III. By substance, I understand that which is in itself and is conceived through itself; in other words, that, the conception of which does not need the conception of another thing from which it must be formed. IV. By attribute, I understand that which the intellect perceives of substance, as constituting its essence. V. By mode, I understand the affections of substance, or that which is in another thing through which also it is conceived. VI. By God, I understand Being absolutely infinite, that is to say, substance consisting of infinite attributes, each one of which expresses eternal and infinite essence. _Explanation._--I say absolutely infinite but not infinite in its own kind (_in suo genere_); for of whatever is infinite only in its own kind (_in suo genere_), we can deny infinite attributes; but to the essence of that which is absolutely infinite pertains whatever expresses essence and involves no negation. VII. That thing is called free which exists from the necessity of its own nature alone, and is determined to action by itself alone. That thing, on the other hand, is called necessary, or rather compelled, which by another is determined to existence and action in a fixed and prescribed manner. VIII. By eternity, I understand existence itself, so far as it is conceived necessarily to follow from the definition alone of the eternal thing. _Explanation._--For such existence, like the essence of the thing, is conceived as an eternal truth. It cannot therefore be explained by duration of time, even if the duration be conceived without beginning or end. _Axioms_ I. Everything which is, is either in itself or in another. II. That which cannot be conceived through another must be conceived through itself. III. From a given determinate cause an effect necessarily follows; and, on the other hand, if no determinate cause be given, it is impossible that an effect can follow. IV. The knowledge (cognitio) of an effect depends upon and involves the knowledge of the cause. V. Those things which have nothing mutually in common with one another cannot through one another be mutually understood, that is to say, the conception of the one does not involve the conception of the other. VI. A true idea must agree with that of which it is the idea (_cum suo ideato_). VII. The essence of that thing which can be conceived as not existing does not involve existence. _The Essence of God_ God, or substance consisting of infinite attributes, each one of which expresses eternal and infinite essence, necessarily exists. [This can be proved in the following manner]: