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; 1/7 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;”
