Spinoza, 1 substance=1 attribute?

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There was an interesting thread a while back about Spinoza, this is an essay I wrote for a class on him. Warning: if you haven’t read Spinoza, this will be incomprehensible.

“In the universe there cannot be two or more substances of the same nature or attribute.” (The Ethics, 1p5)
Discuss.

1p5 is a proposition vitally important to Spinoza’s metaphysics. In this essay I am going to discuss his attempted demonstrations in 1p5dem and 1p8sch2. I contend that both demonstrations fail. However, I do think the proposition makes sense within Spinoza’s system, and I will attempt to indicate why. To begin, it will be necessary to explain the meaning of three key terms, and to place 1p5 within the context of Book 1 of The Ethics.

The three key terms are substance, attribute and mode. What precisely Spinoza means by these terms is a controversial matter. However, for our purposes this isn’t important. I propose we understand these terms in what would be the natural way, i.e. similar to the use in Descartes and other philosophers of the period. So: a substance is both ontologically and epistemically independent of anything else. In contrast a mode is both ontologically and epistemically dependent on a substance. All this means is that a mode requires a substance in which it exists and it requires the prior conception of a substance before it can be conceived. Every substance has attribute(s) . Put simply, an attribute is the nature of a substance: the type of substance it is. To make this clearer, a (un-Spinozistic) example: our body is a substance with the attribute of extension (by its nature an extended thing). Its modes are just the determinate way in which it exists, its shape, size etc - what makes this body a body of a certain type. We cannot conceive of the shape of the body without the body itself, i.e. the substance, and the shape can’t exist without the body. In contrast, the body requires nothing else for its existence, and can be conceived through itself. There are complications with attribute I pass over, for my purposes an attribute expresses an essence or nature of something.

1p5 plays a major role in Spinoza’s argument for substance monism: there is only one substance, God (or Nature). The first fourteen propositions of The Ethics are intended to establish substance monism, and the argument can be summarised as follows :
(1) 1p5: There cannot be two substances of the same attribute.
(2) There exists a substance with infinite (i.e. all) attributes.
(3) Consequently, there can be only one substance, as no substance can have no attributes, any other supposed substance would need to share one of God’s attributes, so contradicting (1).

The argument for substance monism isn’t what concerns us here; I shall focus on 1p5. However, it should be clear what is at stake for Spinoza here. He needs 1p5 to establish his substance monism, without it his official argument fails . I shall now examine his argument for 1p5, starting with 1p5dem.

1p4 states that two substances are distinguished either by a difference of attributes or of affections (modes). This is uncontroversial: there exists nothing other than substances (with their attributes) and modes. The difference must lie in one or the other. There are two parts to the argument for 1p5, corresponding to the two ways we can distinguish. The first part deals with a difference of attributes, which I shall label the argument from attributes. Basically, all Spinoza says is that if two substances are distinguished by a difference of attributes then we obviously have two different substances, as they have different attributes (remember, an attribute expresses what a substance is). There is a problem with this, attributed to Leibniz . Say we have two substances, X and Y, where X has attributes {A1, A2}, Y has {A1, A3}. Clearly X and Y have something in common (A1) but are distinguished by virtue of possessing a different second attribute. Generally, the problem is that for cases with substances of more than one attribute Spinoza’s argument just doesn’t work. I will briefly return to this later.

The second part deals with a difference of affections. The argument, which I shall label the argument from affections, is less clear, stating:

“if they are [two substances] distinguished by a difference of affections, then, since substance is by nature prior to its affections (Pr.1), disregarding therefore its affections and considering substance in itself, that is (Def.3 and Ax.6), considering it truly, it cannot be conceived as distinguishable from another substance.”

Obviously, if we can disregard the affections the conclusion follows. The question is why can we do this? The key inference is clearly from “considering substance in itself” to “considering it truly”. As Don Garrett points out , this inference is not valid. By “in itself” here is meant we can conceive substance as not existing in something else (as a mode does). To conceive something truly is to have an idea of it agreeing with the object of the idea (1Ax6). The claim is that substance conceived in itself, in the above sense, is substance considered truly. This is false: substance doesn’t exist “in itself” in the sense that its not with anything else, a substance will always have certain affections i.e. ways that it is. The substance is truly with its affections, so a true idea of a substance must include them. I am going to focus on this problem, for reasons that shall become clear.

In the literature there are many attempted solutions. Don Garrett, in his Ethics 1p5, gives a nice summary, and reasons for rejecting. What interests me is his solution, which is the best attempt I have found. I shall present it, then show it fails.

Garrett begins by asking what the priority of substance over its attribute involves. As stated earlier, it involves a mode being both in and conceived through its substance. We could disregard the affections if the relation of mode to substance was such that any difference in affections would be conceived through a difference of attributes (for our purposes here we can take substance and attribute as synonymous). The basic idea is that if the affections of substance X differ from the affections of substance Y without this difference being conceivable through a difference in the attributes of X and Y themselves then there will be something about the affections of X not conceivable through X. It will be helpful to state this in argument form.

(1) The affections of a substance X are completely conceived through X (1def5).
(2) These affections cannot be completely conceived through X unless all of their features are conceived through X.
(3) Features of affections cannot be fully known (or conceived) without knowledge of their cause.
(4) The knowledge of the cause of its effect is knowledge of what determines the effect to happen.
(5) Any feature in which the affections of X differ from Y must be conceived through some difference in the attributes accounting for this difference.

This argument seems valid. Consequently, the distinction in affections is only an apparent one. Since we only had a distinction of affections, we don’t have a distinction of attributes. Thus, part of 1p5 is established. Garrett himself helpfully points out the assumptions involved here, and answers an objection he feels one might have. Rather than consider all of this, I wish to consider one assumption that I think we should reject. (1) and (2) can be seen as leading to what Garrett calls a “strong” version of 1def5, which is that any feature of the affections of X can be conceived through X. The feature we are here talking about is that the affections of X differ from those of Y. But, if we wish to include this feature it seems that we run into problems. How can this be a feature of the affections of X? That the affections of X differ from those of Y is surely a feature of X and Y jointly, not X alone. At this point nothing stops us positing another substance, Z. Say the affections of Z differ from those of X: this is now, for the same reason, a feature of X. And so on ad infinitum. Does X possess the feature for every such substance we can posit? Also, how are we meant to conceive of a difference of affections through a difference of attributes? Do we conceive of the affections of Y through X, and so compare? But Spinoza’s system does not allow this. Maybe we conceive of the affections of X through X, of Y through Y, but in what sense are we conceiving of the difference of affections through a difference of attributes here? But my main point is that a difference of affections between X and Y is not a feature of just X, or of just Y, and so the argument does not go through. This objection to me seems valid. So, Garrett’s attempt to rescue this part of the argument for 1p5 fails. As I mentioned, none of the other attempts look convincing so I will conclude that no attempt I am aware of provides a solution.

I will not consider Garrett’s attempted solution to the argument from attributes. Most importantly, we can’t find any reason to think the argument from affections is valid, so the proposition has not been established. This is not to say that the Leibniz objection is necessarily decisive, I shall just not consider any attempts at an answer here. Indeed, Garrett’s attempt isn’t obviously false, but I wish to note that it’s far from simple, whereas Spinoza seems to think the argument is obvious. As such, I have my doubts about Garrett’s attempt as an interpretation of Spinoza’s thought. Therefore, I would prefer to look for an alternative instead of examining this other solution. I will now turn to 1p8schol2 for an alternative argument for 1p5.

Spinoza argues as follows. Let us suppose a fixed number, say twenty, of individuals exist (i.e. more than one substance of the same nature). Spinoza is a causal rationalist: for everything that exists there needs to be a cause, through which we conceive the effect i.e., we need a cause for the existence of each individual. Spinoza also thinks that a true definition of X expresses only the nature of X. Therefore, no true definition expresses a fixed number of individuals: the definition of a triangle states that it is a 3-sided shape, not a fixed number of triangles. So, the cause of the existence of the twenty individuals cannot be the nature of the individuals (the nature can’t state twenty exist). If the cause isn’t in the nature of a thing, it must be in something else, by elimination. But to say the cause is external to the individuals is to say they aren’t ontologically independent: they aren’t causally self-sufficient (self-caused). This contradicts what it is to be a substance (1p6), so these twenty individuals cannot be substances. This argument clearly applies generally, so Spinoza concludes that there cannot be two substances of the same nature. The proposition is established.

What are we to make of this? Well, I think there is a problem. A substance is, for Spinoza, necessarily existing. Its essence involves existence (1p7). Spinoza’s demonstration of this is simple: no substance can be caused to exist by anything external to it, as if it were it wouldn’t be ontologically independent. But it needs a cause to exist, so it is self-caused. To be self-caused is just to exist necessarily (1Def1). Now, say we have twenty substances of the same nature. We need a cause for the existence of each, due to Spinoza’s causal rationalism. But, each substance has the same nature, and if it is a substance then its nature is such that it involves existence: it is necessarily existing. The nature which all twenty share doesn’t cause twenty to exist, but given we have twenty existing, we can explain the existence of each. The existence of each is just explained by the fact that each is a substance, and substance necessarily exists. Now, maybe we could counter: why do twenty exist in the first place? Surely causal rationalism demands an answer to this. But, for that matter, why should one substance exist? What is different about saying twenty substances exist and saying one does? In both cases we can explain the existence of each substance by its nature as substance, in neither case can we explain why we have the number we do. There does seem to be one possible objection here. Given substance necessarily exists, one substance of a particular nature must exist. So this explains the existence of one substance. But the essence, as stated, says nothing about a number greater than one. So there is a cause for one substance, but not for twenty. However, we can counter here too. Given that substance by its very nature exists, what stops twenty substances existing? Nothing external to the substances can, as this contradicts their nature as substances. As their essence isn’t self-contradictory (as a square triangle would be) nothing can stop them existing. Given nothing stops twenty substances existing, they exist. It seems to me reasonable to conclude that this demonstration of 1p5 fails. Now, my above argument looks like it would allow us to show as many substances of the same nature as we want exist. This is true, but I contend that I have argued above using principles Spinoza holds. The problem is with Spinoza’s notion of substance, not my argument.

Of course, Spinoza may well have other reasons for holding 1p5. I shall end this essay by considering what they could be, having shown that neither of his official demonstrations succeed. What I wish to say here shall be sketchy, but I believe I can point in the right direction . I wish to show why 1p5 might at least make sense in the context of Spinoza’s system, rather than conclusively demonstrate it. I shall focus on extended substance, and forget about thought . As I have said earlier, substances cannot enter into causal relations with each other (1p6). Not only can one substance never be the cause of another but also, if X causes Y, then for Spinoza, conception of Y requires conception of X (1Ax4). But substance is epistemically independent i.e. requires the conception of nothing else. So, in principle, no two extended substances can causally interact. So, however many extended substances we have they are completely independent of each other. But what is the prime candidate for the name extended substances (if we want more than one)? Bodies. But causally interacting with each other is one of the main characteristics of bodies. Indeed, the concept of substance was used historically to explain what exactly remains unchanged in such interactions. I contend that to say we can have more than one extended substance leads, within Spinoza’s system, to a nonsensical conclusion: that they cannot interact at all. If we only have one extended substance we have no problem, as there isn’t anything to interact with. Consequently, it seems we have good reason to believe that there cannot be two substances of extended nature. Of course, 1p5 is more general than this, and I am not sure if any version of the above can work with Thought. Also, Spinoza does seem to hold that there are other (unknowable) attributes, so this will cause further problems. My conclusion here is just that we are justified in asserting a limited version of 1p5: there cannot be two extended substances.

Of course, the above argument appeals to certain principles (mainly that substances can’t causally interact) that Spinoza accepts but others may not. My aim is not to show that Spinoza is right, just that there are good reasons to accept the limited version of 1p5, based upon Spinozistic principles. However, as indicated I am unsure as to whether a version of this argument can apply for other attributes. Certainly the idea of thinking substances (minds) being unable to causally interact poses no obvious problems. Our best hope maybe lies in the Parallelism that exists between the attributes, but there is no room for any development along these lines here. To conclude, in this essay I have demonstrated why both of Spinoza’s official demonstrations of 1p5 fail. I have then gone on to suggest a weakened version of 1p5 which we may think Spinoza has good reasons for holding. Whether we can extend our argument here I am unsure. A real problem will be that 1p5 occurs at such an early point in The Ethics that the Geometrical Method just won’t allow taking later propositions, such as the mentioned Parallelism, in order to provide support. As such major revisions to the order of Spinoza’s thought are needed.

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Spinoza has already responded to you; (I change the wording to help you understand)

PROP. VIII. Note II.

  1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined. From this it follows that–
    2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle: it does not imply any fixed number of triangles.
    3. There is necessarily for each individual existent thing a cause why it should exist.
    4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.
    It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. For example, if twenty substances exist in the universe (your example), and we want to account for the existence of these twenty substances, it will not be enough to show the cause of substances existence in general; we must also show why there are exactly twenty substances, neither more nor less: for a cause must be assigned for the existence of each individual substance. Now this cause cannot be contained in the actual nature of substance, for the true definition of substance does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty substances, and, consequently, of each of them, must necessarily be sought externally to each individual substance. Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition (as we have shown, Notes ii., iii.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D.

You are welcome.

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Yes, I am aware of that, its exactly what I was responding too. If you look closely you’ll see that this objection of mine comes straight out of a discussion of Prop 8 Note 2 i.e. the passage you cited.

The problem, as I have stated, is that even though we don’t have a reason for the existence of 20 men, we don’t have a reason for them not existing. Given the hypothesis is that the 20 men are substances, and that nothing can stop a substance existing save internal inconsistency, these 20 men must exist, by Spinoza’s own use of the principle of sufficient reason. The idea is that for each of the 20 men, nothing can stop them existing, hence all 20 exists, despite the fact that the essence of man doesn’t make 20 exist. Spinoza is completely committed to the principle that if there is nothing stopping a substance existing it exists, by his own definitions. Whether a thing exists or does not exist, there must always be a reason for it. To say that the essence of man doesn’t posit 20 men doesn’t give a reason for 20 men not existing, and in any case, as I have argued, if each is a substance then all that can prevent each existing is internal inconsistency which we don’t have here.

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You are mistaken, we do have a reason for 20 substances not existing; it would require an external cause which is contrary to the definition of a substance; having no external cause.

Spinoza is pointing out that men are not substance because they have an external cause.

Mind you Spinoza has proven the existence of a substance two hundred years before it was empirically demonstrated. Today we call that substance energy.

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But thats not the point, of course men aren’t substances. At this point Spinoza isn’t entitled to his substance monism, or to the claim that you can only have 1 substance under each attribute, as he presents this as an alternative proof of 1p5: that no 2 substances can share an attribute. The proof he offers is meant to be completely general i.e. take the essence of anything, we can only explain the existence of 1 of them, therefore there cannot be substances sharing attributes (essence and attribute seem to be equated, more or less). So we take the essence of a given substance and there can only be 1 of them. The objection is that, although the essence of a thing doesn’t posit 20, or 40, or whatever, our hypothesis is that we have the essence of a substance. Given substance exists in itself it cannot causally interact with anything else, so nothing else can stop any substance existing, so nothing can stop 20 substances of the same essence, or attribute, existing. Therefore we can have 20 substances of the same attribute. The argument is run using men as an example. Men aren’t substances, for the reason you give, but this argument is part of what establishes substance monism. So there is nothing objectionable about 20 substances existing, and if nothing stops them existing, then they do.

The reason why Spinoza uses the word ‘externally’:

is that, because the essence cannot explain the existence of 20, something else must, therefore something external. My objection is that this is false. Just because the essence doesn’t posit 20 doesn’t mean that we cannot explain the existence of each individual thing through itself. We can explain this just by the fact that each is, by hypothesis, a substance. Substance exists necessarily. So there is an internal cause for the existence of each. Causal rationalism is satisfied, as we have a cause for the existence of the 20, and the cause is internal so each is a substance. Hence, Spinoza has not established that no 2 substances can share an attribute.

I don’t wish to come across as arrogant here, but I’m pretty sure that this is correct. Its really just a special case of the general problem of Spinozistic substance. Spinoza defines substance so that it cannot be caused by anything else, so it can only be a cause, not caused. This leads to his claim that substance necessarily exists. Now, given substance necessarily exists, any given substance must necessarily exist, just in virtue of being a substance. This is just how his argument for God works. But because Spinoza holds this view about substance, we can come up with any type of substance we want, and unless its contradictory (in a logical sense, eg a square triangle) it must exist. So, in the case here, Spinoza is arguing generally, but if we have a set of 20 substances what applies for 1 substance applies for all 20, therefore they all exist. The point is that Spinoza, in p8 note 2, needs to show that there is no reason for 20 substances to exist. He can’t do this, as above.

I like the equation of substance with energy, or the equation that Jonathan Bennett draws with space(I don’t know if you’ve read him on Spinoza, but its a similar idea I’d imagine). The problem I have with that type of view is how it really captures the causal role of substance. God, or nature, is meant to be the cause of everything (i.e. the total cause, as it must, as all modes are conceived through their cause, the substance). There is a sense in which energy is causally active, but it doesn’t seem to really match Spinoza’s. Aren’t there problems with quantum indeterminacy here? Spinoza thinks everything is necessitated by its effect, QM doesn’t seem to say this, in that individual events aren’t. Spinoza holds such a strict determinism here.

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To “explain the existence of each individual thing through itself” means that it is it’s own cause. But there are twenty of them. What is the cause of the twenty? The cause must be sought after external to the 20 individual things because the number 20 cannot be in the essence of a thing. Therefore they by necessity cannot be their own cause. Therefore there can be no more than one substance. QED

If a local indeterminacy exists in the quantum field it is caused by energy.

From the observational frame of energy with respects to energy… energy is self-deterministic… i.e. teleological.

That energy causes local indeterminacy allows our own observational frame with respects to ourself to experience the self-determinism of energy itself. i.e. that we can be teleological.

Spinoza may not have understood teleology… But Christopher Michael Langan has demonstrated it, and I would say at least on the same level of cogency of Spinoza’s ethics.

Introduction to the CTMU

The Cognitive-Theoretic Model of the Universe

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But thats the point, the number 20 can’t be in the essence of a thing, but the essence of each thing involves independent existence, i.e. the essence of each individual in the set of the 20 involves necessary existence. Each individual thing must have an essence, and to suppose that this essence doesn’t involve necessary existence is to suppose what we are trying to prove, that they aren’t substances. So each individual thing must have an essence, which must involve necessary existence (by our hypothesis), hence we have a cause for the existence of the 20, i.e. each is self-caused. My point is that there seems to be no less reason to affirm the existence of 20 than 1 substances, given in each case we can show the essence of each existing thing involves necessary existence. To assume that it can’t is to beg the question.

All you seem to be doing is repeating what Spinoza says in various ways. Where is the point in my reasoning where I go wrong? I’ve out pointed where I think Spinoza goes wrong: he seems to forget that he has postulated 20 substances, and he attempts to derive a contradiction by showing we can’t have 20 substances (of the same attribute), but forgets that each substance just does necessarily exist, so there’s no explanatory gap.

Note that this, in any case, cannot show there is only 1 substance because we could have another substance, of a different essence (attribute), such that there is only 1 of that different essence. Nothing Spinoza says in this scholium rules that out. Thats the point of the proof of substance with infinite attributes, God.

I’ll have a look at the other thing tomorrow, looks interesting. Of course, what Spinoza was rejecting was Aristotelian style-teleology, which sounds rather different to this so there’s maybe room for it.

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(1) For something to have necessary existence it must be it’s own cause and have no external cause.

Multiple things with the same essence have an external cause by necessity, therefore they cannot be their own cause nor can their essence involve necessary existence.

A thing must be it’s own cause to be a substance. Anything that has an external cause cannot be a substance.

Therefore, multiple things with the same essence cannot be a substance. QED

You are presuming that something that requires an external cause can also be it’s own cause. Contradiction!

(2) Once again, if two substances existed there would necessarily be an external cause for there existence… contradiction!

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At least you’ve stopped paraphrasing Spinoza. You, again, seem to have missed the point. There is no external cause as there is no need for one. Spinoza is just wrong here. Multiple things with the same essence do not have an external cause by necessity. They do not have an external cause by necessity because Spinoza doesn’t make full use of his conception of substance in the argument. He doesn’t use the fact that any purported substance must, in virtue of being a substance, exist necessarily. Given this, nothing over and above each of the 20 substances is required to bring about their existence.

Say we take the essence of a thinking substance. Spinoza hasn’t yet shown we can only have 1 substance, so we can talk about as many as we want. Let us imagine 2 thinking substances. The essence doesn’t posit 2, as Spinoza notes. Everything must have a cause necessitating it in Spinoza’s system. His argument is that because we have the essence of a substance, 1 must exist, but because the essence says nothing about 2, 2 don’t. But, we have 2 thinking things, each of which must have the same essence. Given that both have the same essence, which involves necessary existence, they exist. How could they not? What could the cause of the non-existence of 2 thinking things be? Either internal, i.e. they are contradictory, in which case 1 doesn’t exist; or external, but an external cause cannot be assumed to stop 2 existing because if we assume this then we have assumed that we don’t have 2 substances, which is what we are trying to prove. ‘QED’

Now this is just offensively wrong. Just look at the Ethics again, what does Spinoza say the purpose of this argument is? It is an alternative proof of the proposition that no 2 substances can share an attribute. This proposition is not substance monism, because Spinoza allows at least 2 attributes, so nothing in this proposition stops there being a thinking substance and an extended substance i.e. 2 substances of different attributes. The argument only shows that we can have 1 substance of the same essence. That does not mean we cannot have another substance with a different essence. The reason why we have 1 substance is that God has infinite attributes, hence there cannot be another substance as it would have to share an attribute with God, i.e be of the same essence.

I’m not going to go through my argument again, because I’m just repeating myself. If you don’t buy it, fine, but I’m pretty confident about this. I don’t want to appeal to authority here, but why do you think that, in the secondary literature on Spinoza, everyone seems to find it necessary to provide alternative arguments for substance monism than the ones Spinoza gives? His argument in the Ethics is utterly invalid.

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I think our main disagreement here is that I claim multiple anything requires an external cause… however you claim if those multiple things are presumed to have necessary existence then they don’t need an external cause.

I find that argument lacking greatly because it is the necessary existence that is the thing to be proved not taken as a presumption to disprove external cause.

My proof that multiple anything necessitates external cause is that the essence of a thing cannot have multiplicity in it. This fact I am not sure you are able to understand or comprehend it’s relation to necessary existence.

I would rather end our discussion if we agree on where we disagree.

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Thats exactly the problem, he must assume that he has 20 substances, then derive a contradiction from that. He can’t assume he has 20 non-substances as then his proof is meaningless. If he assumes he has 20 substances, they must all necessarily exist. The 2 are inseperable, hence if he assumes 20 substances, which he must, then he must assume they all necessarily exist. You can’t have a substance without necessary existence, which is why he assigns necessary existence to the essence of a substance. Because of this, he can’t derive the necessary contradiction.

I completely comprehend how its meant to work, your proof is just what Spinoza says. I just think it doesn’t work. As I’ve said constantly, the essence of a thing doesn’t need to have multiplicity in it to explain the existence of multiple things.

But anyway, enough. By the way, do you think his proof of proposition 5 works? I do think there must be something Spinoza can say about the objections I raise in the essay, do you know of anything? It just seems so obviously wrong though.

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It does seem that we agree on where we disagree.

You assume that substance must be presumed in multiplicity to prove that there can only be one substance.

Whereas I claim substance must be proved in multiplicity AND or in only one thing. And that we can intellectually examine a multiplicity of things without having to presume they are or are not substance. And the same goes with intellectually examining only one thing, which does not have to be presumed to be or not be substance. IT MUST BE PROVED.

So, this is where we disagree. Thank you for entertaining the conversation.