Front Page Titles (by Subject) LETTER XXXIX.: Spinoza to Christian Huyghens. - The Chief Works of Benedict de Spinoza, vol. 2
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LETTER XXXIX.: Spinoza to Christian Huyghens. - Benedict de Spinoza, The Chief Works of Benedict de Spinoza, vol. 2 
The Chief Works of Benedict de Spinoza, translated from the Latin, with an Introduction by R.H.M. Elwes, vol. 2 De Intellectus Emendatione - Ethica. (Select Letters). Revised edition (London: George Bell and Sons, 1901).
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Spinoza to Christian Huyghens.
(Treating of the Unity of God.)
The demonstration of the unity of God, on 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—
I. That the true definition of anything includes nothing except the simple nature of the thing defined. From this it follows—
II. That no 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.
III. That for everything that exists there must necessarily be a positive cause, through which it exists.
IV. This cause may be situate either in the nature and definition of the thing itself (to wit, because existence belongs to its nature or necessarily includes it), or externally to the thing.
From these premisses it follows, that if any given number of individuals exists in nature, there must be one or more causes, which have been able to produce exactly that number of individuals, neither more nor less. If, for instance, there existed in nature twenty men (in order to avoid all confusion, I will assume that these all exist together as primary entities), it is not enough to investigate the cause of human nature in general, in order to account for the existence of these twenty; we must also inquire into the reason, why there exist exactly twenty men, neither more nor less. For (by our third hypothesis) for each man a reason and a cause must be forthcoming, why he should exist. But this cause (by our second and third hypotheses) cannot be contained in the nature of man himself; for the true 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.
This, distinguished Sir, has now seemed to me the best method for demonstrating the proposition. I have also proved it differently by means of the distinction between 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.