Spinoza’s Three Kinds of Cognition: Imagination, Understanding, and Definition and Essence in the Treatise on the Emendation of the Intellect

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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.

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 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:

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 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 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 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, 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, 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.

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 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 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:

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.

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 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 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 π is 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 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 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 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 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 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 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), 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”?

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 individualsthese 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 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 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.

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):

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 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 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 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 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.

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.


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