Spinoza: Lecture Two

March 16, 2006

1. More plowing through…

Proposition 12. Substance is not divided according to any attribute.

•   There is a medieval and Aristotelian view that the parts of a substance cannot be substances.  One way to argue for this is just that the part gets its identity from the whole--an arm is defined by its function within the whole body.  But a substance cannot get its identity from anything outside it.  This isn’t quite S.’s argument.

•   S. argues that the parts, if they were substances, would have nothing in common with the whole (Prop. 2 and 5).  The whole could be conceived to exist without the parts, then, which is absurd.

•   Moreover, substances can’t be formed from their parts since one substance can’t cause another.

•   What if the parts are not themselves substances?  Then another absurdity results.  S. is not too clear here.  Maybe the argument is that the whole is the sum of the parts, and yet a substance is not a sum of non-substances.  Or maybe S. is worried that one needs to understand the parts to understand the whole.

 Proposition 14. There can’t be any substance other than God.

• God has infinite attributes—we’ll discuss in a moment what that means.  But one thing it means is that there is no limitation on what attributes God has.  Therefore, if there is some other substance, it would have to have an attribute that God has.  But there can’t be two substances with the same attribute.
• Therefore, it easily follows that everything that exists is either God or an affection of God. 
• It follows likewise that everything that follows from God is eternal, insofar as it is considered as following from God. 
• God is the cause of everything, but immanently.  He is not the cause of things as a cause distinct from the effect.  Rather, he is the cause in that they are in him, an aspect of him. 
• Since everything follows from God, and God is the necessary being, everything is necessary—there is no contingency anywhere in nature.  Nothing that is could have failed to be.
• According to S., God is nature, then, i.e., the whole of reality.
• But it is worth distinguishing two aspects of nature: natura naturans, “nature [as] naturing”, and natura naturata, “nature [as] natured”.  Under the first aspect, we think of nature as guiding the development of things, nature as physical “laws” that move things.  Under the second aspect, we think of nature as being guided, as the material objects that are being moved around by the laws, by the natura naturans. 

2. Infinity.  God is defined to be a substance with infinite attributes, each of which expresses eternal and infinite essence.  “Infinite” occurs twice here. 

• The traditional meaning of “finite” means “bounded by something else”.  Thus, if A is contained in B, then A is always finite in this sense.  St. Augustine uses the word “finite” in this sense when he says that the collection of positive integers is finite in the mind of God.  All that means is that it is bounded by the mind of God.
• In this sense, something is infinite if it is not bounded by anything else.  The odd integers are not infinite in this sense, because they are bounded by the integers.
• Spinoza uses this traditional sense of “infinite” in the scholium after Proposition 13 when he says that we can prove substance to be indivisible by noting that the parts of a substance would have to be finite, but there are no finite substances.  The reason, presumably, why the parts of a substance would have to be finite is that they would be bounded by something.
• Spinoza distinguishes three sorts of infinity:
• Something being infinite by its own nature and that can in no way be considered as finite.  Such a thing can’t be divided into parts.  Let me fill out an argument that Spinoza would probably accept:
• If we divided it into parts, the parts would have to be all finite, since an infinite thing cannot be a part of anything else.
• And there would have to be either finitely or infinitely many of the parts.  If there were finitely many parts, then an infinity would be made up of a finite number of finite parts, which is absurd.
• But suppose there is an infinite number of parts.  Then there is one kind of infinity, the infinite number of parts, contained within another kind of infinite, the infinite thing.  And this can’t be.  (This is a dubious part of the argument.)
• So this sort of infinity, which we can call absolute infinite, has nothing to do with number or counting or parts.
• Something being infinite by virtue of their cause, and when we think of them in abstraction from their cause, we can think of them as finite and divided into parts.  Spinoza thinks space and time are like this.  They are caused by God—i.e., their existence is explained when we understand them as following logically from the modes of God—but when we understand them as realities distinct from God, we can imaginarily divide them up into parts.  Such subdivisions are not really real.  It is only when we consider them with the imagination, our powers of visualization which are opposed here to the intellect, that we see them as made up of parts.
• Duration is what corresponds in modes to eternity in the substance.  Time is what we measure duration with.  Time is but an abstraction, something our minds create.  This is why Spinoza is not worried about Zeno’s bisection paradox.  For an hour to pass, first a half hour must pass, then a quarter, then an eighth…  But there is an infinite number of moments there, and an infinite number of moments can’t pass! 
• Spinoza escapes Zeno’s bisection paradox by saying that these divisions in time are merely imaginary.  Time itself is imaginary.  It is our way of measuring Duration when we mentally separate out Duration from Eternity.  Time is not really infinite.
• But in reality not everything can be expressed by number.  There is then a third kind of infinity defined as that which cannot be expressed by number.  Spinoza says this is like indefiniteness.  It is not quite clear how Spinoza’s example in Letter 12 works.  He talks of two non-concentric circles and the distances between them.  It may be that what he is referring to is the fact that the distances are not always rational numbers. Or he may be talking of the set of all pairs of distances, a set that is bounded but clearly infinite.
• In any case, Spinoza is certainly right that some things cannot be expressed numerically.
• When Spinoza says that there are infinite attributes, each expressing infinite essence, he can’t be talking of the second kind of infinity.  This leaves open the first and third kinds. 
• Interestingly, some interpreters think that Spinoza means that the number of attributes is just unlimited, not limited by anything else.  God has all possible attributes—a completeness of possession of attributes not limited by anything.  At least one such interpreter thinks that this infinity of attributes actually comes down to two attributes—we’ll meet these two attributes later and see why someone might think this.  For now, let’s just see if this makes sense.  Could there be just two infinite attributes?
• At first this seems absurd.  Two is not infinite!  But do we actually know this?  Consider the first definition of infinity.  By that definition two is infinite if and only if it is bounded by something bigger.  It seems it is—by three.  But we’re not talking here of an abstract two.  We’re talking of a very concrete two: of two attributes.  For two attributes to be bounded, i.e., finite, there would have to be three attributes that bound them.  But in fact on the theory that there are only two infinite attributes, there are only two.  There is no third attribute that can be brought in to bound the two.  Hence, two could qualify as infinite in the first sense.
• But actually Spinoza would deny us the use of the word “two” in this context.  Number is only understood when we consider things in abstraction from their absolutely infinite root causes.  But the attributes are not thus abstracted.  Thus, we cannot apply the concept of number to them.  So perhaps all we can say is: There is this attribute, and that attribute.  Can we add: And that’s all?  I am not sure Spinoza’s philosophy allows this.  When we say “that’s all” we would be attempting to bound the attributes by an “all”.  Moreover, we would be saying: “There are no others.”  But that’s a purely negative statement, and as such on Parmenidean grounds to be rejected.
• So probably Spinoza would not say there are only two attributes.  Within his system, it may be impossible to say such a thing…  But that does not mean that it is true within his system that there are more than two attributes.  If the category of number cannot be applied to God’s ultimate reality, then we can neither say there are two attributes nor that there are more than two attributes.  All we can do is say that the attributes aren’t limited by anything, either intensively or extensively.  So, on this view, we have both the first and the third meanings.

3. A step back.  We have a system rather like that of Parmenides in outline.  There is only one substance in existence.  This one is unchanging—indeed, there is no such thing as time.  This one substance has no parts.

• But unlike in Parmenides, we have an account of what we are.  Since plainly I do exist, and since everything is either God or a mode of God or a mode of a mode of God and so on, and since I am not God, I am a mode of God (or a mode of a mode of God, etc.)  We are not substances.
• Observe how the claim that we are not substances is the diametrical opposite of Leibniz’s view that we get the very concept of a substance by reflection on ourselves.  Here we see how Spinoza is further from Descartes than Leibniz is.  Descartes’ Meditations start with thinking about himself—that he thinks and hence that he is—and proceed outward.  Leibniz’s official epistemology says we start with apperception of ourselves and reflect on the concepts implied by this: being, substance, causation, etc.  This is not Spinoza’s approach.
• We have arrived at monism: the view that there is exactly one thing.  If we wish to resist this conclusion, we need to go back over the argument and see if it has gone wrong anywhere.  So, let us step back. 
• The conclusion that everything is either God or a mode of God follows from Spinoza’s Proposition 14 which claims that there is only one substance, namely God, since the only things that exist according to Spinoza are substances and their modes.

• One could resist the argument at this point.  Perhaps in addition to substances and their modes, there are quasisubstances, things that cannot be completely understood without their context but that are such that they can be meaningfully spoken of in isolation from their context.

4. So how does Spinoza argue for Proposition 14?  Well, God has all attributes of all substances.  Therefore, if there were another substance, its attributes would have to be God’s attributes.  But two distinct substances can’t share an attribute.

• Why not?  Because if they did, then they wouldn’t be distinct.  An attribute completely characterizes a substance.  If two substances had an attribute in common, then by understanding one substance, one could understand the other, and this goes against the independence of substances.
• But we have here another sticky point.  The assumption that God exists and God has all attributes—infinite attributes, each expressing infinite essence.  The fact that the attributes are infinite does imply on Spinoza’s view that every possible attribute of a substance is an attribute of God.
• Compare here Leibniz’s view that God has all perfections.  The two views are similar, but there is a crucial difference.  Any one perfection, say, knowledge, does not completely express the essence of a substance.  Attributes do completely express the essence of a substance.
• We can’t really question Spinoza’s view that God has infinite attributes.  The reason we can’t question it is that it is one of his definitions.  Even if one is a theist who thinks that God doesn’t have infinite attributes, one will have to agree that Spinoza’s God by definition does.  One might not want to call this being “God”, but instead give it some other name.  Let’s call it “Bob.”  So, Spinoza defines “Bob” as a being with infinite attributes.  Then he tries to show that Bob exists.  Then he shows that if Bob exists, no other substance exists.  In particular, the God of theism does not exist if Bob exists.
• Where’s the catch, then?
• The catch seems to be in the argument for the existence of Bob.  Spinoza’s system essentially depends on this argument.  If this argument fails, then Spinoza is not entitled to assume the existence of Bob, a being with all possible attributes.
• Recall Leibniz’s criticism of Descartes’ ontological argument.  Leibniz criticized the claim that we have a concept of a being with all perfections, though he thought that he could prove that such a concept is consistent.
• One might use the very same criticism as applied to Spinoza’s argument.  Can Spinoza prove that it is possible for Bob to exist?  In Leibniz’s case, to prove this involved showing that all perfections are mutually compatible.  In Spinoza’s, it should involve showing that all possible attributes can co-exist.
• But it is not obvious that even two attributes can co-exist.  Can a substance have more than one characterization?
• Well, if the characterizations are purely positive, then the answer may be affirmative as in Leibniz’s case—why should positivities conflict?
• If one is a theist, one also can’t quite dismiss this possibility.  After all, the theist does believe that God has all perfections—God is infinite in every way.  Doesn’t that mean that God has the attributes of all substances?
• But why should all possible attributes of substances be purely positive?  For instance, Thomas Aquinas will say that the essences of created things are in a sense negative: they limit being, they say what being is not.  Thus, a human is a rational animal: the animality is a limitation of our being.  Thus, our attribute, rational animality, is limitive and hence in a sense negative.  It would not be fitting, then, for God to have such an attribute.  Our being is limited, finite, and thus in a sense negative.  Hence it is no lack in God that He does not have our attribute: having our attribute would in fact imply a limitation in God.
• Spinoza might insist, however, that in defining a human via limitation, we are making reference to the unlimited thing of which the human is a limited variant. A substance can, however, be understood on its own. (Look how Descartes’ arguments about infinity and the existence of God set up this Spinozistic point.)
• This is the central issue. Is a substance something that can be understood on its own, or is it something that exists not in another? Leibniz’s monads all make reference to everything else: knowing one lets you know about the others. You can’t just separate one off. But they exist not as affections of other things.
• Spinoza, however, identifies the relation of affection to substance with the relation of explanation.

5. Spinoza distinguishes eternity, duration and time.  Saying that something is eternal is more than just saying it exists at all times.  It also says it is necessary on Spinoza’s view.  Duration is passage through, as we might say, time.  Time is the measure of duration—we talk of time whenever we have cut up duration into bits.  So when I say that the Bush presidency or the Battle of Waterloo are realities lasting through time, speaking timelessly and without distinguishing when they are realities, I am speaking of duration, since the Bush presidency and the Battle of Waterloo are something that endures through time.  But when I am more specific and say that the Battle of Waterloo happened or that the Bush presidency started in 2001, I am dealing with time. 

• How we cut time up is up to us.  In this sense, time is a concept of the imagination.  Time is our way of dividing up duration for the convenience of our measurement.  This is how Spinoza resolves the Zeno paradoxes.  There would be a problem, he thinks, if there actually was an infinite number of moments of time in reality.  It’s just that we can divide up duration in an infinite number of ways, and in fact we do when we think of time as a continuum of infinitely many points.

6. Spinoza criticizes the traditional concept of God as having an intellect and will.  He says that the intellect in God would have to be very different, and so saying that God has intellect and we have intellect would in fact be making two radically different claims, as when we say that the river has a bank and when we say Chevy Chase is a bank. 

· If we wish to disagree here, we might make use of a concept of analogy.  God’s intellect while different from ours is analogous to it, in the sense that roughly it fulfills roughly the same role in God as ours does in us: God is to his intellect as we are to ours. 

· Spinoza, however, will not allow the use of analogy, because he won’t let us use facts about one substance to understand another substance.  If there were more than one substance, the substances would be completely distinct and unconnected.

· This allows Spinoza to have another argument for his monism.  Even if there are other substances, we cannot understand anything about them—presumably, not even that they are substances.

o The culprit here seems to be Spinoza’s definition of a substance as something that can be understood and explained completely on its own.  If instead we understand substance as something such that in principle one can talk about it while talking only about it and not about anything else, then we do not have this problem.  For it might be that to completely understand one substance, one needs to understand another.  But one can meaningfully talk of one substance without making any implicit reference to another substance.  The substance itself is the truthmaker of claims about it.  But Sean’s strength is not the truthmaker of claims about Sean’s strength—Sean is the truthmaker of such claims.

o [Here Hume erred.  Hume thought that just because we could think about one substance without thinking of another, the former could exist without the latter.  But this is incorrect: one can think of the number 49 without thinking of the number 7, but the number 49 depends on the number 7, and one does not fully understand the number 49 without understanding the number 7, since 49=7×7.]