d. In the fourth place Spinoza defines attributes, which, as the moment

coming second to substance, belong to it. “By attribute I understand that which the mind perceives as constituting the essence of substance;” and to Spinoza this alone is true. This is an important determination; the attribute is undoubtedly a determinateness, but at the same time it remains a totality. Spinoza, like Descartes, accepts only two attributes, thought and extension. The understanding grasps them as the reality of substance, but the reality is not higher than the substance, for it is only reality in the view of the understanding, which falls outside substance. Each of the two ways of regarding substance—extension and thought—contains no doubt the whole content of substance, but only in one form, which the understanding brings with it; and for this very reason both sides are in themselves identical and infinite. This is the true completion; but where substance passes over into attribute is not stated.

e. The fifth definition has to do with what comes third in relation to substance, the mode. “By mode I understand the affections of substance, or that which is in something else, through the aid of which also it is conceived.” Thus substance is conceived through itself; attribute is not conceived through itself, but has a relation to the conceiving understanding, in so far as this last conceives reality; mode, finally, is what is not conceived as reality, but through and in something else.

These last three moments Spinoza ought not merely to have established in this way as conceptions, he ought to have deduced them; they are especially important, and correspond with what we more definitely distinguish as universal, particular and individual. They must not, however, be taken as formal, but in their true concrete sense; the concrete universal is substance, the concrete particular is the concrete species; the Father and Son in the Christian dogma are similarly particular, but each of them contains the whole nature of God, only under a different form. The mode is the individual, the finite as such, which enters into external connection with what is “other.” In this Spinoza only descends to a lower stage, the mode is only the foregoing warped and stunted. Spinoza’s defect is therefore this, that he takes the third moment as mode alone, as a false individuality. True individuality and subjectivity is not a mere retreat from the universal, not merely something clearly determinate; for, as clearly determinate, it is at the same time Being-for-itself, determined by itself alone. The individual, the subjective, is even in being so the return to the universal; and in that it is at home with itself, it is itself the universal. The return consists simply and solely in the fact of the particular being in itself the universal; to this return Spinoza did not attain. Rigid substantiality is the last point he reached, not infinite form; this he knew not, and thus determinateness continually vanishes from his thought.

f. In the sixth place, the definition of the infinite is also of importance, for in the infinite Spinoza defines more strictly than anywhere else the Notion of the Notion. The infinite has a double significance, according as it is taken as the infinitely many or as the absolutely infinite (_infra_, p. 263). “The infinite in its kind is not such in respect of all possible attributes; but the absolutely infinite is that to whose essence all belongs that expresses an essence and contains no negation.” In the same sense Spinoza distinguishes in the nine-and-twentieth Letter (Oper. T. I. pp. 526-532) the infinite of imagination from the infinite of thought (_intellectus_), the actual (_actu_) infinite. Most men, when they wish to strive after the sublime, get no farther than the first of these; this is the false infinite, just as when one says “and so on into infinity,” meaning perhaps the infinity of space from star to star, or else the infinity of time. An infinite numerical series in mathematics is exactly the same thing. If a certain fraction is represented as a decimal fraction, it is incomplete; ⅐ is, on the contrary, the true infinite, and therefore not an incomplete expression, although the content here is of course limited. It is infinity in the incorrect sense that one usually has in view when infinity is spoken of; and even if it is looked on as sublime, it yet is nothing present, and only goes ever out into the negative, without being actual (_actu_). But for Spinoza the infinite is not the fixing of a limit and then passing beyond the limit fixed—the sensuous infinity—but absolute infinity, the positive, which has complete and present in itself an absolute multiplicity which has no Beyond. Philosophic infinity, that which is infinite _actu_, Spinoza therefore calls the absolute affirmation of itself. This is quite correct, only it might have been better expressed as: “It is the negation of negation.” Spinoza here also employs geometrical figures as illustrations of the Notion of infinity. In his _Opera postuma_, preceding his Ethics, and also in the letter quoted above, he has two circles, one of which lies within the other, which have not, however, a common centre.

“The inequalities of the space between A B and C D exceed every number; and yet the space which lies between is not so very great.” That is to say, if I wish to determine them all, I must enter upon an infinite series. This “beyond” always, however, remains defective, is always affected with negation; and yet this false infinite is there to hand, circumscribed, affirmative, actual and present in that plane as a complete space between the two circles. Or a finite line consists of an infinite number of points; and yet the line is present here and determined; the “beyond” of the infinite number of points, which are not complete, is in it complete and called back into unity. The infinite should be represented as actually present, and this comes to pass in the Notion of the cause of itself, which is therefore the true infinity. As soon as the cause has something else opposed to it—the effect—finitude is present; but here this something else is at the same time abrogated and it becomes once more the cause itself. The affirmative is thus negation of negation, since, according to the well-known grammatical rule, _duplex negatio affirmat_. In the same way Spinoza’s earlier definitions have also the infinite already implied in them, for instance in the case of the just mentioned cause of itself, inasmuch as he defines it as that whose essence involves existence (_supra_, p. 258). Notion and existence are each the Beyond of the other; but cause of itself, as thus including them, is really the carrying back of this “beyond” into unity. Or (_supra_, p. 259) “Substance is that which is in itself and is conceived from itself;” that is the same unity of Notion and existence. The infinite is in the same way in itself and has also its Notion in itself; its Notion is its Being, and its Being its Notion; true infinity is therefore to be found in Spinoza. But he has no consciousness of this; he has not recognized this Notion as absolute Notion, and therefore has not expressed it as a moment of true existence; for with him the Notion falls outside of existence, into the thought of existence.

g. Finally Spinoza says in the seventh place: “God is a Being absolutely infinite, _i.e._ a substance consisting of infinite attributes, each of which expresses an eternal and infinite essence.” Does substance, one might here ask, possess an infinite number of attributes? But as with Spinoza there are only two attributes, thought and extension, with which he invests God, “infinite” is not to be taken here in the sense of the indeterminate many, but positively, as a circle is perfect infinity in itself.

The whole of Spinoza’s philosophy is contained in these definitions, which, however, taken as a whole are formal; it is really a weak point in Spinoza that he begins thus with definitions. In mathematics this method is permitted, because at the outset we there make assumptions, such as that of the point and line; but in Philosophy the content should be known as the absolutely true. It is all very well to grant the correctness of the name-definition, and acknowledge that the word “substance” corresponds with the conception which the definition indicates, but it is quite another question to determine whether this content is absolutely true. Such a question is not asked in the case of geometrical propositions, but in philosophic investigation it is the very thing to be first considered, and this Spinoza has not done. Instead of only explaining these simple thoughts and representing them as concrete in the definitions which he makes, what he ought to have done was to examine whether this content is true. To all appearance it is only the explanation of the words that is given; but the content of the words is held to be established. All further content is merely derived from that, and proved thereby; for on the first content all the rest depends, and if it is established as a basis, the other necessarily follows. “The attribute is that which the understanding thinks of God.” But here the question is: How does it come that besides the Deity there now appears the understanding, which applies to absolute substance the two forms of thought and extension? and whence come these two forms themselves? Thus everything proceeds inwards, and not outwards; the determinations are not developed from substance, it does not resolve itself into these attributes.

2. These definitions are followed by axioms and propositions in which Spinoza proves a great variety of points. He descends from the universal of substance through the particular, thought and extension, to the individual. He has thus all three moments of the Notion, or they are essential to him. But the mode, under which head falls individuality, he does not recognize as essential, or as constituting a moment of true existence in that existence; for it disappears in existence, or it is not raised into the Notion.

a. The main point then is that Spinoza proves from these Notions that there is only One Substance, God. It is a simple chain of reasoning, a very formal proof. “Fifth Proposition: There cannot be two or more substances of the same nature or of the same attribute.” This is implied already in the definitions; the proof is therefore a useless and wearisome toil, which only serves to render Spinoza more difficult to understand. “If there were several” (substances of the same attribute) “they must be distinguished from one another either by the diversity of their attributes or by the diversity of their affections” (modes). “If they are distinguished by their attributes, it would be directly conceded that there is only one substance having the same attribute.” For the attributes are simply what the understanding grasps as the essence of the one substance, which is determined in itself, and not through anything else. “But if these substances were distinguished by their affections, since substance is by nature prior to its affections it would follow that if from substance its affections were abstracted and it were regarded in itself, _i.e._ in its truth, it could henceforth not be regarded as distinct from other substances.” “Eighth Proposition: All substance is necessarily infinite. Proof: For otherwise it must be limited by another substance of the same nature, in which case there would be two substances of the same attribute, which is contrary to the fifth proposition.” “Every attribute must be conceived for itself,” as determination reflected on itself. “For attribute is what the mind conceives of substance as constituting its essence, from which it follows that it must be conceived through itself,” _i.e._ substance is what is conceived through itself (see the fourth and third definitions). “Therefore we may not argue from the plurality of attributes to a plurality of substances, for each is conceived by itself, and they have all been, always and at the same time, in substance, without the possibility of the one being produced by the other.” “Substance is indivisible. For if the parts retained the nature of the substance, there would be several substances of the same nature, which is contrary to the fifth proposition. If not, infinite substance would cease to exist, which is absurd.”[195]

“Fourteenth Proposition: No other substance than God can either exist or be conceived. Proof: God is the absolutely infinite substance, to whom can be denied no attribute which expresses the essence of substance, and He exists necessarily; therefore if there were a substance other than God, it must be explained by means of an attribute of God.” Consequently the substance would not have its own being, but that of God, and therefore would not be a substance. Or if it were still to be substance, “then there would necessarily follow the possibility of there being two substances with the same attribute, which according to the fifth proposition is absurd. From this it then follows that the thing extended and the thing that thinks” are not substances, but “are either attributes of God, or affections of His attributes.” By these proofs and others like them not much is to be gained. “Fifteenth, proposition: What is, is in God, and cannot exist or be conceived without God.” “Sixteenth proposition: By the necessity of the divine nature infinite things must follow in infinite modes, _i.e._, all that can fall under the infinite understanding. God is therefore the absolute First Cause.”[196]

Spinoza then ascribes freedom and necessity to God: “God is the absolute free cause, who is determined by nothing outside of Himself, for He exists solely by the necessity of His nature. There is no cause which inwardly or outwardly moves Him to act, except the perfection of His nature. His activity is by the laws of His Being necessary and eternal; what therefore follows from His absolute nature, from His attributes, is eternal, as it follows from the nature of the triangle from eternity and to eternity that its three angles are equal to two right angles.” That is to say, His Being is His absolute power; _actus_ and _potentia_, Thought and Being, are in Him one. God has not therefore any other thoughts which He could not have actualized. “God is the immanent cause of all things, not the transient (_transiens_),” _i.e._, external cause. “His essence and His existence are the same, namely, the truth. A thing which is determined to perform some action, is, since God is cause, necessarily determined thereto by God; and a thing which is thus determined cannot render itself undetermined. In nature nothing is contingent. Will is not a free cause, but only a necessary cause, only a mode; it is therefore determined by another. God acts in accordance with no final causes (_sub ratione boni_). Those who assert that He does so, appear to establish something apart from God, which does not depend on God, and which God in His working keeps in view, as though it were an end. If this view is taken, God is not a free cause, but is subject to fate. It is equally inadmissible to subject all things to the arbitrary pleasure of God, _i.e._, to His indifferent will.”[197] He is determined solely by His own nature; the activity of God is thus His power, and that is necessity. He is then absolute power in contrast to wisdom, which sets up definite aims, and consequently limitations; particular aims, thoughts of what is about to come to pass, and the like are therefore put out of the question. But beyond this universal, no advance is made; for it must be noticed as specially singular, that Spinoza in the fiftieth Letter (Oper. T. I. p. 634) says that every determination is a negation. Moreover, if God is the cause of the world, it is implied that He is finite; for the world is here put beside God as something different from Him.

b. The greatest difficulty in Spinoza is, in the distinctions to which he comes, to grasp the relation of this determinate to God, at the same time preserving the determination. “God is a thinking Being, because all individual thoughts are modes which express God’s nature in a certain and determinate manner; there pertains therefore to God an attribute the conception of which all individual thoughts involve, and by means of this they also are conceived. God is an extended Being for the same reason.” This means that the same substance, under the attribute of thought, is the intelligible world, and under the attribute of extension, is nature; nature and thought thus both express the same Essence of God. Or, as Spinoza says, “The order and system of natural things is the same as the order of the thoughts. Thus, for instance, the circle which exists in nature, and the idea of the existing circle, which is also in God, are one and the same thing” (they are one and the same content), “which is” merely “expressed by means of different attributes. If we therefore regard nature either under the attribute of extension or of thought, or under any other attribute whatever, we shall find one and the same connection of causes, _i.e._, the same sequence of things. The formal Being of the idea of the circle can be conceived only by means of the mode of thought, as its proximate cause, and this mode again by means of another, and so on infinitely; so that we must explain the order of the whole of nature, or the connection of causes, by the attribute of thought alone, and if things are considered by the attribute of extension, they must be considered only by the attribute of extension,—and the same holds good of other causes.”[198] It is one and the same system, which at one time appears as nature, and at another time in the form of thought.

But Spinoza does not demonstrate how these two are evolved from the one substance, nor does he prove why there can only be two of them. Neither are extension and thought anything to him in themselves, or in truth, but only externally; for their difference is a mere matter of the understanding, which is ranked by Spinoza only among affections (Eth. P. I. Prop. XXXI. Demonst. p. 62), and as such has no truth. This has in recent times been served up again by Schelling in the following form: In themselves, the intelligent world and the corporeal world are the same, only under different forms; so that the intelligent universe is in itself the whole absolute divine totality, and the corporeal universe is equally this same totality. The differences are not in themselves, but the different aspects from which the Absolute is regarded are matters external to it. We take a higher tone in saying that nature and mind are rational; but reason is for us no empty word, for it means the totality which develops itself within itself. Again, it is the standpoint of reflection to regard aspects only, and nothing in itself. This defect appears in Spinoza and Schelling in the fact that they see no necessity why the Notion, as the implicit negative of its unity, should make a separation of itself into different parts; so that out of the simple universal the real, the opposed, itself becomes known. Absolute substance, attribute and mode, Spinoza allows to follow one another as definitions, he adopts them ready-made, without the attributes being developed from the substance, or the modes from the attributes. And more especially in regard to the attributes, there is no necessity evident, why these are thought and extension in particular.