Everything is one substance — and that substance is God
Baruch Spinoza (1632–1677) was a Portuguese-Jewish philosopher from Amsterdam. As a child, he received a traditional Jewish education, learning Hebrew and studying sacred texts. However, in 1656, he was excommunicated from the Jewish community for persistently challenging religious authority and orthodoxy. This expulsion led him to pursue philosophy rather than solely focusing on theology. Additionally, Spinoza worked as a lens crafter and known as one of the three great rationalists in philosophy.
The content of Spinoza’s works made him a target — not only socially, but also physically as he survived an assassination attempt that was motivated by his controversial views. As a result, Spinoza published little under his own name during his lifetime, fearing persecution. Nevertheless, his contributions are profound. He first published Principles of Cartesian Philosophy in 1663, a textbook-style summary of Descartes’ thought. In 1670, he anonymously published the Theological-Political Treatise, a criticism of religious dogma and the misuse of scripture. After his death in 1677, his friends published his remaining works, including his most influential text, Ethics, which will be discussed in this blog post.
This blog will proceed with an analysis of Part One of Ethics to explore how Spinoza’s substance monism manifests. Unlike Parmenides’ more poetic or abstract approach, Spinoza employs a highly structured method, beginning with precise definitions, followed by axioms, and culminating in 36 logically deduced propositions. Part One is explicitly laid out in a geometric format, emphasizing the rigorous nature of Spinoza’s philosophical method.
I will go over each definition and axiom, however, the 39 propositions will take time, so I plan on continually updating the propositions section until it is complete.
Note I: I am using The Project Gutenberg EBook of The Ethics as my source. In this version, the term “definition(s)” is abbreviated inconsistently as both “Deff.” and “Def.” Since I will be quoting directly from the text, both abbreviations will appear in this blog as they do in the original.
At any rate, Spinoza begins Ethics by offering eight definitions.
Definitions
I. By that which is self — caused, I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent.
Causa sui is a Latin term meaning “self-caused.” This initial definition is foundational to the rest of the text, as it allows Spinoza to identify God as being that exists by virtue of its own nature. He defines “self-caused” as the essence involving existence. By linking this with his definition of substance (Def. III), Spinoza establishes that Nature — or God — is self-caused and thus the necessary foundation of all that exists.
II. A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body.
Spinoza carefully defines the concepts of finiteness and infinity. He argues that something is finite if it can be limited by another thing of the same nature. For example, any given body is finite because there is always a larger body that can contain or surpass it. This framework begins to challenge Cartesian dualism, which privileges the mind over the body. Spinoza asserts that thought can only be limited by another thought, just as a body can only be limited by another body — neither can serve to limit the other.
III. By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception.
Substance plays a central role in many metaphysical frameworks. For example, Parmenides views all of reality as one unchanging substance, which he calls Being. Spinoza also embraces the idea of a single substance, and understands it as “that which is in itself” and “conceived through itself” — meaning that it exists independently and does not depend on anything else for its existence. Substance is independent of everything else.
IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance.
An attribute is the specific way in which the intellect perceives the essence of substance. Spinoza acknowledges that, as finite beings, we are incapable of fully grasping substance in its entirety. Instead, we understand substance through attributes, which serve as conceptual lenses for accessing its nature. As we will eventually learn, God — or substance — has infinite attributes, but human beings can perceive only two: thought and extension.
V. By mode, I mean the modifications of substance, or that which exists in, and is conceived through, something other than itself.
A mode is a modification of substance that cannot exist independently; it is entirely dependent on substance for its existence and conception. One way to understand modes is as the particular forms substance takes. For instance, the human body is a mode of the attribute of extension, while a specific idea is a mode of the attribute of thought. Modes are finite expressions that exist in and through substance.
VI. By God, I mean a being absolutely infinite — that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.
God is defined as an absolutely infinite substance — that is, a substance with infinite attributes, each of which expresses eternal and infinite essence. This means that God is not solely infinite in size, but in every possible manner. Each attribute reveals an entirely different aspect of substance, all being equally necessary. When Spinoza says that each attributes “expresses eternal and infinite essentiality,” he is indicating that the attributes are unchanging and timeless — there is no finality.
VII. That thing is called free, which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. On the other hand, that thing is necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or action.
This definition explains the distinction between what is free and what is constrained. A thing is considered free if it exists by the necessity of its own nature, meaning it acts solely according to its own essence and is not influenced by anything external. In contrast, something is constrained when its actions or existence are determined by an external force, which limits how it acts.
VIII. By eternity, I mean existence itself, in so far as it is conceived necessarily to follow solely from the definition of that which is eternal.
Eternity refers to existence as existence is what is required from the nature of substance. Since the essence of substance is existence itself, substance must exist eternally. Fundamentally, substance cannot not exist.
After establishing his definitions, Spinoza proceeds with seven axioms.
Axioms
I. Everything which exists, exists either in itself or in something else.
This axiom is relatively straightforward. Everything that exists either exists in itself — such as substance, which is self-caused — or in something else — such as a mode, which depends on substance for its existence.
II. That which cannot be conceived through anything else must be conceived through itself.
Another straightforward axiom: if a thing cannot be explained or understood by reference to something else, it must be conceived through its own nature.
III. From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow.
Spinoza addresses causality by stating that if there is a definite cause, an effect must necessarily follow. Conversely, if no definite cause is given, then no effect can occur. Effects cannot happen without causes, and given any cause, an effect must surely follow.
IV. The knowledge of an effect depends on and involves the knowledge of a cause.
To fully understand an effect, one must be knowledgeable of its cause.
V. Things which have nothing in common cannot be understood, the one by means of the other; the conception of one does not involve the conception of the other.
Furthermore, if two things are unrelated — if they share no attributes or essence — then it is impossible for either to have conceived the other.
VI. A true idea must correspond with its ideate or object.
When Spinoza says “true idea,” he refers to an idea that accurately reflects reality. Such an idea must correspond to the object it represents, which exists in the real world. Truth is a matter of correspondence between the idea and the actual object.
VII. If a thing can be conceived as non — existing, its essence does not involve existence.
Spinoza argues that if it is possible to conceive of something that does not exist, then we clearly cannot attribute it with the quality of existence.
Spinoza continues by detailing his 39 propositions for the existence of God as Nature.
Propositions
Proposition I
PROP. I. Substance is by nature prior to its modifications.
Proof. — This is clear from Deff. iii. and v.
Substance is a priori as Def. III highlights that substance is “conceived through itself,” meaning that the forms in which this substance take presuppose the existence of the substance. Furthermore, Def. V isolates that things which are understood in relation to something else cannot be conceived separately from it. This means that, as modes are forms of substance, the modes depend upon substance and are conceived of by substance.
Proposition II
PROP. II. Two substances, whose attributes are different, have nothing in common.
Proof. — Also evident from Def. iii. For each must exist in itself, and be conceived through itself; in other words, the conception of one does not imply the conception of the other.
If there were two substances with different attributes, they would share nothing in common. Building from Prop. I and Def. III, Spinoza argues that substances must be conceived through themselves. Therefore, if two substances existed, each would have to be entirely self-causing and independent, meaning they would have no relation to the other.
Proposition III
PROP. III. Things which have nothing in common cannot be one the cause of the other.
Proof. — If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.
If two things are completely unrelated, one cannot be the cause of the other. Spinoza draws on Ax. V to argue that something cannot be conceived through another if they share nothing in common. He also relies on Ax. IV, which states that understanding an effect requires knowledge of its cause. Therefore, if two things are entirely unrelated, there can be no causal relationship between them.
Proposition IV
PROP. IV. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances, or by the difference of their modifications.
Proof. — Everything which exists, exists either in itself or in something else (Ax. i.), — that is (by Deff. iii. and v.), nothing is granted in addition to the understanding, except substance and its modifications. Nothing is, therefore, given besides the understanding, by which several things may be distinguished one from the other, except the substances, or, in other words (see Ax. iv.), their attributes and modifications. Q.E.D.
In this proposition, Spinoza explains how two things can be distinguished from one another. First, two things may differ in attributes, meaning that two different things have different attributes from one another. Second, they may differ in modifications, meaning they are different modes or expressions of a substance. Per Ax. I, everything that exists must either in itself or something else. Def. III and V clarify this further: substance exists in and is conceived through itself, while modifications (or modes) exist in something else — namely, substance. Therefore, things are distinguished either by having different attributes or by being different modifications of the same substance.
Proposition V
PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.
Proof. — If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications — as substance is naturally prior to its modifications (Prop. i.), — it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii. and vi.), there cannot be conceived one substance different from another, — that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.
No two substances can share the same attribute. Even if we assume the existence of distinct substances, they must be distinguishable in some way. According to Prop. IV, substances can be distinct either by their attributes or their modifications. It is impossible for two substances to have identical attributes because an attribute expresses the essence of a substance. Therefore, substances with identical attributes would have identical essences and would not be truly different. The only remaining possibility for distinction would be through modes. But modifications depend on substance and, as Prop. I states, substance is prior to its modifications. When we set the modes aside and analyze Def. III and VI, it is evident that substance is conceived through itself and God is a substance with infinite attributes, meaning that we can conclude that only one substance exists. The modes are solely expressions of this one substance.
Proposition VI
PROP. VI. One substance cannot be produced by another substance.
Proof. — It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop. ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.
Corollary. — Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications (as appears from Ax. i. and Deff. iii. and v.). Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D. This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax. iv.), and (by Def. iii.) it would itself not be substance.
Spinoza argues that it is impossible for one substance to be produced by another substance. Since no two substances can share the same attribute (Prop. V), and since substances with different attributes have nothing in common (Prop. II), it follows — based on Prop. III — that substances cannot cause one another. This is the first proposition in which Spinoza introduces a corollary, a secondary proposition that follows directly from a prior one. In the corollary, Spinoza argues that a substances “cannot be produced by anything external to itself.” As stated in Ax. I along with Def. III and V, a substance exists in itself, whereas modes are dependent on substance. Given that substances and modes exist — with substances not being able to be produced by another substance and modes relying on substance — it follows that substances cannot be produced by anything external to it.
Proposition VII
PROP. VII. Existence belongs to the nature of substances.
Proof. — Substance cannot be produced by anything external (Corollary, Prop vi.), it must, therefore, be its own cause — that is, its essence necessarily involves existence, or existence belongs to its nature.
Per the previous corollary, it is evident that substance cannot be produced by anything external to it. And because substance is self-caused, existence belongs to the nature of substance.
Proposition VIII
PROP. VIII. Every substance is necessarily infinite.
Proof. — There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D.
In this proposition, Spinoza explains that every substance must be infinite. As established in Prop. VII, the nature of a substance involves necessary existence. This existence can either be finite or infinite. According to Def. II, something is finite only if it is limited by another thing of the same nature — for example, a body is finite because a larger body can always be conceived. Therefore, for a substance to be finite, it would need to be limited by another existing substance sharing the same attribute because in order for substance to limit another substance, it would have to be of the same nature. But Prop. V highlights the impossibility of the existence of two substances that share the same attributes. Since substance cannot be finite as it would be logically impossible, it must be infinite by nature.
Spinoza provides two notes here that I will briefly explain:
- Note I: Substance exists by its nature so it is contradictory to limit this existence.
- Note II: Spinoza warns against confusing modes and substances.
Proposition IX
PROP. IX. The more reality or being a thing has, the greater the number of its attributes (Def. iv.).
Per Def. IV, attributes constitute the manner in which intellect perceives the essence of a substance. If a thing has more reality or being, it will have a greater number of attributes because this thing would have more essence.
Proposition X
PROP. X. Each particular attribute of the one substance must be conceived through itself.
Proof. — An attribute is that which the intellect perceives of substance, as constituting its essence (Def. iv.), and, therefore, must be conceived through itself (Def. iii.). Q.E.D.
Def. III states that substance is conceived through itself. Since attributes express the essence of substance and are how the intellect perceives it (as per Def. IV), it follows that attributes must be conceived through themselves — as they are inseparable from the self-caused nature of substance.
- Note I: Spinoza warns of a misconception surrounding the existence of different attributes. Although attributes are conceived separately, that does not mean they express the essence of different substances. There can be multiple expressions of the same substance.
Proposition XI
PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.
Proof. — If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. vii.) is absurd. Therefore God necessarily exists.
This proposition presents Spinoza’s argument for the necessary existence of God. At this juncture, Spinoza has established that there must be one substance, and that this substance possesses infinite attributes. This substance must be understood as God. To prove this, Spinoza employs a kind of reductio ad absurdum: suppose that God does not exist. Then, this would entail the essence of a substance with infinite attributes would not involve existence. But this contradicts Prop. VII, which states that existence belongs to the nature of substance.
Spinoza gives two more proofs that I will review now:
In the first additional proof, Spinoza argues that everything that exists or does not exist must have a cause or reason for its existence or non-existence. The reason must either come from the thing’s own nature or something external to it. For example, a square-circle does not exist because its nature is self-contradictory. On the other hand, a shape like a triangle exists because it is dependent on an external cause. When we apply this reasoning to God, we find that God’s nature necessarily involves existence (as shown in Prop. VII). Furthermore, nothing external to God can prevent God’s existence because Prop. II shows that there is no relationship between substances that have nothing in common, so there would be no external force that is capable of creating God.
In the second additional proof, Spinoza discusses the concept of power in relation to existence. For Spinoza, to exist is to express power, while non-existence is a negation of power. If only finite beings exist, then we would be saying that beings with limited power exist, while an absolutely infinite being — which would have infinite power — does not have power. (Per Def. II, finite beings are necessarily limited by a being of the same nature.) This view would imply that finite beings are more powerful than an infinite being, which is absurd. Spinoza draws on Ax. II and Prop. VII to show that things either exist in themselves or something else. Therefore, either nothing exists at all, or an infinite being necessarily exists.
- Note I: Spinoza explains that while he begins with a proof that moves from affect to cause (a posteriori) to demonstrate God’s existence, he believes the argument is stronger when approached a priori — starting from the definition of God and reasoning outward. Many people find this difficult to grasp because they are accustomed to understanding things only in terms of external causes. This view, however, does not apply to substances which exist by their own nature.
Proposition XII
PROP. XII. No attribute of substance can be conceived from which it would follow that substance can be divided.
Proof. — The parts into which substance as thus conceived would be divided either will retain the nature of substance, or they will not. If the former, then (by Prop. viii.) each part will necessarily be infinite, and (by Prop. vi.) self — caused, and (by Prop. v.) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Prop. vi.) is absurd. Moreover, the parts (by Prop. ii.) would have nothing in common with their whole, and the whole (by Def. iv. and Prop. x.) could both exist and be conceived without its parts, which everyone will admit to be absurd. If we adopt the second alternative — namely, that the parts will not retain the nature of substance — then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by Prop. vii.) is absurd.
In this proposition, Spinoza questions whether it is even possible to conceive of substance as divisible. If we were even able to conceptualize this division of substance, Spinoza notes that the parts of substance must either A) retain the true nature of substance or B) not retain the true nature if substance. Let us consider both options:
- A) If the parts contain the nature of substance, that implies that each part is infinite (Prop. VIII), each part is self-caused (Prop. VI), and each part must have a different attribute or attributes that are distinct from other parts (Prop. V). This is absurd because, per Prop. VI, one substance cannot produce another. Moreover, per Prop. II, substances with different attributes have nothing in common, indicating that parts would share nothing with the whole. Also, Def. IV shows that attributes are the manner in which the intellect expresses a substance’s essence, and Prop. X shows that each attribute must be conceived through itself. Therefore, a substance cannot be divided into separate parts because each attribute expresses the essence of substance and multiple parts cannot share the same attributes.
- B) If the parts do not contain the nature of substance, then dividing the substance would imply the dissolution of the substance’s nature. According to Prop. VII, substance’s essence involves existence and cannot cease to be.
Proposition XIII
PROP. XIII. Substance absolutely infinite is indivisible.
Proof. — If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which (by Prop. v.) is absurd. If the latter, then (by Prop. vii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd.
Corollary. — It follows, that no substance, and consequently no extended substance, in so far as it is substance, is divisible.
This proposition is a direct extension of the previous proposition. Prop. XII explained how substance cannot be divided. Again, if substance were divided into parts, these parts would retain the nature of an absolutely infinite substance which is absurd because Prop. V explains how multiple substances of the same nature cannot exist. If the parts do not retain the essence of substance, then that would entail the parts not retaining existence (because existence is the essence of substance) per Prop. VII. Per this view, God would cease to exist, which Prop. XI finds to be absurd. Therefore, substance is both absolutely infinite and indivisible.
In the corollary, Spinoza argues that it is impossible for any substance to be divisible because the same logic explained above would apply to every substance.
- Note I: Spinoza simplifies this proposition by noting that Prop. VIII explains how substance is necessarily infinite. The attempt to divide substance would be to understand a part of substance as finite which he finds to be contradictory.
Proposition XIV
PROP. XIV. Besides God no substance can be granted or conceived.
Proof. — As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd. Therefore, besides God no substance can be granted or conceived. Q.E.D.
Corollary I. — Clearly, therefore: 1. God is one, that is (by Def. vi.) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to Prop. x.).
Corollary II. — It follows: 2. That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God.
This proposition makes an important claim: the only substance that exists is God. In Def. VI, Spinoza defines God as absolutely infinite, and per Prop. XI, God necessarily exists. If we were to conceive of a substance other than God, it would have to be explained by an attribute of God (because God is already infinite). This would require the existences of two substances with the same attribute, but as Prop. V isolates, it is impossible for two substances to exist with the same attribute. Therefore, God can be the only substance that exists. It is impossible to conceive of any other substance because this other substance would have to exist, but as the first part of the proof shows, that is impossible.
In the first corollary, Spinoza reiterates that God is a single substance, and that substance is infinite.
In the second corollary, Spinoza builds on the first corollary by explaining the extension and thought must either be attributes of God because Ax. I highlights that everything that exists must exist in itself or in something else. Or, extension and thought are accidents of the attributes of God.
- The term “accidents” appears here for the first time, without much explanation or contextual background. In medieval European philosophy, particularly within the Scholastic tradition, “accidents” referred to the qualities of things. In this context, it is safe to say that “accidents” simply refers to modes.
Proposition XV
PROP. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived.
Proof. — Besides God, no substance is granted or can be conceived (by Prop. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself. But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived. Q.E.D.
Everything that exists must exist in God. According to Prop. XIV, God is the only substance that can be granted or conceived. By Def. III, this substance — God — can only be conceived through itself. Def. V states that modes are modifications of substance, meaning they depend on substance and cannot be conceived without it. Since substances and modes together comprise all of existence — and as Ax. I establishes that whatever exists must exist either in itself or something else — it follows that without God, nothing would be able to exist.
Note I: Spinoza addresses a common anthropomorphic view of God — one that conceives of God as having both a body and a mind, like a human being. He rejects this view on the grounds that a body is defined by finite dimensions — length, breadth, depth — and a specific shape. Since God is, by definition, absolutely infinite, it is absurd to describe God in terms of finiteness. Another claim he refutes is that corporeal or extended substance (i.e., the physical world) is separate from God, created by God. Spinoza argues that those who hold this view do not understand the meanings behind the concepts of “God” and “creation.” He refers back to the corollary in Prop. VI, which states that a substance cannot be produced by anything external to itself, and to Note II or Prop. VIII, where he warns against confusing modes with substances. Further, in Prop. XIV, Spinoza demonstrates that no substance can be conceived apart from God. From this, he concludes that extended substance is one of God’s infinite attributes.
He then proceeds to refute other various arguments posed by his opponents:
- The argument for divisibility: The first argument Spinoza addresses from his opponents is the claim that substance is composed of parts. He explains how his opponents show that if we divide substance into two parts, the parts must either be finite or infinite. If the parts are finite, then it would be absurd to claim that two finite parts equal an infinity. If the two parts are infinite, then it would be absurd to put these parts together and have an infinity that is twice as large as another infinity. The opponents give the example of an infinite line measured out in foot lengths. In this case, there will be an infinite number of feet. However, if we divide this foot into 12 inches, then we get an infinite number of inches. This would be absurd because there would be an infinity that is 12 times more than another infinity (because 12 inches equals one foot). Lastly, Spinoza shows another argument his opponents give dealing with a single point where two diverging lines are drawn from it (like a V shape). At first, these lines are a definite distance apart, but when these lines are drawn for infinity, the length between the two lines will change from being definite to indefinable. In this way, measuring or defining infinity is absurd when applied to a physical quantity. Therefore, extended substance cannot be infinite.
- The argument for God’s perfection: The second argument Spinoza addresses from his opponents is the argument that, because God is perfect, it is impossible for God to be passive. Unlike God, the opponents argue, extended substance or matter is divisible, therefore making it passive. Because of this, they argue that extended substance does not pertain to the active essence of God. Spinoza explains that he already disproved this argument because it relies on the hypothesis that “extended substance is composed of parts” which is absurd per Prop. XII and the corollary of Prop. XIII. The foundation that his opponents’ argument hinges on is the idea that infinity can be measured; for example, they say splitting infinity into two parts means that each part cannot be infinite. Other arguments pertaining to the measurability of infinity can be found in the argument for divisibility found above. However, Spinoza disproved this in Prop. XII which shows that an attribute cannot be conceived if it would entail a division of substance. Spinoza says that his opponents’ arguments are akin to measuring a circle using the properties of a square. It is impossible to measure infinity in finite terms and quantifications. Instead, substance is only understood as infinite, one, and indivisible per Props. VIII, V, and XII.
Ultimately, Spinoza criticizes the common misconception that most people have: the idea that a solid is made of surfaces, surfaces made of lines, and lines made of points. For instance, a point has no length, so it would be impossible for a line to be composed of points. Or, a line has length but no width, so it would be impossible for a surface, which has width, to be composed of lines. Spinoza’s argument is that if substance was composed of parts, you could theoretically separate one part from the others which would leave a gap.
If one asks why people tend to divide quantity, Spinoza explains that we conceive of substance in two different ways. First, we view it abstractly and superficially through imagination. Second, we can understand substance through the intellect, which is much harder to do, but reveals substance as infinite, unified, and indivisible. Spinoza notes that when we encounter things like water or rocks, it is easy to mistakes them for separate parts of matter, when in fact they are merely modes — modifications of a single extended substance. Even though modes can ultimately be destroyed, substance is fundamentally eternal.
Spinoza concludes his criticisms by referring to Prop. XIV: “besides God, no substance can be granted.”
Proposition XVI
PROP. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways — that is, all things which can fall within the sphere of infinite intellect.
Proof. — This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined); and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.
In this proposition, Spinoza explains that everything that exists must follow necessarily from God’s infinite nature. Just as the intellect can deduce properties from a finite thing, so too must infinitely many things follow from the essence of God. For example, if one defines a triangle, there are a certain number of properties to be deduced from this definition (such as all angles adding up to 180 degrees). This entails that there are an infinite number of things that follow from God’s essence as God has infinite attributes (per Def. VI), each of which expresses eternal and infinite essence. Therefore, from the necessity of this nature, an infinite number of things follow — that is, everything that can be grasped by an infinite intellect. Spinoza identifies three corollaries that follow:
In the first corollary, Spinoza notes that God is the “efficient cause of all” that have the capacity to “fall within the sphere of an infinite intellect.”
In the second corollary, Spinoza states that God is a cause in and of itself, not through a mode or accident.
In the third corollary, Spinoza argues that God must be the first cause.
Proposition XVII
PROP. XVII. God acts solely by the laws of his own nature, and is not constrained by anyone.
Proof. — We have just shown (in Prop. xvi.), that solely from the necessity of the divine nature, or, what is the same thing, solely from the laws of his nature, an infinite number of things absolutely follow in an infinite number of ways; and we proved (in Prop. xv.), that without God nothing can be nor be conceived but that all things are in God. Wherefore nothing can exist; outside himself, whereby he can be conditioned or constrained to act. Wherefore God acts solely by the laws of his own nature, and is not constrained by anyone. Q.E.D.
In this proposition,
Corollary I. — It follows: 1. That there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act.
Corollary II. — It follows: 2. That God is the sole free cause. For God alone exists by the sole necessity of his nature (by Prop. xi. and Prop. xiv., Coroll. i.), and acts by the sole necessity of his own nature, wherefore God is (by Def. vii.) the sole free cause. Q.E.D.
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