The Logic of Hegel

by Georg Wilhelm Friedrich Hegel

This contradiction in the syllogism exhibits a new case of the infinite progression. Each of the premisses evidently calls for a fresh syllogism to demonstrate it: and as the new syllogism has two immediate premisses, like its predecessor, the demand for proof is doubled at every step, and repeated without end.

186.] On account of its importance for experience, there has been here noted a defect in the syllogism, to which in this form absolute correctness had been ascribed. This defect however must lose itself in the further specification of the syllogism. For we are now within the sphere of the notion; and here therefore, as well as in the judgment, the opposite character is not merely present potentially, but is explicit. To work out the gradual specification of the syllogism, therefore, there need only be admitted and accepted what is at each step realised by the syllogism itself.

Through the immediate syllogism I—P—U, the Individual is mediated (through a Particular) with the Universal, and in this conclusion put as a universal. It follows that the individual subject, becoming itself a universal, serves to unite the two extremes, and to form their ground of intermediation. This gives the second figure of the syllogism, (2) U—I—P. It expresses the truth of the first; it shows in other words that the intermediation has taken place in the individual, and is thus something contingent.

187.] The universal, which in the first conclusion was specified through individuality, passes over into the second figure and there now occupies the place that belonged to the immediate subject. In the second figure it is concluded with the particular. By this conclusion therefore the universal is explicitly put as particular—and is now made to mediate between the two extremes, the places of which are occupied by the two others (the particular and the individual). This is the third figure of the syllogism: (3) P—U—I.

What are called the Figures of the syllogism (being three in number, for the fourth is a superfluous and even absurd addition of the Moderns to the three known to Aristotle) are in the usual mode of treatment put side by side, without the slightest thought of showing their necessity, and still less of pointing out their import and value. No wonder then that the figures have been in later times treated as an empty piece of formalism. They have however a very real significance, derived from the necessity for every function or characteristic element of the notion to become the whole itself, and to stand as mediating ground.—But to find out what 'moods' of the propositions (such as whether they may be universals, or negatives) are needed to enable us to draw a correct conclusion in the different figures, is a mechanical inquiry, which its purely mechanical nature and its intrinsic meaninglessness have very properly consigned to oblivion. And Aristotle would have been the last person to give any countenance to those who wish to attach importance to such inquiries or to the syllogism of understanding in general. It is true that he described these, as well as numerous other forms of mind and nature, and that he examined and expounded their specialities. But in his metaphysical theories, as well as his theories of nature and mind, he was very far from taking as basis, or criterion, the syllogistic forms of the 'understanding.' Indeed it might be maintained that not one of these theories would ever have come into existence, or been allowed to exist, if it had been compelled to submit to the laws of understanding. With all the descriptiveness and analytic faculty which Aristotle after his fashion is substantially strong in, his ruling principle is always the speculative notion; and that syllogistic of 'understanding' to which he first gave such a definite expression is never allowed to intrude in the higher domain of philosophy.

In their objective sense, the three figures of the syllogism declare that everything rational is manifested as a triple syllogism; that is to say, each one of the members takes in turn the place of the extremes, as well as of the mean which reconciles them. Such, for example, is the case with the three branches of philosophy; the Logical Idea, Nature, and Mind. As we first see them, Nature is the middle term which links the others together. Nature, the totality immediately before us, unfolds itself into the two extremes of the Logical Idea and Mind. But Mind is Mind only when it is mediated through nature. Then, in the second place, Mind, which we know as the principle of individuality, or as the actualising principle, is the mean; and Nature and the Logical Idea are the extremes. It is Mind which cognises the Logical Idea in Nature and which thus raises Nature to its essence. In the third place again the Logical Idea itself becomes the mean: it is the absolute substance both of mind and of nature, the universal and all-pervading principle. These are the members of the Absolute Syllogism.

188.] In the round by which each constituent function assumes successively the place of mean and of the two extremes, their specific difference from each other has been superseded. In this form, where there is no distinction between its constituent elements, the syllogism at first has for its connective link equality, or the external identity of understanding. This is the Quantitative or Mathematical Syllogism: if two things are equal to a third, they are equal to one another.

Everybody knows that this Quantitative syllogism appears as a mathematical axiom, which like other axioms is said to be a principle that does not admit of proof, and which indeed being self-evident does not require such proof. These mathematical axioms however are really nothing but logical propositions, which, so far as they enunciate definite and particular thoughts, are deducible from the universal and self-characterising thought. To deduce them, is to give their proof. That is true of the Quantitative syllogism, to which mathematics gives the rank of an axiom. It is really the proximate result of the qualitative or immediate syllogism. Finally, the Quantitative syllogism is the syllogism in utter formlessness. The difference between the terms which is required by the notion is suspended. Extraneous circumstances alone can decide what propositions are to be premisses here: and therefore in applying this syllogism we make a pre-supposition of what has been elsewhere proved and established.

189.] Two results follow as to the form. In the first place, each constituent element has taken the place and performed the function of the mean and therefore of the whole, thus implicitly losing its partial and abstract character (§ 182 and § 184); secondly, the mediation has been completed (§ 185), though the completion too is only implicit, that is, only as a circle of mediations which in turn pre-suppose each other. In the first figure I—P—U the two premisses I is P and P is U are yet without a mediation. The former premiss is mediated in the third, the latter in the second figure. But each of these two figures, again, for the mediation of its premisses pre-supposes the two others.

In consequence of this, the mediating unity of the notion must be put no longer as an abstract particularity, but as a developed unity of the individual and universal—and in the first place a reflected unity of these elements. That is to say, the individuality gets at the same time the character of universality. A mean of this kind gives the Syllogism of Reflection.