1p11 and the principle of plenitude (the second proof)

God, or a substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists.

Deus sive substantia constans infinitis attributis, quorum unumquodque aeternam et infinitam essentiam exprimit, necessario existit [II/22].

tl;dr : it’s the Principle of Plenitude, not the Principle of Sufficient Reason that is doing the work in the second proof of God’s necessary existence:

Alternatively: 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 1p11dem.

I’ve been dreading this proposition. I suspect that it’s the only proposition that gets this many proofs. Three different ones in the main section and then another in the scholium. Spinoza gives three different kinds of proofs. The first one:

If you deny this, conceive, if you can, that God does not exist. Therefore (by 1a7) his essence does not involve existence. But this (by 1p07) is absurd. Therefore God necessarily exists, q.e.d.

I’m not yet going to deal with this first proof in any detail. It is of a type with others of the ‘ontological proofs of God’ species. Yet it’s not precisely Descartes’; it’s not Anselm’s, or Aquinas’, or Scotus’. So while I was digging around in scholastic ontological proofs for God’s existence, I was reminded of something else that I think offers me an interesting take on the second proof. This is what this post is going to be about. The second proof really has three components:

1. A super-strong version of what appears to be the PSR that says that there must be a reason not just for something’s existence but also for its non-existence;

2. Derived from this: that this reason must be internal or external. There is nothing external to God/substance, so it must be internal;

3. But for something to have an internal reason for its non-existence is for it to be essentially self-contradictory and this is absurd.

Q.E.D.

The last two we’ve kind of already been over. The second one relies on Spinoza’s notion of the attributes for why nothing external to God could be a cause of, or in any way interact with, God. The third one is going to be important for his theory of the conatus but it’s necessary to note it’s first appearance here. So it’s the first point I want to focus on. In the past, I’ve normally, just shrugged at this – Spinoza’s a rationalist; this is the PSR; what did you expect? nothing to see here! – in my less nonchalant moods, I do recognise that it’s a really strong version of the PSR. Leibniz may be committed to everything having a reason and I suppose in a loose sense he can be said to explain thing’s non-existence in as much as ‘the best of all possible worlds’ functions as this kind of ur-reason. But actually I don’t think he either needs to, or would want to affirm this strength of the PSR. In fact I think he’d be opposed to it.

I’m being too cryptic for my own good. What I think is this: that Spinoza’s claim that we need to be able to explain something’s non-existence as well as its existence is not really the PSR at all, but actually the Principle of Plenitude (PP). Leibniz, at least according to Hintikka (1981b) absolutely rejects this principle. I don’t actually have any doubts concerning Hintikka’s argument for Leibniz rejecting the PP. The textual evidence is basically incontrovertible (see quote immediately below). This also opens an interesting wedge between Spinoza and Leibniz. It is, I am now starting to think, worthwhile to throw into question whether Spinoza does hold onto the PSR at all. That what is commonly taken to be the PSR, is actually the PP. It is helpful to quote the Leibniz passage that Hintikka opens with (1981b, 259). The passage is from a letter Leibniz wrote to Philipp in January 1680. It’s on page 273 of the Philosophical Papers and Letters collection (I’m quoting the letter directly, as Hintakka removes a couple of phrases – they’re not important but to save anybody the bother of checking to see what Hintakka removed, I’ve quoted the letter directly).

I esteem Mr. Descartes almost as much as one can esteem any man, and, though there are among his opinions some which seem false to me, and even dangerous, this does not keep me from saying that we owe nearly as much to Galileo and to him in philosophical matters as to the whole of antiquity. At present I recall only one of the two dangerous propositions, the location of which you want me to indicate. It is in the Principles of Philosophy, Part III, Article 47, in the following words:

And, after all, it makes very little difference what we assume in this respect, because it must later be changed in accordance to the laws of nature. Hardly anything can be assumed from which the same effects cannot be derived, though perhaps with greater trouble. For, due to these laws, matter takes on, successively, all the forms of which it is capable. Therefore if we considered these forms in order, we could eventually arrive at that one which is our present world, so that in this respect no false hypothesis can lead us into error.

I do not believe that a more dangerous proposition than this could be formulated. For if matter takes on, successively, all possible forms, it follows that nothing can be imagined so absurd, so bizarre, so contrary to what we call justice, that it would not have happened and will not some day happen. These are precisely the opinions which Spinoza has expounded more clearly, namely, that justice, beauty, and order are things relative to us but that the perfection of God consists in the magnitude of his activity by virtue of which nothing is possible or conceivable which he does not actually produce. These are also the opinions of Mr. Hobbes, who asserts that everything that is possible is either past or present or future, and that there will be no place for trust in providence if God produces everything and makes no choice among possible beings. Mr. Descartes was careful not to speak so plainly, but he could not keep from revealing his opinions incidentally…. In my opinion, this is the ‘first falsehood’ and the basis of atheistic philosophy, though it always seems to say the most beautiful things about God.

Hintakka continutes:

The thesis Leibniz here brands “the first falsehood and the basis of atheistic philosophy” was not original with Descartes and Hobbes. It is a version of one of the most famous metaphysical principles in Western philosophy and speculative theology, somewhat misleadingly labeled by A. O. Lovejoy the “Principle of Plenitude”.

(Godfried Wilhelm Leibniz 1875, 4:283–84; translation from Gottfried Wilhelm Leibniz 1975, 273; cited in Hintikka 1981b, 259–60).

Lovejoy propounds his thesis in: The Great Chain of Being (Lovejoy [1936] 1964). Explaining exactly what this thesis is, without falling into simple falsity, contradiction, or paradox is really quite hard. The difficulty is that the thesis relates principles of necessity and possibility, and, in its more paradoxical formulations both rigorously distinguishes and identifies these two modalities. Perhaps the least paradoxical, though also the most obscure formulation is that: there are no eternal accidents. But what does this even mean? Let’s tackle this another way. What Aristotle was trying to get at with this principle, is that when you say something is possible, there is an important sense in which it cannot not-happen (as I flagged: this is where it starts to tie possibility and necessity into a knot). This is where we run into the first problem with explaining this thesis: simple falsity. If I say that today it is possible that I may win the lottery (I have bought a ticket for the lottery and the lottery happens today) then of course we don’t mean that it can’t not happen that I don’t win the lottery today. That would simply be false. After all it is only possible that I win the lottery today, not necessary!

Trying again: the principle does not include time-bounded possibilities, like my winning the lottery today. It is about a more obscure idea: that if something remains possible, eternally, then at some point it must happen. Why would we think this? Well, consider the converse: if something never-ever-ever (i.e. eternally) never happens, then it must be impossible. Anything not impossible, is possible. But this is precisely where it gets paradoxical. We start with a simple understanding of impossibility: if something never-ever-ever happens, it is impossible. It doesn’t seem much of a stretch to say that anything not impossible is possible. Admittedly the Law of the Excluded Middle is doing a lot of heavy lifting, but that’s what it’s there for. But then having defined:

1. The possible as whatever is not-impossible,

2. But the impossible is what eternally never-ever happens,

So:

3. the (eternally) possible must, at some point, happen;

Because:

4. If it did not, it would be impossible, not possible.

So:

5. So the eternally possible is in fact necessary.

But to say that the possible must happen is to link the possible and the necessary in an, at best, unexpected way. The principle of plenitude says that what is eternally possible, must happen. The eternally possible is, in fact, necessary, at some point.

But once you accept that something being eternally possible means that it is necessary, an explanation for why it is currently not the case is required.

And this is why what looks like a super-strong version of the PSR is in fact the PP.

Couple of final thoughts before more research.

Hintikka goes on to say:

Undoubtedly, Leibniz would have found his judgment confirmed if he could have anticipated the use of what he called ‘the basis of atheistic philosophy’ by David Hume in the Dialogues on Natural Religion or if he had known of its use by Lucretius in De rerum natura. However, it is less obvious what he would have said had he been aware of the acceptance of the Principle of Plenitude by many – perhaps most – pious scholastics (Hintikka 1981b, 260).

I’m not so sure that Hintakka is right about this final point. From memory, and I’m going to have to reread the relevant chapter in the Lovejoy, the PP may have been used by ‘pious scholastics’ but it also seemed to get them into trouble. In particular Abelard who comes very close to anticipating Spinoza’s necessetarianism. The PP seems to be one of those principles that had to be accepted on logical grounds but got everybody into really hot water if they were not super careful.

Hintikka has another paper in the same collection. This one is on Aristotle and why he absolutely is (contra Lovejoy) the source of the PP. I just wanted to flag this gem by Aristotle. I actually don’t think it’s saying the same thing that Spinoza would have meant by this but it is strikingly similar in it’s formulation at least:

“Hence a thing is eternal if it is by necessity; and if it is eternal, it is by necessity. And if therefore the coming-to-be of a thing is necessary, its coming-to-be is eternal; and if eternal, necessary.” (Aristotle 1984, bk. II 11. 338^a1-3; cited in Hintikka 1981a, 65)

which is not the same as:

By eternity I understand existence itself, insofar as it is conceived to follow necessarily from the definition alone of the eternal thing 1d8.

But is also not a gazillion miles away.

OK, so I need to say more about how Leibniz’s version of the PSR differs from the PP – fundamentally, Leibniz has a different sense of what possibility is but I’ll leave that for later.

Bibliography

Aristotle. 1984. ‘On Generation and Corruption’. In The Complete Works of Aristotle, edited by Jonathan Barnes, translated by H. H. Joachim, The Revised Oxford Translation. One Volume Digital Edition. Princeton, N.J: Princeton University Press.

Hintikka, Jaakko. 1981a. ‘Aristotle on the Realization of Possibilities in Time’. In Reforging the Great Chain of Being: Studies of the History of Modal Theories, edited by Simo Knuuttila, 259–86. Synthese Historical Library 20. Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-015-7662-8_7.

———. 1981b. ‘Leibniz on Plenitude, Relations, and the “Reign of Law”’. In Reforging the Great Chain of Being: Studies of the History of Modal Theories, edited by Simo Knuuttila, 57–72. Synthese Historical Library 20. Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-015-7662-8_7.

Leibniz, Godfried Wilhelm. 1875. G. W. Leibniz. Philosophische Schriften. Edited by C. I. Gerhardt. Vol. 4. 7 vols. Berlin.

Leibniz, Gottfried Wilhelm. 1975. Philosophical Papers and Letters. Edited and translated by Leroy E. Loemaker. Dordrecht: Springer Netherlands.

Lovejoy, Arthur O. (1936) 1964. The Great Chain of Being: A Study of the History of an Idea. William James Lectures. Cambridge, Mass.: Harvard UP.

1p10 and 1p10s

1P10: Each attribute of a substance must be conceived through itself.

Dem.: For an attribute is what the intellect perceives concerning a substance, as constituting its essence (by 1d4); so (by 1d3) it must be conceived through itself, q.e.d.

I think the proposition is straightforward. Attributes constitute the essence of substance. Substance is conceived through itself, so anything that is essentially the same as substance also has to be conceived through itself. At this point, that doesn’t seem problematic to me. Extension is just extension. Thought is just thought in the way that quantity is just quantity or quality is just quality (yes, I’m still running the attributes=categories line). What does the scholium say?

From these propositions it is evident that although two attributes may be conceived to be really distinct (i.e., one may be conceived without the aid of the other), we still cannot infer from that that they constitute two beings, or two different substances. For it is of the nature of a substance that each of its attributes is conceived through itself, since all the attributes it has have always been in it together, and one could not be produced by another, but each expresses the reality, or being of substance.

I need to start by pointing out that the term ‘really distinct’ is a technical term. Employing ideas from scholastic philosophy, there are a number of different ways in which two things may be distinct for thinkers like Descartes or Spinoza. Spinoza lists three of them in chapter five of part two of the ‘Metaphysical Thoughts’ appendix to his Principles of Cartesian Philosophy (see Appendix 1). They are ‘real distinction’, ‘modal distinction’ and ‘distinction of reason’. The latter one is really no distinction at all. Spinoza gives the example of the difference between a substance and its attribute as being only one ‘of reason’. We can have a definition of substance and a definition of attribute that are not identical but we are not thinking of two different things. We are dealing with the difference between explaining what a thing is without saying what kind of thing it is and explaining what kind of thing that thing is. This is only a distinction ‘of reason’. Real distinction on the other hand is where two things can be conceived of independently and, for most versions of real distinction, can exist independently. So in scholastic philosophy two horses are really distinct because one can exist without the other and we can conceive one without the other. More relevantly, a substance whose attribute is extension and a substance whose attribute was thought, would be really distinct. Finally, there is modal difference. This is the difference between substance and its modes. Spinoza also says that it is the difference between one mode and another – even though two modes may often fit the definition of real distinction, Spinoza wants to keep that term only for substantial difference. That’s the position in the ‘Metaphyisical Thoughts’ but it’s no longer exactly the position in the Ethics. Spinoza has weakened the definition of ‘real distinction’ so that rather than meaning the difference between two things that can both be and be conceived independently of one another, it now only means that they can be conceived independently of one another. In the ‘Metaphysical Thoughts’ if two things could be conceived as really distinct, then they really were distinct. In the Ethics, Spinoza says: no, you cannot make that assumption any more. This is a direct contradiction to what he says in ‘The Metaphysical Thoughts’:

That distinction is called real by which two substances are distinguished [25] from one another, whether they have the same or different attributes, e.g., thought, and extension, or the parts of matter. This is known from the fact that each can be conceived, and consequently, can exist, without the aid of the other.

In the case of attributes and substance(s) we can no longer infer the consequent that just because two attributes are really distinct, then their substance are also really distinct. This is very odd as, if you recall, the difference between a substance and its attribute is only one ‘of reason’. Now if we were in the mood to be hyper precise, we could point out that Spinoza only says that they ‘can exist’ not that they do exist, or must exist ‘without the aid of the other’. In the scholium that I’m discussing, Spinoza says, look: just because two attributes are really distinct, we cannot infer that they must be the attributes of two really distinct substances. But if the difference between a substance and its attribute is only one of reason, then surely this inference is valid? What to do? Well, we need to modify our understanding of what Spinoza might mean by a ‘real distinction’, or what the distinction is between a substance and its attribute. Luckily there is a slightly different version of a real distinction to hand. This would be Scotus’ idea of a ‘formal distinction’ (formal distinctions are a species of real distinction). The idea that Spinoza is using formal distinction to explain what the difference between the attributes is not my idea. Deleuze argues this (though not in a way that I wholely agree with) in his Expressionism book. More recently, and much more to my liking, Andreas Schmidt has written a great chapter ‘Substance Monism and Identity Theory in Spinoza’ which goes into this idea at some length and detail (Schmidt 2009). I’m not going to go into all the ins and out of formal distinction but it does basically do what Spinoza is describing here: two independently conceivable attributes of the same substance.

Why have I gone on at such length about a single paragraph of a scholium? Well because it’s sneakily utterly crucial to the entire enterprise of the Ethics. The opening sentence of the next paragraph makes clear what is at stake here:

So it is far from absurd to attribute many attributes to one substance.

At various points I’ve mentioned a Leibnizian critique of Spinoza, namely that Spinoza has not shown that his concept of God (a substance consisting of an infinity of attributes) is not self-contradictory (i.e. that it is possible). What Spinoza explicitly claims here is only that we can attribute ‘many’ attributes to one substance, not that we can attribute an infinity of them. I suspect he doesn’t see that there is any further problem. Real distinction implies a strict one attribute per substance limit. If we do not have that kind of distinction in place, then there does not seem to be a reason why a substance could not have an infinity of attributes because there could not be anything that could limit substance in that way. I’m not sure how good an arugment this is. But you can see why, once you accept that thought and extension are attributes of the same substance, then it’s going to be hard to think of more opposed attributes that could pose a problem in their attribution to the same substance.

This is all such an important set of claims, that sticking it in a scholium seems slightly underhand almost – not least because he is using a variant (formal) of real distinction that is not the same as the one he used in the ‘Metaphysical Thoughts’.

Bibliography

Schmidt, Andreas. 2009. ‘Substance Monism and Identity Theory in Spinoza’. In The Cambridge Companion to Spinoza’s Ethics, edited by Olli Koistinen, 79–98. Cambridge: Cambridge University Press.

Spinoza, Benedictus de. 1985a. ‘(Curley) Ethics’. In The Collected Works of Spinoza, translated by Edwin M. Curley, I:408–617. Princeton: Princeton University Press.

———. 1985b. ‘Descartes’ Principles of Philosophy’. In The Collected Works of Spinoza, translated by Edwin M. Curley, I:224–98. Princeton: Princeton University Press.

———. 1985c. The Collected Works of Spinoza, Volume I. Translated by Edwin M. Curley. Vol. 1. 2 vols. Princeton: Princeton University Press.

Appendix 1

(Spinoza 1985b, chap. V Of God’s Simplicity [I/257-8]).

Chapter V Of God’s Simplicity

The threefold Distinction of Things: Real, Modal, of Reason

We proceed to the Simplicity of God. In order to understand this [20] attribute of God rightly, we need to recall what Descartes has taught (Principles I, 48, 49), viz. that there is nothing in nature but substances and their modes. From this a threefold distinction of things is deduced (I, 60-62), viz. real, modal, and of reason.

That distinction is called real by which two substances are distinguished [25] from one another, whether they have the same or different attributes, e.g., thought, and extension, or the parts of matter. This is known from the fact that each can be conceived, and consequently, can exist, without the aid of the other.

The modal distinction is shown to be twofold: there is that between [30] a mode of a substance and the substance itself, and that between two modes of one and the same substance. We know the latter from the fact that, although either mode may be conceived without the aid of the other, nevertheless neither may be conceived without the aid of the substance whose modes they are. The former is known from the fact that, although the substance can be conceived without its mode, [35] nevertheless, the mode cannot be conceived without the substance.

[I/258] Finally, that distinction is said to be of reason which exists between substance and its attribute, as when duration is distinguished from extension. And this is also known from the fact that such a substance cannot be understood without that attribute.

Appendix 2

DISTINCTION, REAL
distinctio realis

onderscheid, dadelijk

The definitions Spinoza gives of a real distinction seem to follow the Cartesian usage of the Second Replies (AT VII, 162) and the Principles (AT VIII-1, 28), but it is difficult to see how Spinoza could allow that any two things might be really distinct in the Cartesian sense. For Descartes a real distinction can occur only between two or more substances, but for Spinoza there is really only one substance. Of course, each of the attributes satisfies the definition of substance, and each is really distinct from every other, but there is no possibility of any attribute existing without the others.

(Spinoza 1985c, 1:634)

DISTINCTIO; DISTINGUERE; DISTINCTUS; DISTINCTE

onderscheid(ing); onderscheiden; onderscheiden; onderscheidelijk

distinction; to distinguish; distinct; distinctly, I/145, 237, 244, 257, 259, 266, II/17, 21, 28, 96, 97, 99, 100, 120, 121, 123, 181, 210, 211, 249, 285, IV/55

DISTINCTIO MODALIS

wijzige onderscheid

modal distinction, I/248, 257, 258, II/59

DISTINCTIO RATIONIS

onderscheid van reden

distinction of reason, I/248, 258, 259, 280, II/282

DISTINCTIO REALIS

zakelijke onderscheid

real distinction, I/146, 151, 248, 257, 258, II/33, 52, 59, IV/55

DISTINCTIO VERBIS

onderscheid door woorden

verbal distinction, I/248

(Spinoza 1985c, 1:673)

real distinction

[I/146] In this way he would discover easily the real distinction between the soul and the body

[I/151] D10: Two substances are said to be really distinct when each of them can exist without the other.

[I/248] Why some have maintained a Metaphysical good

[I/257] However, those who eagerly seek some Metaphysical good, needing no qualification, labor under a false prejudice, for they confuse a distinction of reason with a real or modal distinction. They distinguish [5] between the thing itself and the striving that is in each thing to preserve its being, although they do not know what they understand by striving. For though the thing and its striving to preserve its being are distinguished by reason, or rather verbally (which deceives these people very greatly), they are not in any way really distinct.

[I/259] That God’s Attributes are distinguished only by reason

And from this we can now clearly conclude that all the distinctions we make between the attributes of God are only distinctions of reason [5] —the attributes are not really distinguished from one another. Understand such distinctions of reason as I have just mentioned, which are recognized from the fact that such a substance cannot exist without that attribute. So we conclude that God is a most simple being. For the rest, we pay no attention to the hodgepodge of Peripatetic distinctions [10] but go on to God’s life.

[II/33] great errors, who have not accurately distinguished between imagination and intellection. Such errors as: that extension must be in a place, that it must be finite, that its parts must be really distinguished from one another

[IV/59] For if corporeal substance could be so divided that its parts were really distinct, why, then, could one part not be annihilated, the rest remaining connected with one another as before? And why must they all be so fitted together that there is no vacuum? Truly, of things which are really [15] distinct from one another, one can be, and remain in its condition, without the other. Since, therefore, there is no vacuum in nature (a subject I discuss elsewhere),41 but all its parts must so concur that there is no vacuum, it follows also that they cannot be really distinguished, i.e., that corporeal substance, insofar as it is a substance, cannot be divided.

[IV/55] Hence they talk utter nonsense, not to say madness, who hold that Extended Substance is put together of parts, or bodies, really distinct from one another. This is just the same as if someone should try, [15] merely by adding and accumulating many circles, to put together a square or a triangle or something else completely different in its essence.

1p9

Quo plus realitatis aut esse unaquaeque res habet, eo plura attributa ipsi competunt.

The more reality or being each thing has, the more attributes belong to it. Dem.: This is evident from 1d4.

1d4: By attribute I understand what the intellect perceives of a substance, as constituting its essence.

Wish I had something more competent to say about Spinoza’s use of the Latin ‘competunt’ from competēre. Wiktionary has:

come together, meet

agree, coincide in point of time

be equal to, be capable of

https://en.wiktionary.org/wiki/competo#Latin

and Lewis and Short has

3. To belong, be due to

http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0059:entry=competo

I guess the only thing that really needs flagging here is that part of how we decide to translate competunt is based on what we think the substance-attribute relation is. Philosophical translation is as much interpretation and decision as it is anything else. So I don’t like ‘belongs’ because it implies, to me at least, a property and property-relation that I don’t think is right. Attributes are constitutive of a substance’s essence; they are what kind of substance a substance is.

But in a way this is small beer problem. What we really need to get to grips with is what it means for something to have more being-or-reality. I’ve been recently reading Gilson’s Being and Some Philosophers pretty intensively. Would highly recommend it. You can grab a pdf off of the usual places. One of Gilson’s many points is that we need to recognise and understand how philosophers have distinguished Being from existence. As a good Thomist, he of course has views on what the proper distinction between these two things should be but it’s a historical study that looks at a number of options. I’m pretty convinced that Spinoza doesn’t think Being and existence are the same things – which is why the conatus preserves a thing in its being, not its existence. So an initial plausible hypothesis (that I’m not going to challenge here and now, and reserve the right to massively revise at some point in the future if I decide this is bollocks) is that Being means something like self-identity. This does make this claim look a little odd:

The more reality or being each thing has, the more attributes belong to it.

Means:

The more a thing is itself, the more attributes belong to it.

Which isn’t a transparently not-nonsense sentence. But we’ve sort of been seeing this kind of idea play out in the previous scholium when we consider substance as being self-causing and therefore being unique (as in: there cannot be more than one substance per attribute). So there is a sense in which, qua necessary existence or self-caused, a substance is as much itself as it could possibly be; I mean something quite simple here: a substance can’t interact with anything else; it can’t be produced by anything else. On Spinoza’s version of substance, a substance cannot suffer; it cannot be acted upon. So I think I understand what he’s going on about – except why would having/being more than one attribute make substance more itself?

I think I need to back up a bit here. What kind of claim is 1p9? I think part of my problem is that I almost want to read this in a quasi-causal manner, as if adding more reality to a thing *gives* a substance more attributes. I don’t think that can be right though. This is an identity statement. It actually helps if we reverse the claim. So instead of:

The more reality or being each thing has, the more attributes belong to it.

Let’s have:

The more attributes belonging to a thing, the more it is not anything else.

I’m cheating a little bit here because I want to wrap up. We could have got stuck on the idea that if a substance is extended substance then it doesn’t look like it could be any more substantial than that because it’s self-causing and non-interactive. I think Spinoza would want to say: yeah, but if it’s also thinking substance then it’s more not something else and that means more self-identical and that means it has more being. So to unpack this into something resembling a demonstration:

If being = self-identity

and

self-identity = not being anything else [which is dubious, but what can you do?]

then

being more attribute-y means having more being-or-reality because substance is now extended and thinking (and possibly Henry and … and … and … ) and is therefore more not-anything-else because it is now extended and thinking and …

And this idea that this is evident from 1d4? Well being self-identical is a statement about a thing’s essence. So the more ways in which a thing’s essence is not anything else, then the more being-or-reality in this sense of self-identity a thing’s essence will have.

Q.E.D.?

1p7–1p1

1p11 and 1p14 are two key claims for the whole of the Ethics. 1p11 states that, “God, or a substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists” and 1p14 states that, “Except God, no substance can be or be conceived.” Both of these two claims rest on 1p7. The first seven propositions of the Ethics form one single argument that ends with the conclusion that, “It pertains to the nature of a substance to exist”. It can be helpful when reading the Ethics to occasionally read it backwards. By which I mean simply that knowing with what the sequence of an argument concludes, can assist in following the argument that deduces that conclusion. This is how I’m going to read propositions one to seven, or seven to one in this case.

The argument runs (backwards from the conclusion) as follows:

1p7: “It pertains to the nature of a substance to exist”.

Why is this the case?

The demonstration is striaghtforward enough. A substance cannot be produced by anything else. As a substance that exists cannot have been produced by anything else, is must be self-producing or self-causing – and that’s just what is meant by necessarily existing.

But why can’t one substance be produced by another? This is what 1p6 claims.

1p6: “One substance cannot be produced by another substance”.

Why is this the case?

Spinoza says that for one thing to be able to cause another, they must have “something in common”. What does it mean to have something in common? Although Spinoza never explicitly defines this idea, it is pretty clear from his explanation of 1d2, “But a body is not limited by a thought nor a thought by a body” that what having “something in common” means is: conceivable from the same attribute (or perceivable as belonging to the same attribute). So a body can limit a body because bodies are modes of extension. A thought can limit a thought because thoughts are modes of the attribute of thought. Can a body limit, produce, cause, or in in any way interact with a thought? No it cannot. Why not? Because thoughts and bodies have nothing in common i.e. they are modes of different attributes.

OK. So: when Spinoza says that one substance cannot be produced by another substance, this is because each attribute is unique to a substance. Of course Spinoza will eventually show that there is only one substance and it has infinite attributes. But at this stage of the argument, Spinoza is happy to entertain that there may be more than one substance. What there cannot be, is more than one substance per attribute. With this last claim we need to move back to proposition 1p5.

1p5: “In rerum natura non possunt dari duae aut plures substantiae ejusdem naturae sive attributi.”

Why have I given the Latin here instead of an English translation? It is not because anything relevant to the proof hangs on it but I think it is worthwhile to point out that Spinoza uses the phrase “in rerum natura” which can be translated in a number of ways but most straightforwardly as “in the nature of things”. To me the echo of Lucretius’ De rerum natura is unmistakable. However, this is by no means anything resembling proof as in fact “rerum natura” is an all too common Latin phrase. But nevertheless, rather than Curley’s “In Nature” I would have 1p5 read as this:

1p5: “In the nature of things [In Nature] there cannot be two or more substances of the same nature or attribute”.

If this is true, then this indeed means that no substance has anything in common with any other substance and this does mean that no substance can be produced by another substance. So we can see why 1p6, substances cannot be produced by another substance, directly relies on substances having nothing in common i.e. that attributes cannot be shared. This is precisely what 1p5 asserts. Why does Spinoza think that this is the case? 1p4 gives us the arguments as to why not.

1p4: Two or more distinct things are distinguished from one another, either by a difference in the attributes of the substances or by a difference in their affections.

Spinoza needs to show that there cannot be more than one substance with the same attribute. Of course this is an anti-Cartesian proposition. Spinoza wants to claim that Descartes picture of human minds or souls all being distinct substances but sharing the same attribute of thought cannot be the case. Spinoza asks a simple yet devastating question: what difference could there be between two substances that share the same attribute? Well the only things that there are, are substances and modes. What about attributes? Attributes constitute the essence of a substance; they are what kind of substance the substance is, not a separate thing. So two substances can be distinguished by their attributes because this is simply saying that they are two different kinds of substance, e.g. extended substance and thinking substance. But we can’t use their attributes to distinguish substances because ex hypothesi, we are considering only one attribute that they have in common. But what about modes? Surely we can distinguish substances by their modes? After all, if we have two men, then we can distinguish them by their accidents: Socrates is pale, and Plato is strong. But Spinoza insists that this is wrong. Of course his concept of substance does not map onto the Aristotelian idea of substances that underlies my Socrates & Plato example (in this case, Spinoza would say that Socrates & Plato are both modes and that qua modes they are distinguished from one another in a number of ways i.e. modally). But even so, Spinoza’s objection would hold. When we correctly conceive what a substance is, it is what is conceived through itself. So to say that two substances could be different because their modes are different is muddled, given Spinoza’s definition of substance. What kind of distinction does Spinoza think is at play here? It is a version of the ‘identity of indiscernibles’. Importantly though, this is not a psychological or epistemological claim (not that I think the IofI is for Leibniz either) but a logical one. Spinoza is not claiming that we cannot tell the difference between two substances that are only distinguished by their modes, and so we should treat them as one. He is making a logical point and metaphysical point. When we properly understand the definition that Spinoza gives for a substance, what is in itself and conceived through itself (metaphysical and logical) then if we want to find a ‘difference maker’ then we cannot appeal to modes because they are posterior to the substances that they are modes of [this is precisely what 1p1 claims]. Again: we could have appealed to attributes to distinguish substances, but we were ruling that out ex hypothesi. The only thing that there are, are substances (assuming that each substance is differentiated by its attribute) and modes. We have ruled out attributes. We, logically, cannot use modes to differentiate substances, so it cannot (a strong logically cannot) be the case that there are two substances that have only the one attribute in common.

1p3: If things have nothing in common with one another, one of them cannot be the cause of the other.

This is one of those classically annoying Spinoza propositions which looks like it almost could be an axiom, but then you read his explanation and you’re like, eh?

Dem.: If they have nothing in common with one another, then (by 1a5) they cannot be understood through one another, and so (by 1a4) one cannot be the cause of the other, q.e.d.

1a4: The knowledge of an effect depends on, and involves [involvit], the knowledge of its cause.

1a5: Things that have nothing in common with one another also cannot be understood through one another, or the concept of the one does not involve the concept of the other.

I think it’s really easy to misunderstand the argument that is being made here – so much so that I’m half tempted to change the translation to make it easier to understand. To me at least, and maybe this is an idiosyncratic (mis)reading of the argument, it really looks as though Spinoza is saying that one thing not being the cause of the other is because one thing cannot be understood through the other. This would make him a very strong subjective idealist, verging on a solipsist. Now I’m not saying that that solipsism is impossible: actually I am saying that that is impossible, at least within Spinoza’s system as solipsism is literally the position of God, or rather God’s infinite intellect; solipsism would make you or whoever is reading this, God. Which I guess is not impossible, but let’s say that it’s unlikely at best (and if it is the case, why the hell do you need me to explain this to you? Puny god). So if Spinoza is not saying that because one thing cannot be understood through the other that one cannot be the cause of the other as an idealist point of view, what is he saying? In a sense this would be much easier to understand if we invert axiom 5 to this:

if the concept of A implies B, then B can always be understood through A; in this case, then they have something in common

This is an example of how when Spinoza tried to keep things abstract so that the axioms are eternal truths, the actual import of what he is trying to say gets lost. Which is annoying as he is in fact saying something very simple. Let’s take the attribute of extension; any mode of that attribute, i.e. any body is a body precisely because we are considering that modification of substance through the attribute of extension. Because we are so used to bodies actually being (Aristotelian substances) we forget that for Spinoza a body is actually a modification of substance, specifically a mode of the attribute of extension. “Body” is actually a massively compressed piece of short hand. When we think of a body we are thinking of a modification of substance through an attribute. In other words ‘body’ is always really ‘body as a modification of extension’ i.e. body absolutely implies extension in the same way as ‘lion’ implies ‘animal’ (so long as we know what we are talking/thinking about).

So when Spinoza, in axiom 5, suggests that we think about things having nothing in common, what he is saying is quite straightforward: a body cannot be understood through a thought or the attribute of thought and a thought cannot be understood through a body or the attribute of extension.

We really want Spinoza to have said something much simpler: if things have nothing in common with one another, then one cannot be the cause of the other: blue can’t be the cause of eclipses. We are in the realm of what Ryle called ‘category errors’. Which in a way is no surprise. The attributes do function somewhat like Aristotelian categories. Extension really is the mechanist version of the attribute of quantity. Thought is not Quality, true. But quantity does not cause quality – that would actually be muddling three categories ! When we consider substance through an attribute, we are saying what kind of substance it is, or what category of substance it is. The attributes function like categories. To try and explain body through thought is a category error. But it’s not an idealist error, we really do have different ‘whatnesses’ of substance.

There is, unexpectedly to me at least, a beautiful description of what the attribute of extension is and how it functions conceptually in Arnauld and Nicole’s Port-Royal Logic:

if I draw an equilateral triangle on a piece of paper, and if I concentrate on examining it on this paper along with all the accidental circumstances determining it, [57] I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the thought that the triangle is a figure bounded by three equal lines, the idea I form will, on the one hand, represent more clearly the equality of lines and, on the other, be able to represent all equilateral triangles. Suppose I go further and, ignoring the equality of lines, I consider it only as a figure bounded by three straight lines. I will then form an idea that can represent all kinds of triangles. If, subsequently, I do not attend to the number of lines, and I consider it only as a flat surface bounded by straight lines, the idea I form can represent all straight-lined figures. Thus I can rise by degrees to extension itself. Now in these abstractions it is clear that the lower degree includes [comprend] the higher degree along with some particular determination, just as the I includes that which thinks, the equilateral triangle includes [comprend] the triangle, and the triangle the straight-lined figure. But since the higher degree is less determinate, it can represent more things (Arnauld and Nicole 1996, pt. I, chap. 5, p. 38; emphasis added).

There’s a very concise statement from Wikipedia that I want to include:

Among the contributions of the Port-Royal Logic is the introduction of a distinction between comprehension and extension, which would later become a more refined distinction between intension and extension.[1] Roughly speaking: a definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa. The main idea traces back through the scholastic philosophers to Aristotle’s ideas about genus and species,[2] and is fundamental in the philosophy of Leibniz (‘Port-Royal Logic’ 2019).

All I really want to point out is that the notion of ‘inclusion’ that Arnauld and Nichole are using is precisely the inverse of the modern set-theoretical idea of inclusion. This actually does my head in quite a lot. I am so used to thinking of inclusion = sub-set, so that the set of equilateral triangles is a sub-set of all triangles, that seeing somebody write it the other way round keeps producing profound cognitive dissonance. But it’s something to be wary of, as I suspect this is way more common that we’d like in the seventeenth century! I wonder if anybody’s been caught out by this? (Badiou sneeze). I suspect, to bring it back to Spinoza that we need to be v. careful with relations such as ‘involves’.

1p2: Two substances having different attributes have nothing in common with one another.

What is this proposition saying? Attributes constitute the essence of substance; which really is a fancy way of saying they say what kind of substance a substance is: is it extended or thinking substance? Of course we will need to slightly qualify this claim once Spinoza shows us that there is only one substance and it is/has all the attributes. But then we can simply move from considering what kind of substance to a more categorial approach; attributes as categories of the one substance. Are we considering substance through the category-attribute of extension or of thought (quantity or quality?). But to borrow from the Port-Royal example, when we consider what it means to be extended, i.e. what the concept of extension entails, then we can say things like ‘being bounded’ ‘having a size’ ‘having a shape’ ‘having a location’ but if we consider the concept of thought then we can only think of intentional concepts that is, ideas. We will never find a concept that plays for both teams. This is what it means to have nothing in common: there are no concepts that include (in the backwards sense that the C17^th uses) both extension and thought.

1p1: A substance is prior in nature to its affections.

As I remarked earlier, this is a crucial claim for Spinoza as he thinks this is true both logically and metaphysically. In fact he thinks it follows straightforwardly (“is evident”) from definitions three and five:

1d3: 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.

1d5: By mode I understand the affections of a substance, or that which is in another through which it is also conceived.

It is worth pointing out, again, just what an abstract notion Spinoza’s definition of substance is. It really is Locke’s “a supposed, I know not what” (Locke 2004, bk. II, chap. XXIII, §15). Spinoza makes this a positive principle however. Of course we don’t know what substance is when we are conceiving it through itself – to think otherwise would be a logical error. If we want to press the button to know more, then we need to add the concept of attribute and then of affection. I suppose Locke could retort that there is a weird inversional misuse of Ryle going on here. Locke’s point is that people who use the term substance are like those who think that there must be a ‘university-I-know-not-what’ remaining after you take away everything that we think belongs-to or makes-up a university. But actually that is to misunderstand just how abstract Spinoza’s notion of substance is. Locke is here confusing substance with modes. It’s quite true that qua modes, if we take away everything that makes up a university, we have no university. But this is a discourse that applies only to modal entities. Substance is not an entity. It is not a being. It is the being of beings. It is being qua being – if we do not think being through any of it’s categories but conceive it purely through itself then we are thinking of substance. This is what it means to have a definition of substance. This is not what it means to have a representation of substance. As Spinoza somewhat sharply points out, just because people cannot form a picture in their brains of an absolutely infinite being i.e. God, does not mean they have no idea of God. To have an idea in this sense is to have a good definition of a thing.

Bibliography

Arnauld, Antoine, and Pierre Nicole. 1996. Logic, or, The Art of Thinking: Containing, besides Common Rules, Several New Observations Appropriate for Forming Judgment. Edited and translated by Jill Vance Buroker. 5th ed., rev. And newly augmented. Cambridge Texts in the History of Philosophy. Cambridge [England] ; New York, NY, USA: Cambridge University Press.

Locke, John. 2004. An Essay Concerning Human Understanding. Edited by Roger Woolhouse. London: Penguin Books.

‘Port-Royal Logic’. 2019. In Wikipedia. https://en.wikipedia.org/w/index.php?title=Port-Royal_Logic&oldid=878443878.

Axioms 1-7 book one

What is an axiom?

One thing Spinoza does not address in the Ethics is the difference between a definition, axiom, or a proposition (scholia, corollaries, and lemmas I will lazily take to be self-explanatory). This does not mean that he never addresses it. The relevant paragraph is from letter 9 to Simon de Vries (March 1663). In it, Spinoza responds to a query de Vries had made in letter 8 about, “the nature of definition” [IV/38]. Spinoza begins by distinguishing two different kinds of definition. The second kind is a hypothetical, or perhaps to borrow a term that Spinoza used a lot, a feigned definition. This need not be true and in fact may have no referent at all (i.e you can define a pegasus, even though one does not, has not, and never will exist). But a true definition defines the essence of some thing (where ‘thing’ is, as ever, understood as widely as possible; by which I mean a ‘thing’ doesn’t have to be a material object). For instance, Spinoza tells us that love is, “[N]othing but joy with the accompanying idea of an external cause” 3p13s. This is a true definition of the essence of love. But it is not given as a definition because it needs to be demonstrated. Spinoza presumably doesn’t bother telling us that his propositions on the affects are telling us what their essences are (though he does tell us in the Preface to book three that he is telling us what the affects’ “nature and powers” are) because he would have thought that this was so obvious as to be not worth saying. Nevertheless, he does say it, once, in the explanation to the sixth definition of the affects:

Love is a joy, accompanied by the idea of an external cause. Exp.: This definition explains the essence of love clearly enough [emphasis added].

In the letter to de Vries, Spinoza goes on to explain the difference between hypothetical and actual definitions. He asks us to consider two different temples: Solomon’s and one he is imagining. Interestingly, but I don’t believe, importantly, his terminology shifts from ‘definition’ [definitionum] to ‘diagram’ [descriptionem].¹ When giving a description of Solomon’s temple, Spinoza has to give a “true description of the temple unless [he wants] to talk nonsense”. But when it comes to his hypothetical temple, then then true and false no longer really properly apply.² To suggest that somebody’s hypothetical diagram of a temple is false, would be equivalent to saying that they have not conceived what they have conceived. One possibility here that Spinoza does not discuss are impossible objects like chimerae or the goat-stag. Although we may say what a goat-stag is, we actually cannot conceive such a thing. The seventeenth century doctrine of ideas does not allow for ideas of contradictory objects. In this, the doctrine of ideas follows in a long Scholastic tradition that had thought about the relationship between signification and conceptualisation. For a thorough and entertaining overview of the Scholastic debates see Ebbesen’s ‘The Chimera’s Diary’ (Ebbesen 1986). After this discussion of the temples, Spinoza goes on to differentiate definitions from axioms and propositions:

So a definition either explains a thing as it is [NS: in itself] outside the intellect—and then it ought to be true and to differ from a proposition or axiom only in that a definition is concerned solely with the essences of things or of their affections, whereas an axiom or a proposition extends more widely, to eternal truths as well—or else it explains a thing as we conceive it or can conceive it—and then it also differs from an axiom and a proposition in that it need only be conceived, without any further condition, and need not, like an axiom [NS: and a proposition] be conceived as true.

Hopefully the time spent explaining eternal truths for 1d7 now pays off. Definitions explain a “thing as it is”. Axioms and propositions can both do this, but they may also explain ‘eternal truths’; which, if you recall, are necessarily true (for different values of necessarily). Axioms (and presumably propositions) have to be conceived of as true – that’s what being an eternal truth means. Definitions though, can be merely conceived, hypothetically or ‘feignedly’ and in that case do not have to be conceived of as true. If we wanted to be schematic about this, we could have this picture:

So that explains the difference between a definition, a proposition and an axiom. A definition may be true or hypothetically-feignedly false. A proposition must be true, but needs proving. An axiom must also be true, but because of its status as an ‘eternal truth’ does not need to be proved because, “if it is affirmative, will never be able to be negative” (Spinoza 1985b, para. 54, fn. u) [II/20].

The axioms:

I’m splitting my discussion of the axioms as they fall into different levels of difficulty of comprehension (and explanation). So I will not discuss them in the order that Spinoza presents them. First I will discuss axioms 1, 2, 5 & 7 as these are pretty straightforward.

Then I will discuss axiom 3 as this is moderately straightforward in that the content of the axiom is easy enough to understand, but the historical context – as in why Spinoza thought it was an eternal truth and why this a very motivated claim – need some lengthy discussion.

Axioms 4 is not too bad, but again needs some historical background so we can understand just what Spinoza is and is not claiming.

Axiom 6 is a problem. There is a perfectly straightforward interpretation of it – which I will give. I just don’t think that this interpretation is right but don’t want to write an article length discussion on why the standard and straightforward interpretation may not be the best one.

Axioms 1, 2, 5 & 7 (the easy ones)

Axioms one and two reconfigure definitions 3 and 5 – those of substance and mode. They are now eternal truths (I guess we need to throw in some caveat about accepting the law of the excluded middle, but I don’t think anybody before the twentieth century thought that it might be problematic).

Axiom 1

Axiom 1 states that, “Whatever is, is either in itself or in another.” As a definition, this would work for both substance and modes. As an axiom, it is an eternal truth because it is asserting that everything is either ‘A or ~A’ where A=in itself and ~A=in another. We might well wonder what this ‘in’ relation is but Spinoza is relying on us knowing that he is only re-describing the definitions of substance and mode (defs., 3 and 5). Substances are ‘in themselves’; modes are ‘in another’ because a mode has to be a mode of a substance. Everything is either a substance or a mode. Therefore everything is either in itself or in another.

Axiom 2

The same goes for axiom 2, “What cannot be conceived through another, must be conceived through itself.” We are still talking about substance and modes, but now we’re talking about how we conceive substance and its modes. We have shifted from the metaphysical register to the logical one. One interesting thing to note: Spinoza doesn’t simply mimic the structure of the previous axiom. He could have written: “Whatever can be conceived must be conceived through itself or through another”. He doesn’t say this. He starts with a negative: what cannot be conceived through another. This matters as what cannot be conceived through another will turn out to be the attributes of substance. We cannot think extension through anything other than extension. We cannot think thought through anything other than thought.

Axiom 7

Axiom 7 continues the axiomatic approach to substance: “If a thing can be conceived as not existing, its essence does not involve existence.” I suppose the surprising thing about this axiom remains that it appears to be making an axiomatic claim, that is that something is an eternal truth, on the basis of what appears to be flimsy psychological grounds. After all, why can’t I conceive God or substance as not existing? It turns out, that there is a long, complicated and, I will claim, still relevant, set of arguments over whether or not you can actually conceive an impossible, or nonsensical thing. A recent adherent to the claim that you cannot, and I realise that this is a slightly left-field reference, is Daniel Dennett in his article, ‘The Unimagined Preposterousness of Zombies’ (Dennett 1995). His point there is that although you can define a zombie-Spinoza as a creature which is physiologically (down to the last sub-atomic particle) indistinguishable from a human-Spinoza, nonetheless that zombie-Spinoza will lack qualia. There will be nothing it is ‘like’ for that zombie-Spinoza. However, zombie-Spinoza will not know that it is a zombie-Spinoza and will always report that it feels things in just the way it imagines others do. Likewise there is no physical test we can do, because, ex hypothesi, it is physically identical to human-Spinoza. At which point Dennett throws his hands up in despair and says, look: you may imagine that you can conceive of such a thing, but you really can’t. This concept is nonsense; it refers to an impossible thing. Note that there is a suppressed, because mutually-agreed-on-by-both-sides premiss, namely that dualism is false. Descartes thinks that animals are zombies. Descartes can think. Descartes can conceive of zombies because he believes that because two things being physically identical does not rule-out them being immaterially dissimilar. Animals lack the souls that humans have, and so, strictly speaking, feel nothing. Nevertheless we can (in a Cartesian world) imagine a human soul being attached to a cat and then that human-souled-cat would really feel things. That HSC would not be a zombie. To return to (human) Spinoza then: somebody may say that they can conceive of a non-existing substance, or that God does not exist but Spinoza will always insist that despite what they say, they actually cannot. They mis-conceive because they have mis-understood. If somebody understands that God is a being who necessarily exists, then they cannot also conceive a God who does not exist. There are a fascinating few paragraphs on this in the Emendation §§53-54 (where Spinoza has the footnote that defines what an eternal truth is) but discussing them would take me even further afield.

Final point: we can flip this axiom around and I think it is even clearer. Spinoza says, “If a thing can be conceived as not existing, its essence does not involve existence.”

But we could also say: “If a thing’s essence involves existence it must be conceived of as existing.” This is clearly an eternal truth because both clauses are stating the same claim about the relationship between essence and existence; that is: we are merely asserting A = A, though admittedly not obviously so. Spinoza is making the equivalent claim in the axiom. Though admittedly, even less obviously so!

Axiom 5

Things that have nothing in common with one another also cannot be understood through one another, or the concept of the one does not involve the concept of the other 1a5.

I prefer this slightly modified translation:

Things that reciprocally have nothing in common, also cannot be reciprocally understood, or the concept of the one does not involve the other [trans slightly modified]

This is a slightly odd axiom, especially given that I’m lumping it in to the ‘easy to understand group’ of the axioms of book one. Rather than try and explicate it on its own, the easiest approach is just to cheat and see where Spinoza uses it. He only uses it only once in the demonstration to 1p3:

1p3: If things have nothing in common with one another, one of them cannot be the cause of the other.

Dem.: If they have nothing in common with one another, then (by 1a5) they cannot be understood through one another, and so (by 1a4) one cannot be the cause of the other, q.e.d.

What does Spinoza mean by ‘in common’? He tells us this in 1p2:

Two substances having different attributes have nothing in common with one another 1p2.

So what 1p3 is saying is this:

Consider two substances.

Substance-E has the attribute of extension (only).

Substance-T has the attribute of thought (only).

Then substance-E and substance-T have nothing in common (they do not have some third attribute, ‘Henry’ by which they could have something in common).

Then substance-E cannot be the cause of substance-T and vice versa.

How does this help us understand 1a5? As:

1) having something in common means sharing an attribute and

2) attributes are what the intellect perceives as constituting the essence of a substance and

3) “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” 1d3

then

4) attributes also do not need another concept to be understood

5) Which means that when thinking about extension, I do not need thought and vice versa; this is an informal way of saying what Spinoza actually says which is: “the concept of the one does not involve the concept of the other”.

6) But as there is this complete conceptual separation of the attributes, then one cannot be understood through another. How could they, as there is no common concept?

This does kind of feel like I’ve had to demonstrate the truth of axiom 5, but it can be understood on its own so long as already know how strong this idea of ‘nothing in common’ is. Once we realise this is really talking about the attributes and attriubtes are conceptually primary and independent of one another, then axiom 5 does feel like an eternal truth.

OK, so that’s axioms, 1,2 & 5, 7. The easy ones. What about the other three?

Axioms 3, 4 & 6 (the stranger & harder ones)

Axiom 3

From a given determinate cause the effect follows necessarily; and conversely, if there is no determinate cause, it is impossible for an effect to follow.

Surely this is an easy one too? Well, it is easy to understand, yes. What makes it hard, is not the content, but the context. Spinoza is being a little sneaky in making this an axiom. Sneaky may be the wrong word. It’s half sneaky and half overt provacative intervention.

I will explain why.

This axiom is as close to a statement of the principle of ‘sufficient reason’ where reasons, are of course, causes (slightly unnecessary reference to that closet Spinozist Davidson (1963)) as we will find in the Ethics. Is this an eternal truth? After the discovery of radioactive decay and its inherently quantum-mechanical-probabilistic nature … well let’s just say that when Einstein said, “God does not play dice.” This was his most Spinozistic moment; sadly wrong. So today at least we can no longer hold to the principle of sufficient reason or cause as applying universally. But what of the seventeenth century? Well before pushing it back that far, let’s consider an intermediate but well-known figure: Hume:

When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. We only find, that the one does actually, in fact, follow the other. The impulse of one billiard-ball is attended with motion in the second. This is the whole that appears to the outward senses. The mind feels no sentiment or inward impression from this succession of objects: Consequently, there is not, in any single, particular instance of cause and effect, any thing which can suggest the idea of power or necessary connexion (Hume 2007, VII [6]).

Hume’s critique of the conceptually necessary connection between cause and effect is well-known. It is what legendarily prompted Kant out of his dogmatic slumbers and made him postulate causation (and dependence) as one of the twelve categories of the understanding (grouped under relation with ‘inherence and subsistence’ and community [reciprocity between agent and patient]) (Kant 1999, [A80/B106]).³ Hume’s claim, following the empiricist line laid down by Locke, is that Ideas are utterly dependent upon impressions (though presumably not causally dependent). If we do not have an impression of something, then unless we can form the idea out of other ideas, then we cannot have that idea and so we do not have knowledge. Do we have an impression of the causal relation? Hume claims we do not. All we see is one ball moving, striking a second and then the second ball moving. What we don’t see is the power, force, impetus, or necessary connection between these two events. Now Hume is not the first to break with the idea that there is a necessary connection between causes and events. He is probably just the most familiar. On the topic of causality, Hume has sometimes been described as a “Malebranche without God”, or “occasionalism without God”. Malebranche (1638-1715 – so born just six years after Spinoza, dies a year before Leibniz does), was an occasionalist. Malebranche certainly knew of Spinoza (see Getchev 1932). There is no evidence that I’m aware of that Spinoza knew of Malebranche. So how could Spinoza have known about occasionalism and why would he need to deny it’s truth in the form of an axiom? Occasionalism is not a doctrine that Malebranche invents. The claim that between cause and effect there is no necessary connection goes back to al-Ghazali and his attack on the Falasafia – the Muslim-Aristotelian philosophers, especially Ibn Sīnā (Avicenna). Here is al-Ghazali in his work, The Incoherence of the Philosophers:

The connection between what is habitually believed to be a cause and what is habitually believed to be an effect is not necessary, according to us […] Their connection is due to the prior decree of God, who creates them side by side, not to its being necessary in itself, incapable of separation. On the contrary, it is within [divine] power to create satiety without eating, to create death without decapitation, to continue life after decapitation, and so on to all connected things (Ghāzālī 2009, 166 [Seventeenth discussion §1]; emphasis added).

and:

As for fire, which is inanimate, it has no action. For what proof is there that it is the agent? They have no proof other than observing the occurrence of the burning at the [juncture of] contact with the fire. Observation, however, [only] shows the occurrence [of burning] at [the time of the contact with the fire] but does not show the occurrence [of burning] by [the fire] and [the fact] that there is no other cause for it (Ghāzālī 2009, 167 [Seventeenth discussion §5]).

Occasionalism, in the figure of Malebranche (1997, 2013) is very much a live possibility in the seventeenth century. Could Spinoza have simply been ignorant of it in all it’s historical forms? This seems exceedingly unlikely. There is scholarly debate over the extent to which Maimonides (whom Spinoza definitely knew well) either knew or engaged with al-Ghāzālī’s work (Stroumsa 2009; cited in Pessin 2016). But perhaps the simplest point to make is this: you don’t bother having an axiom asserting a thing, when that thing is actually completely beyond doubt. If a lack of necessary connection between cause and effect was so unthinkable, then it would have been unnoticeable and so, unsaid. Is there more to be said? does Spinoza ever deal directly with occasionalism? I need to back up a bit here. The short answer is yes he does, but never in a, “So this is why occasionalism is wrong” kind of way. I need to back up and explain a bit about occasionalism, specifically the problem it is sort of a solution to because there is actually a one really important overlap in the philosophical preconceptions between occasionalists and Spinoza.

What’s occasionalism all about when you get right down to it really?

This is actually a simple one to answer: God’s omnipotence. As God is omnipotent, then there isn’t any ‘room’ metaphysically speaking for a finite object to act. It’s all been ‘crowded out’ by God’s own mightiness. There’s an important sense in which, for Aristotelian Western monotheism, one way of thinking about God is as infinite act(ing/ion). It’s also the case that for many occasionalists, from al-Ghāzālī onwards, they also want to preserve the possibility of God intervening miraculously in the world and they recognise that if finite corporeal beings act and act according to necessary physical laws, then miraculous intervention seems to make less sense.

Why do occasionalists from al-Ghāzālī to Hume always start with an epistemic claim? : you don’t actually see causation. There’s a certain simple sense in why epistemology trumps ontology. If I claim that there are no birds and you go – but “Tweetie Pie!” – I’m either going to have to admit that there are birds, or argue as to why Tweetie Pie is not a bird. Al-Ghāzālī and Hume both, first, have to argue that we do not in fact have knowledge of necessary causal relations before they can then claim that there are no such relations.

If we take God’s omnipotence seriously, then it may seem – or at least it did seem – that we only have two options. The first one is occasionalism: what appears to be corporeal actions simply is God moving stuff about. The second one, is Aquinas’s ‘concurrentism’ (see for example, Dvořák 2013). Concurrentism says that we do act, as does God, but at the same time – hence ‘concurrentism’. Spinoza offers a third choice – that may perhaps seem to be more similar to Aquinas than it actually is. The reason why Spinoza can offer a third option is that he denies an implicit presupposition that both occasionalists and concurrentists share: that God is transcendent, in the sense of a transitive cause, and immaterial. Spinoza’s God is an immanent cause. It’s sometimes said that Spinoza reduces everything to God. Bayle’s famous assessment:

Thus, in Spinoza’s system all those who say, “The Germans have killed ten thousand Turks,” speak incorrectly and falsely unless they mean, “God modified into Germans has killed God modified into ten thousand Turks,” (Bayle 1991, 312)

is the epitome of this kind of approach. Spinoza’s point is that the first sentence is not incorrect but that it is strictly equivalent to the second. To the charge that everything is ‘reduced to God’ Spinoza can reply: no, that’s occasionalism. To the idea that his is therefore a theory of concurrentism, he can say: not exactly, it is not the case that God acts concurrently with your action, but that your action and God’s action are the (numerically) one and the same action but understood from different perspectives. Neither occasionalist nor concurrentist, Spinoza’s immanent cause is a new solution to the problem of finite freedom and infinite power.

A note for later: Kristin Primus’s thesis Causal Independence and Divine Support in Spinoza and Leibniz (Primus 2013) deals with this issue. Importantly she argues that the dialogue in Spinoza’s Short Treatise (Spinoza 2002a) is dealing with this very problem.

But really, this needs to be looked at more closely later.

To wrap up this axiom:

We might unreflectively think that an axiom asserting the existence of causal relations would be unproblematic. But whether it’s contemporary discoveries like the probabilistic nature of quantum mechanics, or the philosophical tradition of occasionalism, we can’t take this axiom as self-evident.

It only becomes self-evident once a few more pieces of the Spinozist framework are in place: the idea of an immanent cause, the idea that God acts from the necessity of his own nature, the rejection of free-will and the ideas of contingency and possibility, and possibly some other stuff too, but they’re the obvious main ones.

Perhaps the best way to read this axiom is as a deliberate staking out of philosophical territory or an Althusserian-style intervention. Either way it is fighting talk for an eternal truth.

Axiom 4

The knowledge of an effect depends on, and involves [involvit], the knowledge of its cause 1a4.

Effectus cognitio a cognitione causae dependet et eandem involvit

So many decisions are being made and questions ignored in this straightforward translation of 1a4. What kind of cause is Spinoza thinking of? If it is an efficient cause, then translating effectus as effect is perfectly fine. If, on the other hand, the cause is a formal cause,⁴ then, although formal causes do have effects, these effects are more like results or conclusions than physical effects. What does Spinoza mean by ‘involves’? Deleuze, for one, will read this as part of Spinoza’s logic of expression: complicating, explicating, implicating. But for the sake of my sanity, I’m going to read ‘involves’ as meaning something less obscure. ‘Implies’ is often what it means. This strengthens the claim that we are not necessarily dealing with a claim about the epistemology of physical systems. Spinoza’s axiom needs to be put in the context of Aristotelian claims about knowledge more broadly. There is a fascinating book, Mancosu’s (1996) Philosophy of mathematics and mathematical practice in the seventeenth century. It starts with a discussion of the historical debate around the status of mathematical proof. How could mathematical demonstration fit within the paradigm of Arisotelian science? This paradigm was built around the syllogism.

We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows, when we think that we know the cause on which the fact depends, (10) as the cause of that fact and of no other, and, further, that the fact could not be other than it is […] What I now assert is that at all events we do know by demonstration. By demonstration I mean a syllogism productive of scientific knowledge, a syllogism, that is, the grasp of which is eo ipso such knowledge. Assuming then that my thesis as to the nature of scientific knowing is correct, (20) the premisses of demonstrated knowledge must be true, primary, immediate, better known than and prior to the conclusion, which is further related to them as effect to cause Posterior Analytics I,2 (Aristotle 2001; final emphasis added).

Mancosu goes on to explain:

It is immediately evident that the requirements set down on the premisses-conclusion relation are much stronger than simple logical consequence. In particular, there are several valid forms of inference that do not yield, in Aristotle’s theory, scientific knowledge. In Posterior Analytics 1.13 Aristotle introduced an important distinction between two types of demonstrations—demonstrations tou hoti and tou dioti—which are translated as demonstration ‘of the fact’ and demonstration ‘of the reasoned fact’. In the later Latin commentaries they were often called demonstratio quia and demonstratio propter quid. The former proceeds from effects to their causes, whereas the latter explains effects through their causes. Aristotle gives the following examples. Suppose one wants to prove that the planets are near the earth. One could argue as follows:

The planets do not twinkle.

What does not twinkle is near the earth.

Therefore, the planets are near the earth.

This demonstration, says Aristotle, is a demonstration of the fact but not of the reasoned fact. Indeed, he explains, the planets are not near the earth because they do not twinkle, but they do not twinkle because they are near the earth. In this case we can reverse the major and the middle of the proof so as to obtain a proof of the reasoned fact.

What is near the earth does not twinkle.

The planets are near the earth.

Therefore the planets do not twinkle.

The second type of syllogism is superior to the first, according to Aristotle, because in it an affection (not twinkling) is predicated of a subject (the planets) through a middle term (being near the earth) which is the proximate cause of the effect (Mancosu 1996, 11).

Are we definitely in the realm of the Aristotelian syllogism? No, not definitely. Ascribing Aristotelianism to Spinoza is always tricky. But I think it makes sense to read Spinoza, if not explicitly appealing to a syllogistic account of scientific explanation (that would be taking things too far), then at least being in the ballpark where to understand an effect-result means understanding the implicative reasons stemming from the cause of that effect-result.

Axiom 6

A true idea must agree with its object [ideato]

Fair warning: I think I am about the only person who doesn’t think that this is a straightforward definition of a correspondance theory of truth. It does, I admit, look like a correspondance theory of truth, but a big part of that comes from translating ‘ideato’ as ‘object’ and ‘convenire’ as ‘agree’. Again, full disclosure: everybody (in the English translation) does and only Shirley flags that there might be something odd about this by leaving ‘ideatum’ in the Latin:

A true idea must agree with that of which it is the idea (ideatum) (Spinoza 2002b, 218).

Idea vera debet cum suo ideato convenire [II/47].

I don’t have a fully worked out replacement for this axiom giving us a correspondance theory of truth; nor do I have an absolute knock-down argument as to why it is not. I’m going to restrict this discussion to a list of points for consideration:

1. This isn’t a definition of truth.⁵ It is an axiom telling us what a true idea must do.

2. ‘ideatum’ is an odd bit of scholastic terminology and mostly means the product of another (divine) idea – we could translate it as ideation

3. ‘convenire’ again has a technical history in scholastic philosophy, Heereboord and Burgersdijk use it in a logical context to mean ‘the same’ or ‘identity’

4. what makes this really tricky is how this axiom interacts with other moments in the Ethics, especially the definition of adequate idea in 2d4

5. and that raises a whole new set of questions – especially about the difference, or not, between ‘objectum’ and ‘ideatum’

6. 1a6 is used in the following six places: 1p5dem, 1p30dem, 2p29dem, 2p32dem, 2p44dem, 2p44c2dem

7. we can’t truly understand what Spinoza means in this axiom without looking at those six uses, and that would take me too far afield

So I’m going to leave this axiom there. It may be a statement of a correspondance theory of truth, but if it is, it’s an odd one.

Bibliography

Aquinas, Thomas. 1998. ‘Disputed Question on Truth, 1’. In Thomas Aquinas: Selected Writings, edited and translated by Ralph McInerny. London; New York: Penguin Books. https://www.overdrive.com/search?q=39FD7D27-A542-4EAD-A41B-FADCDBE199DD.

Aristotle. 2001. The Basic Works of Aristotle. Translated by Richard McKeon. The Modern Library Classics. New York: Modern Library.

Bayle, Pierre. 1991. Historical and Critical Dictionary: Selections. Translated by Richard H. Popkin. Hackett Publishing.

Burgersdijk, Franco Petri. 1640. Institutionum metaphysicarum. Amsterdam: apud Hieronymum de Vogel.

———. 1701. An Introduction to the Art of Logick. Translated by Anon. London: T. Ballard, at the Rising Sun in Little Britain.

Davidson, Donald. 1963. ‘Actions, Reasons, and Causes’. The Journal of Philosophy 60 (23): 685–700.

Dennett, Daniel C. 1995. ‘The Unimagined Preposterousness of Zombies’. Journal of Consciousness Studies 2 (4): 322–26.

Dvořák, Petr. 2013. ‘The Concurrentism of Thomas Aquinas: Divine Causation and Human Freedom’. Philosophia 41 (3): 617–34. https://doi.org/10.1007/s11406-013-9483-9.

Ebbesen, Sten. 1986. ‘The Chimera’s Diary’. In The Logic of Being: Historical Studies, edited by Simo Knuuttila and Jaakko Hintikka, 115–43. Dordrecht: D. Reidel Publishing Company.

Getchev, George S. 1932. ‘Some of Malebranche’s Reactions to Spinoza as Revealed in His Correspondence with Dourtous de Mairan’. The Philosophical Review 41 (4): 385–94. https://doi.org/10.2307/2179800.

Ghāzālī, Abū-Ḥāmid Muḥammad Ibn-Muḥammad al-. 2009. The incoherence of the philosophers =: Tahāfut al-falāsifa. Translated by Michael E. Marmura. 2. ed. Islamic translation series. Provo, Utah: Brigham Young Univ. Press.

Hübner, Karolina. 2015. ‘On the Significance of Formal Causes in Spinoza’s Metaphysics’. Archiv Für Geschichte Der Philosophie 97 (2): 196–233. https://doi.org/10.1515/agph-2015-0008.

Hume, David. 2007. An Enquiry Concerning Human Understanding. Edited by P. J. R. Millican. Oxford: Oxford University Press.

Kant, Immanuel. 1999. Critique of Pure Reason. Edited and translated by Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.

Macherey, Pierre. 2001. La premières partie, la nature des choses. Vol. I. V vols. Introduction à l’éthique de Spinoza. Presses Universitaires de France – PUF.

Malebranche, Nicolas. 1997. Elucidations of the Search After Truth. Edited and translated by Thomas M. Lennon and Paul J. Olscamp. Cambridge Texts in the History of Philosophy. Cambridge ; New York: Cambridge University Press.

———. 2013. Dialogues on Metaphysics and on Religion. Translated by Morris Ginsberg. Abingdon, Oxon ; New York, NY: Routledge.

Mancosu, Paolo. 1996. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. New York ; Oxford: Oxford University Press.

Parkinson, George Henry Radcliffe. 1977. ‘“Truth Is Its Own Standard”: Aspects of Spinoza’s Theory of Truth’. Southwestern Journal of Philosophy 8 (3): 35–55.

Pessin, Sarah. 2016. ‘The Influence of Islamic Thought on Maimonides’. In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Spring 2016. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2016/entries/maimonides-islamic/.

Primus, Kristin. 2013. ‘Causal Independence and Divine Support in Spinoza and Leibniz’. http://dataspace.princeton.edu/jspui/handle/88435/dsp01h415p966c.

Robinson, Lewis. 1928. Kommentar zu Spinozas Ethik. Leipzig: F. Meiner.

Sangiacomo, Andrea. 2016. ‘Aristotle, Heereboord, and the Polemical Target of Spinoza’s Critique of Final Causes’. Journal of the History of Philosophy 54 (3): 395–420. https://doi.org/10.1353/hph.2016.0061.

Spinoza, Benedictus de. 1985a. The Collected Works of Spinoza, Volume I. Translated by Edwin M. Curley. Vol. 1. 2 vols. Princeton: Princeton University Press.

———. 1985b. ‘Treatise on the Emendation of the Intellect’. In The Collected Works of Spinoza, translated by Edwin M. Curley, I:7–45. Princeton: Princeton University Press.

———. 2002a. ‘Short Treatise on God, Man, and His Well-Being’. In Spinoza: Complete Works, edited by Michael L. Morgan, translated by Samuel Shirley, 31–107. Cambridge: Hackett.

———. 2002b. Spinoza: Complete Works. Edited by Michael L. Morgan. Translated by Samuel Shirley. Cambridge: Hackett.

———. 2016. The Collected Works of Spinoza, Volume II. Translated by Edwin M. Curley. Vol. 2. 2 vols. Princeton: Princeton University Press.

Stroumsa, Sarah. 2009. Maimonides in His World Portrait of a Mediterranean Thinker. Jews, Christians, and Muslims from the Ancient to the Modern World. Princeton, N.J.: Princeton University Press.

Notes

 

1 Curley has ‘description’ here, but, given what Spinoza goes on to say, ‘diagram’ or ‘plan’ is a more apt word than the non-descriptive ‘description’.

2 When it comes to a temple, a thing’s definition-diagram, is what it takes to make a temple and this really is not so different from the non-artificial example of love (or any of the other affects); what Spinoza’s definition of love gives us, is a causal account of the production of love.

3 Doctrine of Elements. Pt. II. Div. I. Bk I. Ch. I

4 [A] formal causal relation is the relation between the essence of a thing and the necessary properties inferable from that essence. Causality so understood thus has to do first and foremost with the essential natures of things, and their implications, rather than with bodies entering into collisions according to certain laws […] Spinoza’s views about explanation and intelligibility are also best approached through the lens of this formal-causal model (Hübner 2015, 197).

5 The only person I’ve read who has picked up on this point is Macherey. In the first volume of his Introduction à l’éthique de Spinoza, he comments on Axiom 6 that:

“Il faut surtout noter que cet énoncé, ainsi compris, n’est pas une définition de la vérité” (Macherey 2001, I:60).

“It is important to note that this statement, thus understood, is not a definition of the truth.”

1d8

By eternity I understand existence itself, insofar as it is conceived to follow necessarily from the definition alone of the eternal thing.

Exp.: For such existence, like the essence of a thing, is conceived as an eternal truth, and on that account cannot be explained by duration or time, even if the duration is conceived to be without beginning or end.

Per aeternitatem intelligo ipsam existentiam, quatenus ex sola rei aeternae definitione necessario sequi concipitur.

Explicatio. Talis enim existentia ut aeterna veritas, sicut rei essentia, concipitur, proptereaque per durationem aut tempus explicari non potest, tametsi duratio principio et fine carere concipiatur.

So many questions. I’m not going to start with the definition itself, but with a question that plagued me for years about the explanation, and given that I have a possible answer, I feel I should share, rather than make anybody else suffer. What the hell does Spinoza mean by an eternal truth? Is this sense of ‘eternal’ the same as eternity? What is, for want of a better phrase, the ‘existential import’ of eternal truths? Are they things? Spinoza will tell us that, “For in the nature of things nothing is given except substances and their affections” 1p6c [translation slightly modified]. Does that mean an eternal truth is an affection of substance? an idea in/of God? It would have been nice, whilst Spinoza was defining things, to have defined ‘eternal truth’. Luckily, he does give us a definition, only not in the Ethics. In a footnote to the unfinished Treatise on the Emendation of the Intellect, Spinoza writes:

By an eternal truth I mean one, which, if it is affirmative, will never be able to be negative. Thus it is a first and eternal truth that God is [esse]; but that Adam thinks is not an eternal truth. That there is no Chimera is an eternal truth; but not that Adam does not think (Spinoza 1985b, para. 54, fn. u). [II/20]

Per aeternam veritatem talem intelligo, quae, si est affirmativa, nunquam poterit esse negativa. Sic prima et aeterna veritas est Deum esse, non autem est aeterna veritas Adamum cogitare. Chimaeram non esse est aeterna veritas, non autem Adamum non cogitare.

It’s tempting, but misleading to collapse eternal truths into analytic truths. The temptation comes from Spinoza’s frequent allusion to triangles: “the concept of a triangle involves [implies] that its three angles are equal to two right angles” (Spinoza 1985a, [I/158]). The reason that I’m hesitating is that, and this is a very fine(in both fine’s senses: both pretty and precise) distinction I wish to make. 1) Whereas the classic analytic statement, “All bachelors are unmarried men” invokes some idea of synonymy (with all the Quniean-caveats in mind) that the three internal angles of a triangle sum to two right angles seems to not so much be a case of synonymy as a result that needs to have been demonstrated. 2) Similarly it is because the concept of a chimera is inherently self-contradictory that one cannot exist. 3) When we consider the concept of ‘Adam’ does thinking necessarily follow? No, because at some point there may be no Adam thinking (it is unclear whether by this Spinoza means that Adam may not be, and therefore does not think, or because Adam may be doing something other than thinking – and what that other thing would be, dreaming or imagining? There is a tricky post-Cartesian debate over whether minds can not-think). 4) Fourth example: it is because the concept of God’s essence involves existence that he necessarily exists. 5) Final example and this is a particularly tortured bit of prose:

This intellectual love follows necessarily from the nature of the mind

insofar as it is considered as an eternal truth, through God’s nature 5p37dem

Hic intellectualis amor ex mentis [f.gen] natura [f.nom] necessario sequitur,

quatenus ipsa [f.nom] ut aeterna veritas per Dei naturam consideratur

I’ve left the Curley translation, as is, because sometimes it helps to work from a strictly literal translation so that when I start to muck about with it, we can all see what liberties I’ve taken in order for it to make a bit more sense. I’ve split this (first sentence of the) demonstration into two because the first part is absolutely clear. It is what is going on in the second half of the sentence that I think needs some clarification. The problem with this second half of the sentence is that it doesn’t quite fit the model of how the other examples of eternal truth work. The problem is what is that final clause of ‘through God’s nature’ doing? For instance, this formulation:

It is an eternal truth that, from the nature of the mind, intellectual love necessarily follows

fits the ‘concept of a triangle’ model. Except that this, by itself, is not strictly true (and therefore definitely not a candidate for eternal truth!). This is why Spinoza adds the ‘through God’s nature’ clause. Think of it like somebody who adds “but only in a Euclidean plane” to the claim that the internal angles of a triangle add up to two right angles. It is only because God loves himself with an infinite intellectual love, our minds are a part of God’s infinite intellect and therefore also partake in this infinite intellectual love, that from the nature of the mind intellectual love follows. I think we can rewrite the demonstration like this:

From the nature of the mind, considered through the nature of God, that intellectual love necessarily follows, is an eternal truth.

Right, so this discussion of eternal truth has taken me a long way away from the definition I am supposed to be discussing. So then, back to the definition:

By eternity I understand existence itself, insofar as it is conceived to follow necessarily from the definition alone of the eternal thing.

There’s a great article by Yitzhak Melamed (2016) ‘Eternity in Early Modern Philosophy’ (to be fair pretty much any article by Melamed on Spinoza is great) which does two important things. First, it takes seriously the claim that Spinoza makes, that his understanding of eternity really does have nothing to do with time. It’s fascinating how people can fail to read what is right there in front of them because they know what is right there in front of them cannot be saying what it says. There’s a (fortunately) small body of literature arguing over whether or not Spinoza’s concept of eternity could be sempiternal (ever-lasting) or atemporal in the sense of outside of time. I’m not linking to it, because Spinoza is as explicit and clear as it is possible to be: his concept of eternity has nothing to do with duration or time, not even “if the duration is conceived to be without beginning or end”. The only thing to remark on here, is that Spinoza does distinguish between duration and time, but this distinction is not explained until book two (duration is defined in 2d5, time is sort of explained in 2p44s as a consequence of our imagination of motion). Secondly it shows how this definition of eternity was used, in the sense that Spinoza gives it, by philosophers immediately after Spinoza. Following / repeating Melamed, I think we can say that ‘eternity’, ‘eternal thing’ and ‘eternal truth’ all carry the same import: that of necessity. Some have charged Spinoza with circularity in this definition, deriving a concept of eternity from that of the eternal thing. But the only ‘thing’ that has this property of its existence following necessarily from its definition is whatver may fit the definition of cause-of-itself in 1d1 (“By cause of itself I understand that whose essence involves existence, or that whose nature cannot be conceived except as existing.”). Although, yes, of course, this is going to turn out to be God, we don’t yet know this. The definition of 1d6, does not actually tell us that God’s essence involves existence. Spinoza has to show that in later propositions. So we can, via a simple substitution rewrite 1d8:

By eternity I understand existence itself, insofar as it is conceived to follow necessarily from the definition of ‘cause of itself’ i.e. in the case where a thing’s essence necesssarily involves existence, we could say its essence involves eternity instead.

Eternity is ‘essentially necessitated existence’. Later on in the Ethics we’re going to meet a term: ‘species of eternity’ which will need to be added to this discussion of eternity, eternal thing, and eternal truth, but I don’t want to deal with that now.

Melamed, Yitzhak Y. 2016. ‘Eternity in Early Modern Philosophy’. In Eternity, edited by Yitzhak Y. Melamed, 129–67. Oxford University Press.

Spinoza, Benedictus de. 1985a. ‘Descartes’ Principles of Philosophy’. In The Collected Works of Spinoza, translated by Edwin M. Curley, I:224–98. Princeton: Princeton University Press.

———. 1985b. ‘Treatise on the Emendation of the Intellect’. In The Collected Works of Spinoza, translated by Edwin M. Curley, I:7–45. Princeton: Princeton University Press.

1d7

That thing is called free which exists from the necessity of its nature alone, and is determined to act by itself alone. But a thing is called necessary, or rather compelled, which is determined by another to exist and to produce an effect in a certain and determinate manner.

Ea res libera dicitur, quae ex sola suae naturae necessitate existit et a se sola ad agendum determinatur; necessaria autem vel potius coacta, quae ab alio determinatur ad existendum et operandum certa ac determinata ratione.

Not my favourite definition (not sure I have a favourite definition, but the next one is pretty great). One of the hurdles to Spinozism – one that Spinoza was himself well-aware of, is his absolute necessetarianims and determinism. There no sense to somebody claiming, “I could have done that differently.” Or, “I could have done otherwise.” That is his determinism.  Not only can we not ‘do otherwise’, the entire universe has to be the way it is and could be no other way. This is his necessetarianism. So obviously no free-will. But this is the Ethics. So not so obviously no freedom; what would be the point otherwise? We must not confuse fatalism with determinism. Fatalism says: whatever you do, it will turn out the same (the lazy corollary being: so do nothing, why bother it can make no difference). Determinism on the other hand says: whatever you do will have some effect, so choose wisely.

The obvious problem with this definition, though, is that it appears to make the bar for calling something ‘free’ way too high. In fact, the only thing, given this definition of freedom, that is absolutely free, is God. Modes on the other hand, at least all finite modes (and as we are finite modes, we only really care about them for now), cannot not be determined to act. Calling this ‘necessary’ wouldn’t itself necessarily be a problem. Compatibilism simply is the claim that freedom and necessity go together. Spinoza is, I would argue, a compatibilist. But this claim that your actions are not merely necessary but forced, compelled or constrained (all possible translations of ‘coacta’) is really unpalatable. The big question then, is: will Spinoza ameliorate, change, or refine this definition later on in the Ethics to allow for finite freedom, or not?

1p6

P6: One substance cannot be produced by another substance.

Dem.: In Nature there cannot be two substances of the same attribute (by 1p05), that is (by 1p02), which have something in common with each other. Therefore (by 1p03) one cannot be the cause of the other, or cannot be produced by the other, q.e.d.

Una substantia non potest produci ab alia substantia.

Demonstratio. In rerum natura non possunt dari duae substantiae ejusdem attributi (per prop. praeced.), hoc est (per prop. 2.), quae aliquid inter se commune habent. Adeoque (per prop. 3.) una alterius causa esse nequit, sive ab alia non potest produci. Q.e.d.

Don’t want to make too big a deal of this, but think it’s worth pointing out, as it’s something I missed with regard to 1p5. 1p5 and the demonstration to 1p6 both open with the phrase,

In rerum natura

now I can’t but hear “De rerum natura” because that’s the kind of thing I look out for. The English translations really obscure this, Curley has, “In nature”; Kisner has “in the universe” (bleurgh); Eliot just misses this phrase out altogether. Now I can see why, from the point of view of a translator that you’d be tempted to have it as “In nature” as it reads better than a more literal translation which would be:

In the nature of things there cannot be two substances of the same attribute

But why wouldn’t you want to keep a possible Lucretius reference alive in the English?

OK. So the first thing to remember is that I don’t think that Spinoza has quite shown what he wants to show in 1p5. 1p5 says that, “In Nature there cannot be two or more substances of the same nature or attribute” and if you recall I gave this example:

substance A with attributes C & D

substance B with attributes D & E

to show how we could have two substances that were distinguishable by their attributes and yet shared one. So all Spinoza has really shown is that, “In Nature [the nature of things] there cannot be two or more substances with ONLY the same nature or attribute(s)”. So the question is, does 1p6 still follow? Well it does, and at first I thought that the initial demonstration didn’t work, but the alternative one probably does. Now I think that the alternative demonstration in the corollary is tricksy but the initial one is fine. Let me explain. So the reason I was initially hesitant about the demonstration to 1p6 is that I was thinking too much about 1p5 and how this complicates the proof. But 1p2 and perhaps even more so 1p3 are just as important. Consider my example of substances A & B. Can substance A produce substance B? Well they do have something in common with one another – attribute D, but substance B has attribute E, which substance A does not; this means, by 1p2 and 1p3 that substance A can’t produce substance B. It doesn’t have the right stuff. Note that giving substance A both attributes D & E doesn’t help as then substance B can’t be distinguished from substance A, so we’d be supposing that substance A produces something that is and is not different from itself; and that’s a reductio ad absurdum. Even though, as I said, I wasn’t initially too sure that the proof works, as it stands, I thought it Spinoza thought it held because of a suppressed premise that was the kind of thing that he would have thought such a commonplace that there was no need to have it as an axiom, namely:

For things that come to be from external causes—whether they consist of many parts or of few—owe all the perfection or reality they have to the power of the external cause 1p11s

This would also rule out my scenario of substance A producing substance B (because to produce a substance with any particular attribute, the producing substance must have that attribute), but, as I hope I’ve shown, Spinoza actually doesn’t need to appeal to this idea for his proof to work. All he needs is 1p2 and 1p3 working in concert.

Cor.: From this it follows that a substance cannot be produced by anything else. For in Nature there is nothing except substances and their affections, as is evident from 1a1, 1d3, and 1d5. But it cannot be produced by a substance (by 1p06). Therefore, substance absolutely cannot be produced by anything else, q.e.d.

Alternatively: This is demonstrated even more easily from the absurdity of its contradictory. For if a substance could be produced by something else, the knowledge of it would have to depend on the knowledge of its cause (by 1a4). And so (by 1d3) it would not be a substance.

The first part of the corollary seems pretty straightforward. A substance cannot be produced by anything else, because as Spinoza points out, all that there is, is substance and their affections but we can rule out affections as they are posterior to their substances, and we’ve just shown that a substance cannot be produced by another substance. Q.E.D. The alternative demonstration I think holds, but only because of Spinoza’s absolute realism when it comes to the definitions. How does the argument hold? Spinoza maps a relationship of production to a relationship of implication; one substance produces another, one substance implies another – and this latter idea contradicts Spinoza’s definition of a substance, so the idea that a substance could produce another is also contradictory nonsense.

1d4

By attribute I understand what the intellect perceives of a substance, as constituting its essence.

Per attributum intelligo id, quod intellectus de substantia percipit tanquam ejusdem essentiam constituens.

It’s funny how some secondary-literature philosophical arguments die. It’s almost never because the position that spawned them, or the problem that generated them disappeared or was refuted; it’s more like everybody gets bored and stops talking about it.

Spinoza’s theory of the attributes has seemed problematic to his readers ever since the seventeenth century. The problem is usually presented as a matter of choosing between two alternatives, the “objective interpretation” and the “subjective interpretation”, and it is notorious in Spinoza studies: Francis S. Haserot calls it “The schism that cuts deepest into the interpretation of Spinoza”.¹ Objectivists see the attributes as inherent characteristics of substance, revealing its real nature; subjectivists see them as the result of the way in which substance is apprehended, reflecting just the apprehending intellect and not the real nature of substance. There are many different formulations of both positions (Mark 1977, 55).

But, and I think that this is more the case here, it’s not the case that everybody got fed up and moved on. It’s more the recognition that what may have appeared to be one long continuous argument really wasn’t. Mark suggests that there are two main stumbling blocks to getting past the objective/subjective debate. The first is seeing the attributes as a kind of property. The second is seeing them as “representational entities”. The second in particular points out how, when Spinoza discusses the relationship between mind and body, he refers to them being, “one and the same thing, but expressed in two ways” 2p7s. Mark points out that this kind of terminology leaves open the question of what that thing is, that is being expressed; that when we talk of something being an expression, the natural thing to do is to wonder what it is an expression of. Once this move has been made, then the relationship of expression appears to be a representative one, “an intentional or sematic gap is set up between them [the mind and body and what they are expressions of]” (Mark 1977, 60). The definition of the attribute, as “what the intellect perceives” also seems to open up this question. Could the intellect be wrong? Could we be mis-perceiving the attributes? Defenders of the objective view say no, because this is the intellect we are using in the definition. But whether we agree with the response or not, both objective and subjective responses to this question agree that the question makes sense; they disagree only over their respective answers. As Mark wishes to show, this approach is quite wrong. This “gap” isn’t the only reason why people are muddled about the attributes. Mark also suggests that one reason why the argument has been so protracted is that attributes are seen as properties. He points out that if they are, then the question of whether they are accidental, or essential properties, should be answerable. They cannot be accidental because they are necessary. But they’re not essential either because each attribute is sufficient and complete in itself. Mark concludes that this contradiction means that they simply are not properties at all.

I really like Mark’s paper, and it has been hugely influential on my reading of the attributes for many years. But despite agreeing with both of his conclusions: that 1) the attributes are not properites (though this is more complicated than Mark realises, a point I’ll return to shortly) and that 2) there is not any kind of “gap” between substance and its expressions, we need to supplement his argument with a more historical approach. I think it’s simply wrong to read the seventeenth (and most of the eighteenth) centuries arguments (not that there were that many of them) over the attributes as being the same arguments that happened post-Kant. The very framework of the question as Mark has read it, is Kantian-inflected through and through – and twentieth century post Fregean-Kant even more so. The problem with Mark’s paper is that it is ignorant of the problem-tradition in which Spinoza’s definition of the attributes actually fits. Mark insists that Spinoza breaks with what he calls, loosely as he recognises, a traditional Aristotelian metaphysics. This is sort of true, but it’s as false as it is true. Spinoza was not the first to recognise that there is a problem with the substance-accident or subject-predicate model for talking about God. This problem is especially acute if one also believes that God is absolutely simple in a way that does not allow for these kind of distinctions to hold. When we say that I am tall, we attribute the quality tallness to me. There is a me who has the property tallness. When we say that God is wise, because of a commitment to divine simplicity, we don’t have that subject-predicate gap. It might be better to say that God is wisdom … and neo-Platonic understandings of God beckon … This double-problem of attribution and simplicity, is a problem that on the one hand we could say bedevils Christain Aristotelian scholastic philosophy; on the other hand it is precisely this kind of apparently intractable problem that leads to the most inventive and fruitful of philosophical speculation. I’ll return to this double-problem below. In recontextualising Spinoza’s definition of the attributes in this way, I am not saying that there is no problem with how Spinoza understands them. This is a problem-tradition after all! But the problem moves from an argument over how we should read Spinoza – objectivist or subjectivist – to one over whether Spinoza could legitimately claim what he thinks he needs to claim about the attributes.

Attributes are also names. They can be predicates. They can be properties. But when we say that God is good, or wise, or just, what is it that we are saying? There is a long and complex history within Western monotheism of worrying about how we can talk about God. One part of this history is the problem of divine names. An additional wrinkle to this problem was the philosophical commitment to a notion of “divine simplicity”.

“Hear, O Israel: The Lord our God, the Lord is one!” Deuteronomy 6:4.

There’s a particularly great article on how Spinoza’s Ethics is part of, partakes in, the tradition of divine simplicity, Andreas Schmidt’s ‘Substance Monism and Identity Theory in Spinoza’ (Schmidt 2009). Schmidt argues that Spinoza’s concept of substance or God, is simple in the way previous scholastic philosophers had understood God to be. This means that there is no real difference between substance, substance’s essence and the attributes that constitute the essence of substance. Schmidt also claims, following Deleuze’s own similar argument in Expressionism in Philosophy (Deleuze 1990) that Spinoza is implicitly using a Scotian idea of ‘formal distinction’ to explain how the attributes can be distinct from one another, yet also express the same essence. Something like this must be in play for a substance to have more than one attribute. I’m not going to discuss the ins and outs of this claim, though I think it’s right. This notion of divine simplicity gives the missing historical and philosophical background to Mark’s recognition that there can’t really be a ‘gap’ between the attributes and the essence of substance (despite whatever the grammar of Spinoza’s pronouncements in 2p7s might suggest) and why the attributes do not function like properties in a ‘standard’ sense.

Perhaps surprisingly, given the amount they are discussed in book one of the Ethics, we don’t actually learn what any of these attributes actually are, until the first two propositions of book two, namely thought and extension (though there is a reference to ‘corporeal substance’ in 1p13c) and despite Spinoza’s claim that God has an absolutely infinite number of attributes, we only ever learn of two. I think, as one almost final comment on 1d4, it’s worth mentioning just how much the idea both that God has an absolutely infinite number of attributes and that two of them are thought and extension breaks with this tradition of divine names. I think Spinoza breaks with this tradition is three distinct ways (though I’m not 100% sure about the third one).

1) Although this will be developed further in the first eleven propositions of the Ethics, that God has to be corporeal or that one of his attributes has to be extension is something that nobody prior to him has argued (though see Fraenkel’s great article, ‘Ḥasdai Crescas on God as the Place of the World and Spinoza’s Notion of God as “Res Extensa” ’ (Fraenkel 2009) which finds a precursor in this Judaic notion of ‘place of the world’). The first half dozen propositions of the Ethics can be read as arguing that if God is purely immaterial-incorporeal, then the corporeality of the world that He is supposed to have created is strictly mysterious-miraculous and that is properly unacceptable for Spinoza.

2) Historically, there have been three distinct non-anthropomorphic approaches to the understanding of God: negative theology, analogy and univocity.

[given that I’m about to sum up three enormous and enormously complicated traditions in three bullet points, liberties are about to be taken]

2.1) Negative theology, says that our understanding of what, for instance, goodness is, is strictly finite and creaturely. This means that strictly speaking you have to say that God is not good (hence the negative part of negative theology). More interestingly, even our concept of being is finite (this is what Scotus denies and why Deleuze calls him the first, though still inadequate, thinker of univocity (Deleuze 1994, 35)) and therefore God is not. God is the being beyond being. But God is still the cause and therefore also the explanation of our goodness in as much as we are good, this is only because we partake-participate in the super-emminently transcendent (not)-goodness of God. It’s all very neo-Platonic.

2.2) The method of analogy which Aquinas develops says although there is no univocity of concept between Creator and creature, nonetheless there is not a complete equivocity either. Instead, we have analogical relationships. Just as the being of a substance is superior to the being of a mere potentiality, so God’s being is superior to ours.

2.3) The third approach is Scotus’s univocity: there is a common concept of being applicable to both God and finite beings. Spinoza is one of the great thinkers of univocity, despite this being a term he never uses, as both thought and extension apply in the same logical manner to both infinite and finite modes-beings.

3) The absolute infinity of God’s attributes. That each attribute has to be infinite in its own kind is nothing new. God is infinitely wise, for instance. That God can be described / has / or better is an infinity of attributes is new. I think. Watch this space as I actually check / ask a friend.

One final, final comment as this has gone on far too long. One of our post-Kantian prejudices about the attributes is that we think that when the intellect perceives we must be adding something to the essence of substance in the way that space, time and the categories are ‘added’ to the noumenal. Added is the wrong word, of course. But Kant’s point is that they are not properties of the noumenal, which is why he is an idealist, not a realist. Spinoza’s approach is as different as it’s possible to be, whilst not quite being the opposite. To sum it up in a simple slogan:

Attributes are subtractive.

When we consider substance as thought or as extension, we are thinking a fraction of substance’s reality. We are thinking a ‘part’ of substance’s actually absolute infinity. Deleuze has this great analogy (see Deleuze 1998) of substance being like white light and each attribute being a single wave-length, each one of which is necessary to constitute the essence of substance as white light yet each wave-length can be considered on its own.

Deleuze, Gilles. 1990. Expressionism in Philosophy: Spinoza. Translated by Martin Joughin. New York: Zone Books.

———. 1994. Difference and Repetition. Translated by Paul Patton. London: Athlone Press.

———. 1998. ‘Spinoza and the Three “Ethics”’. In Essays Critical and Clinical, 138–51. London: Verso.

Fraenkel, Carlos. 2009. ‘Ḥasdai Crescas on God as the Place of the World and Spinoza’s Notion of God as “Res Extensa”’. Aleph, no. 9.1: 77–111.

Haserot, F. S. 1953. ‘Spinoza’s Definition of Attribute’. The Philosophical Review, 499–513.

Mark, Thomas Carson. 1977. ‘The Spinozistic Attributes’. Philosophia 7 (1): 55–82. https://doi.org/10.1007/BF02379992.

Schmidt, Andreas. 2009. ‘Substance Monism and Identity Theory in Spinoza’. In The Cambridge Companion to Spinoza’s Ethics, edited by Olli Koistinen, 79–98. Cambridge: Cambridge University Press.

1(Haserot 1953, 28)

1d3 & 1d5

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 1d3.

Per substantiam intelligo id, quod in se est et per se concipitur; hoc est id, cujus conceptus non indiget conceptu alterius rei, a quo formari debeat.

By mode I understand the affections of a substance, or that which is in another through which it is also conceived 1d5.

Per modum intelligo substantiae affectiones, sive id, quod in alio est, per quod etiam concipitur.

1d3 and 1d5 really need to be read together as although Spinoza defines a substance as that “whose concept does not require the concept of another thing, from which it must be formed”, that is not the same claim as saying that it needs no other contrastive concept to be so understood. Spinoza is making a logical point, I am making a pedagogical one.

Substance is a term that Locke famously pronounced that it is a “something, he knew not what” (Locke 2004, II, xxiii). Of course, in that same discussion, Locke does explain why the concept was invented. If we have a quality, then it seems natural (a logico-grammatical fact of the kind that Nietzsche was rightly suspicious of, “it is a falsication of the facts to say: the subject ‘I’ is the condition of the predicate ‘think.’ (Nietzsche 2014, vol. 8, sec. 17)) to suppose that this quality is a quality of something. A similar argument is that when we wish to consider change through time (I am, in some sense, despite the changes, the same, numerically identical person I was twenty years ago) we suppose that there is some stable ‘me’ that undergoes these changes. In both cases: attribution of change to the subject of change, and the attribution of numerical identity through change, the supposition is that there is a substance that remains numerically identical through change and is the subject of change. Locke’s objection to the idea, is that as all we have knowledge of is the qualities themselves, we can know nothing of what a substance is, behind, beyond, below, these qualities. Spinoza has none of these worries. If the definition seems obscure, it really needs to be read in contrast to 1d5 which defines what Spinoza calls a mode.

The standard Aristotelian picture is one of substance and accidents. Accidents, inhere is a substance. They are what make a substance white, aged, wise, fat etc. Modes are a refinement of this idea. They were needed to do two jobs: one, should we wish to talk about different shades or intensities of a colour then this kind of difference was described as modal. Second: there was this weird problem around transubstantiation for Aristotelian scholastic philosophy. The problem was that when the bread and wine was changed into the body and blood of Christ this was a change in the substance: what was bread and wine is not body and blood. Nonetheless we don’t want to say that the body of Christ is now a bit stale – the accidents that previously inhered in the substance of the bread can’t inhere in the substance of Christ without a lot of theological upset. So this means that in this one miraculous case, we do have ‘free-floating’ qualities. We have bread-iness and wine-iness not inhering in any substance. This phenomenon was known as ‘real accidents’. In contrast, modes, even by the omniscient power of God, had to inhere in something (God can’t break logical laws, normally, for most people, except Descartes). I suspect, though don’t know for certain that this is why Spinoza uses a substance / mode ontology not a substance / accident ontology. Modes have to be, logically and conceptually have to be, modes of a substance. This explains why a mode has to be “in another through which it is also conceived”. That thing it is, through which it is conceived, is substance. A substance, unlike a mode does not require anything else to either exist, or to be thought of (though of course we might still consider Locke’s worry that you’re not thinking of anything at all, and Nietzsche’s that you’re positing something unnecessary; in a way these two worries are dealt with in definition 4). Hence Spinoza’s definition in 1d3.

Two final remarks: just as in 1d1, Spinoza gives us a definition of what a thing is (substance and mode) and how we conceive it. When we conceive a substance, we conceive it as a subject; when we conceive a mode, we conceive it as a predicate of a subject. This is the grammatical-logico subject, not the political or epistemological subject-with-a-capital-S.

Finally, as a pure excessive aside: it now amuses me that however radical Nietzsche’s comments vis à vis Kant or Descartes are, and they are, that before them were thinkers happy to conceive of free-floating accidents/predicates independent of grammatical or logical constraint (albeit, only in the miraculous case of transubstantiation, but still).

Locke, John. 2004. An Essay Concerning Human Understanding. Edited by Roger Woolhouse. London: Penguin Books.

Nietzsche, Friedrich Wilhelm. 2014. Beyond Good and Evil: On the Genealogy of Morality. Translated by Adrian Del Caro. Vol. 8. The Complete Works of Friedrich Nietzsche. Stanford, California: Stanford University Press.