19 Dec 2008

Figure and Negation in Spinoza's Letter 50 to Jelles

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Hegel Entry Directory]

[The following summarizes the first part of the letter. After which, I include the text of the letter in full.]

Spinoza explains his claim that God is not properly called one or single. He writes, "a thing can be called one or single only in respect of its existence, not of its essence. For we do not conceive things under the category of numbers unless they are included in a common class."

To explain this, I will begin first with what I summarize from § 395 of Hegel's Science of Logic:

Quantity comes about when something is related to something else in such a way that both are taken to be identical. Given that they are numerically different, they in a sense repel each other. But there is also an attraction between the two whereby they are taken as qualitatively identical even if they are not numerically identical. Thus each one unifies with its "self-externality" (its qualitatively but not quantitatively identical counterpart), and hence "Attraction is in this way the moment of continuity in quantity."

[(my summary is not based on a full read of the book, so confer with the original text for this section:
Quantity is sublated being-for-self; the repelling one which related itself only negatively to the excluded one, having passed over into relation to it, treats the other as identical with itself, and in doing so has lost its determination: being-for-self has passed over into attraction. The absolute brittleness of the repelling one has melted away into this unity which, however, as containing this one, is at the same time determined by the immanent repulsion, and as unity of the self-externality is unity with itself. Attraction is in this way the moment of continuity in quantity.)]

For Spinoza, two essences are not taken together as though they formed groups, because essences are a part of each other in a continuum [for more, see chapter 13 of Expressionism; Cours Vincennes: 10/03/1981; Cours Vincennes: 20/01/1981; and Cours Vincennes: 24/01/1978.] So essences cannot be grouped as units. However, we can think abstractly about existences as being discrete units that can be grouped [see Gueroult's "Spinoza's Letter on the Infinite" for more on this abstraction.] When we "group" essences, we are arbitrarily sectioning off region of intensive variation, like commonly shaded white areas of a white wall. But we cannot think of intensities individually. We can, although inaccurately, imagine existing extensive modes existing apart from each other, hence we can group them and take different existences as being of one category. This would seem to apply even more so to Spinoza's notion of simple bodies grouped together into compound bodies. These compound bodies can be imagined as complete and discrete, but their essences to which they correspond are part of an intensive continuum. Let's see how Hegel defines continuum in § 396 of Science of Logic:

I summarize this section as saying:

Continuity is a non-immediate unity of ones. What differentiates the ones does not interrupt their sequence. Continuity is the "the self-continuation of the different ones into those from which they are distinguished."

[Hegel actually writes:
Continuity is, therefore, simple, self-same self-relation, which is not interrupted by any limit or exclusion; it is not, however, an immediate unity, but a unity of ones which possess being-for-self. The asunderness of the plurality is still contained in this unity, but at the same time as not differentiating or interrupting it. In continuity, the plurality is posited as it is in itself; the many are all alike, each is the same as the other and the plurality is, consequently, a simple, undifferentiated sameness. Continuity is this moment of self-sameness of the asunderness, the self-continuation of the different ones into those from which they are distinguished.]

For Spinoza, the continuum of essential intensive degrees of power is not essentially made up of a plurality, because there are no discrete units to make up any such plurality. Rather, there is an infinite whole that is infinite because no number applies to it; for it cannot be divided (it is a continuum), but it is also not limited by anything else, because it has itself as its own cause.

Hegel seems to think that the infinity of Spinoza's substance is like what he means by pure quantity, because he writes in § 401:

It is the notion of pure quantity as opposed to the mere image of it that Spinoza, for whom it had especial importance, has in mind when he speaks of quantity as follows:

'Quantity is conceived by us in two manners, to wit, abstractly and superficially, as an offspring of imagination or as a substance, which is done by the intellect alone. If, then, we look at quantity as it is in the imagination, which we often and very easily do, it will be found to be finite, divisible, and composed of parts; but if we look at it as it is in the intellect and conceive it, in so far as it is a substance, which is done with great difficulty, then as we have already sufficiently shown, it will be found to be infinite, without like, and indivisible. This, to all who know how to distinguish between the imagination and the intellect, will be quite clear.'

So the infinite substance cannot be grouped with anything else, because it is unlimited and hence is nothing discrete. So we cannot "count" it: we cannot count any real parts in it, nor can we count it as a part of a broader group.

To illustrate, Spinoza has us imagine a man holding a penny and a dollar in his hand. He only counts these as two if they are two homogenized things (like how Hegel thinks that things must be taken as identical first before we can assign them a quantity). So no number can be assigned to the penny and dollar unless the man can firstly conceive the two as agreeing with each other through his applying a common name to them both, for example, "pieces of money or coin."

But God's existence is his essence, because his existence follows from his essence; for his essence is the cause of his existence. It is in his nature that his existence be involved in his essence, because he is productively defined that way. But essences are not divisible -- certainly not his essence, which is unlimited and infinite. So we cannot group God with something else, both of which taken to be things of a common sort. Therefore we cannot properly consider God as one or single, because this is applying number to something which is infinite and hence cannot be assigned a numerical value.

Spinoza then addresses his claim that figure is negation and is not something positive. Matter (extension?) considered in its totality, that is, considered without limitation, can have no figure, because figure can only be applied to finite and determinate bodies. When we apprehend a figure, that means we have apprehended a determinate thing along with its manner of determination. The thing has its own being, but when we apprehend it as a figure, we are not apprehending what it's being is, but everything that the being is not, because we are apprehending all that stands over-against it and serving to delimit it, that is, we are apprehending all that is opposed to it, all that negates it. So something's determination does not pertain to its being, but rather to its non-being.

So since figure is nothing but determination, and determination is negation, figure can be nothing other than negation, as has been said.

The letter's text:



[Of the difference between the political theories of Hobbes and Spinoza, of the Unity of God, of the notion of figure, of the book of a Utrecht professor against the Tractatus Theologico-Politicus.]

Most courteous Sir,—As regards political theories, the difference which you inquire about between Hobbes and myself, consists in this, that I always preserve natural right intact, and only allot to the chief magistrates in every state a right over their subjects commensurate with the excess of their power over the power of the subjects. This is what always takes place in the state of nature.

Again, with regard to the demonstration which I establish in the appendix to my geometric exposition of Cartesian principles, namely, that God can only with great impropriety be called one or single, I answer that a thing can only be called one or single in respect of existence, not in respect of essence. For we do not conceive things under the category of numbers, unless they have first been reduced to a common genus. For example, he who holds in his hand a penny and a crown piece will not think of the twofold number, unless he can call both the penny and the crown piece by one and the same name, to wit, coins or pieces of money. In the latter case he can say that he holds two coins or pieces of money, inasmuch as he calls the crown as well as the penny, a coin, or piece of money. Hence, it is evident that a thing cannot be called one or single, unless there be afterwards another thing conceived, which (as has been said) agrees with it. Now, since the existence of God is His essence, and of His essence we can form no general idea, it is certain, that he who calls God one or single has no true idea of God, and speaks of Him very improperly.

As to the doctrine that figure is negation and not anything positive, it is plain that the whole of matter considered indefinitely can have no figure, and that figure can only

p. 370

exist in finite and determinate bodies. For he who says, that he perceives a figure, merely indicates thereby, that he conceives a determinate thing, and how it is determinate. This determination, therefore, does not appertain to the thing according to its being, but, on the contrary, is its non-being. As then figure is nothing else than determination, and determination is negation, figure, as has been said, can be nothing but negation.

The book, which a Utrecht professor wrote against mine, and which was published after his death, I saw lying in a bookseller's window. From the little I then read of it, I judged it unworthy of perusal, still less of reply. I, therefore, left the book, and its author. With an inward smile I reflected, that the most ignorant are ever the most audacious and the most ready to rush into print. The Christians seem to me to expose their wares for sale like hucksters, who always show first that which is worst. The devil is said to be very cunning, but to my thinking the tricks of these people are in cunning far beyond his. Farewell.

The Hague, 2 June, 1674.

Spinoza. The Letters. Transl Samuel Shirley. Cambridge: Hackett Publishing Company, Inc., 1995, pp.259-260.

Text reproduction from R. H. M. Elwes translation, available online at:

Hegel. Science of Logic. Transl. A.V. Miller. George Allen & Unwin, 1969.
Text available online at:

No comments:

Post a Comment