficult topic that, I presume, he wished to set aside for

purposes of the TdIE. According to Spinoza, the nature of the dent is more a

function of my body than the foreign body, but, even so, the idea of the dent does

“tell” me something about the foreign body (2p16c). The dents themselves, and, so

too, the ideas of the dents, are associated in various ways. For example, if my body

gets dented by light reflected from a piece chocolate cake at the same time my

olfactory system is impacted by aroma in the air, then the two images will be

associated in my brain and the ideas of those images will be associated in my mind. I

think this means, for example, that when I picture the cake on the table, I will also

recall its aroma. Spinoza allows that the mechanisms he provides are somewhat

speculative, but thinks that they are good enough for his purposes, and suspects that

they are not far from the truth (see 2p17cs).

Let’s suppose my belief that oil feeds fire arises from casual experience, that

is, from past associations of oil’s being poured on fire with fire’s increasing.2

Spinoza’s main idea seems clear enough: in such a situation I don’t understand why

oil feeds fire, I have no insight into the matter. What would having that involve? For

Spinoza, it would require perceiving oil through its essence, and perceiving fire

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though its essence, which, he thinks, would make manifest why oil has the effect on

fire that is does. And this is something that dent cognition does not do.

Let’s suppose, instead, that I have acquired my belief that oil feeds fire “from

hearsay, or from some sign conventionally agreed upon,” say, through some

combination of reading textbooks and being told so by teachers. In this case, the

situation is more complicated, but Spinoza’s basic point remains the same. The

relevant associations are more complex in that they now include linguistic dents, an

intricate network of associations of sound traces and inscription traces left on my

brain.3 But if I rely on external testimony for the view and don’t myself grasp the

essence of fire and the essence of oil, then I don’t understand why oil feeds fire.4

Connection between subject and predicate runs through essence

Spinoza’s own examples of hearsay raise some interesting questions. Recall,

they include things like knowing who your parents are and the date of your birth. It

is perhaps consistent with the presentation of the three kinds of cognition that

Spinoza holds that your cognition of when you were born or who your parents are is

irredeemably consigned to the bottom level. I doubt that this is in fact Spinoza’s

view. I think that he thinks there is a sort of understanding of such matters available

at least to certain intellects, if not to us. But, what would it mean for me to

understand these things—to have insight into them in the way that I might

conceivably have insight into oil’s feeding fire?5

I would like to pursue this question in a couple of steps. First, I want to

consider some suggestive remarks that help to bring out the role that the plenum

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physics and essence are playing in Spinoza’s thinking; and then, I want to consider

Spinoza’s treatment of things whose essences don’t include existence.

In §62, in the course of a discussion of “fictitious ideas,” Spinoza offers an

analysis of what happens when someone makes a statement like “men are suddenly

changed into beasts.” Spinoza writes:

[T]hat this is a statement of a very general kind, such that there would be in

the mind no conception, that is, no idea or connection [cohaerentia] of

subject with predicate. For if there were such, the mind would at that time

see the means and cause, the ‘how’ and the ‘why’ such a thing took place [quo

et cur tale quid factum]. Then again, no attention is given to the nature of

subject and predicate.

It is interesting to see Spinoza couch his discussion in terms of the connection of a

subject with a predicate; I believe this is rather unusual for him. Here is what I think

his point is.

Let’s say someone, fresh from A Midsummer’s Night Dream, reports that

Bottom was turned into an ass. Spinoza regards such a statement as general,6

because she has “no idea of the connection of the subject with the predicate.”

Moreover, it is only because she has no idea that she is able to form this fiction.

Well, what sort of thing would give her an idea of the connection? Evidently,

some sense of the “means and cause” of the transformation or “the ‘how’ and the

‘why’” of this event’s taking place. This, in turn, Spinoza implies, requires paying

attention to the nature of Bottom—probably both the nature of the pre-

transformation human being and the nature of the post-transformation ass. Now,

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for Spinoza, understanding Bottom’s pre- and post-transformation natures involves

knowing the pre-transformation plenum structure and the post-transformation

plenum structure; and having the “how” and the “why” involves understanding how

basic principles of the plenum gave rise to such a transformation—i.e., “the means

and the cause.”

As I mentioned, this is part of Spinoza’s account of how we form fictitious

ideas. His ultimate point is that as we understand these matters better—as we

understand what the human Bottom is, what the donkey Bottom is, and what the

“how” and the “why” would have to look like—it will eventually become impossible

for us to entertain this fiction; the plenum order won’t support such

transformation.7 This last point reinforces something that Spinoza said earlier in the

TdIE, at §58:

the less men know of Nature, the more easily they can fashion numerous

fictitious ideas, as that trees speak, that men can change instantaneously into

stones or springs, that ghosts appear in mirrors, that something can come

from nothing, even that gods can change into beasts or men, and any number

of such fantasies.

The better we understand Nature, the harder it is for us to make sense of fictions.

Before I have studied chemistry, it might have been easy for me to entertain the

fiction of water unfrozen at ten degrees below zero, but after I study chemistry such

a fiction becomes unintelligible.

There are two points I want to pull out of this discussion, for the moment.

First, the connective tissue between subject and predicate comes via their nature,

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which I am taking in this context, to be their essences. Second—encouraged by

Spinoza’s comment about the need to see “the means and cause, the ‘how’ and the

‘why’ such a thing took place [quo et cur tale quid factum],” I think we ought to

understand these natures in terms of plenum theory. In other words, plenum theory

gives Spinoza his picture of what these essences look like and, through that, what a

connection of subject with predicate looks like.8,9

Existence and the Order of Nature

To the extent that things concerning you can be traced back to your essence

(which I am taking here to be your geometrico-kinetic constitution), we have some

idea of what it means to have insight into those things and their relation to you. But

not everything about you can be traced back to your essence. In particular, your

existence cannot be traced to your essence. So, what might cognition of the third

kind of your existence look like?

There’s a notion that surfaces at a couple of points in the TdIE that I think is

helpful here, namely, the order of Nature.10 In §40, Spinoza says “the better [the

mind] understands the order of Nature, the more easily it can restrain itself from

useless pursuits.” This idea of the order of Nature comes up again in §65:

if the existence of thing is conceived is not an external truth, [in order to

avoid to determine whether our idea is true and not a fiction] we need only

to ensure that the existence of the thing is compared with its essence,11 while

at the same time attending to the order of Nature.

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In order to tell whether my idea of an individual is a true or a fiction, I need to see

whether that individual’s essence fits into the order of Nature.12 Spinoza’s appeal to

the order of Nature in the TdIE is similar to an appeal to the “order of universal

corporeal Nature” in 1p11d2 of the Ethics:

But the reason for the existence or nonexistence of a circle or a triangle does

not follow from their nature, but from the order of universal corporeal

Nature. For it is from this latter that it necessarily follows that either the

triangle necessarily exists at this moment [iam] or that its present [iam]

existence is impossible.

The article “the” in “the triangle” is not found in the Latin, of course, but it is clear

that Spinoza in talking about the existence of some individual triangle, at some

particular place and time (as the two iam’s indicate). And what he is saying here is

its existence is settled by the “order of universal corporeal Nature.”

That can seem puzzling. We sometimes tend to think of the Nature’s order as

generic, so that it is comprised by some set of basic laws. I think there is a stratum of

Spinoza’s metaphysics that corresponds to this level. Such structure is due either to

the attributes of substance itself, or the immediate infinite modes (“motion and

rest”). The existence or nonexistence of the triangle is consistent with these very

general features of the universe.

However, as we have seen, there is another layer of structure, what Spinoza

calls the order of Nature, which is consistent only either with the existence or the

triangle or with its nonexistence (but not both). I think this stratum corresponds to

the mediate infinite mode that Spinoza calls the face of the whole universe in Letter

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64. He links this mode to the conception of “the whole of Nature” as “one individual

whose parts—that is, all the constituent bodies—vary in infinite ways without any

change in the individual as a whole.” This individual exhibits an order, but a fully

determinate one. Whether the triangle exists depends on whether its essence is

integrated into that determinate order.

To return to our question, then, what might it mean for an intellect to have

insight into the date of your birth? A full understanding of your appearing on the

seen when you did, requires locating you within the face of the whole universe, and

then tracing back the face of the whole universe (or the infinite individual) to God’s

or substance’s essence. In order to do this, one would have to have a purchase on

the face of the whole universe, that is, on “the whole of Nature” conceived as “one

individual” with all its “constituent bodies.” This is something that lies beyond us,

but not beyond God or Nature.13

Part 2 Definition and Essence

The best form of cognition involves perceiving a thing “through its essence” alone,

which is often connected to knowing the thing’s proximate cause. This is in line with

the traditional view that to understand a thing is to grasp its essence. It is easy to

feel, however, that Spinoza leaves us in the dark about how he looks at essence.14

And in fact Spinoza allows in §22, “the things I have hitherto been able to know by

this kind of knowledge [i.e., the third kind of knowledge] have been very few.”

Even so, I think Spinoza does try to provide some help with this topic in the

TdIE. This comes mainly through his extensive remarks on definition. In this

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context, a definition is supposed to be an account of an essence, so if we know what

a definition looks like we will know something about what an essence looks like.

Essence, definition, mode and substance

Let’s begin by recalling the general framework for thinking about essences that

Spinoza inherits from the Aristotelian tradition.

A thing’s essence is its basic, structural features: it is what makes the thing be

the thing that it is. An essence is a worldly item, as opposed to a representational

item. A logos or real definition is an account of an essence. It, in contrast with the

essence itself, it is a representational item. A logos or real definition is supposed to

track the worldly item, that is, it is supposed to provide a perspicuous

representation of a thing’s essential structure. In contrast with a real definition, a

merely nominal definition tells you how to apply a word.15 Aristotelians supposed

rational animal got at a human being’s core or constituting powers: it sets the

parameters for the theory of what a human being is; by way of contrast, featherless

biped doesn’t. Spinoza is implicitly ridiculing the Aristotelian theory when he places

my cognition of man as a rational animal at the lowest level of cognition and groups

it with my cognition of a dog as barking animal in (TdIE §20): No one would have

thought barking revealed the dog’s essence; rather the ability to bark is a

consequence of more fundamental features of the dog. Spinoza does something

similar toward the end of the scholium on universals in the Ethics (2p40s1), where

he writes:

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For example, those who have more regarded with admiration the stature of

men will understand by the word man an animal of upright stature, while

those who are wont to regard a different aspect will form a different common

image of man, such as that man is a laughing animal, a featherless biped, or a

rational animal. . . . Therefore, it is not surprising that so many controversies

have arisen among philosophers who have sought to explain natural

phenomena through merely the images of these phenomena.

Spinoza implies here that rational animal is no better than laughing animal or

featherless biped as an account of a man: all three are misguided attempts to “explain

natural phenomena through merely the images of these phenomena.”

The Aristotelian account of definition and essence interact with the

Aristotelian substance-accident ontology in an important way. The dependence of

an accident on a substance is included in the accident’s essence. In other words,

saying what an accident is involves making reference to the substance in which it

exists. Aristotle’s favorite example is snub: snubness, in virtue of what is, must exist

in a nose. This dependence is reflected in the (real) definition of snub—thus, the

Aristotelian thesis that substances are “prior in definition” to accidents.

Although snub is a toy example, it is worth trying to hear it as “realistically”

as possible. So, snubness, we may suppose, is a certain arrangement of the soft

tissue and cartilage found in certain animal’s noses. And, an account of what

snubness is—what we might think of as a theory of snubness—will involve an

account of what the thing to which snubness belongs is—that is, a theory of the

animal, including a theory of the arrangement of the soft tissue in its various organs.

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The relation of snub to nose is not criterial or merely conceptual. Aristotle’s

point is not that it is part of our “concept” of snub, or perhaps part of the “meaning”

of the word “snub,” that snub belong only to noses. Rather, we should think of snub’s

being related to noses as world dependent, perhaps a matter of biology, more or less

as we think of water’s being H2O as world dependent, a matter of chemistry, and not

grounded in the “concept” of water or the “meaning” of the word water.

Spinoza accepts both of the ideas I’ve discussed so far, namely, that definitions

ought to reveal essences and that the definition or essence of an accident (for him, a

mode) depends on the definition or essence of its substance (for him, God or

Nature). In TdIE §95, Spinoza says that we must be careful when defining a thing to

avoid using what is merely a coextensive property in an explanation of an essence:

For a definition to be regarded as complete [perfecta], it must explain the

inmost essence of the thing, and must take care not to substitute for this any

of its properties. To explicate this . . . I shall choose only the example of an

abstract thing [rei abstractae] where the manner of definition is unimportant,

a circle, say. If this is defined as a figure in which the lines drawn from the

centre to the circumference are equal, it is obvious that such a definition by

no means explains the essence of a circle, but only one of its properties. . . .

For the properties of things are not understood as long as their essences are

not known.16,17

Spinoza is using the term property here in its technical Aristotelian sense. A

property is an accident (or mode) that necessarily flows from a thing’s essence. The

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stock example was risibility in a human being: the Aristotelians supposed the ability

to appreciate the incongruence involved in humor flows from a more basic rational

capacity. Spinoza is saying here that we need to be careful not to mistake a property

—something derivative from a thing’s essential structure—for the essential

structure itself. He says at the end of the passage that we won’t be able understand,

in particular, a thing’s properties without understanding its essence first.18

Spinoza’s example is a bit puzzling. Why isn’t figure in which the lines drawn

from the centre to the circumference are equal a perfectly good account of the

circle’s essence? After all, it picks out all and only circles, and does so necessarily.

What sense can we make of the idea that this feature of circles is grounded in

something more fundamental? To answer this question, we need to look at what

Spinoza regards as a good account of the circle’s essence. This comes in the next

section (TdIE, §96), where he makes the general point that, in a case of created

thing, its definition must involve its proximate cause:

1. If the thing be a created thing, the definition, as we have said [cf. §92], must

include its proximate cause. For example, according to this rule a circle

would have to be defined as follows: a figure described by any line of which

one end is fixed and the other moveable. This definition clearly includes the

proximate cause.

2. The conception or definition of the thing must be such that all the

properties of the thing, when regarded by itself and not in conjunction with

other things, can be deduced from it, as can be seen in the case of this

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definition of a circle. For from it we can clearly deduce that all the lines

drawn from the centre to the circumference are equal.

Why does Spinoza think that figure described by any line of which one end is fixed

and the other moveable expresses the essence of a circle, whereas figure in which

the lines drawn from the centre to the circumference are equal does not?

Spinoza says that a good definition includes the circle’s proximate cause.

Here he thinks of that cause as a Euclidean construction procedure. One idea, which

comes up in the period, but which Spinoza does not mention, is that the construction

procedure makes evident the possibility of a thing. By showing how to make a circle,

the procedure of fixing one end of a line and moving the other end makes clear that

a circle is a possible geometrical structure. The characterization figure in which the

lines drawn from the centre to the circumference are equal does not do this. As far

as that characterization goes, such a figure might be like a plane figure bounded by

exactly two straight sides19 or like the fastest possible motion.20

Beneath this thought, is, I think, the following this idea: If you know what

goes into the construction of something—if you know how something is produced—

you have a good picture of its basic structure. Moreover, since there is no more to

the circle structure than what is put into it to by its construction procedure, the

construction procedure must ground all of its properties (as required by point 2 in

the extract). So if, for example, having an area equal to its radius squared times is π

a property of the circle structure, this property must be a byproduct of the circle’s

being the result of rotating a line about a fixed endpoint. By way of contrast, it is not

obvious that all of the properties associated with the figure picked out by the

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characterization figure in which the lines drawn from the centre to the

circumference are equal depend on that feature as opposed to some other aspect of

the figure. For this reason, it is natural to think that the definition explains why the

circle has the property of being a figure in which the lines drawn the centre to the

circumference: the figure has this property because it was generated by rotating a

line about a fixed end point.

The difference between the two formulations can be hard for us to hear

today, because we have become accustomed to think about geometry in a very

different way. But I don’t think it is impossible for us to put ourselves in Spinoza’s

shoes and think of geometry in this less formal way.

Be that as it may, I want to point out something implicit in Spinoza’s picture

that is easy to easy to overlook. This is the real work that space (an aspect of

extension) is doing in the theory. The constructions implicitly rely on space and its

nature. For consider: Why is that there is a construction procedure for producing a

triangle but no procedure for constructing a biangle (a two-sided closed plane

figure)? Spinoza’s answer is that space (or extension) admits of the one construction

but not the other. What a geometrical essence is is a way of describing space (or

extension). What the definition, the construction procedure, or “proximate cause,”

does then is to make clear that space (or extension) admits of a certain carving or

description. The essences presuppose space; they are fundamentally space

involving. They theory of the triangle depends on the theory of space. Notice that we

have here Spinoza’s version of the Aristotelian priority in definition of substance to

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accident. Geometrical essences are conceived through space in the way that, for

Aristotle, the definition of snub involves that of nose.

Spinoza tells us in TdIE §95 that his example concerns an abstract thing as

opposed to a real physical being, and says, “in the case of an abstract thing the

manner of definition is unimportant”? How does this qualification affect things?

Well, the sort of abstraction involved here is similar to that which Berkeley

discusses when he considers abstracting the shape of a thing from its other

qualities, as opposed the abstraction involved when human is abstracted from Peter,

James, and John.21 In other words, we are thinking about an individual, this circle,

and not the universal circle. So, consider a fully determinate individual within the

plenum, say, Baruch Spinoza’s body. This structure is governed not only by

geometrical principles that characterize Euclidean space, but also by kinetic and

dynamic principles that characterize motion within in the plenum. We can abstract

the geometrical structure from the rest of the structure and consider, for example,

only this body’s shape and volume, ignoring the rest of its features. When we do so,

talk of the geometrical construction procedure as being the shape’s “proximate

cause” becomes metaphorical, because the real causes of the body’s shape depends

on the kinetic and dynamic principles from which we are abstracting.

Even so, the relation of a circle to its construction procedure is analogous to

that of Spinoza’s body to the real motions in the plenum that give rise to the

particular pattern of motion and rest that is Spinoza’s body. For example, in the way

that the possibility of the circle depends on what constructions the general structure

of space admits of, the possibility of Spinoza’s body depends on what physical

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constructions the general structure of the plenum admits of.22 In the same way the

theory of the triangle depends on the theory of space, the theory of Spinoza’s body

depends on the theory of plenum. (In Spinoza’s terminology, Spinoza’s body is

conceived through the extension, which includes all of extension’s basic structural

features.) In the same way that the construction procedure for the triangle grounds

all of its properties, the proximate cause of Spinoza’s body grounds all its

properties.23,24

On Spinoza’s picture, the geometrical essences are grounded in a real being,

space (or extension), which necessarily exists of its own nature. If what a

geometrical essence fundamentally is, is the carving of space (or extension)—a

“description,” in the technical Euclidean sense—then, without space there would be

no carvings or descriptions, and so no procedures. This point is related to a remark

that Spinoza makes in 1p8s2. If people thought correctly about substance and mode,

Spinoza writes:

by substance they would understand that which is in itself and is conceived

through itself . . . . By modifications they would understand that which is in

another thing, and whose conception is formed from the thing in which they

are. Therefore, in the case of nonexistent modifications we can have true

ideas of them since their essence is included in something else, with the

result that they can be conceived through that something else, although they

do not exist in actuality externally to the intellect.

While we can make sense of there being nonexistent modifications of substance, we

cannot make sense of substance’s nonexistence. Similarly, while we can make sense

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of there being a nonexistent of description of space—perhaps the existence of the

triangle considered above was precluded by the order of Nature—we cannot make

sense of there being no space (or extension). This is because the essence of a

modification is included in, or conceived through, that of substance.

I want to separate this point from the thorny question of whether all possible

such carvings are at some point actualized, i.e., whether all essences are realized.

Perhaps, Spinoza has other reasons for thinking all possible carvings of the plenum

are actual.25 The point he is making here (in 1p8s2) is that our having a “true idea”

of a modification—which is in this context would amount to having a definition of its

modification’s essence—depends only on substance or extension and not on the

existence of the modification.

To a certain extent, Spinoza’s picture of the reality of finite essences is

continuous with a medieval Aristotelian picture. The Aristotelians share with

Spinoza the idea that essences are not merely representational entities: they are not

concepts, meanings of words, or whatnots along those lines. Essences require an

extra-mental ground. The Aristotelians, like Spinoza, ground finite essences in a self-

sufficient necessary being, God. According to them, each finite essence is a different

way of imitating or limiting God’s unbounded essence.26 This idea is familiar in the

subsequent tradition. It is at work, I suspect, in Leibniz’s well-known arguments

from possibility to the existence of a self-sufficient necessary being. It also shows up

in Kant. In his early work, “The Only Possible Argument in Support a Demonstration

of the Existence of God,” Kant discusses God as providing the matter for possibility, a

theme that continues into the First Critique, when he provides an explanation how

20

of reason is brought to form the idea of ens realissimum (an idea that Kant maintains

cannot be given “objective reality”).27

But there is a difference between Spinoza and the Aristotelians as well. For

Spinoza, the dependence of a finite essence on the ur-essence is such that the finite

thing must be understood through the ur-structure: You can’t understand a triangle

unless you understand the basic Euclidean structure of which the triangle is a

determination. More to the point, you can’t understand the Spinoza’s body—how it’s

put together and what it is doing—unless you understand the basic geometric,

kinetic, and dynamic principles that order the plenum, of which Spinoza’s body is a

determination. The same is not true for Aristotelians who regard a finite being like

Socrates as a substance in its own right. As a substance, Socrates is not defined

through—his essence does not involve—something else. So my attempt to

understand Socrates’ essence—to work through what a rational animal is—does not

take me to God’s essence.28

Let’s consider the Aristotelian picture of essence more closely. How is a finite

being like Socrates structured on their theory? We begin with a perfection or reality,

say, that of being a substance. The possession of this perfection involves a having

certain (relative) self-sufficiency, so something possessing this perfection does not

need to be in something else in order to exist.29 Now, the perfection substantiality

can be determined through the addition of further perfections. For example, one

perfection that can be added to substance is corporality. Certain further powers or

abilities come with this perfection, for example, the ability to occupy space and

mobility.30 Corporeal substance can be determined still further, by the addition of

21

other perfections, for example, living. With these perfections come new abilities, the

abilities to assimilate nourishment and to reproduce. And so on, until we get to the

nature human being, by adding the powers of locomotion and sensation and the

power of rationality.

For the Aristotelians, rational, sensitive and locomotive, living, corporeal

substance is supposed to be a real definition of human being, that is, an account of

the essence of a human being. As a human being is not simply a property bucket, its

definition does not simply list a hodgepodge of features. There’s causal order or

coherence here: the power of locomotion and sensation presupposes life and the

power of (human) rationality presupposes sensation. This is part of what’s involved

in the idea that sensation and locomotion are (real) determinations of living

substance, and rationality is a (real) determination of animal.

Now, I ended the account of the real essence of Socrates at human rather than at

Socrates. This is appropriate in view of the Aristotelian doctrine that individuals

cannot be defined: only the essence of the species to which to individual belongs can

be defined. Perhaps the thought behind this claim is this: There will, of course, be

found in Socrates’ essence some individuating principle that grounds his distinction

from other conspecific individuals, say, Plato and Glaucon. (Aquinas, for example,

thought this principle was “designated matter,” and Scotus thought it was a

principle of “thisness”.) Understanding or theory, however, ends at the level of the

species. While the theory says that Socrates and Plato must each have his own

individuating principle (his own designated matter or his own principle thisness),

22

there is no further understanding or theory to be had concerning Socrates’ principle

and how it differs from Plato’s. Any further account of how they differed would be

anecdotal and occasional rather than belonging to systematic knowledge (episteme

or scientia).

Aristotelian essences are, then, very different from the essences envisioned

by Spinoza. There is nothing in the Aristotelian scheme corresponding to the

geometric, kinetic, and dynamic structure that Spinoza thinks plenum essences

involve. The materials that the Aristotelians build their essences out of—perfections

like living, animal, rational—look to Spinoza very odd candidates for the ingredients

in a theory of an individual’s basic structure. I think this difference sets much of the

context for what Spinoza has to say about essence and definition.

So: In §98, Spinoza says that the “best basis for drawing a conclusion” is a

“particular affirmative essence.” That emphasis continues in the next section (§99):

Hence we can see that it is above all necessary for us always to deduce our

ideas from physical things, i.e., from real beings, advancing, as far as we can,

in accordance with the chain of causes from one real being to another real

being, and in such a manner as never to get involved with abstractions and

universals, neither inferring something real from them nor inferring them

from something real.31

What is the point behind Spinoza’s emphasis on “a particular affirmative essence”

and “real beings” and his comment on the need to avoid becoming “involved with

abstractions and universals”?

23

I think Spinoza’s point’s is that if I want to understand some plenum

structure—say, the Spinoza body, or that rainbow over there, or the solar system—I

should attempt to characterize the geometrical-kinetic-dynamic structure of that

individual, without worrying about other individuals in the plenum that are like it

(or unlike it) in various respects. This is a natural (if not unproblematic) line of

thought given Spinoza’s geometrical orientation. Let me explain.

When I am working out a geometrical argument—say, constructing a

diagram that exhibits the relationship between the three interior angles of a triangle

and a straight line, I am focused on individuals—these angles in that triangle

bearing some relation to that line. I see the necessity of the relationship in this case

and, if I so choose, I generalize to other the similar cases. The generality seems to

come from the necessity rather than the necessity from generality. That’s true of

geometry, but it also true of geometric-kinetic-dynamic account of real motion-and-

rest structures in the plenum. When I come up with an account of the mechanics of

the rainbow in front of me that explains why the drops of water in that mist in the

sky have a certain effect on the light, I attempt to work out the relevant

relationships for this arrangement of drops. If I succeed, my theory works

irrespective of whether there are any other rainbows in the plenum.32

Now, to be sure, my theory is, let’s say, repeatable, in the following sense: if

there are similar structures in the plenum that happen to be similarly situated with

respect to light, and so on, they too will form rainbows. But this repeatability is in a

certain sense beside the point: it is not of the essence of the explanation, of the

understanding acquired through working out the mechanics of this rainbow. The

24

repeatability comes from seeing why it holds in this case, and noting that if other

cases are similar, then the same things will be true of them.33

Let’s contrast this with an Aristotelian approach. For them, generality seems

to lie at the heart of the human scientific endeavor. It is the fact that all dogs share

certain properties that clues us into there being an intelligible necessity somewhere

at work—whether this necessity is to be found in the dog’s essence or in the

following of certain propria from the dog’s essence. Aristotelian metaphysics makes

room for nonrepeatable finite essences—Aquinas’s views on angels come to mind

here—but the general direction of their natural philosophy sees human

understanding, human scientia, as the result of the abstraction of universals from

particulars. This orientation is captured in the point we noticed earlier that

systematic knowledge (scientia or episteme) ends at the species: everything else is

anecdotal and occasional.

This context helps us see the point of Spinoza’s call to focus on the “particular

affirmative essence.” It is not, as I have said, that he thinks that the structure in the

rainbow is not repeatable. Rather, the point of this remark is to have us think about

the plenum-mechanico structure of a given individual instead of having us focus on

what it has in common with structures of the same kind or species and seeing what

commonalities we can extract. Accordingly, the point of Spinoza’s call to focus on

particulars is not to get us to focus on those aspects of the rainbow that are, we

might say, inherently individual—says, its being located at this place at this time. He

is not advising that we should, for example, focus on the circle qua being a

description in this quadrant of the Euclidean plane instead of being a description in

25

that quadrant.34 To be sure, it is in some sense a condition of being this circle as

opposed to that circle that it be a description of this region as opposed to that

region. But there does not seem to be much of theoretical interest here, beyond the

observation that spatio-temporal location matters to the identity of finite modes of

extension.

Now, this might be disputed. Spinoza after all emphasizes the importance of

the “interrelation of things” (§41) or the “interconnection of things” (§95) for

getting Nature right. You are the offspring of your parents, and they are the

offspring of their parents, all the way back to Lucy, and things go back from there all

the way back to the big bang. A full understanding of you, it seems, should bring into

account the myriad and manifold relations and events that brought you on the scene

—your parents, your species, your ecosystem and so forth. And, if this is so, it is

plausible to think Spinoza might hold that your essence should inherit some or all of

these relationships and events. And, indeed, there is a passage in §99, which

concerns definition and essence, that indicates that a “series of causes” is involved in

the essence of finite things:

our mind, as we have said, will reproduce Nature as closely as possible; for it

will possess in the form of thought the essence, order, and unity of Nature.

Hence we can see that it is above all necessary for us always to deduce our

ideas from physical things, i.e., from real beings, advancing, as far as we can,

in accordance with the chain of causes from one real being to another real

being.

26

While the exact meaning of this passage may be obscure, it indicates that a “chain of

causes” is involved in the definition of the essence of a finite thing.

Now, I think there is something right about the suggestion that a full

understanding of you involves the connections you have with the rest of Nature. In a

way, this was something we saw earlier in this talk, when we considered what it

might mean to understand when you were born or who your parents are. But it does

not follow that such relations are a part of your essence. The drift of our earlier

argument, at any rate, is that it was a consequence of God’s essence to produce a

certain order in which my body would emerge in the plenum at a certain place and

time.

Well, then, what about the remark from §99, which suggests that the

definition of a mode involves a series of causes? Doesn’t this show that the causal

grid is implicated in the essence of a (plenum) mode? Well, Spinoza goes on in the

next section (§100) to make clear that this is not his meaning. He says there, “it

should be noted that by the series of causes and real beings I do not here mean the

series of mutable particular things, but only the series of fixed and eternal things.”

There are, he writes, “an infinite number of factors affecting one and the same thing,

each of which can be the cause of the existence or nonexistence of the thing.” No

human could grasp such a series, but this does not matter for the project of grasping

a particular essence. This is because, Spinoza tells us, “the existence of mutable

particular things has no connection with their essence.”

Spinoza explains further in the next section (§101):

27

But neither is there any need for us to understand their series. For the

essences of particular mutable things are not to be elicited from their series

or order of existing, which would furnish us nothing but their extrinsic

characteristics, their relations, or, at the most, their circumstances. All these

are far from the inmost essence of things.

Here Spinoza draws a firm line between the series of mutable things that furnish the

“extrinsic characteristics,” “relations,” and “circumstances” of a thing as opposed to

its “inmost essence.” But, if we don’t think of “the series of causes and real beings”

mentioned in §100 as the spatially and temporally extended causal nexus, as the

causal grid, how are we supposed to think of it? Spinoza goes on to explain (in

$101):

This essence is to be sought only from the fixed and eternal things, and at the

same time from the laws inscribed in these things as in their true codes,

which govern the coming into existence and the ordering of all particular

things. Indeed, these mutable particular things depend so intimately and

essentially (so to phrase it) on the fixed things that they can neither be nor be

conceived without them. Hence, although these fixed and eternal things are

singular, by reason of their omnipresence and wide-ranging power they will

be to us like universals, i.e., the genera of the definitions or particular

mutable things, and the proximate causes of all things.

But, how do the fixed and eternal things form a “series”? Here’s a suggestion.

Perhaps the series runs along these lines: first, there is the basic geometrical

(Euclidean) order found at the level extension. A second layer of kinetic structure is

28

introduced through the immediate modes, which includes motion and rest.35 Beyond

these layers of global structure, there must also be, of course, local structure,

peculiar to the individual—the structures involved in maintaining the particular

ratio of motion and rest that the individual is.36 If this is correct, the local structure

is conceived through the immediate modal structure (motion and rest) and,

ultimately, through extension, an attribute of substance. This would be part of

Spinoza’s reworking of the idea that the essence or theory of the mode involves the

essence or theory of its substance.37 We cannot understand a ratio of motion and

rest without understanding the principles of motion and the principles of extension.

Spinoza has systematic reason to want to recover a notion of my essence that

is to a certain extent detachable from the causal grid. In Parts 3 through 5 of the

Ethics offers a theory of those things that tend to enhance our conatus and those

things that tend to diminish our conatus, which conatus identifies with our essences.

This theory requires that I have a nature that is to a certain extent to work out

separate from the rest of the causal grid. (I have in mind, in particular, Spinoza’s

theory of being active and being passive.) That said, it is important not to overstate

my independence. At the end of the day, according to Spinoza, I am a profoundly

dependent being and that dependence, as we have seen, is registered in the fact that

my essence must be conceived through the Nature’s geometric, kinetic, and dynamic

order. Indeed, Spinoza thinks we have tendency to overlook our dependence and

exaggerate our (relative) independence, so that at times we come to see ourselves

as somehow in opposition with Nature’s order—as if we could be in an antagonistic

relationship with the very geometric, kinetic, and dynamic fabric out of which we

29

are cut. I see Spinoza’s account of essence as meant to strike a balance: It preserves

my reality as an individual thing while simultaneously making clear my status as an

utterly dependent thing.38

Spinoza concludes §101 with an important and interesting remark. He says:

Hence, although these fixed and eternal things are singular [singularia], by

reason of their omnipresence and wide-ranging power they will be to us like

universals, i.e., the genera of the definitions or particular mutable things, and

the proximate causes of all things.

Earlier I remarked that there was a way in which repeatability was not at the heart

of the Spinozistic explanatory enterprise: my account of the workings of this

rainbow is focused on it, rather than what it may or may not have in common with

all other rainbows. What about the basic principles of geometric, kinetic, and

dynamic order themselves? It might be felt that here is something that is

fundamentally repeatable or universal.

I take it that Spinoza is agreeing here with that suggestion, albeit it in a

qualified way. They “will be,” he says, “to us like universals, i.e., the genera of the

definitions or particular mutable things.” Why only “like,” though?

Here we should keep an eye on the way in which the fixed and eternal things

function within Spinoza’s theory. The universe’s basic geometric, kinetic, and

dynamic structure is “omnipresent” in a special way: this structure is invariant

throughout the plenum. Take, for example, something as simple as the triangle law.

Any three points in the plenum, no matter where than are located, and no matter

30

how far they are from one another, obey the following principle: the path going from

the first to the second and then from the second to the third is longer than the path

going from the first to the third. The same invariance is found in the kinetic and

dynamic as well as the geometric structure: we might put it that the universality

here is a universality of uniformity rather than one of repeatability of features or

predicates. As there is nothing corresponding to this uniformity of structure in the

Aristotelian scheme, Spinoza’s omnipresent fixed and eternal things are like

Aristotelian universals, but only like.

This colors Spinoza’s thinking about the problem of universals. On one

understanding of the problem, the issue concerns whether the kind human is

grounded in similarities found among certain individuals (we may call this position

“nominalism”) or whether the similarities among certain individuals are grounded

through in the kind (“realism” or “moderate realism”).

So, for example: Is the perfection corporeality a sort of ingredient in my

nature and in your nature, which is why you and I are similar in certain ways: e.g., I

like you, have shape and size and occupy space? Or, is corporeality merely a way of

cognitively or linguistically marking that we are similar in certain ways: that we

both have size and shape and take up space?

It seems to me that neither option fits Spinoza’s metaphysics. Consider two

extended things, say, the Spinoza body and the solar system. What they are, are two

different “motion-and-rest” determinations of extension. As determinations of

extension they inherit the order made for by the “omnipresent” “fixed and eternal

things”. (Each of them obeys the triangle law, for example.) So their similarities are

31

not primitive; they have a deep explanation. But, and this seems crucial, this

explanation does not come through kind membership: rather, it comes their relation

to a certain base object, namely the substance through which their essences are

conceived. Here it is important to note that Spinoza describes the “fixed and eternal

things” as “singular” in §101.

Well, one might wonder, could we, Spinoza not withstanding, think of the

extend things as inherited their similarities through their relation to the kind

extended—so that the Spinoza body and the solar system are similar in various

respects in virtue of their belonging to the kind extended? But now we need to ask,

how are we thinking of the kind extended? A natural way for us to think of it

nowadays is as embodying criteria for sorting things into extended and not

extended: Solar system, in; my thought of Michelle Obama, out. The Spinoza body,

in; the number two, out. And so on. That is, we would be viewing the kind as a sort

of “quasi-concept.” If so, then this proposal is inadequate from Spinoza’s point view.

He does not think that a sorting principle that grouped things into extended and

nonextended captures the richness of extension—explained, for example, why all

extended things obey the triangle law. The point I have in mind is closely related to

Kant’s famous claim that geometry is not analytic but synthetic: that we cannot get

at the geometrical relationships by analyzing the concept of extension.39 Perhaps,

there are other ways of thinking of extension, available in the period, which capture

its richness, but the only ones I am aware of are those that, like Spinoza’s view, cast

extension or space as a singular thing.

32

33

1 Imagination, reason, and intuition for Spinoza, I think, have primarily a taxonomical status. He does not think in terms of faculties, so that, for example, imagination is the result of the exercise of one power or faculty, reason another, and intuition, a third. He regards faculties in this sense as mere beings of reason as opposed to real items. It is hard to tell whether Spinoza regards the boundaries between the different kinds as sharp or gradual.

2 As matter of fact, we probably pick these views up through a combination of hearsay—which includes what our teachers tell us about such matters—and casual experience, but let’s leave that aside.

3 Or so I suppose. Spinoza does not say a lot about how language works. He does seem to think that language plays a role in cognition involving traditional universals—notions, like dog, horse, and man. The dents that dogs leave on me coalesces into a blurry imagine, somewhat like an over exposed photograph, I think, and words are useful both for picking out a given blurry image and for (partially) coordinating my blurry images with yours.

4 Even though the first level of cognition does not involve seeing the “how” or the “why,” it can be quite secure. Spinoza, for example, is quite happy to say to use scio—I know—in connection with it. I know who my parents are and I know when I was born. Indeed, Spinoza writes “it is in this way [i.e., via the first sort of cognition] that I know [novi] almost everything that is of practical use in life.” Although it is secure in this way, it the only level where error can be found. This is because Spinoza views understanding as incompatible with the possibility of error. Spinoza’s idea that is that certainty is coextensive with understanding: on the one hand, if I don’t understand why it is that I will die someday—it is just that I have noticed that people do, without my catching on to the rhyme or reason of the thing—than it is possible for me to wrong about this, no matter how, as we might put it, well-grounded my conviction is. But if I understand why this I will die—say, if I see how mortality is built into the nature of an animal—then error is impossible. It is easy to think to think that Spinoza’s point about certainty following understanding is that “understanding,” like knowledge, is a success term, so that if I really understand why s is p then it follows that s is p. I take it that, however, that Spinoza’s point concerns the nature of understanding: there’s something that goes on when I see that three is related to six in the same way that two is related to four that doesn’t go on when I take this on authority, and what goes on in the former case doesn’t admit of error. Spinoza thinks certain subject matters—including mathematics, metaphysics, and theology—are such that when one is thinking clearly only trivial mistakes, akin to slips of the tongue, are possible. This has to do with the nature of our cognitive relationship to those subject matters.

5 And, as a matter of fact, I think it would have struck many in Spinoza’s audience as odd: understanding is of the universal—animal and dog—and the idiosyncratic features of Rover and Spot are only anecdotal, and part of the subject matter of science. Many medieval philosophers thought there was a divine plan, but this is not what science was about, or the proper object of human understanding.

6 I think “general” here probably means something like vague and indeterminate, as when we criticize our students for not being specific enough in their papers.

7 One might wonder whether it makes a difference whether we think of the fictional statement as “Men can turn into asses” or as “This man suddenly turned into that ass.” I don’t think so. I think for Spinoza one can understand this man’s turning into that ass—detailing the

mechanical transformation—without become involved with the goings on in other (perhaps only superficially) similar events, if there are any such events. I think Spinoza presumes other superficially similar transformations would be similar underneath, but this is only a presumption to be born out or refuted by detailed mechanical accounts.

8 The idea that the connection between a subject and predicate runs through the relevant natures or essences makes for a similarity between Spinoza and Leibniz. Leibniz thinks that Caesar’s crossing the Rubicon is something that can be traced to Caesar’s complete concept, and Caesar’s complete concept is in certain ways akin to an account of his essence. I’ve argued elsewhere the Caesar’s complete concept bears a certain intimate relation to the physics of the world that Caesar inhabits, so I think there is a way in which my emphasis on the plenum mechanics is not alien to Leibniz’s outlook. To be sure, for Leibniz, the monadic order is more fundamental than the phenomenal order, but the only way in which are able to give determinate content to Caesar’s concept is by thinking of Caesar as a being with a particular point of view on a certain physical order.

9 [PROBABLY OMIT Spinoza returns to the idea of the connection in his discussion of false ideas. In §73, he asks the reader to consider the “concept [conceptu]” of a sphere, as given by the motion of semi-circle. He deems that that to be a “true perception.” But, he goes on to say, if that motion is taken in isolation from the larger concept or from some real cause in nature, then its “affirmation” would be false. {This is reminiscent of Descartes’s remarks in the First Replies that a triangle inscribed in a square does not have a true and immutable nature, unless it is considered “with a view to examining only the properties which arise out of the conjunction,” say, for example, that the triangle’s area is half of that of the square (7:118; 2:84—for discussion see BTW, pp. 301-306). It seems to me that Spinoza’s case of a true perception where the connection between subject and predicate is effected by some essence corresponds to the situation where Descartes says there is a true and immutable nature; and the case where Spinoza is thinking of the motion as not connected to the circle through a definition is like that case where triangle inscribed in the square does not count as true and immutable nature. (Notice, that essence seems to be doing some of the work for Spinoza in effecting a connection between a subject and a predicate that gets done in other ways in more propositionally oriented theories.)} While exactly how Spinoza is thinking about “affirmation” here is perhaps puzzling, his basic point is clear. The connection between subject and predicate in a true idea must be grounded; it cannot be left simply hanging. One possible ground is the plenum, which might provide a “real cause” for the sphere’s motion. Another possible ground might be the definition of a sphere, which specifies that sphere be the result of the rotation of a semi-circle: according to Spinoza, this essence serves connects the semi-circle to its motion. Without some such connecting principle—the real cause or the linkage through the sphere’s definition—we have no basis for attributing motion to the semi-circle. Spinoza writes:

when we affirm of a thing something that is not contained in the concept we form of the thing, this indicates that our perception is defective, or in other words that we have thoughts or ideas that are, as it were mutilated and fragmentary. For we saw that the motion of the semicircle is false when taken in isolation, but true if it is conjoined with the concept of a sphere, or the concept of some cause determining such motion.

{ Interestingly, Spinoza goes immediately moves from this observation to his central thesis that finite cognition is part of an infinite (global) cognition. The passage continues:

Now if it is in the nature of a thinking being, as seems apparently to be the case, to form true or adequate thoughts, it is certain that inadequate ideas arise in us from this, that we are part of some thinking being, some of whose thoughts constitute our mind in

their entirety, and some only in part.

His idea seems to be that if falsity results from our thoughts being disconnected—lacking the cause or essence that glues the predicate to the subject—and if our thought is fundamentally truth oriented (that is, “if it is in the nature of a thinking being . . . to form true or adequate thoughts”), then (1) the cognition of an unlimited thinking being will contain all of the relevant essences and causes and (2) our incomplete cognition will be some part of its cognition. Alanen calls attention to this interesting passage, p. 18, n. 23.}

{Here, too, Spinoza seems to be thinking of the connection between a subject and predicate in terms of plenum structure, whether the connection is forged through an essence or through the causal goings on in the plenum.) Notice that Spinoza seems to be operating with two levels. There is (a) the level of essence—which includes that plenum structure—and there is (b) our level of our cognition. Since, his level of essence is closely akin to our level of theoretical science, this is akin to trying to provide an account of understand in terms of (a’) theoretical science and (b’) our better or worse grasp of it. There’s water in all of its H2O glory, with all of the chemistry implicit therein, and there is my cognitive grasp if it, which can either reproduce this structure accurately or in a confused and mutilated way. There doesn’t seem to be, for Spinoza, a distinct, semi-autonomous, representational level, say, our “concept” of water, or the “meaning” of the term water.}

10 The order of Nature comes up in §§40, 55, and 65

11 I am not sure what Spinoza has in mind by ensuring that “existence of the thing is compared with its essence”—perhaps his thought that when I am trying to figure out whether you are existing I need to be working with your deep structure rather than your surface features. What I am interested in here, however, is the second part of the sentence.

12 I don’t think Spinoza’s point is generic. When we are talking about existence, we are talking about individual: so the question is not whether the order of Nature makes room for individual similar to you, say, an individual of the same kind as soon. Rather the question is whether the determinate order of Nature admits of your existence (or my existence, or Yeti, the abominable snowman’s existence).

13 [POSSIBLY OMIT Some might feel this excursion through the plenum physics in order to figure out what an understanding of when you born might look like is unnecessary. Spinoza is, it might be suggested, committed to the Principle of Sufficient Reason. So, there must be a reason why I was born when I was. And understanding that reason, whatever it is, is just what having the third kind of cognition my birthday must amount.

I don’t find this way of looking at things helpful. Putting aside the fact the “Principle of Sufficient Reason” a term of art that Spinoza himself rarely uses, it is important to realize that the Principle of Sufficient Reason is a only a schema. In order to give content to the schema, we need to look at the clues Spinoza provides as to how he would fill things out. And, he thinks that people who go on about trees talking and men turning into beasts are talking nonsense, I take it, because there are no principles and essences in the plenum to underwrite such a thought. One can add, if one likes, that such occurrences would violate the Principle of Sufficient Reason, but I don’t think that is adding much. Similarly, oil feeds fire because of the mechanical constitution of each and the way the plenum is ordered: understanding those constitutions and their behavior in the plenum is understanding the “reason” for oil’s feeding fire. Finally, you were born when you were because of that’s how the face of universe is order.

Understanding that order, in all of its determinate detail, is to understand the “reason” for the place and time of my birth.]

14 In “Spinoza on the Human Mind,” p. 22, Lilli Alanen writes, “Spinoza, as Margaret Wilson remarks, says too little about essence for one to know what exactly all this is supposed to mean or how the ascent from common notions to intuitive cognition of essences is supposed to work, but clearly Spinoza thinks of rational knowledge through common notions as a necessary condition for intuitive science, which is the highest kind of cognition.”

15 In this discussion, I will be using the word definition in the sense of a real definition, as opposed to nominal definition.

16 Spinoza also emphasizes the interconnection of things with nature in §41.

17 As Spinoza points out, his example concerns an “abstract thing [rei abstractae]” as opposed to a “real and physical beings [entia physica et realia],” and that raises some interesting questions. We’ll want to look at those questions later, but first let’s try to figure out what Spinoza is trying to say about definition and essence.

18 This might mean we won’t understand why a thing has the properties it has until we understand its essence (so that, we won’t understand why the circle has the property of having all the lines drawn from the center to the circumference being equal until we grasp its essence). Or it might mean we won’t understand what the properties themselves are until we know the essence (so that, we can’t understand what snubness is until we understand what animals are). Or perhaps both.

19 Kant’s example.

20 Leibniz’s—perhaps unfortunate, in view of relativity theory—example.21 Introduction to PHK, §7 and §9.

22 That is, now taking into account not only basic geometric structure but also basic kinetic and dynamic structure.

23 I note that it is not clear to me whether we are to think of those causes diachronically—so that they involve, e.g., embryology—or synchronically—so that they involve the processes responsible for the internal motions that preserve his ratio of motion and rest, say, things like his circulatory and respiratory system. Perhaps, Spinoza sees a place for both.24

The end of §95 suggests that When one stops thinking in terms of the abstract motion involved in a construction procedure and begins thinking in terms of the real motions within the plenum that give rise to finite bodies, the “interconnections of Nature” are brought into view, and reproduced in our intellect.

25 This divides, in turn, into two possible views: actual at all times or actual at some time or the other.

26 And God knows the finite essences through knowing his own essence. Not even God gets essences for free, via some divine representational system. There is the thing that is represented.

27 See “The Only Possible Argument in Support a Demonstration of the Existence of God,” Section 1, Second Reflection, 2:77-81, and Section 2 of “The Ideal of Pure Reason” in the Critique of Pure Reason (A571/B599-583/B611).

28 A good thing, since according to medieval Aristotelians, I cannot understand God’s essence in this life, in any event.

29 One should think of the perfection as involving something broadly causal—a sort of power or ability—and not simply a matter of logic. Perhaps there are is some logical correlate having to do with predication, so that substances, for example, are not predicated of anything else, but, if so, the correlate is byproduct of the substance’s being self-sufficient (rather than the other way around).

30 Certain limitations come with this perfection, too, but that is another story.

31 I think that there is a difference between an abstraction and a universal. A particular circle—the circle described here in this region of Euclidean space—may be an abstraction in that we are leaving out the kinematic and dynamic aspects of the situation: we are leaving out the “real” cause of the circle, perhaps some motion in plenum. Although it is an abstraction, the circle, the one that describes this region of space, it is not a universal.

32 Indeed, if there are other rainbows in the plenum, it is in principle possible that their mechanics are different: it is in principle possible that their drops are structured or arranged differently, so that there is some other mechanism at work which produces the same effect as the rainbow whose structure I am attempting to characterize.

33 This emphasis can also be found in Berkeley’s account of generality (see Introduction to PHK, §160). No one in the period seems drawn to a classical picture of abstraction according to which essences are extracted from experience.

34 Similarly, I suppose, it would seem to be a condition of my being me, as opposed to being that structurally identical individual halfway across the universe, that I am the ratio of motion and rest here and that other individual is the ratio of motion and rest way over there.

35 Spinoza instances in Letter 64 “motion and rest” in the case of extension as an example of an immediate infinite mode.

36 Spinoza provides a sketch of a complex individual in the material on physics in Part 2 of the Ethics. I think Letter 32, about the worm in the blood, suggests a similar picture. There seem to be different levels of structures, where sometimes a macro is set up to that in can “regulate” the micro levels, so that, for example, the blood’s nature regulates the proportion and arrangement of the lymph and chyle particles.

37 This is signaled in the passage by the remark, “Indeed, these mutable particular things depend so intimately and essentially (so to phrase it) on the fixed things that they can neither be nor be conceived without them.”

38 [PROBABLY SKIP Although ingenious, Spinoza’s account is not without difficulty it seems to me. In particular, he is asking a lot of the idea of a ratio of motion and rest, a pattern of motion and rest. It is not obvious that the notion is robust enough to do the work he requires of. Purely geometrical essences, for example, do not admit of the flexibility that Spinoza

requires: you stop being a circle as soon as you start being an ellipse. So there is something difficult here. By pointing this out, I don’t mean to be saying it is clear that Spinoza’s project can’t be made to work. Rather, I think find his few discussions of this topic too schematic to be able to tell.]

39 We won’t, he thinks, be able to account for in this way why it is not possible to find more than three mutually perpendicular lines through a common point, for example.