Spinoza on Why There Can Only Be One Substance

Curtis Brown

Classical Modern Philosophy


Oval: R's mindOval: M's mindOval: your mindOval: my
Spinoza’s view about substance differs in two main respects from Descartes’.  Descartes thinks that there are two main kinds of substance (three if you count God), while Spinoza thinks that there is only one kind; and Descartes thinks that there are many particular substances, while Spinoza thinks that there is only one particular substance.  We might represent Descartes’ view like this:





Oval: my body Oval: your body Oval: M's body Oval: R's body






The chart illustrates the idea that there are two main kinds of substance, mental and physical, and many particular substances of each kind.  It also captures the idea that each of us has a substance of each kind, a body and a mind.  (More precisely, for Descartes, each of us is a mind and has a body.)

            Spinoza modifies this picture in two ways.  In proposition 5, he argues that there cannot be more than one substance with the same attribute.  (Attributes are more or less the same as Cartesian essences; unlike Descartes, Spinoza appears to believe that there are more than two attributes, but he also thinks we only know of two, namely thinking and extension; the supposed further attributes play no role in the argument.)  So, so far, it looks as though for Spinoza there can be at most one mind and one body.   But even this is too generous; in Proposition 14, he argues that there cannot be different substances with different attributes either, so that there can only be one particular substance.  So we get something like this picture:

The idea that the very same substance has both the attributes of thinking and of extension doesn’t sound particularly odd to modern ears; after all, materialistic theories of the mind are now very common.  What does seem odd is not the idea that mind and body are really the same thing differently thought of, but rather the idea that there is only one mind and only one body (which of course are both really the same substance).

            We should now look a little more carefully at Spinoza’s reasons for this odd doctrine.  A good place to start is with proposition 14; we can work backward to the propositions on which it rests.

            We can understand proposition 14 as essentially offering the following argument (Jonathan Bennett’s formulation):


1.  There must be a substance with all possible attributes.

2.  There cannot be two substances with an attribute in common.

so,        3.  There cannot be more than one substance.


The first premise, that there must be a substance with all possible attributes, is argued for in propositions 7 and 11, which offer Spinoza’s version of the ontological argument.  The second premise, that there cannot be two substances which share an attribute, is argued for in proposition 5.


Why must there be a substance with all possible attributes?


The argument that there must be a substance with all possible attributes is similar in some ways to Descartes’ version of the ontological argument (which itself derives from St. Anselm).  But whereas Descartes (and Anselm) argue that existence is part of the notion of God because existence is a perfection and God has all perfections, Spinoza argues that God must exist because God is a substance and existence is part of the notion of substance.

            The question why there must be a substance with all possible attributes decomposes into two further questions:  (a) why must there be a substance?  (b) why must it have all possible attributes?


(a) Why must there be a substance?  In proposition 7, Spinoza argues that “it pertains to the notion of substance to exist.”  We might take the argument to be this:


1.  Nothing outside a substance can cause it to exist.

2.  Everything must have a cause.

so,        3.  Substance must cause itself to exist.


The second premise, a version of what is often called the “principle of sufficient reason," is simply taken for granted by Spinoza:  he apparently takes it to be so evident as hardly to require mentioning.  The first premise, most helpfully argued for in the second demonstration of proposition 6, is virtually a consequence of the definition of substance.  Substances must be independent; as Descartes put it, they can depend on nothing else for their existence.  (Of course Descartes has to fudge this a bit, since he thinks minds and bodies depend on God for their existence; Descartes says that only God is a substance in the strict sense, but minds and bodies can be called substances by virtue of the fact that they depend on nothing except God for their existence.)  If a substance was brought into existence by something else, it wouldn’t have the right kind of independence.  To put this in a more explicitly Spinozistic terminology, if something else brought a substance into existence, then we would have to “conceive it through” its cause.  But substance can be "conceived through itself” (def. 3). 

            If a substance cannot be caused by anything else, and has to be caused by something, then it must be caused by itself.  It’s hard to see how something can cause itself to exist.  (For one thing, we normally think that causes precede their effects, but a thing cannot precede its own existence.)  But Spinoza identifies two things that we think of as different, namely causation and logical necessity.  It is causally necessary that if one billiard ball hits another, the second billiard ball begins to move (other things being equal).  It is logically necessary that, given that ‘P’ and ‘if P, then Q’ are true, ‘Q’ must be true as well.  We think of these as two very different kinds of necessity, but for Spinoza they come to the same thing.  So for a thing to cause its own existence is for its existence to be logically necessary because of some fact about it rather than because of any facts about other things.  If something about a substance makes it the case that it has to exist, then its essence must include existence (much as Descartes thought God’s essence had to include existence).

            (Given that we do now distinguish between the two sorts of necessity, must we regard Spinoza’s argument as resting on an equivocation?  No; we can simply restate the entire argument in terms of logical rather than causal necessity.  Nothing outside a substance can explain its existence; everything must have an explanation; so a substance must explain its own existence.  If to explain something requires making it logically necessary, then this seems to show that substance necessarily exists.)


There is still something odd about the argument.  If there is a substance, the argument seems to show that it must cause itself to exist, i.e. it must necessitate its own existence.  The argument began with a purported fact, namely that a substance existed, and then consisted of looking for the reasons for this fact.  But what if it weren’t a fact?  Why couldn’t there simply be no substance, and so no fact which needs explaining?  I suppose Spinoza could argue empirically that we know there is at least one substance; we perceive properties (modes), but modes cannot exist without a substance to exist in, so there is a substance.  But the empirical flavor of this line of reasoning would not appeal to Spinoza.  It is probably better to regard the proof as not requiring the factual premise that a substance exists.  It is really just an investigation into the concept of substance.  If a substance were to exist, it would have to necessitate itself; but this shows that the essence of substance would have to include existence, which is to say that substance would necessarily have to exist.  So if it is possible for substance to exist, then it is necessary that substance exist.  (The argument would then resemble what Norman Malcolm has identified as Anselm’s second ontological argument [Philosophical Review 69 (1960), reprinted in Plantinga, ed., The Ontological Argument].) However, this still seems to leave open the possibility that it is not possible for substance to exist, that substance necessarily does not exist.


(b) Why must the substance have all possible attributes?    We know that God exists because he is a substance and substance necessarily exists.  But why must there be an existing substance with all possible attributes?

            One answer is “by definition.”  God is by definition “substance consisting of infinite attributes” (def. 6).  But there is something very fishy about this step.  Just because God is defined as “substance with all attributes” and there necessarily is a substance, it doesn’t follow that anything fits the definition of God.  If it were that easy to prove the existence of things, we could prove the existence of a lake a thousand miles long by defining it as “substance consisting of fresh water and extending for a thousand miles.”  There must be some other reason for thinking God has all attributes.

            The second demonstration of proposition 11 helps to fill the gap.  Spinoza there says that if something doesn’t exist, there must be an explanation of why it doesn’t exist.  (A negative application of the principle of sufficient reason!)  This explanation must come from the thing’s own nature or from something outside it.  The reason for the nonexistence of the thousand-mile lake comes from outside it:  it doesn’t exist because of causal laws and the course of geological history.  But the reason for the nonexistence of a substance with all attributes cannot come from outside the substance, since two substances with different attributes have nothing in common with each other (proposition 2), and things with nothing in common cannot cause each other to exist or not exist (proposition 3).


There is something deeply messed up here, though.  What is the reason that there is no substance with only the attribute of thinking?  As we’ll see later, it is that there is a substance with all attributes, and there cannot be two substances with overlapping attributes.  But then the reason why there is no substance with only the attribute of thinking comes from outside the nature of such a substance:  it is essentially prevented from existing by the fact that there is a substance with all attributes.  But then this looks like a case of a substance with one attribute being prevented from existing by something with a different set of attributes:  so either things with nothing in common can cause each other (contrary to proposition 3) or else the substance with one attribute and the substance with all attributes do have something in common (namely the one attribute), in which case proposition 2 must be interpreted in such a way that it does not apply to substances with overlapping attributes, in which case it will not support the conclusion that nothing external to God could prevent his existence.


Why can’t two substances share an attribute?


That two substances cannot have “the same nature or attribute” is argued in proposition 5.  It goes like this: 


1.  The only things that can distinguish two substances (i.e. make them different) are attributes and modes (proposition 4).

(But why whould we think this?  Why couldn’t two substances be numerically distinct even though they have exactly the same attributes and modes?  We might take Spinoza to be appealing to something like Leibniz’s principle of the identity of indiscernibles:  if two substances are exactly alike, they can’t really be different substances.  But Spinoza also has a kind of independent argument that there couldn’t be two substances with the same nature toward the end of note 2 to proposition 8.  In a nutshell, the idea is that there couldn’t be any explanation of why there were two as opposed to one or three or . . ..)


2.  If two substances have different attributes, then they are not two substances with “the same nature or attribute.”  So the first of the two means of distinguishing between substances is of no use here.


3.  Substance is “prior to its modifications.”  So what we really need to consider is the essence of the substance rather  than its modifications.  But two substances with the same attribute have the same essence (even if they have different modes).  So, “the modifications . . . being placed on one side,” the supposed two substances must really be the same thing.

(Huh?  This part of the argument is a bit mysterious.  I’m inclined to think the best way to fix it is to appeal again to the end of note 2 to proposition 8 (see tiny note to premise 1) to explain why there can’t be more than one thing with the same essence.)                                                                                                                                     


So,       4.  Since our supposed two substances with the same attribute cannot be distinguished by either attributes or modes, and since those are the only two ways they could be distinguished, there cannot really be two substances with the same attribute.


Premise 1 and premise 4 are both rather suspicious, as indicated in my notes to them.  But the most serious problem concerns premise 2, which Spinoza deals with in a single brief sentence.  The trouble is that 2 is ambiguous.  To say there cannot be two substances with “the same attribute” might mean (a) that two substances could not have all their attributes in common, or it might mean (b) that two substances cannot have any attribute in common.  The phrase “nature or attribute” suggests that Spinoza must mean (a), since presumably two things would not have the same nature unless they shared all their attributes.  And his argument is a good argument for (a):  if two substances are distinguished by means of their attributes, then they cannot have all their attributes in common.  The only trouble with interpretation (a) is that it will not give him the conclusion he needs.  For, to return to the main argument of proposition 14 sketched at the beginning of this handout, the existence of a being with all attributes will not rule out the existence of substances with just one attribute unless we can rule out substances having any attributes in common.

            Interpretation (b), then, is the one Spinoza needs for his one-substance argument.  But his one-line defense of premise 2 does not support (b).  If one substance had attributes a, b, and c, and a second substance had attributes c, d, and e, then they would have an attribute in common but would nevertheless be distinguishable by means of their attributes.  So the short argument does not show that there could not be different substances which shared some but not all of their attributes.  This looks disastrous for the argument.  (Bennett suggests that the only place to look for a possible rescue is to proposition 2, “two substances with different attributes have nothing in common with each other.”  Of course this too is ambiguous, but if it means that two substances which differed in any of their attributes could have nothing in common, then it would rule out the possibility of substances with some but not all attributes in common.)