Spinoza's Proof for an Infinity of Attributes of One Substance

by Corry Shores
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From Ethics Book I

I.Def.3 “By substance, I mean that which is in itself, and is conceived through itself : in other words, that of which a conception can be formed independently of any other conception.”

I.Def.4 “By attribute, I mean that which the intellect perceives as constituting the essence of substance.”

I.Def.5 “By mode, I mean the modifications of substance, or that which exists in, and is conceived through, something other than itself.”

I.5 “There cannot exist in the universe two or more substances having the same nature or attribute.”

If there were several distinct substances, we could only distinguish them by means of a difference in their attributes or in their modes.

If each substance were different because it possessed a unique attribute that the other substances lacked, then to each substance there would belong at least one distinguishing unique attribute.

But then, they are differentiated according to the ways that each substance lacks some attribute another one has; in other words, they would have to be co-defined. Yet, a substance is conceived by itself, and thus it cannot be that there are different substances differing only in attributes.

Then substances would have to be distinguished according to their modes.

We know that substances are prior to modes; for, modes are in substance and conceived through them, but substances are conceived in themselves, hence substances must be prior to modes.

But this means that modes are not involved in defining a thing’s essence, hence they cannot be used to distinguish substances.

But, if substances can be distinguished neither by attribute nor by mode, then there is no means to differentiate substances, hence there is but one substance.

I.10. "Each particular attribute of the one substance must be conceived through itself."

Attributes are what the intellect grasps as an essence of substance. But substances must be conceived by themselves, and hence one of its essences must as well, for if instead it required that one essence be conceived in terms of another, then it would no longer be an essence of a self-conceivable substance.

I.8. “Every substance is necessarily infinite.”

A substance would be either finite or infinite. But if it is finite, it would be limited by another substance of the same nature or attribute, but we know that there cannot be multiple substances of the same attribute.

I.9 “The more reality or being a thing has, the greater the number of its attributes (Def. iv.).”

There more being something has, the greater its nature, hence the greater its number of attributes.

I.Schol.10 Infinite attributes express one substance.

Substance, as infinite, would have an infinity of essence, hence infinite attributes.

And thus:

I.11 "God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists."

Spinoza. Ethics. Transl. Elwes. available online at:

http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html

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