the ground that His nature involves necessary
existence, which you
asked for, and I took note of, I have been prevented by various
business from sending to you before. In order to accomplish my
purpose, I will premise-
definition of anything includes nothing except the simple nature of the thing defined. From this it follows-
definition can involve or express a multitude or a given number of individuals, inasmuch as it involves and expresses nothing except the nature of the thing as it is in itself. For instance, the definition of a triangle includes nothing beyond the simple nature of a triangle; it does not include any given number of triangles. In like manner, the definition of the mind as a thinking thing, or the definition of God as a perfect Being, includes nothing beyond the natures of the mind and of God, not a given number of minds or gods.
definition of the thing itself (to wit, because existence belongs to its nature or necessarily includes it), or externally to the thing.
definition of man does not involve the number of twenty men. Hence (by our fourth hypothesis) the cause for the existence of these twenty men, and consequently for the existence of each of them, must exist externally to them. We may thus absolutely conclude, that all things, which are conceived to exist in the plural number, must necessarily be produced by external causes and not by the force of their own nature. But since (by our second hypothesis) necessary existence appertains to the nature of God, His true definition must necessarily include necessary existence: therefore from His true definition His necessary existence must be inferred. But from His true definition (as I have already demonstrated from our second and third hypotheses) the necessary existence of many gods cannot be inferred. Therefore there only follows the existence of a single God. Which was to be proved.
essence and existence; but bearing in mind the object you mentioned to me, I have preferred to send you the demonstration given above. I hope it will satisfy you, and I will await your reply, meanwhile remaining, &c.
Voorburg, 7 Jan., 1666.