Spinoza's main work 'The Ethics' is not an easy work, partially because of the content but mostly because of the form. Spinoza argues in a rigorously logical deductive form, that is to say, starting with definitions and axioms which are held to be self-evidently true, then proceeding to propositions (claims) and finally proofs (arguments for the claims). Unlike Descartes who proceeded to do this in an informal conversational style, Spinoza's style is highly formalized, and is written like a work of mathematics.

His main starting and most famous point, is that there is only one substance in all of existence - God. God, according to Spinoza, is the whole universe and everything in it - you and I included. We are all just parts of a whole, and that whole is God. Clearly Spinoza's conception of God is not the traditional one; he equates God with the universe, not with Jehovah, the Trinity or Allah; not with one being who stands outside and beyond the universe in other words.

His argument for God being all that exists occurs in the first 15 propositions of 'The Ethics'. It is complex, and if I were to restate it with all the details (many of which are only introduced for later arguments in 'The Ethics') it would make a longer essay than Spinoza's extremely economical phrasing produces! So instead I will outline the main form of the argument, and then briefly mention some objections to it.

His Second Definition, listed at the start of the work, is that a thing is finite when something else of the same nature exists. This might seem contrary to the usual conception of finite, consider an infinitely large object - with such an object there would of course, be no more room for any other objects, for the infinite object would fill all infinity of space. Therefore if there is room for something else, the original object cannot really be infinitely large. This is what Spinoza has in mind. To him, infinite means having all of something; infinitely large means having all the space, infinitely red means having all the red, and so on.

His fourth definition is that of attributes, which he considers constitute the essence of a substance (a thing/object); these are seperate from what he calls affectations. The only attributes we can discover (not the only ones which exist) are thought and extension. Things like colour, position, weight, etc, which we might usually call attributes, are only affections according to Spinoza, and do not constitute the essence of a substance. This is basically the difference between attributes and affections; an attribute is fundamentally what an object is, whereas an affection is just the way it happens to be at the moment. An object without attributes cannot exist, for since attributes are what an object is, an object with no attributes is nothing.

The sixth definition describes God as an infinite being (substance) - that is, an object with infinite attributes. This was a common belief in Spinoza's day.

In his fifth proposition, Spinoza claims that there cannot be two or more substances with the same attributes. This is because the attributes form the essences of substances, and thus for two or more substances to have the same attributes would mean they have the same essence - which is another way of saying that they are the same thing. Obviously the same thing cannot exist in two different places at once, being two different things and one thing all at the same time - that is absurd.

Now consider what has so far gone. If you accept what Spinoza has so far said, then you must accept that, if God exists, then he is the only thing that exists. For if God has infinite attributes, to put it more plainly and in the way Spinoza meant, then God has all possible attributes. If we hold that no two substances can have the same attributes, then there can only be God, for there are no attributes left outside of him for another substance to consist of.

So clearly what Spinoza now has to prove is that such a being, an infinite God, does indeed exist. Then all the rest of the conclusions follow inexorably (or so it would seem).

In his third definition he describes a substance as that which can be conceived through itself, i.e. something which does not need something else to allow us to conceive it. In his fourth axiom he claims that knowledge of an effect requires knowledge of its cause, which seems evident. Therefore, if you accept these definitions, you can see that no substance can be caused by another - for then it could not be conceived through itself alone. All substances have themselves as their cause, which means existence belongs to their essence. In other words, they necessarily exist.

Since Spinoza defined God as a substance, it follows from this that God must necessarily exist.

Therefore, since God exists, and since his existence precludes anything else from existing, God is all that exists.

Objections

Logical arguments are unarguably true - if you agree with the propositions. In Spinoza's case what this means is that if you accept his definitions and axioms, you will find it difficult not to agree with his conclusions (unless you can find a flaw in his reasoning, which is not at all easy - although not impossible).

One such flaw was identified almost immediately by another great philosopher, Leibniz. He pointed out that while it seemed true that no two substances could have the same attribute make up, why couldn't they differ in one or more, while still being the same in others? A substance with attributes AB is undoubtedly the same as any substance with AB, but is it really the same as a substance with BC? This was Descartes' view - he held that all things shared the same attribute of extension, but were not the same substance, because they differed in thought (or souls).

Since The Ethics was published after Spinoza's death, he could make no reply to this objection. However I proffer the idea that Spinoza thought of this objection and ignored it. Not because it isn't valid, but because if he can prove that God exists, it becomes moot. Yes, substance AB and BC do share an attribute yet are different. But if God contains ABC, he precludes the existence of those two substances. Since God contains all the possible attributes, it is not possible for any other substance to differ in even one from him.

A much more damaging objection comes from our more modern concept of God. Nowadays, we would not accept as self-evident that God is an infinite being with infinite attributes - and we might well reject Spinoza's sixth definition. Even in Spinoza's day many would have thought twice before accepting that an infinite God would have infinite physical attributes; God was rather viewed as a spiritual being. Without this keystone definition, the rest of his argument collapses.

Spinoza's definition of substance as that which can be conceived through itself, also seems rather arbitrary and self-serving. What are the grounds for holding this to be true? He might have held it because a substance is something which is separate from anything else, but surely a substance X is still separate from another substance Y, even if that Y was the cause of X. The cue ball in a pool game might hit and move the black ball, but does that mean neither is really separate from each other?