Selection from – Ethics – Part I. Of Deus sive Natura (Page 4)
Spinoza's Words: (without (Deus sive Natura) nothing can be)
Proposition. XIII. Substance absolutely infinite is indivisible.
Proof.—If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which is absurd. If the latter, then substance absolutely infinite could cease to exist, which is also absurd.
Proposition. XIV. Besides (Deus sive Natura) no substance can be granted or conceived.
Corollary I.—Clearly, therefore: 1. (Deus sive Natura) is one, that is only one substance can be granted in the universe, and that substance is absolutely infinite..
Corollary II.—It follows: 2. That extension and thought are attributes of (Deus sive Natura).
Proposition. XV. Whatsoever is, is in (Deus sive Natura) and without (Deus sive Natura) nothing can be, or be conceived.
Comment:
Infinity is a concept that is notoriously difficult to handle. Substance is that something out of which everything. including mental concepts, come. Spinoza's proof of the proposition that infinite substance is indivisible goes like this: suppose that something infinite is divided in two - if they are both infinite there would be two fundamental infinities. He considers that impossible. And for infinite substance to lose its infinite attributes by division is equally impossible. Therefore, he concludes, infinite substance is indivisible. The following propositions and corollaries are straight forward and important to his system of philosophy.
The doctrine of substance has a long history in philosophical thought, especially in metaphysical discussions. Thinkers have long struggled with efforts to try to describe ultimate reality. The persistent thought is that there must be some one thing out of which everything is made. It has been a struggle to define an underlying unity which the human mind seems to long for.