Spinoza's Monism

Descartes’s & Spinoza’s Conception of Substance

Descartes’s official definition of substance in terms of an independent individual:

By substance we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence. (Principles, §51)

However, Descartes denies that the conception of something’s being “independent” applies in the same way to God and to finite (created) beings. Consider three points.

Hence the term ‘substance’ does not apply univocally, as they say in the Schools, to God and other things; that is, there is no distinctly intelligible meaning of the term which is common to God and his creatures. (Principles, §51)

First, Descartes holds that every substance has what he terms a “principal attribute.” A principal attribute is the “one principal property which constitutes its nature and essence, and to which all its other properties are referred.” (Principles, §53) Thought and extension are the only two principal attributes for Descartes; there are no others. They are really distinct—i.e. they are both conceptually and existentially distinct from one another. In other words, thought may be conceived independently of extension (and vice versa) and a thinking substance may really exist independently of an extended substance (and vice versa).

Second, Descartes distinguishes between conception and causation: there can be causal relations in the absence of conceptual relations. This permits him to distinguish inherence—the dependence of a mode or property on a substance—from causal dependence. In fact, Descartes absolutely needs to distinguish inherence from causal dependence, because the second argument for God’s existence in the Third Meditation requires that God is constantly causally involved in maintaining our existence. If inherence were the same as causation, then we would all, by virtue of our dependence on God’s causal activity, inhere in God.

Third, Descartes thinks that multiple substances can have the same principal attribute, and thus such substances must be individuated by their modes. In other words, what makes two substances ultimately distinct from one another are their modes, not their attributes.

Spinoza adopts the Cartesian definition of substance in terms of independence:

By substance I mean that which is in itself and is conceived through itself; that is, that the conception of which does not require the conception of another thing from which it has to be formed. (E1d3)

But Spinoza applies the definition univocally and rigorously. So in the end, as he argues, there can be only one substance. Let’s look at that argument.

Spinoza’s Monism Argument

Important Definitions

In what follows, the following three definitions will be important:

  • D3: By substance I understand what is in itself and is conceived through itself, that is, that whose concept does not require the concept of another thing, from which it must be formed.
  • D4: By attribute I understand what the intellect perceives of a substance, as constituting its essence.
  • D5: By mode I understand the affections of a substance, or that which is in another through which it is also conceived.

Important Axioms

As will these axioms:

  • A1: Whatever is, is either in itself or in another.
  • A2: What cannot be conceived through another, must be conceived through itself.

Important Proofs

And these proofs:

  • P5: In Nature there cannot be two or more substances of the same nature or attribute.
  • P7: It pertains to the nature of a substance to exist.
  • P11: God, or a substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists.
  • P14: Except God, no substance can be or be conceived.

The Argument in Three Steps

Spinoza’s argument for monism ultimately looks like this:

  1. No two substances share an attribute
  2. God has infinite attributes (i.e. God has all the attributes, whatever they are)
  3. ∴ There can be no substance other than God

Let’s break this argument up into three steps and see what we think of each part:

  • Step 1 (E1p5): No two substances can share an attribute
  • Step 2 (E1p11): God is a substance with infinite attributes
  • Step 3 (E1p14): God is the only substance

Spinoza’s Proof: Step 1

Spinoza’s argument that no two substances can share an attribute looks like this:

  1. If two substances exist, then they can be distinguished (from the Identity of Indiscernibles)
  2. E1p4: If two substances can be distinguished, then they are distinguished either by a difference in attribute or a difference in mode
  3. No two substances can be distinguished by a difference in mode (from E1d3, E1a6, E1p1)
  4. ∴ Two substances are distinguished by their attributes (from 1, 2, and 3)
  5. If two substances are distinguished by their attributes, then they cannot share an attribute
  6. ∴ Two substances cannot share an attribute

Premise (1) would have been seen as relatively uncontroversial. The Identity of Indiscernibles says: (∀F)(Fx ↔ Fy) → (x = y). In English: for any property, if a thing (x) has that property just in case a thing (y) has that property then x and y are identical. Put another way: no two things are entirely qualitatively identical.

The key premises are thus (3) and (5). Here is an interpretation of Spinoza’s argument for (3) – the claim that, contra Descartes, substances cannot be distinguished by a difference in their modes:

  1. E1d3: Substance is conceived through itself
  2. E1d5: Modes are conceived through something other than the substance to which they belong
  3. E1p1: ∴ Substances are (conceptually) prior to their modes
  4. ∴ Substance considered in itself excludes consideration of modes (from A, B & C)
  5. ∴ Substances cannot be distinguished by a difference in their modes (= 3 above)

The basic idea behind this argument is that if a conception of a substance can be formed without including anything that is dependent upon the substance, then that which is dependent upon the substance is not required to distinguish (epistemically) one substance from another nor can it be the basis of a (metaphysical) distinction between one substance and another.

Now, Leibniz has a famous objection to premise (5) that if two substances are distinguished by their attributes, then they cannot share an attribute:

the case is different if these two substances have some attributes different and some in common, as when c and d are the attributes of A, and d and f the attributes of B. If he denies that this is possible, he must demonstrate its impossibility. (Leibniz 1969), 198

In other words, suppose Substance 1 has attributes A, B, & C, and Substance 2 has attributes C, D, & E. Can’t we individuate 1 from 2 on the basis of the attributes that they do not share (namely A, B, D, & E) while allowing that they still share attribute C?

Michael Della Rocca makes the following response on behalf of Spinoza:

…[L]et’s assume that Leibniz’s scenario is possible. If so, then attribute Y would not enable us to pick out or conceive of one substance in particular. The thought “the substance with attribute Y” would not be a thought of one substance in particular, and thus attribute Y would not by itself enable us to conceive of any particular substance. For Spinoza, such a result would contradict the clause in the definition of attribute according to which each attribute constitutes the essence of substance. As Spinoza says in 1p10s, a claim that he clearly sees as following from the definition of attribute, “each [attribute of a substance] expresses the reality or being of substance.” So for Spinoza, if a substance has more than one attribute, each attribute by itself must enable us to conceive of the substance, and this can be the case only if each attribute that a substance has is unique to that substance. Thus Leibniz’s scenario is ruled out. (Della Rocca 2008), 29

If Della Rocca is correct then Spinoza can successfully avoid Leibniz’s challenge to (5), and the first step of his proof goes through.

Spinoza’s Proof: Step 2

In step two Spinoza must defend the claim that God is a substance with infinite attributes (E1p11). Here’s his argument:

  1. E1p7: Existence belongs to the essence of substance
  2. E1d6: By God I understand a being absolutely infinite, that is, a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence
  3. E1p11: ∴ God necessarily exists and has infinite attributes (from E1p7 & E1d6)

So the reasoning here seems to be that since God is defined as a substance with infinite attributes, and E1p7 establishes that substances necessarily exist, God necessarily exists. So how does Spinoza establish E1p7? Consider the following.

  1. Substances are caused either by themselves or by other substances (from the PSR)
  2. E1p6: No substance is caused by another substance (from E1p2, E1p3 & E1p5)
  3. ∴ E1p7: substances are self-caused

One might object that this argument seems only to show that existing substances are self-caused. It doesn’t show that all possible substances are self-caused, and thus necessarily exist. But that is surely what Spinoza means to establish in E1p7.

Spinoza’s reply:

For each thing there must be assigned a cause, or reason, both for its existence and for its nonexistence. For example, if a triangle exists, there must be a reason or cause why it exists; but if it does not exist, there must also be a reason or cause which prevents it from existing, or which takes its existence away. (Ethics 1:p11d)

Thus: by the PSR, even the non-existence of something must be explained. But the non-existence of a substance cannot be explained by appeal to the existence or non-existence of another substance (E1p3, E1p5). So its existence or non-existence must be explained by its own nature. But, according to Spinoza, substances by nature are conceivable, and thus have natures that do not include contradictions. So, given that a substance cannot be concieved through its own nature not to exist (because this would require appealing to something distinct from the substance that limits it, thus contradicting the requirement that we appeal only to the substance’s nature), there can be no reason why a putatively possible substance does not actually exist. So it must be self-caused, and exist necessarily.

But is the nature of God as possessing all attributes coherent (this is another worry of Leibniz’s)? What would have happened had Spinoza proved the existence of some other substance, e.g. an extended substance, first? Would he have been able to then prove God’s existence—i.e. from the proof of extended subtance could he prove that there is still only one substance and it is God? By the claim that no two substances can share the same attribute (E1p5) it seems that he would not be able to prove God’s existence from such a starting point. So why isn’t the argument Spinoza offers an arbitrary one (see (Garrett 1979) for discussion)?

One issue that is worth considering is the role that E1p8 (i.e. that every substance is necessarily infinite) plays (if it does at all) in the argument for E1p11.

Another issue is the sense in which Spinoza thus denies the thesis that explanatory relations are irreflexive. God or substance, unlike other beings, is self-explanatory – i.e. it is explained through itself. Is this a fully coherent notion?

Spinoza’s Proof: Step 3

In light of the foregoing, we can easily see now how Spinoza puts the entire proof together in order to establish that there is a single substance and it is God.

  1. No two substances share an attribute
  2. God has infinite attributes
  3. ∴ There can be no substance other than God

All finite beings are thus modes of the one – God (see E1p15).


Della Rocca, Michael. 2008. Spinoza. London: Routledge.

Garrett, Don. 1979. “Spinoza’s ‘Ontological’ Argument.” The Philosophical Review 88 (2):198.

Leibniz, Gottfried Wilhelm. 1969. “On the Ethics of Benedict De Spinoza.” In Philosophical Papers and Letters: A Selection, edited by Leroy E Loemker, 196–206. Dordrecht: Kluwer Academic Publishers.

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