Spinoza's Ethics: I.P14: Nothing But God

Here Spinoza raises the word affectiones which has been translated as "modifications" here, but is variously translated "accidents," "affections" and "states" by other translators. As I commented earlier, modifications seems most applicable. The concepts rem extensam, "extended thing" and rem cogitatem, "thinking thing" make their first appearance here. It is interesting that such profound distinctions are introduced in a Corollary 2 note.

Praeter Deum, nulla dari neque concipi potest substantia.

Translated as,

Except God, no substance can be nor be conceived.

Demonstratio: Cum Deus sit ens absolute infinitum de quo nullum attributum quod essentiam substantiae exprimit, negari potest (per definitionem 6) isque necessario existat (per propostionem 11) si aliqua substantia praeter Deum daretur, ea explicari deberet per aliquod attributum Dei sicque duae substantiae ejusdem attributi existerent, quod (per propositionem 5) est absurdum adeoque nulla substantia extra Deum dari potest et consequenter non etiam concipi. Nam si posset concipi, deberet necessario concipi ut existens; atqui hoc (per primam parem huius demonstrationis) est absurdum. Ergo extra Deum dari neque concipi potest substantia. Q.E.D.

Translated as,

Since God is an absolutely infinite being, about which no attribute that expresses the essence of substance can be denied existence (by D6). And God exists necessarily (by P11). If any substance except God were to exist, it would have to be explained through some attribute of God, and so two substances of the same attribute might exist, which (by P5) is absurd. And to such an extent, no substance beyond God can exist and consequently even be conceived. For if it could be conceived, it must necessarily be conceived as existing. But this conception (by the first part of this demonstration) is absurd. So, beyond God, substance can neither be nor be conceived.

Corollarium I: Hinc clarissime sequitur I Deum esse unicum hoc est (per definitionem 6) in rerum natura non nisi unam substantiam dari eamque absolute infinitam esse, ut in scolio propositionis 10 iam innuimus.

Translated as,

From this it follows most clearly, first, that God is one and only, that is (by D6), that in the nature of things there is only one substance and it is absolutely infinite, as we intimated in P10S.

Corollarium: Sequitur II rem extensam et rem cogitatem vel Dei attributa esse vel (per axioma 1) affectiones attributorum Dei.

Translated as,

It follows, second, that an extended thing and a thinking thing are either attributes of God, or (by A1) modifications of God's attributes.