From the traditional view of one substance with infinite attributes to Gueroult’s reinterpretation of each attribute as a distinct substance

Martial Gueroult (1891–1976) was a French philosopher and historian of philosophy whose reading of Baruch Spinoza’s Ethics is, in my view, among the most brilliant ever produced. The Ethics is Spinoza’s rationalist attempt to conceptualize the nature of God. The traditional interpretation holds that Spinoza identifies God as a single substance — an absolutely infinite being that expresses itself through an infinite number of attributes. Finite things, in turn, are modes: determinate expressions of this substance under particular attributes. My blog post on Book I of Spinoza’s Ethics can be found here.

Gueroult, however, argues that attributes themselves pertain to their own substance. Because there are infinitely many attributes, this would mean that there are an infinite number of single-attribute substances. For example, Spinoza identifies Thought and Extension as attributes; on Gueroult’s reading, Thought and Extension are each substances in their own right, with an infinite number of finite modes populating them. God, then, is the unity or culmination of all these single-attribute substances taken together — an absolutely infinite substance composed of all attributes.

At any rate, Martial Gueroult’s monumental work Spinoza remains an unfinished project, covering only Books I and II of the Ethics. Even so, it spans over a thousand pages of close, systematic commentary. Gueroult’s interpretation has been influential but also frequently criticized for not adhering to the traditional interpretation of Spinoza. When I first encountered Spinoza’s Ethics, I read it through what I later learned was the traditional lens — one that assumes a single, infinite substance expressing itself through attributes and modes. This blog will instead take up Gueroult’s distinctive interpretation of the Ethics.

Of course, this blog cannot hope to treat the entirety of Gueroult’s vast commentary. Adding to the challenge, his text remains untranslated; the only complete version exists in the original French. This makes the task difficult, but not impossible. My discussion will therefore draw on a handful of key sources:

1. David Smith in 2012 published a text titled Spinoza, Gueroult, and Substance. In this, he examines the controversial nature of Gueroult’s reading and explains why he ultimately sides with Gueroult.
2. In Spinoza: A Collection of Critical Essays edited by Marjorie Grene, there is an English translation of Gueroult’s commentary regarding Spinoza’s Letter on the Infinite (Letter XII, to Louis Meyer) which Gueroult finds integral to Spinoza’s concept of the infinite.

• *This blog will focus on Gueroult’s reading of Book I.

Let us move forward with the brilliance of Gueroult’s interpretation.

I will be drawing from Smith’s article (it is quite amazing).

Gueroult’s Argument

I. “Substances” as Plural

Per the traditional interpretation, Spinoza is famous for saying that there is only one substance — and that substance is God. However, in the earliest pages of the Ethics, Spinoza repeatedly speaks of “substances” in the plural. Let us look at some examples:

PROP. II. Two substances, whose attributes are different, have nothing in common.

…

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.

…

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.

…

The problem should be stated in the clearest terms possible: If there is only one substance, why does Spinoza speak of “substances” in the plural? To speak of substance in the singular sense is a serious error that ultimate makes the text look clumsy. This is where Gueroult’s reading comes in. The idea of an infinite number of single-attribute substances resolves this dilemma.

II. The “Leibniz Situation” (1p5)

Let us examine 1p5 (Proposition V of Book I):

PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.

The traditional interpretation of 1p5 is that Spinoza is ruling out the possibility of two different Gods. If there is one substance, it would be impossible to have another, since that other substance would necessarily share an attribute with God — which would be contradictory. How could two distinct things share the exact same nature without being one?

Smith describes this traditional view as Spinoza’s way of avoiding a “Leibniz situation.” Here is what such a situation would look like:

Substance X has attribute A.

Substance Y has attributes A and B.

On the traditional reading, this is excluded by 1p5, since both X and Y would share attribute A. But there is a problem. If Y has both A and B, then Y does not actually share the same nature as X. Attributes, for Spinoza, define the essence of a substance. So if one substance has more attributes than another, their natures are not identical. Essentially, calling this “two substances of the same nature” is inaccurate because they are not of the same nature.

This makes Spinoza’s wording in 1p5 feel erroneous if one only follows the traditional interpretation. Gueroult offers an alternative. He argues that at this stage of the Ethics, Spinoza is speaking only about single-attribute substances. In other words, one should read the text as if Spinoza is considering:

The substance of Thought

The substance of Extension

(And so on, for each of the infinite attributes.)

On this reading, 1p5 becomes clear: there cannot be two distinct Extension-substances, nor two distinct Thought-substances. Each attribute corresponds to exactly one substance.

Ultimately, then, Gueroult explains that Spinoza continues to argue that the only substance that is truly multi-attribute is God, who unifies all of the single-attribute substances into one absolutely infinite being. Gueroult’s interpretation, therefore, makes sense of the plural “substances” in the early propositions and removes the oddity that troubles the traditional view.

III. “Indivisible” Substance

Following 1p5, one must examine the demonstration of 1p12d. For clarification, here is 1p12 (and part of the demonstration):

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…

In the demonstration of 1p12, Spinoza explains why substance cannot be divided. If one divides substance into parts, those parts would either still count as part of the same substance or they would not. If these parts did consist as parts of the same substance, then each part would be infinite, self-caused, and “consist of a different attribute.” That would mean several substances could come from one substance, which Spinoza calls “absurd.” If the parts did not retain the nature of substance, then substance itself would be destroyed — which is also impossible. This must align with Gueroult’s argument: substances are not born from one substance; it would be absurd for several substances to be formed from one substance because substances are self-caused (as Spinoza says).

Spinoza adds this puzzling line: if a substance is divided, and the divided parts retain the nature of the substance, then each part of the substance must “consist of a different attribute.” On the traditional reading, this wording feels strange. Why would Spinoza phrase it as if each substance “consists of” a single attribute (albeit a ‘different’ one)? If there is only one infinite substance with all attributes (God), this language seems clumsy and misleading — almost as if Spinoza were imagining a plurality of single-attribute substances. (Because the demonstration in 1p12 refers to 1p5, it only makes sense to interpret attributes as pertaining to their own substance).

Gueroult’s interpretation is that — in these early propositions — Spinoza is treating each attribute as having its own substance: a substance of Thought, a substance of Extension, and so forth. Read this way, Spinoza’s statement that different substances “consist of a different attribute” means exactly what it says. Each substance has one attribute, distinct from the others, and there cannot be two of the same kind of substance.

IV. “Infinite” Substance

Now that we have examined the quirky readings pertaining to the traditional interpretation, let us move to more definitive reasons as to why Gueroult’s interpretation is correct. This means beginning with 1p12 and 1p13:

PROP. XII. No attribute of substance can be conceived from which it would follow that substance can be divided.

…

PROP. XIII. Substance absolutely infinite is indivisible.

Both of these propositions appear to be duplicates of one another. In both of them, substance is indivisible. And, the demonstrations of each proposition follows the same structure: if substance is divisible, then the parts of this division either retain the nature of substance or they do not. Thus, the only difference between these propositions is that 1p13 refers to an “absolutely infinite” substance, while 1p12 does not.

If Spinoza is a monist from the start (i.e., if one takes up the traditional reading), meaning that only one absolutely infinite substance (God or nature) exists, then 1p12 and 1p12 collapse into the same claim. Given Spinoza’s detailed analysis, one must ask: Why would Spinoza write two separate propositions that say the same thing?

According to Gueroult, the substance(s) being discussed in 1p12 are the single-attribute substances (a substance of Thought, a substance of Extension, etc.)— not the “absolutely infinite” substance. Each of these single-attribute substances are infinite in their own kind, but not absolutely infinite. Following 1p12 — in 1p13 — Spinoza moves to describe the “absolutely infinite” substance (God or nature) which unifies (contains) all attributes. In this case:

• 1p12: A single-attribute substance (e.g. Though or Extension) cannot be divided.
• 1p13: The absolutely infinite substance (God or nature) cannot be divided).

V. “Unique” Substance

Another argument that justifies Gueroult’s interpretation stems from 1p8d:

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.

The bolded phrase in 1p8d effectively says: “A substance of one attribute can only exist if it is unique.” (This is how Edwin Curley renders the Latin, and as Smith notes, the wording really does appear in Spinoza’s text.) On the standard one-substance reading, however, this does not make sense. Why would Spinoza even speak of “a substance of one attribute,” if the only true substance is the absolutely infinite God who has all attributes?

Gueroult takes the line seriously. He argues that in these early propositions Spinoza is still treating attributes as corresponding to their own single-attribute substances: one unique substance of Thought, one unique substance of Extension, and so on for the infinity of attributes. Each is infinite in its own kind.

Not everyone accepts this. André Doz, for instance, argues that one should not read Spinoza literally here. Instead, Doz suggests that the clause should be taken to mean: “for any given attribute, there is only one substance that has it.” In other words, if you pick any attribute, only one substance (God) possesses it.

Smith points out, however, that this is a forced reinterpretation. The Latin itself refers directly to “substance of one attribute,” and the context of Proposition 8 reinforces this: “every substance is necessarily infinite.” That phrasing makes more sense if Spinoza is describing substances that are infinite “in their kind” (single-attribute substances) rather than an already absolutely infinite God. This is because Spinoza does talk about God as “absolutely infinite,” but the Latin here indicates that this is discussing “infinite in its own kind.”

VI. “Every” Substance

To continue, let us examine the interaction between 1p7 and 1p8:

PROP. VII. Existence belongs to the nature of substances.

…

PROP. VIII. Every substance is necessarily infinite.

For 1p8, Spinoza draws directly from 1p7, which established that the essence of substance is existence. From this, he concludes that “every substance is necessarily infinite.” The word “every” implies that there are multiple substances. Once again, Gueroult argues that Spinoza is not talking about God as “absolutely infinite,” but about single-attribute substances. Each of these substances necessarily exists (1p7), and each is infinite within its own attribute (1p8).

VII. Letter to Hudde

Spinoza’s correspondence with Johann Hudde sheds further light on the argument of 1p7. While Smith cites this letter only in fragments, I consulted the full text and selected the most relevant passages.

In Spinoza’s June 1666 letter (Letter XXXVI), he explains what follows if we treat attributes like Extension or Thought as existing “by their own sufficiency.” Spinoza writes:

What I take to say, then, is that if we assert that something that is only unlimited in its own kind, and perfect in its own kind exists by its own sufficiency, then we’ll have to concede the existence also of a being that is absolutely unlimited and absolutely perfect. This being I call ‘God’. For example, if we maintain that extension or thought (each of which can be perfect in its own kind…) exists by its own sufficiency, we will also have to concede the existence of God, who is absolutely perfect — i.e. of an absolutely unlimited being. (Ep. 36)

A few lines later, he adds:

If we assert, for example, that extension involves existence, it must be eternal and unlimited, expressing absolutely no imperfection but only perfection. Therefore, extension will … express God’s nature in some way. (Ep. 36)

Here Spinoza is clear: if Extension involves existence, it must be eternal, unlimited, and express God’s nature. And, he explicitly states that this attribute can exist “in its own kind,” but this would require the existence of a being that is “absolutely unlimited.”

On Gueroult’s reading, this confirms that 1p7 (“Existence belongs to the nature of substances”) applies not only to the absolutely infinite God but also to single-attribute substances such as Extension or Thought. Each is infinite “in its kind” and necessarily exists, and together they express the essence of God.

Incorporation vs. Exclusion

After reviewing Gueroult’s main arguments, it is necessary to turn to a crucial debate between the traditional reading and Gueroult’s interpretation.

Spinoza writes in 1p7:

PROP. VII. Existence belongs to the nature of substances.

Now, if this proposition applies to any substance, then one could infer the existence of a single-attribute substance such as Thought-substance or Extension-substance. But by definition God consists of all attributes, including Thought and Extension. This leads to a tension with 1p5:

PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.

If Thought-substance already exists “on its own,” then God cannot also have Thought as an attribute without violating 1p5. Yet in 1p11d Spinoza moves directly to proving God’s existence:

PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

Spinoza says this without first proving or denying the existence of single-attribute substances (at least explicitly proving or denying their existence). The puzzle, then, is: if 1p7 applies universally, why does Spinoza privilege God in 1p11 instead of starting with the single-attribute cases? Of course, one can take Gueroult’s approach and assume that Spinoza is discussing single-attribute substances, but the question that ought to be begged is this: Why is Spinoza not more clear on this question?

Two main responses have been offered:

Exclusion (traditional view): Only God counts as a possible substance. On this reading, 1p7 applies to God and God alone; the very idea of a single-attribute substance is incoherent.

Incorporation (Gueroult’s view): Proving God’s existence does not exclude the existence of single-attribute substances, but rather includes them. God is the unification of all such substances. On this reading, 1p5 and 1p14…

PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.

…

PROP. XIV. Besides God no substance can be granted or conceived.

… are not contradictions but clarifications: there can be no substance outside God. The single-attribute substances are precisely God’s attributes taken together. For Gueroult, the single-attribute substances are not in competition with God; God is their unification.

Thus, for Gueroult, God is the only Multi-Attribute Substance.

Gueroult’s Own Words…

As stated earlier, Gueroult’s Spinoza — which analyzes Books I and II of the Ethics — has never been translated into English. In fact, very little of his work in English is available. One exception appears in Spinoza: A Collection of Critical Essays, edited by Marjorie Grene, which includes a translation of Gueroult’s analysis of Letter XII — Spinoza’s famous “Letter on the Infinite” to Louis Meyer. While this section does not touch on Gueroult’s thesis of single-attribute substances, it exemplifies his careful treatment of Spinoza’s argument that substance is infinite and indivisible. As Gueroult explains:

Existing necessarily by virtue of its essence, substance cannot without contradiction be conceived as finite, because in so doing one would deny that by its essence substance necessarily posited its existence in the entire expanse of its being; nor could it be conceived as divisible, for partitioning implies finitude. Thus, it is by nature absolutely indivisible. (Spinoza’s Letter on the Infinite, Gueroult’s Interpretation)

Gueroult truly emphasizes substance as both infinite and indivisible. When one turns to his analysis of the Ethics, it becomes clear that he extends this logic by giving each single-attribute substance full weight: each is infinite in its own kind and absolutely indivisible.

Conclusion

Gueroult offers a profound and unconventional reading of Spinoza’s Ethics. His work remains untranslated into English, making the task of grappling with it difficult, but not impossible. This blog has drawn on Smith’s excellent account to salvage some of Gueroult’s insights for an English-speaking audience.

In the end, the real issue may not be whether Spinoza explicitly intended his philosophy to rest on single-attribute substances, but whether Gueroult’s interpretation provides a more coherent picture of the relationship between substance, attributes, and modes. If nothing else, Gueroult forces us to reread Spinoza, reconsidering whether the “one substance” model is the only, or even the most compelling, way to understand God.