UC Davis Philosophy 22 Lecture Notes


Picture of Spinoza

Spinoza's Signature

Spinoza at first worked within the framework of the Cartesian philosophy, publishing in 1663 a book entitled Principles of the Philosophy of René Descartes. Another early work, the posthumously published Treatise on the Emendation of the Intellect, contains themes that were central to Descartes's investigation of knowledge. It also contains hints of the metaphysics unfolded in the posthumously published Ethics, the capstone of Spinoza's philosophical career.

True Ideas

In the Emendation of the Intellect, Spinoza (like Descartes) was concerned with the improvement of human knowledge, which requires that we be able to distinguish the true from the false in a reliable way. Descartes had claimed that if an idea is perceived very clearly and very distinctly, it is true. Spinoza, by contrast, did not look at the relation of the idea to the mind, but only to the idea itself, for assurance of its truth. He claimed that truth shines forth on its own: the criterion of the true idea is the true idea itself. (This notion is discussed in more detail below .)

A method of seeking truths is most perfect when it begins with the idea of a most perfect being. The truth of the idea lies in the essence it expresses. The idea of a perfect being is a true idea, corresponding to something existing, because the essence of a perfect being implies its existence. Further, whatever follows from the idea of such a being is also true. Thus the best method will produce an order of ideas, flowing from the idea of a perfect being. To this ideational order corresponds an order of existing things. The description of that order occupies the first two parts of the Ethics.

Cartesian Substance

Spinoza's metaphysical system can be understood in terms of its similarities and differences to the system of Descartes (Principles I, 51ff). The objects of Descartes's ontology, that is, the things Descartes held to exist, are substances. The only substance properly so-called, that is, the only being that does not depend on anything else for its existence, is God. God's existence is contained in his essence, so there is no need for anything but the essence to insure God's existence. Substances in a relative sense are God's creations, which depend only on God's will to exist. In particular, substances improperly so-called do not depend on one another for their existence. A human mind exists due to the will of God, but its existence does not depend on the human body.

Each Cartesian substance has a principal attribute, which makes it the kind of thing that it is. God has the attribute of thinking (which includes understanding and willing). Some created substances (humans and angels) also have the attribute of thinking, while others (physical objects and non-human animals) have the attribute of extension. Descartes believed that thinking and extension are mutually exclusive: no substance can have both attributes. Thus I myself am a thinking substance and my body is an extended substance. The composite of the two (the "union of mind and body") is not a substance, on Descartes's view, though it was on the view of Aristotle.

According to Descartes, created substances of the same kind are differentiated from one another by their modes, or the ways in which they have their attributes. Thinking a series of particular thoughts, willing a series of particular acts, all of which go into making a thinker a unique individual, though there are other thinkers with their own modes of thinking. Similarly, extended things are differentiated by their modes: a certain size, shape, state of motion or rest, etc.

Spinozistic Substance

Spinoza agreed with Descartes about substance proper; like Descartes, he believed that the essence of God includes God's existence. But he broke with Descartes by asserting that there are no created substances. Rather, God is a being with infinitely many attributes, including thinking and extension. Each of these attributes is infinite "in its own kind," in the sense that it is not limited by anything else of the same kind. Thus, there is no limit to God's thought and none to the divine attribute of extension.

Differences arise only at the level of modes. The individual thoughts that Descartes assigned to his own mind as a substance are on Spinoza's view thoughts in the mind of God. Similarly, individual physical things are modes of God's attribute of extension.

The Independence of Substance

Spinoza's system is supposed to follow from a few definitions and axioms. If one rejects the system (and if Spinoza's inferences are valid), one must reject the starting point. One of the interesting tasks for the student of Spinoza is to discover the sources of those of his conclusions that seem objectionable.

Through Propositions 1 and 2, Descartes and Spinoza are in agreement. Substance is prior to its affections (or modes), and two substances with different attributes have nothing in common. It is with Proposition 3 (what has nothing in common cannot causally interact) that Spinoza breaks ranks with Descartes, at what was an admitted weak point in Descartes's metaphysics.

Spinoza argues for Prop. 3 on the basis of Axioms 4 and 5. The absence of a common element prevents us from understanding one kind of thing through the other. I think Descartes would have to concur with this claim. We do not understand bodies through minds or minds through bodies. Actually, we would only understand both through God's mind, but we have no access to the mind of God.

If we do not know bodily events through minds, if we could never tell merely by consideration of an act of will which bodily motion would follow it, how can we know that the two are connected? Only by noticing that one does in fact follow the other, in a systematic way. But this is not enough to establish a causal connection, as Spinoza recognized in the Emendation of the Intellect. In order to know that a connection exists, one must discover that in the cause which brings about the effect. Where two things have nothing in common, this is impossible. An "empiricist" might object to Spinoza's claim that two things cannot stand in a causal relation if the knowledge of one does not involve knowledge of the other. Perhaps causal relations are simply not intelligible.

The next move against Descartes's scheme is the claim in Proposition 5 that no two substances can share an attribute. This means that if there is a mental substance, it is unique, and the same for extended substances (and this holds in general for any other kind of substance). Descartes held that there can be a real difference between substances due to the fact that we can conceive one clearly and distinctly without the other (Principles I, 60). This might be thought to work for different kinds of substance (though Spinoza will deny this too), but how can it work for the same kind of substance? I can conceive of another mind, for example, by conceiving of its principal attribute, thinking. But this is not enough to distinguish it from any other thinking thing. So it must be the modes of thinking which distinguish them.

Here Spinoza plays his trump card. To consider a substance as a substance we must conceive it through itself (Definition 3). But then we do not conceive it through its modes, for by Definition 5, a mode is something other than the substance itself. So (to use Descartes's language against him) no modal distinction can amount to a real distinction. A possible objection here is that Spinoza is misusing the expression "conceived through itself." There is no real distinction between a substance and its modes, the objection would run. To conceive a substance through its modes is to conceive it "through itself," in that the modes are modes of the substance, not something distinct from the substance.

There remains the possiblity of more than one substance, and this is the next target. In Proposition 6, Spinoza claims that production of one substance by another (creation) is not possible. The reason is the created substance would have to be conceived through the creating substance, which is contrary to the meaning of 'substance.' This corresponds to Descartes's admission that created beings are not substances in the full-blooded sense, so he should have nothing to complain of here. However, one might object that two distinct substances might exist independently of each other, without standing in any causal realtion (such as creation) at all.

The Existence of Substance

It was Aristotle who first made substance the centerpiece of metaphysics. He began with things he took to exist and asked what they are. Spinoza reverses the order, beginning with the concept of substance and moving to its existence. Proposition 7 establishes that the nature of substance includes its existence. This is the germ of the ontological argument, though it differs in form from both Anselm's and Descartes ' versions. Spinoza's claim is that because nothing else can produce substance, substance is self-produced, and hence that it exists from its very nature. But this is a questionable argument, for it does not consider the question why substance has to be produced at all. In Definition 1, Spinoza equates a self-caused being with a being whose nature includes its existence. But this is an odd notion of "cause," since there is no production or change involved in the relation between nature and existence.

Infinite Substance

We have reached the point where Spinoza claims to have shown that substance exists necessarily, but it is still an open question how many substances there are. Spinoza's answer will be that there is only one, but to arrive at this conclusion, he had to make some further claims about attributes.

The first claim is that substances are infinite, in the sense that they are not limited by anything of their own kind. Finite things are limited in the sense that there can be something greater than them. For example, for any cube of any given size, there could be another cube that is larger (Part One, Definition 2). Since a thinking substance is the only thinking substance, it is not limited by any other thinking substance. The same holds for extended substance. There is nothing greater than the cosmos (whole extended universe), since there is only one extended thing: the cosmos itself.

After showing the unlimited character of each attribute singly, Spinoza introduces the notion of degrees of reality, corresponding to number of attributes. A substance may have more than one attribute, since each attribute is conceived through itself. A maximal substance (identified with God) would have infintely many attributes, each one of which is infinite. It has already been argued that substance exists, but does God, maximal substance, exist?

Spinoza has several proofs that a maximal substance exists, but perhaps the most important one is from the mere possibility of a maximal substance. Its nature does not involve a contradiction, so its existence is possible (Leibniz will make much of this point). And if some other thing were able to prevent its existence, that thing would limit the maximal substance. But by definition each attribute is unlimited, so no thing of the same attribute can prevent the existence of maximal substance. Further, there can be no conflict among the different attributes, since they have nothing in common. So from the mere possibility of a maximal substance, the conclusion is drawn that it must exist.

Substance is Unique

Moreover, there is only one maximal substance. This is not surprising, given the argument for its existence. A maximal substance has all the attributes that can be had, so that if there were another one, it would have to share in these attributes, which would be a limitation and contrary to the nature of the maximal substance.

Substance is Indivisible

Maximal substance is also indivisible. This claim is very important to Spinoza, given his idenfitication of maximal substance with God. The attributes are not parts of substance, and so there is no division of substance in that which constitues its essence. It is true that the attributes themselves may exist in a way that allows division. If thinking is an attribute of substance, there may be individual thoughts which are distinct from one another. And if extension is an attribute of substance, there may be extended things (e.g. the blocks making up the wall of a tower) which are distinct and indeed are themselves divisible.

But the divisibility of the modes of substance do not mean that substance itself is divisible. For substance is conceived through itself, not through its modes or affectations. This distinction is absolutely critical to Spinoza's thought: it is what prevents him from falling into the view (first expressed in Western philosophy by Parmenides) that reality is homogenous. Spinoza was a monist, in that he held that only one thing (maximal substance or God) is ultimately real, but he wanted to hold at the same time that the appearance of plurality is not an illusion. To do so, he gave a place to plurality at the level of modes.

At this point we need to consider the specific question of whether God can be extended. Spinoza counted as his opponents those philosophers who argued that God is incorporeal. He granted that it would be wrong to think of God as having a body like a human being, as do the gods of the ancient Greeks and Romans. This would be to make God finite. But this does not rule out the possibility that the infinite expanse of extended nature is the "body" of God. Still, perhaps the very nature of extended things precludes God from being extended.

The argument is that nothing extended can be infinite, and so extension is not suited to be an attribute of God. If there were infinite extension, it is claimed, paradoxes would arise (Galileo, for one, was aware of such paradoxes). For example, take any unit of measurement of a finite length, say an inch. Then an infinite length would consist of infinitely many inches. On the other hand, it would also have infinitely many feet, and hence be twelve times larger! Modern philosophers (following the nineteenth-century mathematician Cantor) would deny that the conclusion follows from the premises. They maintain that since there is a one-to-one correspondence between feet and inches, the number of feet and the number of inches is the same.

Spinoza's approach was quite different. He maintained that all the argument establishes is that "infinite quantity is not measurable and cannot be made up of finite parts" (Ethics, Part I, Proposition 15, Scholium). But in that case, what about the parts we perceived extended objects to have? Spinoza again draws a distinction between how we view extension abstractly through the imagination (whence they have parts) and through the the intellect (as unitary substance). This recalls the distinction made earlier, that "matter is everywhere the same, and there are no distinct parts in it except in so far as we conceive matter as modified in various ways. Then its parts are distinct, not really but only modally" (Ethics, Part I, Proposition 15, Scholium).

Substance as Cause

Spinoza considered a number of other arguments on this topic, but we will pass over them in the interests of time. The next topic is Spinoza's claim that everything that is or can be conceived, is in God. This is really only an elaboration of his position that God is maximal substance. Whatever exists either is God or a mode of one of God's attributes. As mentioned above, Spinoza denies that there is a creation of other things. The notion that God has an intellect which allows the conception of an uncreated world, and a will which creates the world is denounced by Spinoza as anthropomorphic. God as rational creator is as much a myth as Jupiter or Zeus.

At the same time, Spinoza held that God is the cause of all things. Obviously this is possible only on a very specific understanding of the notion of a cause. In the primary sense, something is a cause when its nature is responsible from the existence of something. Thus because everything follows from the nature of God, God is the cause of all things (including God, for substance is said to be "self-caused"). Moreover, God causes all things that are in the scope of the divine intellect, since an infinite number of things flow from an infinite substance. Later, at Proposition 35, Spinoza claims that whatever is in God's power necessarily exists.


Since God is a cause in the sense that what exists follows from God's essence, God can be said to be a free cause. Freedom here is understood in the sense of a lack of external constraint. God is free because there is nothing to interfere with the unfolding of the Divine essence. (Hobbes made use of this notion of freedom to say that humans are free although their wills are determined.)

This notion of freedom does not involve any notion of will or choice; indeed, Spinoza denies that God has a "will" or makes choices. To attribute will and choice to God is anthropomorphic, a projection of (alleged) human characteristics onto the divine being. In fact, will is only a mode, not an attribute of substance. In Part II, Spinoza maintains that there is nothing more to will than individual acts of volition. Thus will is not a "faculty" of God (and this holds for "intellect" as well).

It might be objected that without choice, God is not free. Because they follow necessarily from God's essence, things cannot be otherwise than what they are, and this is a limitation of God's power. Spinoza turns the tables on this objection, stating that if things were otherwise than what they are, they would have to be the product of a God with a different nature, in which case two Gods would be possible, and God would not be the maximal substance.

Types of Causality

In the succeeding propositions, Spinoza discusses a number of aspects of the causality of God. What is most important is a distinction between two ways in which God is a cause. From the essence of God, some things are said by Spinoza to follow directly. In this sense, God is a "proximate" cause. But with finite existing things, essences are not sufficient for existence. The essence of an individual human being, Peter, is not such that Peter's existence follows from it necessarily. Rather, the existence of finite things has as its cause the existence of other finite things. Nevertheless, since all things are in God, God must be considered their cause.

In general, there are two ways of thinking of God, as a being conceived through itself ("natura naturans") and as a being conceived through its affections ("natura naturata"). Considered in the first sense, God is free (in the sense noted above). But in the realm of finite things, which are only affections of God, there is only necessity. Each thing exists as it does solely by virtue of some cause which necessitates it. Nothing can determine itself to action.

Finite existence and action is determined by prior causes, to infinity. There is no first cause of finite things. If it is supposed that there is a first cause, then it would have to be of the same kind as what it causes. Then it would be limited by that thing and hence finite. But every finite thing has a cause.

Things must be as they are, so there is no contingency in the world. A contingent existence or action would be one that neither must occur of necessity nor cannot occur of necessity. But everything is either necessary or impossible. What we think is contingent (e.g. that I was born at the exact minute that I was) really depends on our ignorance of the chain of causes (Corollary to Prop. 23, Pt. II).

Mistaken Conceptions of God

Part I of the Ethics concludes with a remarkable discussion of the origin of the common way in which God is conceived. Belief in God is the result of a combination of an ignorance of causes and a desire to get one's way. When we do not know the cause of the occurrence of a favorable event, we deem it a sign of God's favoring of us. In general, events are understood as dependent on God's ends, and systems of worship are built up with an eye to gaining God's favor. The universe is understood in terms of final causes (for example, as in Aristotle's philosophy). Moreover, since disaster sometimes befalls the pious and fortune sometimes favors the impious, God's real plan for the universe is deemed mysterious.

On Spinoza's view, there are no final causes: the universe is utterly indifferent to the fortunes of any individual. There is no distinction between good and bad, right or wrong, except as relative to the interests of the individuals who use those labels. Since these interests are tied to the favor of God, people call "good" that which is consistent with their conception of God and "bad" that which is not. The same applies to evaluative concepts such as order and disorder, beautiful and ugly. We can never define the prefection of God using these relative concepts. Only an intellectual understanding of God's nature as a maximal substance adequately characterizes God's perfection.

The Attributes of Thought and Extension

In Part II of the Ethics, Spinoza turns from the general nature of God to the two specific attributes which we human beings understand: thought and extension. It is taken as an axiom that "Man thinks" (Axiom 2, Part II), and individual thoughts are modes. So there is something, the attribute of thought, of which individual thoughts are modes. Axiom 4 states that we feel bodies, and from Definition 1 we have it that bodies are modes of extension. So substance, or God, has the attributes of thought and extension, and we have no information about any other modes (Axiom 5), and hence about any other attributes of substance.

Though the announced goal of Part II is to show "The Nature and Origin of the Mind," carrying it out involves a description of the nature of bodies. The relation between thoughts and bodies in the human being is considered in two ways. The metaphysical relation between the two is explored in the earlier propositions of Part II. In the later propositions, the attention shifts to the way in which thought represents extended things, and finally, how it represents things in general.

Spinoza begins the discussion by explaining the way in which God can be said to be the cause of the modes of thought and extension. Specifically, God is the cause of a mode of thought only insofar as God is conceived under the attribute of thought, and God is the cause of a mode of extension only insofar as God is conceived under the attribute of extension. This causal "insulation" of the modes means that a body has no causal influence on an idea, and vice-versa, contrary to the view of Descartes and most other philosophers.

Psycho-Physical Parallelism

Not wishing to deny that there is a correlation between ideas and states of the body, Spinoza devised a scheme whereby ideas and corresponding states of the body change in parallel. This is embodied in Proposition 7, which states that "the order and connection of ideas is the same as the order and connection of things." In the Scholium to Proposition 7, Spinoza notes that thought and extension are attributes of the same substance. It follows from this, he claims, that the modes of thoughts and extension are the modes of the same thing. "And so, whether we conceive Nature under the attribute of Extension, or under the attribute of Thought or under any other attribute, we find one and the same order, or one and the same connection of causes--that is, the same things following from one another." This view is sometimes called "neutral monism," in that there is only one thing which is both mind and body, and that neither mind nor body takes precedence over the other.

The proof of the proposition, however, proceeds along different lines. Modes of thought are existing ideas, and insofar as they exist, they have a "formal reality." But ideas have content, or "objective reality," as well. (This distinction was also made by Descartes and his scholastic predecessors.) The formal reality of ideas is embedded in a necessary chain of causes, modes of the attribute of thought. He claims, further, that the objective reality of the ideas (including the bodies which are the objects of our ideas) follows a parallel chain.

This claim is justified by Axiom 4 of Part I, "The knowledge of an effect depends on, and involves, the knowledge of the cause." Suppose one has an idea which is knowledge of a body at a given time. Then one also has an idea which is knowledge of the cause of that body. So there is a connection of cause and effect holding for bodies, and this is paralleled by a connection between the idea of the cause of the body and the idea of the body as effect.

This argument seems problematic, even if we grant the truth of Axiom 4. It must be understood as a conditional: if there is knowledge of a body as an effect, then there is knowledge of the body of as a cause. Now human knowledge of bodies as effects is pretty limited, but Proposition 7 is completely general: it is not restricted to those cases where humans have knowledge. To establish this thesis, Spinoza must appeal to God's idea of bodies as effects. That he has this in mind is suggested by the Corollary, where Spinoza that states that what follows formally (i.e., in the order of existence) from God's nature "follows from the idea of God with the same order and the same connection, as an object of thought in God." Since God's thought comprehends everything, any connection in the idea of God is reflected in those things (including bodies) that the idea is about.

Another aspect of the generality of Proposition 7 is that to every extended thing there corresponds an idea of that thing. Any thing that "is explicated" as a mode of the attribute of extension also can be explicated as a mode of the attribute of thought. "This truth seems to have been glimpsed by some of the Hebrews, who hold that God, God's intellect and the things understood by God are one and the same" (Scholium to Proposition 7). Nature under the guise of extended is to be explained solely in terms of extension, but its order is paralleled precisely by nature explained solely in terms of thought.

In Proposition 9, Spinoza considers ideas of individual things. Such ideas are limited, and as such require a cause in order to exist. Spinoza claims that the cause of an idea must be another idea. We can say that it is God who causes the idea, but this must be understood only in the sense in which there is another idea of an individual thing (or "definite mode of thinking") which is a mode of God's attribute of thought.

The Essence of the Human Being

A human being is not a substance; if so, it would exist necessarily, and by Axiom 1 it does not. "From the order of Nature it is equally possible that a certain man exists or does not exist." So what is "the essence of man?" The essence of man can only be found in modes of God's attributes, since this is all there is other than substance. Spinoza notes that we should not take the essence as "that without which a thing can neither be nor be perceived," since human beings depend on God, which would make God the essence of man.

Instead, what makes up the essence of a thing is that "which, when posited, posits the thing, and by the annulling of which the thing is annulled" (Scholium to Proposition 10). What we are looking for is something which, when present, makes the human being exist, and when absent, causes the human to cease to exist. We are told in Proposition 11 that this is an idea of an existing finite thing. Insofar as all ideas are modes of God's attribute of thought, "the human mind is part of the infinite intellect of God" (Corollary to Proposition 11).

Since the idea that makes up the essence of the human being is about an individual thing, that thing is perceived by the idea. We might ask how well the object is perceived. To this Spinoza replies that it is perceived so that nothing in the thing is not perceived. If the thing is a body, then "nothing can happen in that body without its being perceived by the mind" (Proposition 12). This is a very strong claim, and as might be expected, it can only be backed up by appeal to the fact that ultimately the idea is God's idea.

At this point, Spinoza is ready to make the claim that the object of the idea that is the essence of the human mind is the human body. The basis of this claim is Axiom 4, which states that "We feel a certain body to be affected in many ways." Since we have ideas of these affections in our mind, what has these affections is the object of our ideas, so the body is the object of the idea that is the essence of the human mind. The Corollary to Proposition 13 states that "Man consists of mind and body, and the human body exists according as we sense it." To prepare the way to understanding the union of the mind and body and the way in which the mind knows the body, Spinoza turns to "a brief preface concerning the nature of bodies" (Scholium to Proposition 13).

The Nature of Bodies

The interlude begins with a treatment of bodies in general, which is used to explain how the human body operates, which in turn explains the ideas which we get from experience. After laying out the general notions of motion and rest, Spinoza introduces a new notion, not found in his definitions, of the form of a body. Bodies are extended things which have parts which themselves are extended things. What unifies the parts into one thing is an "unvarying relation of movement" among them. The material constituents of a body may change while the form remains the same. Since Spinoza understood change in bodies in terms of their motion and rest, it is the form which is responsible for the causal relations that bodies have to one another.

To account for the fact that the ideas humans have represent more than merely the states of their own bodies, Spinoza sketched a physiology of bodily parts. The key elements are "soft" parts which can change when the human body is acted upon by another body. The persistence of their changed state accounts for the production of ideas as if the body were still there, thus explaining how memory and imagination are possible.


Also explained is the way in which people commonly understand nature. This "first kind of knowledge" (which is really opinion rather than truly knowledge), comes from casual experience. It is decribed as "external, fortuitous," resulting from the "run of circumstance" (Proposition 40, Scholium 2). Exposure to a pattern of events A-B reinforces the impressions made on us, resulting in the strengthening of the images which follow when A occurs again.

In this way, we make causal judgments which are not really justified because there is no insight into how B comes from A. (David Hume would claim in the Eighteenth Century that this is the only way causal judgments can be made, so that none are justified!) It also leads to a false doctrine of universals. People believe that they know the essence of a thing (say a human being) based on what is common in their experience. Whether a human being is called a rational animal, a featherless two-legged animal or a laughing animal depends entirely on the associations made with instances of humans we have encountered.

Similarly, common language is based on association. When I hear the word 'apple,' there comes to mind an image of a fist-sized fruit with a shiny skin, succulent flesh, etc. There is no reason this association takes place other than my experience in having such a thing pointed out to me when I hear the word. Spinoza maintained that a great deal of the confusion of human thought stems from a failure to recognize the arbitrariness of language which is based on association alone.

Much of our language is comprised of universal terms like 'man,' 'animal,' and 'thing,' which are formed on the basis of imagination. They are convenient for associating images with one another, but they do not denote anything real. Thus Spinoza is a nominalist with respect to general terms. This is not to say that all abstract terms lack reference, however. If an idea, such as that of substance, is formed from the pure intellect, it and the associated word denote something that is real.

With all this in mind, Spinoza states that experience yields inadequate ideas ("images") of other bodies, our own bodies, and our own minds. With respect to bodies, the problem is that our ideas of them pertain to their form, and not their material constituents. So these ideas will always be inadequate. (We have even more inadequate ideas of other bodies, since we know them only through the effects on our own bodies.) And since the mind is the idea of the body, the inadequacy of the idea of the body spills over to the idea of the idea of the body (i.e., the idea of the mind).

What is common to knowledge of the first kind is that it is based on imagination, which in turn comes from experience. What we get in imagination is "dumb pictures." The mind has other ideas, however, which result from its activity. These ideas, such as that of substance, are conceived, not imagined, and it is in them that true knowledge lies.


A higher form of knowledge ("knowledge of the second kind") is that involving common notions and adequate ideas of the properties of things. Ideas of motion and rest are common to all extended body. (Contrast this with the more restricted idea of a human being, which is a universal derived from individual exprerience.) So laws of physics such as the conservation law enunciated in the treatise on body would be known in this way.

The highest form of knowledge is inuitive. We gain "knowledge of the third kind," merely by contemplating the ideas involved. The ideas are those of the attributes of God and the essences of things. Part I of the Ethics exhibits this kind of knowledge.

To illustrate the distinction between the three "kinds of knowledge," Spinoza appeals to a mathematical case, where one is to find a fourth number to complete a proportion, as with 1/2 = 2/x. One could get the solution from a rule that he had been taught, which would yield knowledge of the first kind. If one derived the solution from general principles of mathematics, the knowledge would be of the second kind. Finally, if one were to "see" the solution without doing any calculating or reasoning at all, one would have intuitive knowledge.

The Criterion of Knowledge

Spinoza posed a question considered at length by Descartes: how could he distinguish between opinion and knowledge? Is there a criterion to separate the two? In the case of images, one can have false ideas without being able to tell that they are false. We think that they are true when we lack a reason to think otherwise. We may have no doubt about its truth, but this does not amount to certainty. On the other hand, when we have a true idea, we are certain of its truth. The truth of a true idea is known through its mere possession. Thus the true idea is the criterion of truth. It is like a light which illuminates itself.

There Are No Faculties of Will and Intellect

When one is in possession of a true idea, there is no question about its affirmation or denial. To have a true idea is to affirm it, so in this case, the act of the understanding and the act of will are indistinguishable. This is so with images as well. Spinoza asks us to consider the case of a child with the idea of a winged horse and no other ideas. He claims that the child affirms the existence of the horse simply through the possession of the idea of it. Only the presence of other ideas excluding the existence of the horse would give rise to doubt.

In general, the understanding of an idea is identical to its affirmation or denial. Individual ideas are nothing more or less than individual acts of volition. (Note that in Part II, Spinoza restricts himself to affirming and denying as acts of will, reserving until later a discussion of other volitions, such as pursuing and shunning.) Further, there is nothing over and above individual acts, no "faculty" of understanding or willing, since the mind itself is only a mode of thinking. So the will and the intellect are the same thing.

Alleged Freedom of the Will

The identity of will and intellect undermines Descartes's contention that will is free. One basis for this contention is the claim that one is at liberty to doubt the truth of any idea whatsoever (the project of the First Meditation). Spinoza counters that this liberty is illusory. One's suspension of judgment is a necessary consequence of the recognition that there are reasons that an idea is not true. And if the idea is true, its possession is tantamount to its affirmation.

Spinoza discussed other Cartesian arguments for free will, but here only one other one will be noted. Descartes had rather lukewarmly embraced the "liberty of indifference," which exists when and individual lacks any reason inclining him or her toward one alternative rather than another. If an individual lacks freedom to act in an arbitrary manner, then he or she will be in the same position as an ass who starved to death when faced with a choice between two type of feed, which he likes equally well. Spinoza's response is that in the case where there is no inclining preference, the individual would not indeed act like a rational human being. Any starving to death because he could not decide which restaurant he liked best would be behaving irrationally, like a child, someone insane, or even an ass. (In fairness to Descartes, it should be noted that he considered indifference to be the lowest form of liberty.)

The Benefits of Knowledge

At the end of Part II, Spinoza summed up the advantages of living one's life according to the kind of knowledge described in the Ethics. In general, one has a proper reverence for God, a respect for other people, and a disregard for what is beyond one's power. But he ends paradoxically, stating that citizens should be governed and led "so as to do freely what is best" (Ethics, Part II, Scholium to Proposition 49). It is only in a very rarified sense that people are able to act freely, and only a relative sense in which they may do what is best.

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