The Logic of Hegel

by Georg Wilhelm Friedrich Hegel

People generally speak of the analytical and synthetical methods, as if it depended solely on our choice which we pursued. This is far from the case. It depends on the form of the objects of our investigation, which of the two methods, that are derivable from the notion of finite cognition, ought to be applied. In the first place, cognition is analytical. Analytical cognition deals with an object which is presented in detachment, and the aim of its action is to trace back to a universal the individual object before it. Thought in such circumstances means no more than an act of abstraction or of formal identity. That is the sense in which thought is understood by Locke and all empiricists. Cognition, it is often said, can never do more than separate the given concrete objects into their abstract elements, and then consider these elements in their isolation. It is, however, at once apparent that this turns things upside down, and that cognition, if its purpose be to take things as they are, thereby falls into contradiction with itself. Thus the chemist e.g. places a piece of flesh in his retort, tortures it in many ways, and then informs us that it consists of nitrogen, carbon, hydrogen, &c. True: but these abstract matters have ceased to be flesh. The same defect occurs in the reasoning of an empirical psychologist when he analyses an action into the various aspects which it presents, and then sticks to these aspects in their separation. The object which is subjected to analysis is treated as a sort of onion from which one coat is peeled off after another.

228.] This universality is (2) also a specific universality. In this case the line of activity follows the three 'moments' of the notion, which (as it has not its infinity in finite cognition) is the specific or definite notion of understanding. The reception of the object into the forms of this notion is the Synthetic Method.

The movement of the Synthetic method is the reverse of the Analytical method. The latter starts from the individual, and proceeds to the universal; in the former the starting-point is given by the universal (as a definition), from which we proceed by particularising (in division) to the individual (the theorem). The Synthetic method thus presents itself as the development of the 'moments' of the notion on the object.

229.] (α) When the object has been in the first instance brought by cognition into the form of the specific notion in general, so that in this way its genus and its universal character or speciality are explicitly stated, we have the Definition. The materials and the proof of Definition are procured by means of the Analytical method (§ 227). The specific character however is expected to be a 'mark' only: that is to say it is to be in behoof only of the purely subjective cognition which is external to the object.

Definition involves the three organic elements of the notion: the universal or proximate genus genus proximum, the particular or specific character of the genus (qualitas specified,) and the individual, or object defined.—The first question that definition suggests, is where it comes from. The general answer to this question is to say, that definitions originate by way of analysis. This will explain how it happens that people quarrel about the correctness of proposed definitions; for here everything depends on what perceptions we started from, and what points of view we had before our eyes in so doing. The richer the object to be defined is, that is, the more numerous are the aspects which it offers to our notice, the more various are the definitions we may frame of it. Thus there are quite a host of definitions of life, of the state, &c. Geometry, on the contrary, dealing with a theme so abstract as space, has an easy task in giving definitions. Again, in respect of the matter or contents of the objects defined, there is no constraining necessity present. We are expected to admit that space exists, that there are plants, animals, &c., nor is it the business of geometry, botany, &c. to demonstrate that the objects in question necessarily are. This very circumstance makes the synthetical method of cognition as little suitable for philosophy as the analytical: for philosophy has above all things to leave no doubt of the necessity of its objects. And yet several attempts have been made to introduce the synthetical method into philosophy. Thus Spinoza, in particular, begins with definitions. He says, for instance, that substance is the causa sui. His definitions are unquestionably a storehouse of the most speculative truth, but it takes the shape of dogmatic assertions. The same thing is also true of Schelling.

230.] (ß) The statement of the second element of the notion, i.e. of the specific character of the universal as particularising, is given by Division in accordance with some external consideration.

Division we are told ought to be complete. That requires a principle or ground of division so constituted, that the division based upon it embraces the whole extent of the region designated by the definition in general. But, in division, there is the further requirement that the principle of it must be borrowed from the nature of the object in question. If this condition be satisfied, the division is natural and not merely artificial, that is to say, arbitrary. Thus, in zoology, the ground of division adopted in the classification of the mammalia is mainly afforded by their teeth and claws. That is so far sensible, as the mammals themselves distinguish themselves from one another by these parts of their bodies; back to which therefore the general type of their various classes is to be traced. In every case the genuine division must be controlled by the notion. To that extent a division, in the first instance, has three members: but as particularity exhibits itself as double, the division may go to the extent even of four members. In the sphere of mind trichotomy is predominant, a circumstance which Kant has the credit of bringing into notice.

231.] (γ) In the concrete individuality, where the mere unanalysed quality of the definition is regarded as a correlation of elements, the object is a synthetical nexus of distinct characteristics. It is a Theorem. Being different, these characteristics possess but a mediated identity. To supply the materials, which form the middle terms, is the office of Construction: and the process of mediation itself, from which cognition derives the necessity of that nexus, is the Demonstration.

As the difference between the analytical and synthetical methods is commonly stated, it seems entirely optional which of the two we employ. If we assume, to start with, the concrete thing which the synthetic method presents as a result, we can analyse from it as consequences the abstract propositions which formed the pre-suppositions and the material for the proof. Thus, algebraical definitions of curved lines are theorems in the method of geometry. Similarly even the Pythagorean theorem, if made the definition of a right-angled triangle, might yield to analysis those propositions which geometry had already demonstrated on its behoof. The optionalness of either method is due to both alike starting from an external pre-supposition. So far as the nature of the notion is concerned, analysis is prior; since it has to raise the given material with its empirical concreteness into the form of general abstractions, which may then be set in the front of the synthetical method as definitions.