SPINOZA

ETHICS

RUNNING COMMENTARY

Definition 1

The first thing to note is that the definition is in two parts joined by the word ‘or’. Latin has a variety of words to cover different senses of the English ‘or’: ‘one or the other, but not both;’ ‘one or the other, or both;’ and ‘or to say the same thing in another way.’ Here the Latin word is sive, which carries the last of these meanings. So Spinoza is saying that the two formulations of the definition are equivalent.

The next thing to consider is how these formulations differ. Spinoza tends to use the words ‘essence’ and ‘nature’ interchangeably (except when ‘Nature’, which I usually spell with a capital N in this sense, means the universe, or God); so this change in wording is not significant. Nor is the shift from ‘existence’ to ‘as existing’ significant, since it is merely grammatical. What does matter is the change from ‘involves’ to ‘cannot be conceived except as.’

The difference is that the first formulation treats the essence as a real being which carries its existence with it, whereas the second formulation treats it as a concept of which existence is a necessary component. Many philosophers, past and present, would regard the identification of the two as an outrageous logical confusion which condemns his system from the very first sentence. Maybe it is ultimately an error; but Spinoza was well aware of what he was doing. The lynchpin of his philosophy is his belief that concepts or ideas, and really existing essences, are just different aspects of one and the same thing. You may well find the notion itself difficult to grasp; but you must at least understand that this is what he is deliberately doing, if you are to make any sense of his philosophy at all.

Similarly, you may have difficulty with both formulations of the definition itself. I think the second is rather easier; so let’s look at it first. Here Spinoza is saying that there is a kind of being (he hasn’t yet said that there is only one), such that we cannot conceive its nature except as existing — in other words, it is the concept of a being which necessarily exists. The ‘necessarily’ is important. One of the standard objections to the ontological argument is that you can define anything into existence by including existence in the concept. For example, I might define a ‘Pound’ as an existent pound, as contrasted with the ordinary sort, which might or might not exist. But Spinoza would say that this is not necessary existence. All it means is that I have resolved to call the pounds in my pocket ‘Pounds,’ and the pounds in my empty savings account ‘pounds’. I can have a perfectly clear conception of a ‘Pound,’ while at the same time knowing that there was a time, and will be a time, when the concept has no application.

What Spinoza is saying is that existence is essential to the nature of the concept, in a way that the existence of a pound is not essential to its nature. Now, it might well be that traditional conceptions of God are vulnerable to the above criticisms. If God is an all-powerful, all-wise, all-loving being, who is separate from the world, and created it at some time in the distant past, and is concerned for what happens in it — then there is nothing in this description which prevents us from conceiving his non-existence. There might be rational grounds for saying that such a being must in fact exist, but they do not flow from his very nature.

The only plausible candidate for that which exists by its very nature is being itself. You will find that Spinoza makes a lot more sense if you read terms like ‘God,’ ‘Nature,’ or ‘substance’ as meaning ‘being,’ or ‘being itself.’

As for the first formulation of the definition, Spinoza is considering it as something real, and not as it is conceived. The crucial word is ‘involves’, which means ‘enfolds’, or ‘is integrally bound up with.’ Unlike some other early modern philosophers, Spinoza accepts that things have essences (like Aristotle’s ‘forms’). In the case of everyday objects, there is a sharp distinction between their essence and their existence. For example, every individual horse has the essence or nature of a horse; and we can always wonder whether any given horse actually exists or not. Moreover, there was a time, and there will be a time, when there are no instances at all of the essence of horse. In other words, essence and existence are two distinct modes of being.

But being itself is different, since it transcends the distinction between essence and existence. Strictly speaking, Spinoza ought to say that its existence involves its essence as much as its essence involves its existence. However, he normally gives priority to essence. The primary reality is essence, which is a universal, and general. The existence which this essence involves is utterly different from that of finite and determinate particular things. It is analogous to the difference between the existence of the number 10, and that of any given collection of 10 things. (And if you don’t like the idea that the number 10 exists, consider how it differs from non-existent numbers, like the positive whole number which, when multiplied by itself, gives the number 2.)

Finally, let us go back to the concept of a ‘cause of itself.’ For many people, the concept of a ‘cause of itself’ would be a contradiction in terms, since the cause has to come first. Again for Spinoza, being itself is a special case, since its existence is caused by its involvement in its essence — or, as he puts it elsewhere, its existence ‘flows’ or ‘follows’ necessarily from its essence or nature. You can’t have the one without the other: the essence is incomplete without existence, and the existence is impossible without the essence.

You also need to bear in mind that Spinoza does not normally make any distinction between ‘cause’ and ‘reason’ (and I have sometimes translated ‘cause’ as ‘reason’ or vice versa, because it would read so oddly in English otherwise). It is central to his philosophy that the following of an effect from a cause is the same as the following of a conclusion from a premise, or of an implication from a concept. So one of many possible paraphrases of the Definition could be something like: ‘[Being itself] is the reason for its own existence, since its essence necessarily carries its existence with it, and cannot be conceived without it.’

Spinoza is using the traditional concept of a genus (or highest genus), such that everything must belong to some genus or other, and nothing in one genus has anything in common with anything in another genus.

Although Spinoza uses different words for ‘finite’ and ‘limited’ (more literally, ‘terminated’), they have the same meaning. All three words come from different Latin words meaning an end or limit. So to be finite is to be bounded; and a thing can be bounded only by something which has the same nature. Spinoza expresses the example of a body rather oddly. We might expect him to say that a body is bounded by one or more actual bodies surrounding it, whereas instead he talks of a larger conceivable body. But he phrases it as he does in order to include the extreme case of the whole material universe. If it is finite, it is not bounded by anything larger; but however large it is, we can always imagine a larger one within which it is contained.

Of course, the examples he gives are the only two genera in Descartes’ system. Spinoza is stressing that it is a category mistake to talk of any relation between the two. One body can be terminated by another, and a thought can be terminated by another thought (the first thought ends when the next thought comes into being). But a thought can’t be terminated by something in the brain; nor anything in the brain by a thought.

However, there is an ambiguity as to how one thought is terminated by another. Spinoza may not simply mean that thoughts are finite in duration, but that every individual thought is bounded by the thoughts which it is not. For example, the thought ‘human being’ (or ‘rational animal’) is limited by all the animals which are not rational; and the thought ‘animal’ is limited by all bodies which lack sensation; and so on.

By implication, something is infinite in its genus only if there is nothing else of the same genus to limit it.

Definition 3

Here again we have a double definition: one at the level of existence, and one at the conceptual level.

Latin has neither the definite nor the indefinite article, and it is often a delicate question whether to translate substantia as ‘substance’, ‘a substance’, or ‘the substance.’ In general I prefer the first formulation, since Spinoza held that there is only one substance, and that it is a universal. On the other hand, he hasn’t yet proved that there is only one substance, so it could equally well be read as ‘a substance’.

Next, Latin, like English has two separate verbs: to be, and to exist. I don’t think the difference is philosophically significant, and I sometimes (as here) use ‘exist’ instead of ‘is’, because the word ‘is’ has so much work to do in English. For example, there is no ‘is’ in the Latin for ‘is conceived’ (which is simply concipitur).

A lot of meaning is packed into those little words ‘in itself’ (half the length in Latin!). The meaning is that a substance doesn’t exist in something else, but is entirely self-dependent for its existence (as we shall see, it must be a cause of itself, as defined above). The contrast is with things which do exist in something else, namely qualities, relations, and the suchlike. In this, Spinoza is very close to Descartes’ strict definition of substance (according to which only God is a genuine substance); but at the same time not far adrift from Aristotle’s classic definition, that a substance is that of which things are predicated, but is not itself predicated of anything else.

As for the second half of the definition, it is clear that the ‘in other words’ refers to it, and not to the first half. Just as a substance is existentially self-dependent, so it is conceptually self-dependent. Bearing in mind Spinoza’s conflation of concept or definition with essence, and of essence with existence, we can see that the two parts of the definition are ultimately equivalent for Spinoza.

Note that Spinoza does actually say ‘the concept of any other thing.’ The word ‘thing’ is grossly overworked in English, and it is very difficult for a translator (from any language) to distinguish cases where the word does appear in the original language, and where it doesn’t. So there is a significant difference between ‘any other thing’, and the vaguer ‘anything else’. Similarly, you will have to watch carefully whether I write ‘anything’ or ‘any thing’ — the latter means that the word ‘thing’ occurs in the Latin.

But why does Spinoza deliberately use the word ‘thing’ here? There are a number of possibilities:

• He may (like Descartes before him) be using the word ‘thing’ as equivalent to ‘substance’, and be anticipating his later conclusion that you can’t have an adequate conception of a thing without a conception of its cause. If a substance is self-dependent (i.e. self-caused), it can be conceived without the conception of any other substance which caused it.
• He may be contrasting the concept of a thing, with just a concept. If he had said that the concept of substance could be formed without any other concept, then that would make it an absolutely simple concept, which would therefore be indefinable. He can hardly say that in a definition of it!
  
  
• On the other hand, perhaps his use of the word ‘thing’ is not significant after all. He may be defining the concept of substance as a uniquely simple concept, which is different from all others in being directly conceived through itself, and incapable of further definition.

I think the second possibility is the most likely one, since it is parallel to the first part of the definition. He is denying that the concept of substance is like that of qualities or relations, which can only be conceived as qualities of things distinct from themselves, or relations between things distinct from themselves.

Definition 4

Note that, like Descartes, Spinoza uses the word ‘perceive’ for intellectual awareness, as contrasted with sensation. Although it often means much the same as ‘conceive’, it has the stronger implication that the understanding perceives something as true, rather than merely understanding it as a possibility.

Again, Spinoza follows Descartes in using the word ‘attribute’ for what is essential to a substance, as contrasted with ‘modes’, which are particular instances of an attribute. However, there is a serious ambiguity (Latin and English) in the word ‘constituting’. It would normally be taken as meaning that the attribute makes up the whole of the essence of the substance, so that there is only one attribute per substance. This is certainly Descartes’ position when he says that the attribute of extension is the essence of extended substance or matter; and if he had been more consistent, he would have said that the attribute of thought was the essence of thinking substance or mind (instead of substances in the plural).

However, as will become clear later, Spinoza holds that there is only one substance with only one essence, of which its attributes are different aspects. Consequently, ‘constituting’ must mean ‘being one of the constituents of.’

Spinoza doesn’t explicitly discuss the relation between substance and essence. But he is worlds apart from Locke, who seems to regard substance as an underlying ‘I know not what,’ in which essences and accidental qualities inhere, like pins in a pincushion. Ultimately, for Spinoza, there is no real distinction between substance and essence. By calling it ‘substance’ we focus on its self-subsistence; and by calling it ‘essence’, we focus on its general aspects which are intelligible to the human understanding.

This identification becomes clearer when we see what Spinoza deduces from the Definition. In Proposition 9, he says it is obvious from this Definition alone that 'the more reality or being each thing has, the more attributes belong to it.' It is not obvious at all, unless 'essence' is equivalent to 'reality' or 'being' ; in other words, he is talking at a level which transcends the distinction between essence and existence.

Definition 5

Here, the definition is again in two parts, of which the second is also in two parts.

The first part merely offers alternative terminology: a mode means the ‘affections’ of a substance (yes, he does oddly have ‘mode’ in the singular and ‘affections’ in the plural). What is interesting is that he uses a rather vague term to explain a more precise one. In Descartes, a mode (which literally means ‘way’) or modification is a particular way in which a general attribute is instantiated. For example, being a circle with a radius of one metre is a particular way of instantiating the attribute of extension, or is a mode of extension.

The word ‘affection’ (like the closely related word ‘passion’) was usually used to cover the particular experiences (sensations and emotions) of sentient beings. They were essentially passive, in that they arose when sentient beings were affected by external objects (light striking the retina, or hearing a frightening noise). In the case of humans, the affections were normally contrasted with actions of the soul, namely abstract thought, and free volition. However, the term was sometimes extended to cover anything in a physical object which was caused by something else, and was thus equivalent to ‘accident’, the preferred term of Aristotle and the scholastics. Again, an accident is something which ‘happens to’ a thing, as contrasted with its essential nature, or ‘form’.

Spinoza’s choice of the term ‘affection’ constitutes a significant departure from Descartes. For Descartes, the modes of extension or matter are all passive, and the modes of thought are all active. Here, Spinoza is implying that the modes of all attributes are passive. We shall see the significance of this later.

Note also that Spinoza says that modes are modes of substance rather than of attributes. I don’t think this is significant, since substance is nothing distinct from the totality of its attributes, and elsewhere Spinoza makes it clear that modes are particular instances of general attributes.

As for the second half of the definition, it is once more divided into an existential and a conceptual part. It is the exact counterpart of the definition of substance. Existentially, just as a substance is that which is self-dependent, a mode is that which cannot exist by itself, but has to be in something else. For example, a particular shape can only exist in a thing which has that shape. Conceptually, substance is conceived in itself, whereas a mode can only be conceived through something else. However, as with the definition of substance, there is an ambiguity here. It is not clear whether the ‘something else’ is the thing of which the mode is an affection, or whether it is the general attribute of which it is a particular instance — or both. Ultimately it doesn’t make any difference, given that the one substance is the totality of its attributes; but it does make a difference if we are talking (loosely) about substances in the everyday sense.

Definition 6

This is, of course, the God of the philosophers. I doubt that many monotheistic philosophers of religion would quarrel with the first part of the definition (at least in the Latin) — unless they knew what Spinoza was going to deduce from it. I must admit that I dithered whether to include the indefinite article or not. With the article, it gives the impression that God is one entity among many, who differs from other entities in that his attributes are absolutely infinite. Without the article, it means that God is being itself, without any limitations whatever — which is certainly the conclusion Spinoza comes to, but hardly orthodox theology.

In the second part of the definition, the word ‘infinite’ is ambiguous, since it can mean either ‘infinitely many’, or ‘to an infinite degree.’ However, it is obvious from the context that the first occurrence means ‘infinitely many,’ and the second means ‘to an infinite degree.’

So here we have at least two major deviations from Descartes. The first is to say that all attributes are attributes of God himself. Although this was the direction in which Descartes’ philosophy was pointing, he never himself took the final step. He accepted that thought and extension were not substances in the strict sense, but he drew the line at saying they were attributes of God. He probably believed that God was thinking substance, even if he thought in a way we cannot comprehend.

The second deviation is that Descartes believed that there are only two kinds of substance, or attributes. For Spinoza, these are the only two we know; but God must have infinitely many attributes, otherwise he wouldn’t be infinite.

The phrase ‘each expresses eternal and infinite essence’ is more difficult. ‘Eternal’ is explained in Definition 8, below. ‘Infinite’ means that the essence is expressed to an infinite degree, without any limitation whatever. But ‘expresses essence’ is an odd phrase. However, if we return to the definition of ‘attribute’ in Definition 3, Spinoza says it is what ‘the understanding perceives as constituting the essence of a substance.’ Well, ‘express’ is one of the words used for what is done to make something open to the understanding (e.g. expressing an opinion); so perhaps all that Spinoza means is that each attribute displays, or reveals, or portrays essence in a way in which we can understand it. As for the ‘essence’ which is displayed, it is the being or nature of God.

Note that if I had translated it as ‘an eternal and infinite essence’ (as many translators do), this would imply that God had infinitely many essences — namely one per attribute. I don’t think this is a correct interpretation of Spinoza. I think he holds that there is a single divine essence or being, which can be understood in infinitely many aspects through each of the attributes.

The Explanation makes explicit a crucial point. Some philosophers might define God simply as an infinite being (rather than an absolutely infinite being), on the grounds that this sufficiently distinguishes him from finite beings, such as ourselves and the whole of the created world. But that would mean that he was infinite only in his own genus or kind. He might possess the attribute of divinity to an infinite degree, but lack the attributes of finite beings, such as extension, and thought as we know it (and this would be very similar to Descartes’ position). So here Spinoza is insisting that, for God to be absolutely infinite, he must possess all attributes, and not be limited to just one.

The second sentence of the Explanation reinforces my interpretation of ‘essence’ as ‘being’, since it implies that ‘expressing essence’ is equivalent to ‘involving no negation.’ There is a long philosophical tradition in which ‘negation’ means ‘absence of being,’ and it is clearly what Spinoza means here. So ‘infinite essence’ means something like ‘unlimited fulness of being.’

Definition 7

Spinoza’s definition of freedom is loaded, to put it mildly. He does not (as many would) make a contrast between what is free, and what is determined or necessitated. Rather, he contrasts what is self-determined with what is determined by something else. His definition covers both coming into existence and acting.

As far as coming into existence is concerned, only a cause of itself can be free, even if its existence follows necessarily from its own nature or essence. All other things are ‘determined’ to existence by another. This word ‘determine’ is a difficult one (and it still causes difficulty a century later in Kant’s writings). Literally, it means to put bounds or limits to, and can mean exactly the same as ‘define’ (which simply comes from a different word meaning ‘limit’). As far as I am aware, it wasn’t until the 19th century that it (and its equivalents in other languages) acquired its modern meaning of causally determining in such a way that no alternative is possible (as in ‘determinism’, for example). In Spinoza’s time, the normal meaning was to restrict something general to a particular value.

If you look carefully at the definition, you will see that only unfree things are ‘determined’ to existence. This is because they are particular modes of God’s attributes, whereas God himself is universal, and therefore not ‘determined’.

As for action, God’s actions are particular; therefore they can be said to be ‘determined’ — they are particular instantiations of his attributes, considered as emanating by necessity from his own nature. The actions of unfree things are the other side of the coin, so to speak, and they are unfree because they are determined by God’s nature, not their own.

I have used the ugly word ‘unfree’, since it’s difficult to find one which is the opposite of ‘free’, but without having misleading implications. Spinoza obviously had the same difficulty in Latin, when he wrote ‘a necessary thing, or rather one which is compelled.’ ‘Necessary’ isn’t quite right, since the same word was regularly applied to God as a ‘necessary being’ (i.e. one which necessarily exists). ‘Compelled’ is better, since it implies (in Latin at least) being forced by another.

One final linguistic point is that the last word in the definition is ratio, which is usually translated as ‘reason’, but has many meanings. I may be going too far in translating it as ‘law’ (i.e. law of nature) here, though it does carry this meaning in classical Latin. Other translators prefer something vaguer, like ‘in a fixed and determined manner.’

Definition 8

It’s probably best to take the Explanation first, and work backwards. In the Explanation, Spinoza makes a sharp distinction between eternal existence and temporal existence. Even if temporal existence is infinite (endless in both directions), it still has duration in time — for example, it might be said that the history of the universe is infinite in this sense. Eternal existence is quite different, since it is the sort of existence had by necessary (eternal) truths and the concepts (essences) of which they are composed. So the existence of a truth like 2+2=4, and of the numbers 2 and 4, is timeless, and not an endless duration.

Going back to the Definition, Spinoza is clearly using the word ‘eternity’ as equivalent to ‘eternal existence.’ So existence is eternal if its sole source is the definition of the thing which is eternal. The use of the word ‘definition’ in this context may seem shocking, since we think of a definition as a purely human creation, from which no existence can possibly follow. But you will just have to get used to the fact that Spinoza uses the words ‘definition’, ‘concept’, ‘essence’, and ‘nature’ more or less interchangeably. A true verbal definition corresponds exactly to a concept perceived by the human understanding, and a concept is an idea or mental representation of a real essence. They are all different expressions of one and the same thing.

Consequently, eternal existence is the sort of existence possessed by something the existence of which follows from its essence — i.e. God.

AXIOMS

Axiom 1

Remember that the axioms are supposed to be so obvious (to anyone who understands the language in which they are written) that they require no proof. So provided you understand what is meant by ‘existing in itself’ and ‘existing in something else,’ this axiom should be obviously true.

We have already seen that only substance exists in itself, in that its existence is involved in its essence. Attributes and modes (and relations, which are not explicitly mentioned by Spinoza) exist in something else, namely substance.

One possible quibble is that there might be things which exist partly in themselves, and partly in something else — i.e., some of their characteristics might follow from their own nature, and some from the thing in which they exist (for example, a wooden triangle owes its 180° to its triangularity, but its weight to the wood). But such examples merely show that Spinoza is only talking about existence here: things either have a completely self-dependent existence, or they do not.

Axiom 2

This axiom is complementary to the first, in that the first is about existence, and the second is about concepts. I don’t know why Spinoza didn’t formulate it in the same way, e.g. ‘Everything which is conceived, is conceived either through itself, or through something else.’ It is clearly what he means. Perhaps he assumes that his readers will take it for granted that things are normally conceived through something else, and he is preparing the ground for the special case of God, who is the one being conceived through himself.

Axiom 3

I have already discussed the meaning of ‘determined’ (explanation of Definition 7). In Latin, there is no distinction between ‘determined’ and ‘determinate’; but I think ‘determinate’ brings out the meaning better. A cause must be completely particularised, with no generality or indeterminacy, in order for its effect to follow. Once it is particularised, its effect follows with (logical) necessity. Conversely, if a particular effect is specified, it is impossible for it to happen unless its particular cause is present.

This axiom is obvious only if you already accept Spinoza’s definition of ‘cause’, which he neglects to provide among his definitions. For Spinoza, the relation between cause and effect is a logical relation. For example, given a knowledge of the laws of geometry, you can calculate the length of the hypotenuse of a right-angled triangle, if you know the precise lengths of the other two sides. Similarly, given a knowledge of the laws of mechanics, you can calculate the velocity of a body of a given mass, if you know the precise mass and velocity of another body colliding with it.

Conversely, nothing follows if any relevant factor is left incompletely specified. For example, if you have an equation like x=2+5+8, it follows that x=15. But if you have an equation like x=2+5+ some other unspecified number, then nothing follows at all. Similarly, for Spinoza, if anything in the cause is indeterminate, then no effect will follow.

What all this amounts to is the assumption (which was universally accepted until the 20th century) that everything in Nature is precisely what it is, and that ultimately there is no vagueness. There are no indeterminacies which might allow for a range of different possible outcomes, given a set of initial conditions. Spinoza’s claim is that, if there were any indeterminacy, then it is not the case that a number of different things might happen, but that nothing could happen at all (any more than any particular number can follow from an equation containing an unspecified variable).

Axiom 4

Here again, this axiom is complementary to the previous one, and it is concerned with concepts or knowledge, as contrasted with what is the case in reality.

As we have just seen, for Spinoza, the relation between cause and effect is a logical one; and it is not unreasonable to claim that you can’t be said to fully understand the conclusion of an argument, or the solution to an equation, unless you understand what it followed from, and how.

Take, for example, Pythagoras’s theorem (in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides). It is perfectly possible for someone to make use of the theorem without understanding it. It is said that the ancient Egyptians used to construct right-angles by laying out an equally knotted rope in a triangle, so that one side was 3 lengths, one side was 4 lengths, and the other side was 5 lengths (5²=4²+3², or 25=16+9, therefore it is a right-angled triangle). It took the Greeks to demonstrate why this should be so; and it is fair to say that they were the first to understand it, since they knew the reason — or, in Spinoza’s terms, they knew the cause, of which the theorem was the effect.

The geometrical example is important because Spinoza (like Hobbes and Descartes before him) saw geometry as a major component of natural science: ultimately nature consisted of geometrically shaped volumes of matter in motion. It may also be the case that Spinoza (perhaps influenced by Hobbes) was thinking of the fact that you can only understand a geometrical shape if you know how it was brought into being. For example, the cause of which a circle is the effect is the rotation of a rigid length round a fixed point on a plane surface. If you don’t know this, then you don’t really know what a circle is (even though you may have learned to apply the word ‘circle’ when you see one).

But even in non-geometrical examples, it seems quite reasonable to say that you don’t understand something if you don’t understand its cause (e.g. ‘I don’t understand electricity,’ or ‘the disappearance of the Marie Celeste is a complete mystery.’) Indeed, the most contentious part of the Axiom is the assertion that knowledge of the effect involves (i.e. is logically bound up with) knowledge of the cause.

Axiom 5

The point here is that, for one thing to be understood through another, is for their concepts to be logically intertwined. For their concepts to be logically intertwined, there must be some common element. For example, the concepts of grandparent and grandchild are linked by the concepts of parent and child (the parent of the grandchild is the child of the grandparent). If there is nothing in common (e.g. a toothache, the far side of the moon, and the square root of minus one), then they cannot be logically connected.

In the light of the previous axiom, we can immediately see that Spinoza will use this to prove that things which have nothing in common cannot be related as cause and effect. Then, also bearing in mind that things which have nothing in common belong to different genera, or are modes of different attributes, he will prove that there can be no causal interaction between mind and body.

Axiom 6

The word ‘agree’ is commonly used in modern philosophy; but unfortunately it doesn’t have a fixed meaning. Sometimes it just means ‘to be consistent with;’ sometimes it means ‘to have one or more specified properties in common with’ (e.g. two triangles might agree in shape, but not in size); and sometimes it has the stronger sense of ‘to be qualitatively identical with.’ Clearly Spinoza is using it in this strongest sense: an idea is true if it is identical with that of which it is the idea — apart, of course, from its being an idea rather than a thing. This is an unambiguous statement of what is known as the ‘correspondence theory of truth.’

Axiom 7

This axiom is no more than the converse of Definition 1, except that there is no reference to the ‘cause of itself.’ There he identified ‘that of which its nature cannot be conceived except as existing’ with ‘that of which its essence involves existence.’

Just as an example, I shall take you through this one simple demonstration.

Spinoza says: ‘This is obvious from Definitions 3 and 5.’

If you go to Definition 3 by clicking on Definition 3 in the top frame, you will see that it says: ‘By substance, I mean that which exists in itself, and is conceived through itself; in other words, that of which the concept does not need the concept of any other thing, from which is must be formed.’ If you have forgotten what this means, you can access my explanation by clicking on the 3. Return by clicking BACK on the Netscape toolbar once (or twice if you went to the explanation).

Then if you click on 5, you will see that it says: ‘By mode, I mean the affections of a substance; or that which exists in something else, and through which it is also conceived.’

From this, you can deduce that, when Spinoza says that a substance is ‘prior in nature’ to its affections, he means that it exists in itself rather than in something else, and that it is conceived through itself rather than through the concept of another thing. So the proposition is indeed obvious from the definitions.

Note, however, that ‘prior’ doesn’t mean ‘prior in time,’ but ‘logically prior.’ There is no implication that a substance could originally exist without expressing itself through its affections, and then start expressing them at some later time.

Spinoza normally ends his demonstrations with the letters Q.E.D. (quod erat demonstrandum, or ‘which is what was to be demonstrated’). He doesn’t here, because it is an assertion of the obvious, rather than a formal demonstration with a series of steps.

As it happens, there is only one reference to Proposition 1. If you scroll the text up a little, you should find that you are in the Demonstration of Proposition 5, namely that ‘in the universe, there cannot exist two or more substances which have the same nature or attribute.’ So the sole function of Proposition 1 is as a step in this particular proof (which we shall come to shortly).

Now work through the Demonstrations of Propositions 2–6 in the same way, using the upper frame. Enlage the frame by dragging the lower border downwards with the mouse. You can always reduce it again as necessary. If you have understood the Definitions and Axioms, you should be able to understand the Demonstrations. There is no need to follow up later references to the Propositions (though you can if you wish).

A corollary is a supplementary proposition which follows more-or-less directly from one just proved.

Spinoza uses the heading ‘alternatively’ for a different way of proving the same thing. Here he derives the same corollary from Axiom 4 and Definition 3. He uses the argument form of the reduction to the absurd (reductio ad absurdum): if there are only two possibilities, and one of them is demonstrably absurd, then the other must be true. So, a substance either can or cannot be produced by something else. Since it is absurd to say that it can be produced by something else, it follows that it cannot be produced by something else

Work through Propositions 7–8.

A Scholium (plural: ‘Scholia’) is an explanatory comment. Usually Spinoza reserves them for explaining why people might be prevented by misconceptions or prejudices from accepting the force of the previous Demonstration, and some of them are quite extended.

In fact, Scholium 1 is more of an ‘alternatively’, since it provides an alternative proof of proposition 8.

Scholium 2 is very oddly placed, since it isn’t about Proposition 8 at all. In fact it is in two parts, the first of which is a note on Proposition 7 (that it belongs to the nature of substance to exist), and the second of which is on Proposition 5 (that in the universe, there cannot exist two or more substances which have the same nature or attribute).

In the first part, Spinoza explains that people have mistaken concepts of cause and of substance. If they had true concepts of them, they would regard proposition 7 as a self-evident axiom, or ‘common notion.’ Spinoza cannot treat it as a common notion, since it is not common to all people, precisely because they have false concepts. In fact, hardly anyone before Spinoza would have regarded it even as true.

In passing, Spinoza explains how we can have true ideas of things which do not exist, despite that fact that ‘a true idea must agree with that of which it is the idea’ (Axiom 6). For example, we might have a true idea of a geometrical figure which has never been instantiated, or a true idea of a unicorn (a horse-like creature with a single horn on its forehead, as contrasted with, say, an elephantine creature with three horns). The answer is that their essences are contained in something else which does exist (ultimately, God). But in the case of substances, their ‘truth’, or existence, or essence is contained within themselves, and they cannot be conceived except as existing.

There is then a somewhat odd argument that, if you claim to have a true idea of substance, but wonder whether substance exists, it is the same as to claim that you have a true idea, but wonder whether it might not be false. The point is that the true idea of substance is the idea of substance-as-existing; so you cannot entertain the possibility that it is false, — i.e. an idea of something which does not exist.

Similarly, he says that ‘if you declare that substance is created, you are thereby declaring that a false idea has become a true idea.’ What he means is that, if substance is created, there was a previous time when it did not exist. But if it did not exist, the idea of it was false, and only became true when the substance came into being. So a false idea became a true idea. Now this might be OK for finite beings. You could, in a manner of speaking, say that the idea of a dodo was once true, but is now false. But substance is a timelessly eternal being, and the idea of it can no more switch from truth to falsehood, than 2+2 can equal 4 at one time, and some other number at another time.

After this, he moves to his alternative demonstration of Proposition 5, that there cannot be more than one substance with the same nature. It is a distinctly roundabout argument. In summary, it goes like this. If something is such that there can be more than one of it, the number that actually exists cannot be caused by its nature. For example, the fact that actual triangles all have 180° is caused by their nature; but there is nothing in the nature of triangularity to specify how many instances of triangularity there must be at any given time. So if there are ten, or a thousand, or a million, their actual existence must be caused by something external to the nature of triangularity.

In the case of substance, its existence follows from its nature or definition alone, and not from any external cause. But the existence of any number of substances cannot follow from a definition; therefore only one substance of a given nature can follow from its definition.

All Spinoza says is that ‘this is obvious from Definition 4.’ Definition 4 was ‘by attribute, I mean that in a substance which the understanding perceives as constituting the essence of the substance.’ It is obvious only if ‘reality’, ‘being’, and ‘essence’ have the same meaning. But we should by now be used to the idea that they do coincide in the case of substance, and it is loose of Spinoza to say ‘thing’ instead of ‘substance’ in this Proposition. Moreover, any old thing can have more being within a single attribute (for example, a large, heavy object has more reality than a small one). It is only in the case of substance, which encompasses the whole being of a given attribute, that it can only have more being by having more attributes.

Clearly, in this Proposition, Spinoza is building up to his proof of the existence of a God with infinitely many attributes.

Read Proposition 10 and its demonstration.

This short Scholium is intended as a refutation of Descartes’ argument that mind and matter must be distinct substances, because they are conceived entirely separately. Spinoza’s position is that there is no reason why a single substance should not be conceived under more than one attribute; and an infinite being must be conceived under infinitely many attributes.

As for how we can tell different substances apart, Spinoza’s answer is that the question doesn’t arise, since he is going to show that there is only one substance.

PROPOSITION 11

By now, it’s hardly surprising to learn that God necessarily exists — the only surprise is that it has taken so long to come to this point. Spinoza offers three proofs: the Demonstration, and two Alternative Demonstrations.

The Demonstration itself is a somewhat eccentric version of the ontological argument. Instead of proving God’s existence directly, Spinoza uses a reduction to the absurd. Either God exists, or he does not. The supposition that he does not exist leads to an absurdity. Therefore he necessarily exists. (Spinoza is not sensitive to the distinction between saying ‘therefore necessarily God exists,’ and saying ‘therefore God exists necessarily’ — the latter is certainly what he believed.)

Alternatively [1]

The first alternative demonstration depends on the concept of cause; but it has nothing to do with the traditional ‘first cause’ argument, since it is concerned with God’s nature alone.

Spinoza starts with the assumption that there must be a reason/cause for the existence or non-existence of everything. There are three possible cases:

1. a thing’s existence is logically impossible (e.g. a round square);
2. a thing’s existence or non-existence is contingent upon the order of the universe as a whole;
3. a thing’s existence is logically necessary (i.e. substance).

He then says it follows that a thing exists necessarily, if there is no reason or cause to prevent it from existing. Well, it follows only if the premises are understood in a certain way. What Spinoza is assuming (and we shall find the same assumption in Leibniz) is that essences have a positive striving towards existence. This idea may be difficult to grasp; but it is to do with the idea that ultimately there is no distinction between essence and existence. Only in God is the distinction entirely absent; but finite essences are not merely logically possible, but have a quasi-existence (often called ‘subsistence’) consisting in a positive dynamic towards existence.

So when something is logically impossible, it is not merely that (as Hobbes would say) the words cancel each other out, and nothing is said; rather, there is an eternal struggle between conflicting essences, which prevents the combination from ever existing. So the cause of non-existence is internal to the compound essence itself.

As for essences which contain no internal contradiction, and are therefore logically possible, their striving for existence will result in their actualisation, unless it is prevented by an external cause. With so many competing possibilities, only a tiny proportion can be actualised at any given time. Which are actual, and which are prevented from existing, depends on the ‘order’ (i.e. systematic structure) of the universe as a whole. The existence of those which are actualised follows from their essence only if the order of things has opened a slot for their actualisation by removing all obstacles — so the reason or cause of their existence is not their essence, but the order of things.

So God exists necessarily if there is no reason or cause preventing him from existing. If there is such a cause, there are three possible cases:

1. it is a substance external to God’s nature, and of the same nature;
2. it is a substance external to God’s nature, and of a different nature;
3. it is internal to God’s nature.

(1) collapses into God himself, so there is nothing distinct from God to prevent his existence.

(2) a substance of a different nature could not prevent God’s existence, since there can be no relation between substances of different natures.

(3) requires that God’s nature involves a contradiction, which is absurd since God is absolutely perfect.

Alternatively [2]

The second Alternative Demonstration also depends on the idea that an essence has a positive striving towards existence, or ‘power to exist.’

If it were the case that only finite beings existed, they would be more powerful than God, since they had succeeded in actualising their existence, whereas God had not. But this is absurd, since God is absolutely powerful, and finite beings are not. Therefore either nothing exists, or both God and finite beings exist.

But we do exist, and we cannot exist without God, therefore God necessarily exists.

SCHOLIUM TO PROPOSITION 11, Alternatively [2]

The Scholium to the second Alternative Demonstration starts by saying that the proof is apos]teriori rather than apriori, so that it can be perceived more easily. Spinoza is using the terms in their traditional sense of reasoning from effect to cause, and from cause to effect, respectively. The proof is aposteriori, because it rests on the existence of finite beings, which are an effect of God.

He then gives an equivalent apriori version. The ability to exist is a power or energy. The more reality or perfection the nature of a thing has, the more energy it has for existing. Therefore an absolutely infinite being has infinite energy for existing, and necessarily exists.

Finally, he considers a possible objection. This is that things which have more to them are more difficult to bring into (or out of) existence. Therefore the most perfect being must be the most difficult to bring into existence. (Roughly what he has in mind is the commonsense observation that it is easier to make something small and simple, than something large and complicated. For example, it’s easier to make (and to destroy) a brick than a cathedral. This observation is then generalised to cover all degrees of reality or perfection). Spinoza answers the point by saying that the principle applies only (if at all) to finite things which are brought into being by an external cause. They owe their degree of perfection to that cause; and clearly that cause must have the required power (e.g. an architect and a gang of masons).

In the case of God, who is the cause of himself, his perfection doesn’t make it more difficult for him to exist, but easier. It would be much more difficult for him to exist if he were imperfect, since he might lack the required power, or there might be obstacles which he could not overcome.

PROPOSITION 12

Having established the existence of God, Spinoza now moves on to discuss his nature. Propositions 12 and 13 are intended to prove that no substance is divisible, and hence that God is indivisible. It may seem rather tortuous to establish both propositions, since it is obvious by now that God is the only substance. But he hasn’t yet formally established this (it comes in Proposition 14, although the demonstration doesn’t depend on Propositions 12 or 13).

The wording of Proposition 12 is quite meticulous, and it is as significant for what it doesn’t say as for what it does say. It doesn’t say that no attribute can be divided, since there is an obvious sense in which attributes can be divided. For example, in the case of extension, I can conceive distinct shapes, and not just extension as a whole; and I can saw a plank of wood in half. Again, in the case of thought, I can distinguish one concept from another; and my private thoughts are locked up in my head, and well and truly separated from those of other people.

What he does say is that the division of attributes must not be conceived in such a way that they imply that substance itself is divided. In other words, division of the attribute doesn’t imply division of the substance which has that attribute. For example, when I saw a plank of wood in half, I don’t create two substances out of one; and when I conceived the distinctness of my idea of the plank from your idea of the plank, it doesn’t mean that there are two distinct substances to which the two ideas belong.

As will become clear from the next few Propositions, Spinoza is here primarily concerned with the attribute of extension. To say that extended substance is not divisible amounts to saying that matter as a whole is a single substance (or, once he has proved that there is only one substance, that it is really only one attribute of God). What this means is that it is not an aggregate of parts, such as point-particles, or atoms, or Leibnizian monads (not yet invented!).

In effect, Spinoza is side-stepping the age-old problem of the ‘composition of the continuum’. Like Descartes before him, he regarded matter, space, and extension as really one and the same thing. Now whatever one may say about matter, space and extension are continuous quantities. This means that, however small a volume of space you define (e.g. a billionth of a square centimetre), you can always define a smaller one (e.g. a billionth of a billionth). Indeed, however far you carry this process, you can never reach a perfect mathematical point, which has absolutely no dimensions whatever.

Conversely, if you imagine space as being built up out of infinitely many mathematical points, you won’t get anywhere. It’s not like trying to build a gigantic cube out of minute bricks. If you are building something out of bricks, however small, you will at least make some progress, since two bricks side-by-side are twice as wide as one brick. But since mathematical points have no breadth at all, if you put two of them side-by-side, they are at exactly the same point. And the same goes for a billion points. It’s like trying to draw a line by repeatedly stabbing your pencil on the same point.

From the Greeks onwards, various attempts were made at explaining how space might be built up out of points — in my view unsuccessfully. The alternative (which was adopted by Descartes, Spinoza, and others) was to say that the whole was prior to the parts. In other words, space as a whole is a single, homogeneous thing, within which we can specify any divisions we like, however large or small. But space is not constructed out of these or any other parts — rather, the parts are constructed out of space. Without space as a whole, there can’t be any parts of space. (It’s like the difference between a collection of particles and a wave: a collection of particles is no more than the sum of the particles which constitute it, whereas a wave can only exist as a whole — although you can conceive half a wave, it can’t exist by itself.)

As for matter, the atomists in particular made a sharp distinction between volumes of space which are occupied by matter (atoms and compounds of atoms), and empty volumes of space (the void, or vacuum) into which atoms move. However, atomism gives rise to a number of philosophical and physical problems. For example, however small you specify an atom as being, it must have parts (e.g. a bottom half and a top half). So atoms must be compounds of parts which are magically held together by unknown forces, and they cannot constitute the ultimate building-blocks of the universe. Again, how can the void be absolutely empty if it is filled with light, and gravitational and magnetic forces (to confine oneself to those known in Spinoza’s time)?

By identifying matter with space, and by denying the vacuum, Descartes and Spinoza avoided all these problems. Just as space is a single whole, so is matter. Just as we can arbitrarily define one volume of space at one time, and another at another, so nature can produce one configuration of physical objects at one time, and another at another. But they have no more real and permanent independent existence than, say, icebergs in the Arctic Sea. They stick together for a while, and move through the water; but unlike atoms and the void (which are of utterly opposite natures), icebergs have essentially the same nature as the water through which they move.

This is not to say that the Descartes/Spinoza approach is without its own problems — but we shall look at these more closely when we come to Leibniz.

In the meantime, you should note that Spinoza’s demonstrations that substance is indivisible make no reference at all to these contextual issues. They are internal to his own system, and would not convince anyone who was not already convinced by his Definitions and Axioms. He might have done better to tackle the philosophical issue itself, as Leibniz did shortly afterwards.

Work through Propositions 12–13

COROLLARY TO PROPOSITION 13

Note the qualification ‘in so far as it is substance.’ There are two points here. The first is that corporeal substance isn’t really substance, but only one of infinitely many attributes of the one true substance, namely God.

The second is that, as I explained earlier, there are senses in which matter is divisible, but not in so far as it is considered as an attribute of substance.

SCHOLIUM TO PROPOSITION 13

We shall have to go more deeply into the distinction between the finite and the infinite shortly. For the moment, it is enough to say that Spinoza was writing just before mathematics exploded into the modern era with theories about different degrees of infinity. He, like virtually all his contemporaries, was firmly wedded to the idea that a quantity was either finite or not. If it was finite, then it had determined limits and a specified magnitude. If it was infinite, then it had no determined limits and no specified magnitude, and no more could be said about it.

So, if something is specified as a part of substance, it must have been specified what part. Consequently, it must be finite (specified, determined, delimited); whereas Spinoza has defined substance as infinite — so a part of substance cannot be a substance. Then there are two reasons why substance cannot be composed of parts. First, substance cannot be a compound of not-substances. Second, however many finite parts you add together, the result may be very large indeed, but it is still finite, and therefore not infinite substance.

PROPOSITION 14

Spinoza now comes back to the point (which he could have made earlier) that God is the only substance. Note that, as usual, he makes the double (and very strong) claim that, not only is God the only existent substance, but the only conceivable substance. If you think you can conceive the existence of two Gods, then you have a false conception of God.

Now follow the Demonstration of Proposition 14, and Corollary 1 (which is obvious).

COROLLARY 2 TO PROPOSITION 14

Corollary 2 is rather more difficult. First, the expressions ‘extended thing’ and ‘thinking thing’ are not correct English. They are literal translations of the Latin res extensa and res cogitans, which Spinoza has lifted straight from Descartes. I have deliberately translated them this way in order to preserve the ambiguity as to whether he means ‘an extended thing,’ or ‘extended thing-in-general.’ If the latter, we might prefer the word ‘substance’ in English. But that translation is absolutely excluded, since Spinoza’s whole purpose is to deny the Cartesian thesis that extension and thought are distinct substances. He uses the ordinary-language term ‘thing’ as not implying that they are substances in the strict metaphysical sense.

Next he says that ‘extended thing’ and ‘thinking thing’ are either attributes of God, or affections of attributes of God. But which, for Heaven’s sake? There’s all the difference in the world between an attribute and an affection of an attribute. The answer must lie in the ambiguity of the word ‘thing’. If it is taken as thing-in-general, then it is an attribute. If it is taken as an individual thing, then it is an affection of an attribute. So, for example, extension in general (i.e. space or matter as a whole) is an attribute of God, and individual physical objects are affections, or particular determinate instances, of extension in general.

PROPOSITION 15

Yet again there is a parallel between existence and conception (which are ultimately one and the same in God). Here Spinoza introduces the concepts of ‘existing in’ God and ‘being conceived through’ God. These are not actually very problematic concepts. We are already familiar with the notion that qualities (modes, affections, accidents, or whatever you call them) can only exist in things of which they are the qualities. For example, the brown colour of my table exists in my table, and I can’t strip it off and put it in my briefcase. For Spinoza, the table itself, together with all its qualities, bears the same relation to God as (in everyday experience) the colour does to the table. That is the sense in which my table exists in God.

Similarly, all qualities are modes, or modifications, or particular instantiations of more general concepts. For example, ‘brown’ is a particular instance or mode of the more general concept of ‘colour’. So you can’t have a concept of ‘brown’ without having a concept of ‘colour’ — or, in Spinozistic terms, brown is ‘conceived through’ colour. Here Spinoza is saying that God is the ultimate concept as well as the ultimate existent being. Just as my table is a highly particularised mode of God’s attribute of extension, so the idea or concept of the table is a highly particularised mode of the idea or concept of God, considered under the attribute of extension.

SCHOLIUM TO PROPOSITION 15

This is a long Scholium, in which Spinoza defends his thesis that God is corporeal.

Remember that Spinoza doesn’t hold (as Hobbes does) that God is merely corporeal, since extension is just one of infinitely many attributes, including that of thought. However, the large majority of thinkers, Jews and Christians alike, had held that God was a completely immaterial substance distinct from the material universe.

{1} In the first paragraph (in fact it’s all one paragraph in the original Latin), Spinoza abruptly dismisses the uneducated view of God as a Great Daddy in the Sky. He then turns to what he considers the best argument for denying that God is corporeal, namely that ‘body’ means something of a particular shape and size — and of course God isn’t corporeal in that sense.

{2} Next Spinoza claims that it is one thing to deny that God has a definite shape and size, but quite another to deny that extension/matter in general belongs to the divine nature. His first rebuttal is that, if matter is not an attribute of God, he would have had to have created it as a substance distinct from himself — but it is impossible to conceive how this could be done, therefore it is meaningless to assert it.

{3} He then repeats his proof that matter cannot be created by God, and must be one his attributes.

{4} Spinoza now offers a diagnosis of how his opponents could have come to the mistaken view that God is immaterial. He thinks their arguments can be reduced to two, which he sets down before refuting them.

{5} The first argument is that since matter is a compound of parts, it cannot be infinite, and therefore cannot belong to God. Spinoza then reports three sub-arguments he has found in the literature, which purport to show that matter cannot be infinite.

{7} The second sub-argument is that if the universe is infinite, them it is both infinitely many inches across and infinitely many feet across; but the latter makes it twelve times the size; therefore it cannot be infinite. (Again, this is no more paradoxical than the fact that there are infinitely many numbers, infinitely many even numbers, and infinitely many prime numbers, even though these infinities are different sizes.)

{8} The third sub-argument is rather more puzzling. It is true that if you extend two lines to infinity, the distance between them will cease to be a determinable quantity. But the same is true of the lengths of the lines themselves. I do not see how this adds to the general conceptual difficulty (if it is one) that the concept of extending something to infinity means that the determinate becomes indeterminable.

{9} After this, Spinoza sums up the sub-arguments by repeating that his opponents draw the conclusion that the material universe must be finite, and therefore cannot belong to the essence of God.

{10} He then states the second argument, which at first sight looks rather an odd one. Almost since the beginning of philosophy, it was assumed that matter is essentially passive, and that mind, soul, spirit, or form is essentially active. So why say that corporal substance is passive because it is divisible? The answer is that Spinoza is not thinking of this or that physical object — say, a billiard ball, which moves only when acted upon by a cue or another ball. Rather, he is thinking of the material universe as a whole, which is the only candidate for belonging to God’s nature. Obviously, the universe as a whole cannot be acted on like a billiard ball. But if it consists of parts, it is capable of being divided into its parts, which is a way of being acted on. So the argument is that, assuming that the material universe (whether finite or infinite) is divisible, or composed of parts, its passivity means that it cannot belong to God’s essence.

{11} The next two paragraphs contain the core of Spinoza’s refutation. He says that his opponents make the mistake of assuming that an infinite quantity must be both measurable, and made up of finite parts. Their arguments do not show that the material universe is not infinite, but only that an infinite quantity is neither measurable nor composed of parts — which is precisely what Spinoza himself holds.

{13} The next paragraph doesn’t really add much. The last sentence is an allusion to the point I made above, that you can’t draw a line by putting points in a row, since they will always be at the same point. Similarly, you can’t generate a surface by putting lines side-by-side like matchsticks, since lines have no breadth; nor can you generate a solid by putting surfaces together. Nevertheless, it is fair to say that the fiction that you can do something like this was crucial for the development of the infinitesimal calculus by Leibniz and Newton a generation later.

{14} Now Spinoza gives an entirely different (and at this stage incomplete) argument against the divisibility of matter into discrete parts. It rests on his denial of the vacuum, which he argues for elsewhere. The argument is that, if the parts of matter were really distinct from each other (i.e. independent substances), then you could conceive of one of these parts being annihilated. If so, then either it would leave a vacuum, which is contrary to the hypothesis that there is no vacuum; or the other parts would have to move in to take its place. But if the parts of matter are entirely independent (as they must be if they are separate substances as Spinoza conceives them), they have no reason to react to the disappearance of one of their neighbours. The consequence Spinoza draws is that the possibility of a vacuum can be avoided only if the material universe is an organic whole — i.e. a single, indivisible entity.

{15} Spinoza now moves to a more psychological explanation of why people are naturally inclined to conceiving matter as divisible. He distinguishes between conceiving through the imagination, and conceiving through the understanding. This distinction should by now be very familiar to you — e.g. Descartes’ distinction between the (wrong) idea we have of the sun derived from sensory imagery, as a disk roughly a foot across; and the idea we have from our understanding, which is of a vast sphere.

Spinoza’s language may cause some difficulty here. First, when he talks of ‘imagining’, in common with most other philosophers of the period, he doesn’t mean having a mental image of something which is not present to the senses, but having a pictorial image which might or might not be of something actually present to the senses. The imagination is the faculty of forming images under any circumstances whatever.

He describes a conception derived from the imagination as ‘abstract’ or ‘superficial’. ‘Superficial’ is O.K., since it means ‘concerned only with the surface’ (Latin: superficies), as contrasted with the underlying reality. But ‘abstract’ rings oddly, since we are used to the idea that sensation and imagination are to do with concrete particulars, whereas it is the understanding which deals with abstractions and universals. ‘Abstract’ means ‘considered in separation from’, and so it is a relative term. So when we imagine ‘abstractly’, what is our image considered in separation from? The answer is that it is considered in separation from substance. Our images are just images in the mind, whereas our understanding penetrates to substance itself.

As Descartes had already said in the Principles, we are habituated to conceiving things through the imagination, and it is hard intellectual work to consider things as they really are, through the understanding alone. Our sensory images tell us that the material world is sharply demarcated into discrete physical objects, which can be sawn in half, chopped with knives, and ground into powder. But our understanding tells us that the material universe is a single, organic whole.

{16} Now Spinoza introduces a new point. What is given in sensation is a variegated world of different kinds of thing — my table, my computer, the pussycat on my lap, the glass of wine, the Bach fugue playing in the background (old fogey that I am; and Spinoza never heard Bach) — but from a scientific point of view, they are all manifestations of matter. All the differentiations are in the qualities of things, and not in matter itself. We can distinguish things as perceived through their qualities, but we can’t distinguish ‘matters’. We have no grounds whatever for saying that matter is anything other than one. So the parts of matter are only modally distinct (i.e. distinguished from one another through their perceived qualities), and not really distinct (i.e. in reality they are not distinct things [remember, Latin res = ‘thing’], or substances).

Spinoza illustrates his point with the example of water. His example is intelligible only if we understand him as distinguishing between the particular and the general. Particular instances of water are manifested at different places and at different times. The pond at the bottom of my garden is distinct from the water I make my coffee with. They come and go. The pond might evaporate in a drought, and I drink my coffee. But water considered as H²0 is neither in one place nor another, nor does it come in or out of being.

{17} Finally, Spinoza comes back to the second argument, which was that matter is essentially passive, because it is divisible. He says that he has already answered it, because, in so far as it is considered as substance (rather than as given to the imagination) it is indivisible.

He then adds the point that, even if matter were divisible, its belonging to God would not detract from the divine nature as essentially active, since there can exist no other substance (apart from God himself), which could perform the act of carving material substance into discrete parts. Consequently, God’s status as essentially active is preserved.

PROPOSITION 16

The ‘necessity of the divine nature’ is a common Spinozistic phrase. He uses it to emphasise that the divine nature exists necessarily, and necessarily is as it is. When he says that infinitely many things ‘must follow’ from it, he means that they follow from it necessarily, just as the properties of a triangle follow from its nature. Note the implication of ‘everything which can be subject to the divine understanding.’ Spinoza means everything which is conceivable (even if not by us), and hence everything which is logically possible. Consequently, everything which is logically possible must be actualised (at some time or other).

The most problematic phrase in this Proposition is ‘in infinitely many modes.’ It is unclear to me whether Spinoza means ‘mode’ in the technical sense of a particular instantiation of an attribute, or in the everyday sense of ‘way’. Perhaps he wasn’t even conscious of the ambiguity, since there is just the one word in Latin. Either would make sense, since each attribute will have infinitely many modes. Note that Spinoza doesn’t use the word ‘thing’ (res) here, so he is talking about absolutely anything — qualities and events as much as physical objects.

In the Demonstration, note the reappearance of the concept of degrees of reality (previously mentioned in Proposition 9). This should in any case be familiar to you from Descartes’ proofs of the existence of God. The idea is that some essences have more to them than others (e.g. the specification of a computer has more to it than that of a wheel), and they are said to have a higher degree of reality, independently of whether they actually happen to exist or not.

THE COROLLARIES TO PROPOSITION 16

Taken together, the corollaries state that God is the absolutely first and efficient cause, through himself and not accidentally, of everything conceivable.

‘First cause’ should require no explanation. The ‘efficient’ cause is the agent which brings something into being. If you need to refresh your memory on the Aristotelian 4 causes, go to IHMP Unit 5 [unit5/ancient.html]. He is the cause of things ‘through himself’ in that they emanate from his essence, and not ‘accidentally’, as would be the case if he were merely transferring an effect from some other cause (like a billiard ball which is set in motion, and then transfers its motion to another).

PROPOSITION 17

There are a couple of things to note here.

First, in the Demonstration Spinoza deliberately identifies things’ following from God’s nature, with God’s acting from the laws of his nature (he says they ‘come to the same thing’). The second formulation is more consistent with traditional theology (a purposeful God acting in accordance with his own laws), whereas the former is more consistent with Spinoza’s actual position.

Second, I find the word ‘anyone’ rather odd. I would have expected ‘anything’ — and it is quite unambiguously ‘anyone’, not ‘anything.’ The reason why I find it odd, is because the sort of external compulsion one might possibly suppose a God to be subject to would be things like necessary truths (God can’t do the logically impossible), or absolute values (God can be meaningfully described as good, only if his actions measure up to some external standard of goodness). And Spinoza does indeed deny that God is subject to any such compulsions. Perhaps what he has in mind here is that he can’t be compelled by any other God, since (as he reminds us in the demonstration) nothing else exists. If so, he would be making the very obvious point that since there are no other beings, there are no other beings to compel him to action.

Normally the word ‘anyone’ refers to human beings. It would obviously be absurd to say that any human being could compel God to action. But in Corollary 1, Spinoza dilutes this to ‘incite’. Possibly what he has in mind is that prayer is ineffectual, since nothing can incite God to change his mind.

I’m not quite sure of the force of the qualification ‘whether intrinsically or extrinsically’. I think he means that an ‘intrinsic’ cause distinct from the perfection of his own nature would be an imperfect mode of his being, such as a human at prayer; whereas an extrinsic cause would be another God. This does at least make sense in the context.

COROLLARY 2 TO PROPOSITION 17

The Corollary that God is the only free cause follows inexorably from what has gone before. But it is hardly freedom as we understand it; and it is arguable that, if Spinoza is successful in establishing at least a limited sense of human freedom in Part V, then humans are actually more free than God. If so, then Spinoza is neither the first nor the last philosopher to believe that human beings have a uniquely privileged position in the scale of things. Hunks of matter certainly aren’t free; and a God’s gotta do what a God’s gotta do. But at least we can control our attitudes to the inevitable, and enjoy thinking about philosophy, instead of surrendering ourselves to the pleasures and concomitant displeasures of the senses.

SCHOLIUM TO PROPOSITION 17

This is a longish Scholium (over a page, and all one paragraph in the original), in which Spinoza attacks the mainly Cartesian view that God is free because he chooses between different possible universes.

{1} His first point is that everything which is within God’s power is what follows logically from his nature. It is therefore logically impossible for him to prevent anything. In other words, there is no gap between what is possible and what is actual, which would enable him to actualise only some possibilities.

{2} However, Spinoza is aware that no-one will accept this argument unless they have already accepted what has gone before; so he tackles the issue more directly. First he says that he will argue (a few sentences later) against the thesis that, since understanding and free will are the greatest human perfections, God must have them to the highest degree. In fact, Spinoza will say, God has neither.

{3} Before that, he considers his opponents’ argument that God’s omnipotence would be used up if he created everything he was able to create — i.e. there would come a time when there was nothing left that God could do. Consequently, God has to make a selection from all the possibilities, so that there are always further possibilities remaining. Spinoza adds that they are committed to saying that God’s selection is entirely arbitrary, presumably on the grounds that, since all possibilities are equally possible, there can be no rational grounds for preferring one to another. This was certainly Descartes’ position. For example, Descartes held that any geometry was logically possible, and that God arbitrarily chose to create a Euclidean universe. Spinoza, on the other hand, maintains that Euclidean geometry follows from God’s nature, and that none other is conceivable. As we shall see later in the module, Leibniz held that God made a rational and non-arbitrary choice between different possible universes, namely the best.

{4} Spinoza starts his rebuttal by restating that everything flows from God’s nature ‘from eternity and to eternity.’ He doesn’t say this explicitly, but since eternity is beyond time, there can be no question of there being a time at which God runs of things he can do. Then he says that his position makes God’s omnipotence far more perfect. Again, he doesn’t spell out what he means, but he presumably means that God’s omnipotence is more perfect in the sense of more complete — that God is more omnipotent if he creates everything within his power, and not just a selection from it. However, he may also mean that his omnipotence is more perfect if it is fully rational, and doesn’t involve arbitrary acts of will.

{5} The next paragraph largely repeats what Spinoza has already said, except that he turns his opponents’ position into a logical contradiction, namely that God cannot do everything that he can do. (Later, Leibniz gets round this objection by saying that not all possibles are ‘compossible’ — that a universe in which Adam sins is possible, and one in which he doesn’t sin is possible; but they can’t both be actualised, and God has to decide which.)

{6} Now Spinoza takes up the topic of God’s understanding and will. In fact he only discusses his understanding, and at the end of the Scholium he merely says that same arguments apply to his will.

Theologians had long discussed the question of how we can have any conception of God’s understanding. The conventional view was that it is different from, but analogous to human understanding. We can form some sort of conception of it, however inadequate, by extending our human power of understanding to infinity. Here Spinoza flatly denies this approach. God is so different, that there is nothing in common between our understanding and his understanding, apart from the name. Consequently we have no conception at all of the latter, and it isn’t what we mean by the word ‘understanding’. (Hobbes had already made the same point.)

{7} Spinoza’s demonstration of the difference starts out from the point that, when humans understand something, the thing understood must already exist. By contrast, God’s understanding comes first, and is the cause of both the existence and the essence of the thing. In other words, things exist and are as they are because of the way God understands them, whereas the process is reversed in the case of human understanding.

He approves of those who say that there is no distinction between God’s understanding, will, and power, because for God to understand something is for him to have the power and the will that it should exist. ‘God said , let there be light: and there was light.’ In the beginning was the Word, and the Word was with God, and the Word was God.’ In both the Old and the New Testaments, there is a conflation between the Word (logos = word, reason, or understanding); and God exercises his power by willing that his word be actualised — i.e. that essence becomes existent.

Of course (although again Spinoza doesn’t say this explicitly), we can have no comprehension of what it is for understanding, will, and power to be the same, since they are utterly distinct from each other in us human beings.

{8} Now we have a complicated bit of reasoning. Spinoza wants to argue that, since God’s understanding is the sole cause of our essence, it can have nothing in common with the human understanding which is part of our essence, and therefore cannot be conceived by analogy with it. I personally don’t see how this can be compatible with Spinoza’s thesis that causality is a logical relationship, which can exist only if there is something in common between the cause and the effect.

Anyway, his argument turns on the claim that ‘something which is caused differs from its cause precisely in that which it has from its cause.’ This is made clear by his example of one human being generating another. What is generated is not human nature (which is a timeless essence flowing from the nature of God), but the individual existence of the new human being. The two individual existences are entirely distinct, and have no logical connection with one another. If one is destroyed, it has no effect on the other (as we shall see, Leibniz denies this — and perhaps Spinoza should have too, given his holistic conception of the universe). On the other hand, they share the same essence, and if the essence of the one is destroyed, the essence of the other will also be destroyed. (We have seen the same argument discussed, in much greater detail, and perhaps with more sophistication, by Boethius and Ockham. If you wish to refresh your memory, go to IHMP Unit 3).

Spinoza now says that, whereas human parents are the cause only of the existence of the child, and not of its essence, God the Father is the cause of the essence of humanity, and not merely of its existence. So, just as the human parent is existentially distinct from the child, so God is essentially distinct from humanity, and has nothing in common — including his understanding. There is no way we can argue by analogy from human to divine understanding.

{9} Finally, Spinoza asserts that the same is true of God’s will as of his understanding. In other words, our human understanding of the word ‘will’ can no more be transferred to God than that of the word ‘understanding’.

PROPOSITION 18

‘Immanent’ means ‘residing within’ (not to be confused with ‘imminent’, meaning ‘hanging over’, or ‘impending’). In theological parlance, God is described as ‘immanent’ if he is omnipresent in the created universe, rather than remote from it. In Spinoza’s philosophy, God can hardly be said to be immanent in this sense, since the universe is immanent in him, not the other way round. However, in this particular context, ‘immanent’ has a more restricted meaning. An action or cause is said to be ‘immanent’ if it remains within the agent, and has no external effect — for example, if I have a secret thought, and don’t do anything about it. By contrast, a ‘transient’ action or cause is one which has an effect on something else, as with one billiard ball hitting another. (‘Transient’ means ‘going across’, and in this context it is often spelled ‘transeunt’, in order to distinguish it from another sense, in which it means ‘passing through without stopping,’ or ‘temporary’.)

So God is the immanent, not the transient cause of everything, since everything is in God, and there is nothing separate from God on which he could have any effect.

PROPOSITION 19

It should be pretty obvious by now that God and his attributes are eternal. However, it is odd that the Demonstration doesn’t appeal to Definition 8, in which Spinoza defines eternity. The important point is that eternity is not infinite duration, but timeless, as with the relation between the essence of triangularity and its properties.

SCHOLIUM TO PROPOSITION 19

In the Scholium to Proposition 19, he refers to an alternative proof of God’s eternity in Proposition 19 of his Descartes’ Principles. There the proof depended on God’s having no limits, and infinite existence is what we mean by ‘eternity.’

PROPOSITION 20

Now Spinoza makes explicit what has been implicit all along, that in God there is no distinction between existence and essence. You might say that, in itself, being just is. It is only when you come down to the level of individual things existing in space and time that it becomes meaningful to distinguish the essence (concept, definition, idea) of a thing from the instantiation of that essence at a particular place and time.

COROLLARY 1 TO PROPOSITION 20

The first Corollary is obvious, since it does indeed immediately follow that if God’s essence is an eternal truth, then his existence is also an eternal truth. Although the expression may seem odd to us, I think he does literally mean that his existence itself is an eternal truth, and not merely that the fact that God exists is an eternal truth.

COROLLARY 2 TO PROPOSITION 20

If God is immutable (unchanging), then his attributes are immutable, since they constitute his essence. The argument then becomes rather artificial. If they ‘changed with respect to existence,’ they would have to ‘change with respect to essence’ — fair enough from what he has just said; but what does this mean? I don’t think it makes sense to interpret Spinoza as meaning that the attribute as a whole goes out of being. So he must be talking about modes of the attribute coming in and out of being. Now of course modes do come in and out of being. So he must mean that the attribute itself doesn’t suffer any existential change, but only its modes. So, for example, space or extension itself never changes, but only the individual objects which are modes of extension.

Finally, Spinoza argues that, since existence and essence are the same at the level of the attribute itself, if it changes existentially, it must also change essentially, and the ‘true would give rise to the false.’ His point is that, if, for example, space has a certain essence, then all geometrical truths follow from it, and are eternally and necessarily true. But if its essence can change, the new essence will have followed necessarily from the old one; but it will also give rise to geometrical truths which are inconsistent with the previous ones, and therefore false, since the previous ones were necessarily true.

PROPOSITION 21

This and the following two propositions are rather difficult, and they are not essential for understanding the rest of Part I. Basically, Spinoza is distinguishing two types of mode: those which are infinite, eternal, and necessary, and the rest. They are modes which are more specific than the attribute itself, but still so general as to be present in every particular mode. The only example he gives here concerns the attribute of thought, namely ‘the idea of God in thought’. It is more specific than thought in general, so it is a mode of thought; but it is still absolutely universal, since everything has to be conceived through God.

He doesn’t say so here, but the equivalent infinite mode of extension is ‘motion and rest’. Again, it is more specific than extension in general (it is a way of being extended which is different from having a certain shape or size); but it applies to every portion of matter, and underlies the laws of motion, on which the whole of physics (as conceived at the time) depends.

PROPOSITION 24

Now Spinoza starts discussing God’s relation to things (res) — i.e. the constituents of the universe. Obviously he can’t call them ‘substances’, since God is the only substance.

In Proposition 24 and its corollary, Spinoza proves that the essence of things does not involve existence, and therefore that they must both be brought in to existence and kept in being by God.

PROPOSITION 25

Remember that an efficient cause is one which brings something into being. Having just said that the essence of things is distinct from their existence, he now has to demonstrate that God is the cause of their essence as well as of their existence. Another way of putting it is to say that God is the source of all concepts, as well as of all their actually existing instances.

COROLLARY TO PROPOSITION 25

In the Corollary, Spinoza makes it explicit that individual things are modes of God’s attributes, and that they are particular instances of those attributes. Spinoza often uses the word ‘express’ to mean ‘be a particular instance or manifestation of’. So when he says in Definition 6 that each of God’s attributes expresses essence, he means that each expresses a particular aspect of God’s essence as a whole. As I have said before, the terms ‘definite’ (or ‘defined’) and ‘determinate’ were regularly used to mean a precisely specified particular instance of some something general. So individual material objects are precise specifications of the general attribute of extension.

PROPOSITION 26

Now we have the strange phrase ‘determined to action’, and later we will find the parallel phrase ‘determined to existence’. To take the latter first, determining something to existence means exactly the same as bringing it into existence in a determinate way — and no individual can be brought into existence unless it is fully determinate (it must have exactly the shape and size it has, without any vagueness, or approximation, or indeterminacy). Similarly, if a thing does something, or acts, its action must be absolutely determinate. In effect, what Spinoza is saying here is that God precisely determines not only the existence and essence of things, but also their actions.

Consequently, since things are not the causes of themselves (of their own existence, essence, or action), they can’t act unless they are determined to action by God. Most religious philosophers would agree that matter couldn’t do anything unless God had at least started it off; and most would also agree that every subsequent action is dependent on God, and cannot go against his will. The sting in the tail of this Proposition is that human beings are not exempt, and therefore have no freedom of the will independent of God’s decrees. Humans can no more determine themselves to action than they can determine themselves to existence.

PROPOSITION 27

I think the force of this Proposition is, not so much that things such as human beings cannot acquire freedom by escaping from God’s determination, but rather that the determination is inexorable, and humans haven’t even the freedom to do nothing.

PROPOSITION 28

This proposition amounts to the assertion that God determines the existence and action of each individual thing through an infinite series of material causes and effects.

In effect, Spinoza’s argument is that finite events could not be produced directly by God. Anything which follows immediately from the divine nature is itself infinite and eternal — in other words, it is atemporal. So if all events followed immediately from his nature, they would not be events at all, since events must take place in time. It would be like properties following from the nature of a triangle, which have no temporal sequence, but just exist eternally.

In order to distance the universe enough from God’s nature for things to happen in time, Spinoza, says that the immediate causes of events are finite modes (i.e. other things or events), even though the whole series follows from eternal and infinite modes, which follow from the attributes constituting the divine nature.

SCHOLIUM TO PROPOSITION 28

Spinoza certainly needs a Scholium here, since he is skating on very thin ice if he wants to maintain both that everything is in God, and that things are not immediately caused by God. His account is beginning to look like Neoplatonism, with its hierarchy of emanations from The One, via celestial forms, down to individual material things (saw glimpses of this in Agrippa von Nettesheim, and Della Porta). Only in Spinoza we have God, then his attributes, then infinite and eternal modes, and then finite modes. In this Scholium he is redressing the balance towards everything being in God. He makes three main points.

The first is that, even though some things are produced through the mediation of ‘primary’ things which follow immediately from his nature, everything can only exist or be conceived in God.

Second, he says it follows that, since God’s effects cannot exist or be conceived without their cause, God is the ‘absolutely proximate cause’ of the things immediately produced by him (i.e. the infinite and eternal modes). Here we have again the contrast we first came across in the Explanation of Definition 6, where Spinoza said that God is absolutely infinite, and not in his genus. There the point was that God is not merely one genus (divinity), with the possibility of there being other genera, such as matter. Rather, God embraces all possible genera (extension, thought, etc.), which are his attributes. So here he is saying that God is not just a special kind of being which can create different kinds of being, but that everything is caused by a God who transcends all distinctions into different kinds of being.

Third, he says it is speaking loosely to describe God as the ‘remote’ cause of individual things. It may be useful for drawing attention to the distinction between things which are produced immediately, and those which are produced through their mediation. But he is not their ‘remote’ cause if that is taken as meaning that he is separate from the effects he causes (as, for example, the sun is the remote cause of skin cancer), since everything exists in God.

PROPOSITION 29

By now this Proposition should be relatively straightforward. The Demonstration makes it clear, not merely that nothing is contingent, but that there is no half-way house between what is necessary and what is impossible. Note that, although I have sometimes used the expression ‘logically necessary’ in my explanations, it is strictly anachronistic, since Spinoza had no conception of any distinction between logical and physical necessity. We have to wait for Leibniz to articulate that distinction.

SCHOLIUM TO PROPOSITION 29

This Scholium reads slightly oddly, since it isn’t especially relevant to what has gone before, and Spinoza makes it sound as if he has already used the expressions ‘Nature naturing’ and ‘Nature natured,’ which he hasn’t (though he does use them a lot later). Since they aren’t good English, they are often left in the original Latin: Natura naturans and Natura naturata (not that they are good Latin either). They aren’t Spinoza’s invention, but had been used in scholastic philosophy to distinguish between Nature in its active and in its passive aspects.

What is original to Spinoza (and shocking to his contemporaries) is the identification of Nature naturing with God considered in himself, and of Nature natured with the modes of his attributes. Elsewhere, he sometimes uses the expression ‘God or Nature’ (and the ‘or’ is sive, which means ‘in other words’). If God is Nature, than it’s hard to see how he (or she, or it) can be identified with the personal God of Judaism or Christianity.

PROPOSITION 30

In the Scholium to Proposition 31, Spinoza explains that he is talking about acts of understanding, not the faculty of understanding itself. However, he doesn’t explain the contrast between finite and infinite understanding. By the latter he presumably means acts of understanding in so far as they are in the divine mind. So this proposition states that, whenever we understand anything, the object of our understanding is God, with his attributes and affections.

In the Demonstration, the expression ‘that which is contained objectively in the understanding’ means the object represented by it (it is the same is Descartes’ concept of ‘objective reality’ in his proof of the existence of God).

PROPOSITION 31

As Spinoza explains in the Demonstration, understanding is just one of a number of modes of thought. While absolute thought (or thinking in general) is an attribute of God, and therefore belongs to Nature naturing, its modes belong to Nature natured. This is a way of saying that God doesn’t have acts of understanding, volitions, feelings of love, etc.

SCHOLIUM TO PROPOSITION 31

After explaining that he is talking about acts of understanding, Spinoza says that we ‘perceive’ nothing more clearly than the act of understanding itself. Like Descartes, Spinoza uses the word ‘perceive’ for intellectual awareness or consciousness, as contrasted with sensation, which is concerned with images in the brain.

The last sentence is somewhat obscure. I think he means that every act of understanding enhances our understanding of understanding itself. So, since we are conscious of understanding every time we understand something, we are more familiar with understanding itself than with anything else.

PROPOSITION 32

As Spinoza explains in the Demonstration, this proposition applies equally to finite beings and to God with his infinite will. God’s will does not belong to his essence as absolutely infinite substance, but is only a mode of his attribute of thought. Like any other mode, it requires a cause. Consequently (Corollary 1), God does not act from free will.

COROLLARY 2 TO PROPOSITION 32

Here Spinoza makes the important point that will and understanding are in precisely the same position in relation to God as are motion and rest. In other words, they are infinite and eternal modes — in the one case of thought, and in the other case of extension. They all have to be caused, or be ‘determined to existence and action in a particular way’ (or this could be translated as ‘in a particular [finite] mode.’ Infinitely many things follow from a given act of God’s will or understanding (i.e. infinitely many finite modes follow from a divine act at the level of the infinite and eternal modes). But the same is true of motion and rest, from which infinitely many finite modes follow. Consequently, we should no more say that God acts from freedom of the will, than we say that he acts from freedom of motion or rest. His will follows from the necessity of his nature just like everything else.

In this, Spinoza is very close to Hobbes. Although Hobbes only discusses the will in a human context, he makes essentially the same point, that the will is inexorably caused like anything else. Although we can be said to be free in so far as an act is the consequence of our willing it rather than of some external cause, we don’t have freedom in the sense of being able to will what we will.

PROPOSITION 33

When Spinoza refers to the order of things, he doesn’t simply mean one thing happening after another (e.g. 1,3,2 instead of 1,2,3). The order of things means the systematic orderliness of Nature as a whole, or the system of laws of Nature governing its evolution. Although it would be more a paraphrase than a translation, Spinoza could be read as saying ‘. . . in any other way or in accordance with any other laws of Nature . . .’

The central point in the Demonstration is that the order of things follows necessarily from God’s nature (just as the properties of a triangle follow from the nature of triangularity). If you conceive a different order, you thereby conceive a different divine nature from which it follows. But divine nature is such that it must exist if it can be conceived. So it two different divine natures are conceivable, there must be two Gods — which is a contradiction.

SCHOLIUM 1 TO PROPOSITION P33

Now Spinoza explains the meanings of the terms ‘necessary’, ‘impossible’, ‘contingent’, and ‘possible’. His general thesis is that everything is either necessary or impossible. When we say something is ‘contingent’ or ‘possible’, we shouldn’t mean that it is really neither necessary nor impossible, but merely that we don’t know which it is. For example, if I toss a coin, I might say that heads and tails are equally possible; but all I should mean is that I have insufficient knowledge of its properties and the forces acting on it to be able to calculate which way it will fall on this particular occasion.

I have said elsewhere that Spinoza didn’t have a concept of the distinction between logical and physical necessity. Here he could be interpreted as making just such a distinction, when he says that things are necessary either if their existence follows from their essence, or if the efficient cause of their existence is present. But the distinction he is drawing is not between two kinds of necessity, but between two kinds of thing — abstract objects, and concrete material things.

In the case of abstract objects, he is making the very strong claim that, if they are not impossible, then they necessarily exist. For example, a round square is impossible, since there is no such concept or essence. But the equilateral triangle necessarily exists, since there is such an essence. However, the necessarily existent equilateral triangle is not to be confused with material triangles made out of wood or metal, since we can’t know whether or not the order of Nature permits the existence of a perfect instantiation of equilateral triangularity (almost certainly not, in fact).

As for concrete material objects, their existence doesn’t flow from their essence, otherwise anything could be defined into existence. They can only be brought into existence by efficient causes. But efficient causes are part of the total system of Nature, so that individual things come into being only if their existence is a necessary component of Nature as an organic whole. As we have already seen, for Spinoza the relation between cause and effect is exactly the same as the relation between premise and conclusion; only in the case of an individual physical event, the deduction is infinitely complex. The difference between the existence of abstract and concrete objects is that, in the former case existence follows from the nature of the object alone, whereas in the latter case, it follows from the nature of Nature as a whole, including all other concrete objects.

SCHOLIUM 2 TO PROPOSITION 33

There now follows a long Scholium of over a page (just two paragraphs in the original), in which Spinoza attacks the view that God can only be perfect if he has freedom of the will. Remember, as always, that the primary meaning of ‘perfection’ is ‘completeness’ or ‘fulness of being’, with little or no implication of moral or aesthetic goodness. Indeed, as Spinoza is going to argue in the Appendix to Book I, moral terminology has meaning only in relation to human interests, and cannot be applied to God.

{1} Spinoza starts by reiterating that the universe must be perfect, since it follows necessarily from the perfection of God’s nature. If it were different, God would be different, and therefore less perfect.

{2} However, he accepts that many people (such as Descartes, for example), will have a very different conception of God’s freedom from his own.

{3} In the Scholium to Proposition 17, Spinoza had argued that will doesn’t belong to God’s essence. He now says that, even if will did belong to his essence, it still follows that God could not have created the universe differently — consequently he had no freedom of choice between one possible universe and another.

His first point is that, since God is eternal, he is outside time, and there is no before or after in his nature. Consequently, there cannot have been any time before he made his creative decree, when he contemplated alternative universes, and willed to create one rather than another.

{4} Next, Spinoza counters a possible objection that God would have been no less perfect if he had decreed differently (this is in fact Descartes’ position). His argument is that, if one and the same God could have had a different understanding or will, then they would not follow necessarily from his nature, and he would be able to change his mind. It goes without saying that a God who changes his mind is less perfect than one who doesn’t. But I don’t think Spinoza has an answer to someone who says that, because God is perfect, he doesn’t change his mind; but at the time when he made up his mind, he had a range of possibilities to choose from (this is Leibniz’s position).

{5} But Spinoza then says that, even on their own principles, his opponents cannot allow that God’s understanding and will could have been different. First, it is agreed that God’s understanding is actual, not potential. This means that there can be no period of development from a possible decree to an actual one. Second, it is also agreed that God’s will and understanding are not distinct from his essence. Consequently, if his will and understanding were different, his essence would be different.

{7} Spinoza now considers a possible objection to his claim that the universe must be perfect (and by implication, that there is only one possible perfect universe). This is the (Cartesian) point that good and evil are not objective properties of things, but depend on God’s will. What we mean by ‘good’ is ‘ordained by God’, so whatever universe God willed to create, it would be perfect — even if it were the exact opposite of the actual universe.

{8} Spinoza’s response is that, if what is good depends on God’s will, then it must affect his understanding of what is good, so that he has conflicting understandings of what is good. (I thinks this argument works only if it is assumed that God already has an understanding of what is good — an assumption which Descartes would not accept. For Descartes, there is a single, arbitrary decree as to what is to be created and understood as good.) Spinoza then repeats his (better) argument that only one possible will can follow from the divine nature.

{9} Finally, Spinoza concedes that Descartes’ position has some merit. At least it’s better than saying that God acts in accordance with some objective criterion of goodness. To say this would make God subject to something external to his nature, and completely destroy his perfection.

The consequence (which Spinoza draws explicitly in the Appendix to Book I) is that goodness does not depend on God’s will, because the concept of goodness does not apply to God at all.

PROPOSITION 34

Finally Spinoza ends Book I with three short propositions concerning God’s power.

Proposition 34 identifies God’s power with his essence. Although Spinoza doesn’t explicitly say so here, this makes God’s power prior to his understanding and will, since they are not his essence itself, but follow from it.

PROPOSITION 35

This is little more than a restatement of Spinoza’s thesis that whatever is possible is necessary, and there is no such thing as an unactualised possibility. Here he expresses it in terms of God’s power, whereas previously he had expressed it in terms of God’s essence.

PROPOSITION 36

This last Proposition is the counterpart of the thesis that everything has a cause. Not only does everything have a cause, but everything also has an effect. Its significance is that the universe is a dynamic system, in which nothing is inert, and causal sequences never peter out. The Demonstration rests on the identification of God’s power with his essence — it is inconceivable that any individual thing, as a particular instance or mode of God’s power, could be ineffectual.

THE APPENDIX

{1} In the original, the Appendix is broken up into only 3 paragraphs. The style is much more narrative than the body of Book I, and I suggest you go through it as a whole. I think the argument is straightforward enough for you not to need any explanatory notes on it.