Third subdivision of the Logic: The doctrine of the concept

 Addition. The standpoint of the concept is in general that of absolute idealism, and philosophy is knowing conceptually [begreifendes Erkennen]. It is conceptual knowing insofar as everything that ordinary consciousness regards as an entity, and in its immediacy as independent, is known [gewußt] merely as an ideal moment in it. In logic at the level of the understanding [Verstandeslogik] the concept is usually considered as a mere form of thinking and, more precisely, as a universal representation. The claim, so often repeated from the side of sentiment and the heart, that concepts as such are something dead, empty, and abstract, refers to this low-level construal of the concept. Meanwhile, just the opposite holds and the concept is instead the principle of all life and thereby, at the same time, something absolutely concrete. That such is the case has emerged as the result of the entire logical movement up to this point and hence does not need first to be proven here. As far as the opposition of form and content is concerned in this connection, namely, with respect to the concept as allegedly merely formal, this opposition, like all the other oppositions held fast by reflection, is already behind us as something overcome dialectically, that is to say through itself, and it is precisely the concept which contains all the earlier determinations of thinking as sublated determinations in itself. To be sure, the concept needs to be considered as form, but only as infinite, fecund form that encompasses the fullness of all content within itself and at the same time releases it from itself. By the same token, the concept may also be called 'abstract', if by 'concrete' one understands what presents itself to the senses as concrete – what can be perceived in any immediate way at all. We cannot grasp the concept as such with our hands and, when it comes to the concept, we generally have to take leave of seeing and hearing. Nonetheless, the concept is at the same time, as already noted, the absolutely concrete, and indeed is so insofar as it contains in itself being and essence, and accordingly contains the entire richness of these two spheres in an ideal [ideeller] unity. – If, as previously noted, the diverse stages of the logical idea can be considered as a series of definitions of the absolute, then the definition of the absolute that is the result for us here is that the absolute is the concept. To be sure, one must in this case then construe the concept in a sense different from and higher than occurs in logic at the level of the understanding, for which the concept is regarded merely as a form of our subjective thinking, a form devoid of content in itself. In light of this, there is only one question that could still be raised. If in speculative logic 'concept' has a meaning completely different from the one that would otherwise be ordinarily associated with the expression, why is what is completely different in this sense [dieses ganz Andere] nonetheless called the 'concept' here, when doing so occasions misunderstanding and confusion? The reply to such a question would be that, however great the distance between the concept of formal logic and the speculative concept, it still turns out, on closer inspection, that the profounder meaning of the concept is by no means as alien to the ordinary use of language as might at first seem to be the case. One speaks of the derivation of a content, such as, for example, the derivation of legal determinations concerning property from the concept of property, and one speaks also conversely of tracing such a content back to the concept. With this, however, it is recognized that the concept is not merely a form devoid of content in itself, since, on the one hand, there would be nothing to derive from the latter and, on the other, in tracing a given content back to the empty form of the concept, the content would not only be robbed of its determinacy; it would also not be known.

 Addition. Passing over into an other is the dialectical process in the sphere of being and the process of shining in an other within the sphere of essence. The movement of the concept is, by contrast, the development, by means of which that alone is posited that is already on hand in itself. In nature it is the organic life, which corresponds to the stage of the concept. Thus, for example, the plant develops itself out of its seed. This seed contains the entire plant in itself already, but in an ideal manner and so one should not construe its development as if the various parts of the plant, root, stem, leaves, and so forth were already really in the seed yet merely in utterly miniature fashion. This is the so-called 'Chinese box hypothesis', the deficiency of which consists in the fact that what is only on hand initially in an ideal manner is considered as already concretely existing. What is right in this hypothesis is, by contrast, this: that the concept, in its process, remains with itself and that nothing new is posited by this means with respect to the content. Instead only an alteration of form is brought forth. It is then, too, this nature of the concept (that of demonstrating itself in its process as self-development) that one has one's eyes on when one speaks of ideas innate to human beings or considers all learning, as Plato did, merely as recollection. Yet this likewise should not be understood as if what makes up the content of the consciousness educated by instruction were already on hand previously in the same consciousness in the specific way that that content unfolds. – The movement of the concept is to be considered, as it were, merely as a play; the other posited by it is in fact not an other. In the Christian religious doctrine, this is articulated in such a way that God not only created a world that as an other stands over against him, but also that he has, from all eternity, produced a son in whom he is with himself as spirit.

 Addition 1. When there is talk of concepts, one usually has in view an abstract universality and the concept would then also be customarily defined as a universal representation. One accordingly speaks of colour, plant, animal, and so forth, and these concepts are supposed to arise by way of the fact that, in the process of leaving aside the particular factor through which the diverse colours, plants, animals, and so forth are distinguished from one another, we hold fast to what is common to them. This is the manner in which the understanding construes the concept and it is right for sentiment [Gefühl] to declare such concepts to be hollow and empty, mere schemata and shadows. But the universal factor of the concept is not merely something common, opposite which the particular has its standing for itself. Instead the universal factor is the process of particularizing (specifying) itself and remaining in unclouded clarity with itself in its other. It is of the most enormous importance as much for knowing as for our practical comportment that the merely common is not confused with the truly universal factor [Allgemeinen], the universal [Universellen]. All the reproaches that tend to be raised from the standpoint of sentiment against thinking in general, and then, more particularly, against philosophical thinking, are grounded in this confusion, as is the often-repeated claim about the dangerousness of thinking, allegedly driven to extremes. Moreover, in its true and encompassing meaning, the universal is a thought, of which it has to be said that it cost millennia before entering into human consciousness and which attained full recognition only through Christendom. The Greeks, who were otherwise so highly cultivated, knew neither God in his true universality nor even the human being. The Greek gods were only the particular powers of the spirit, and the universal God, the God of nations, was still the hidden God for the Athenians. So, too, for the Greeks there was an absolute chasm between them and the barbarians, and the human being as such was not yet recognized in his infinite worth and his infinite justification. When, indeed, the question has been posed why slavery has disappeared in modern Europe, first the one and then the other particular circumstance is cited to explain this phenomenon. The true reason why there are no longer slaves in Christian Europe is to be sought in nothing other than the principle of Christendom itself. The Christian religion is the religion of absolute freedom, and only for the Christian is the human being as such valid, in his infiniteness and universality. What the slave lacks is the recognition of his personhood; the principle of personhood, however, is the universality. The master regards the slave not as a person but as a basic matter [Sache] devoid of a self, and the slave himself does not count as an 'I'; instead, the master is his 'I'. – The previously mentioned difference between the merely common and the truly universal is articulated in Rousseau's well-known Contrat social in a quite fitting manner where it is said that the laws of a state would have to proceed from the universal will (volonté générale) without, however, needing at all to be the will of all (volonté de tous). In relation to the theory of the state, Rousseau would have accomplished something more thorough, had he always kept this distinction in mind. The universal will is the concept of the will and the laws are the particular determinations of the will, grounded [begründet] in this concept.

 Addition 2. In regard to the usual discussion in logic [operating] at the level of the understanding, about the emergence and formation of concepts, it remains to be noted that we do not form the concepts at all and that the concept in general is not to be considered something that has a genesis at all. To be sure, the concept is not merely being or the immediate; instead, mediation is also part of it. However, this mediation lies in the concept itself, and the concept is what mediates itself through itself and with itself. It is wrong to assume, first that there are objects which form the content of our representations and then our subjective activity comes along behind them, forming the concepts of objects by means of the earlier mentioned operation of abstracting and gathering together what is common to the objects. On the contrary, the concept is what is truly first and the things are what they are, thanks to the activity of the concept dwelling in them and revealing itself in them. In our religious consciousness this surfaces in such a way that we say, 'God created the world out of nothing' or, to put it otherwise, 'the world and finite things have gone forth out of the fullness of divine thoughts and divine decrees'. In this manner it is recognized that the thought and, more precisely, the concept is the infinite form or the free, creative activity, which is not in need of some stuff on hand outside itself, in order to realize itself.

 Addition. The judgment is customarily regarded as a combination of concepts and, indeed, diverse sorts of concepts. What is right in this construal is this, that the concept forms the presupposition of the judgment and makes its appearance in the judgment in the form of the difference. But it is wrong to speak of diverse sorts of concepts, for the concept, although concrete, is still essentially one and the moments contained in it are not to be considered as diverse sorts. Moreover, it is equally false to speak of a combination of the sides of the judgment since, when there is talk of a combination, then what are combined are thought of as being on hand for themselves even apart from the combination. This external construal is evident then in an even more determinate fashion if it is said of a judgment that it comes about by virtue of the fact that a predicate is attributed to a subject. In this connection the subject counts as something obtaining externally for itself and the predicate as something occurring in our head. Meanwhile, the copula 'is' already contradicts this representation. If we say 'this rose is red' or 'this painting is beautiful', what is thereby said is not that it is we who in some external fashion make the rose red or the painting beautiful, but instead that these are the objects' own determinations. A further deficiency of the usual way of construing judgment (usual in formal logic) consists in the fact that, as a consequence of this construal, the judgment generally appears as something merely contingent and the progression from concept to judgment is not demonstrated. The concept as such, however, is not something in itself stagnant [verharrend], devoid of process, as the understanding thinks. To the contrary, as infinite form, it is absolutely active, as it were, the punctum saliens of all vitality, and accordingly differentiates itself from itself. This diremption posited by the concept's own activity, the diremption of the concept into the difference between its moments, is the judgment, the meaning of which is accordingly to be construed as the particularization of the concept. In itself, the concept is, to be sure, already the particular but, in the concept as such, the particular is not yet posited, but is instead still in transparent unity with the universal. Thus, for example, as earlier noted (§ 160 Addition), the seed of a plant already contains the particular factor of the root, of the branches, of the leaves, and so forth. But this particular factor is at first only on hand in itself and is only posited in that the seed discloses itself, something which is to be considered the judgment of the plant. This example can also serve to draw notice to the fact that neither the concept nor the judgment are merely occurrences in our head and are not fashioned merely by us. The concept is something that dwells within the things themselves, by means of which they are what they are, and to comprehend [begreifen] an object means accordingly to become conscious of its concept [Begriff]. If we then take the next step to judging the object, it is not our subjective doing that accounts for attributing this or that predicate to the object. Instead we consider the object in the determinacy posited by its concept.

 Addition. If one says: 'The subject is that of which something is asserted and the predicate is what is asserted of it', then this is to say something quite trivial. One learns nothing more precise about the difference between the two by this means. As far as the thought of the subject is concerned, it is initially the individual and the predicate the universal. In the further development of the judgment, it then happens that the subject does not remain merely the immediately individual and the predicate merely the abstract universal. Subject and predicate then also acquire a [new] meaning, the former that of the particular and universal, the latter that of the particular and individual. This exchange in the meaning of the two sides of the judgment is what takes place under the two designations of 'subject' and 'predicate'.

 Addition. The various species of judgment are to be construed not merely as an empirical manifold, but instead as a totality determined by thinking. One of Kant's great services is to have provided some validation for this demand. Kant divided judgments, according to the schema of his table of categories, into judgments of quality, quantity, relation, and modality. Although this division set up by Kant cannot be recognized as adequate (in part because of the merely formal application of the schema of these categories, in part also because of their content), underlying this division, nevertheless, is the genuine intuition that it is the universal forms of the logical idea itself through which the diverse species of judgment are determined. Accordingly, we initially obtain three main species of judgment, which correspond to the stages of being, essence, and concept. The second of these main species is then doubled in turn, corresponding to the character of essence as the stage of difference [Differenz]. The inner ground of this systematic [character] of the judgment is to be sought in the fact that, since the concept is the ideal unity of being and essence, its unfolding, as it comes about in the judgment, also has to reproduce initially these two stages in a transformation [Umbildung] that conforms to the concept, while it itself, the concept, demonstrates itself to be the determining factor for the genuine judgment. – The various species of judgment are to be considered, not as standing next to one another with the same value but instead as forming a sequence of stages, whose differences rest upon the logical meaning of the predicate. This sort of consideration is also already at hand in ordinary consciousness to the extent that one does not hesitate to ascribe a very slight capacity for judgment to those only used to making such judgments like 'this wall is green', 'this stove is hot', and so forth. At the same time, by contrast, it will be said that someone truly understands how to judge only if his judgments concern whether a certain artwork is beautiful, an action is good, and the like. In judgments of the first-mentioned species, the content forms merely an abstract quality and the immediate perception suffices to decide on its presence, whereas, by contrast, if it is said that an artwork is beautiful or that an action is good, the objects named are compared with what they ought to be, i.e. with their concept.

 Addition. Correctness and truth are very frequently considered to mean the same thing in ordinary life and one accordingly speaks of the truth of some content where it is a matter of mere correctness. Correctness generally affects merely the formal agreement of our representation with its content; however this content may be otherwise constituted. The truth consists, by contrast, in the agreement of the object with itself, i.e. with its concept. It may be correct anyway that someone is sick or that someone has stolen something. But such content is not true since a sick body is not in agreement with the concept of life, and so too theft is an action that does not correspond to the concept of human action. What is to be taken from these examples is that an immediate judgment, in which an abstract quality is asserted of something immediately individual, however correct it might be, still contains no truth since subject and predicate do not stand in the judgment in the connection of reality and concept to one another. – The lack of truth of the immediate judgment consists, further, in the fact that its form and content do not correspond to one another. If we say 'this rose is red', then it lies in the copula 'is' that subject and predicate agree with one another. But now the rose, as something concrete, is not merely red; instead it also has an odour, a determinate form, and many other sorts of determinations that are not contained in the predicate 'red'. On the other side, this predicate, as an abstract universal, does not apply merely to this subject. There are also, in addition, other flowers and generally other objects that are likewise red. Subject and predicate in the immediate judgment thus come into contact with one another, as it were, only at one point but they do not cover one another. The state of affairs is quite different in the conceptual judgment. If we say 'this action is good', this is then a conceptual judgment. One notices immediately that here, between subject and predicate, there is not this loose and external connection as there is in the immediate judgment. In the immediate judgment the predicate consists in some abstract quality or other which may or may not apply to the subject. In the conceptual judgment, by contrast, the predicate is, as it were, the soul of the subject, by means of which the subject, as the body of this soul, is determined through and through.

 Addition. The negative-infinite judgment, in which no relation at all between subject and predicate is on hand any more, is usually cited in formal logic merely as a senseless [sinnlose] curiosity. Nevertheless, this infinite judgment is in fact not to be considered merely as a contingent form of subjective thinking. Instead it ensues as the very next dialectical result of the preceding, immediate judgments (of the positive and the simply negative), whose finitude and lack of truth explicitly come to light in it. Crime can be regarded as an objective example of the negative-infinite judgment. Whoever commits a crime, more precisely a theft, does not merely negate, as in the civil juridical dispute, the particular right of someone else to this specific matter. Instead he negates the right of that person altogether and, for this reason, he is not merely ordered to restore the matter which he stole, but is instead punished in addition because he violated the right as such, i.e. the right in general. The civil juridical dispute is, by contrast, an example of the simple-negative judgment since in it merely this particular right is negated and right in general is recognized in the process. The connection here is thus as it is for the negative judgment 'this flower is not red', by means of which merely this particular colour, but not colour altogether, is negated in regard to the flower since it can still be blue, yellow, and so forth. Likewise then, too, death is a negative-infinite judgment in contrast to sickness, which is a simple-negative judgment. In a sickness, merely this or that particular vital function is restricted or negated; by contrast, in death, as one would say, body and soul separate from one another, i.e. subject and predicate fall completely outside one another.

 Addition. The judgment of reflection is distinguished generally from the qualitative judgment by the fact that its predicate is no longer an immediate, abstract quality but instead of the sort that, by means of it, the subject demonstrates itself to be related to the other. If we say, for example, 'this rose is red', we consider the subject in its immediate individuality without relation to another. If, by contrast, we make the judgment 'this plant has healing powers', we consider the subject, the plant, as standing in relation with another (the illness to be healed by it) through its predicate, the healing capacity. Matters are similar with the judgments 'this body is elastic', 'this instrument is useful', 'this punishment works as a deterrent', and so forth. The predicates of such judgments are generally determinations of reflection, by means of which one has moved beyond the immediate individuality of the subject while the concept of it is still not given. – The usual sort of rationalizing [Räsonnement] tends above all to immerse itself in this manner of judgment. The more concrete the object of concern, the more viewpoints it presents for reflection, by means of which, meanwhile, the distinctive nature, i.e. its concept, is not exhausted.

 Addition. Since it is determined in the singular judgment as universality, the subject by this means moves beyond itself, past itself as this mere individual. When we say 'this plant has healing powers', this entails not merely that this individual plant has them but that several or some do and this results in the particular judgment ('Some plants have healing powers', 'Some human beings are inventive', and so forth). Through this particularity, the immediately individual [subject] loses its self-sufficiency and enters into a connection [Zusammenhang] with another. The human being is, as this human being, no longer merely this individual human being; instead he stands alongside other human beings and is thus one in a group [Menge]. Precisely by this means, however, it also belongs to the universal and is thereby elevated. The particular judgment is positive as well as negative. If only some bodies are elastic, then the rest are not elastic. – Herein lies, then, again the progression to the third form of the judgment-of-reflection, i.e. to the judgment of the set of all ('all human beings are mortal', 'all metals are conductors of electricity'). The set of all [Allheit] is that very form of universality towards which reflection at first tends. In this connection the individuals form the foundation and it is our subjective act by means of which the individuals are gathered together and are determined [as belonging together] in their entirety [als Alle bestimmt]. The universal appears here only as an external bond which encompasses the individuals subsisting for themselves and indifferent to it. The universal is, nevertheless, in fact the ground and basis, the root and substance of the individual. If we consider, for example, Caius, Titus, Sempronius, and the other inhabitants of a city or a country, then the fact that they are collectively human beings is not merely something common to them, but their universal, their genus, and all these individuals would not be at all without this, their genus. In contrast to this, matters are different with that superficial, only so-called universality that is in fact something that merely accrues to all individuals and is common to them. It has been noted that human beings, in contrast to animals, have this in common with one another, that they are equipped with ear lobes. It is, meanwhile, apparent that if, somehow, one or the other should not have ear lobes, the rest of his being, his character, his capacities, and so forth would not be affected by this. It would, by contrast, make no sense to assume that Caius could somehow not be a human being but be brave, learned, and so forth. What the individual human being is in particular, this is only insofar as he is, above all, a human being as such and in the universal sense [im Allgemeinen], and this universal is not only something external to and alongside other abstract qualities or mere determinations of reflection. Instead it is much more what pervades everything particular, encompassing it within itself.

 Addition. The progression from the reflexive judgment of the set of all to the necessary judgment can be found already in our ordinary consciousness insofar as we say: 'what accrues to everything, accrues to the genus and is, therefore, necessary.' When we say: 'all plants', 'all humans', and so forth, this is the same as if we say 'the plant', 'the human', and so forth.

 Addition. The categorical judgment ('Gold is a metal', 'The rose is a plant') is the immediate judgment of necessity and corresponds, in the sphere of essence, to the relationship of substantiality. All things are a categorical judgment, i.e. they have their substantial nature, which forms the fixed and unchangeable foundation of them. Only when we regard things from the viewpoint of their genus and as determined by it with necessity, does the judgment begin to be a true one. It must be designated a deficiency in someone's training in logic, if judgments like these: 'Gold is expensive' and 'gold is a metal' are regarded as standing on the same level. That gold is expensive concerns an external relation of it to our inclinations and needs, to the costs of acquiring it, and so on, and the gold remains what it is, even if that external relation alters or falls away. By contrast, being a metal constitutes the substantial nature of gold, without which it or anything else that is otherwise in it or asserted of it cannot subsist. Matters are the same if we say 'Caius is a human being'; in this way we declare that everything that he may otherwise be only has value and meaning insofar as it corresponds to this, his substantial nature, to be a human being. – Furthermore, however, even the categorical judgment remains deficient insofar as in it the factor of particularity does not yet receive its due. Thus, for example, the gold is indeed metal, but silver, copper, iron, and so forth are likewise metals, and being metal as such behaves indifferently to the particular character of its species. Herein lies the progression from the categorical to the hypothetical judgment which can be expressed by the formula: 'if A is, then B is'. We have here the same progression as earlier from the relationship of substantiality to the relationship of causality. In the hypothetical judgment, the determinacy of the content appears as mediated, as dependent upon another, and this is then precisely the relationship of cause and effect. The meaning of the hypothetical judgment is then generally this, that through it the universal is posited in its particularization and, with this, we acquire, as the third form of necessary judgment, the disjunctive judgment. 'A is either B or C or D'; the poetic artwork is either epic or lyrical or dramatic; the colour is either yellow or blue or red, and so on. The two sides of the disjunctive judgment are identical. The genus is the totality of its species and the totality of the species is the genus. This unity of the universal and the particular is the concept and it is this, which now forms the content of the judgment.

 Addition. Like the concept and the judgment, the syllogism also tends to be regarded merely as a form of our subjective thinking and, in keeping with this tendency, it is said that the syllogism is the justification [Begründung] of the judgment. Now, to be sure, the judgment points to the syllogism, but it is not merely our subjective doing through which this progression comes about. Instead it is the judgment itself that posits itself as syllogism and, in doing so, returns to the unity of the concept. More precisely, it is the apodictic judgment that forms the transition to the syllogism. In the apodictic judgment we have an individual that relates itself, thanks to its constitution, to its universal, i.e. its concept. The particular appears here as the mediating middle between the individual and the universal and this is the basic form of the syllogism, the further development of which, formally construed, consists in the fact that the individual and the universal also occupy this place, by means of which the transition from subjectivity to objectivity is then formed.

 Addition. In keeping with the construal of the syllogism, mentioned above, as the form of the rational, reason itself has been defined as the capacity to make syllogistic inferences and understanding, by contrast, as the capacity to form concepts. Underlying these definitions is a representation of the spirit as the mere sum of powers or capabilities lying next to one another. Apart from this superficial representation, what is to be noted about this combination of the understanding with the concept and reason with the syllogism is that just as little as the concept is to be regarded merely as a determination of the understanding, so, too, the syllogism is to be regarded without further ado as rational. On the one hand, what is usually treated in formal logic in the doctrine of the syllogism is in fact nothing other than the mere syllogism of the understanding, which in no way deserves the honour of counting as the form of the rational, indeed, as the rational itself. On the other hand, the concept as such is so little merely a form of understanding that it is rather the understanding in the mode of abstracting alone, through which the concept is demoted to this level. In accordance with this, there is also a tendency to distinguish mere concepts of the understanding [Verstandesbegriffe] and concepts of reason [Vernunftbegriffe], which is nevertheless not to be understood as though there were two distinct species of concepts but instead much more so that it is our doing either to stand pat merely with the negative and abstract form of the concept or to construe it, in keeping with its true nature, as at the same time positive and concrete. Thus, for example, the concept of freedom, insofar as it is a mere concept of the understanding, is freedom considered as the abstract opposite of necessity, while the true and rational concept of freedom contains in itself necessity as sublated. Similarly, the definition of God put forward by so-called deism, is the concept of God insofar as it is a mere concept of the understanding, while by contrast the Christian religion, knowing [wissen] God as the triune God, contains the rational concept of God.

 Addition. The syllogism of existence is a syllogistic inference merely at the level of understanding and, indeed, insofar as the individuality, the particularity, and the universality stand opposite one another in an entirely abstract manner here. Thus, this syllogism is then the most extreme way that the concept comes to be outside itself. We have here something immediately individual as a subject; some particular side, a property, in this subject is then emphasized and by means of this property the individual demonstrates itself to be a universal. So, for example, we say 'this rose is red; red is a colour, therefore, this rose is something coloured'. It is this form [Gestalt] of the syllogism, above all, that is typically discussed in ordinary logic. In former times, the syllogism was considered the absolute rule of all knowing and a scientific claim obtained then as something justified only if it was demonstrated in a manner mediated by a syllogism. Today one encounters the diverse forms of the syllogism almost exclusively only in compendia of logic, and acquaintance with those various forms counts as empty pedantry, of no further use of any sort either in practical life or even in science. In this regard, it deserves to be noted, first, that although it would be superfluous and pedantic to enter on the scene at each occasion with the entire elaboration of formal modes of inferring, the diverse forms of inference nonetheless continue to impose themselves on our knowing. For example, if someone waking up in the morning during the wintertime hears carriages clanging on the street and this occasions him to consider that things may well have frozen solid, he performs an operation of inferring and we repeat this operation daily amidst the most manifold complications. Becoming explicitly conscious of this, one's daily actions as a thinking being might thus at least be of no slighter interest than the well-recognized interest in becoming acquainted, not only with the functions of our organic life, e.g. the functions of digestion, production of the blood, breathing, and so forth, but also with the functions of the processes and formations of nature surrounding us. It will undoubtedly have to be conceded in this connection that just as little as a foregoing study of anatomy and physiology is needed in order to digest properly, to breath properly, and so on, one needs to have studied logic first in order to draw proper conclusions. – It is Aristotle who first observed and described the diverse forms and so-called figures of the syllogism in their subjective meaning and, indeed, did so with such sureness and determinacy that essentially nothing further had to be added. Although this accomplishment brings Aristotle great honour, by no means is it the forms of syllogistic inference at the level of understanding or at the level generally of finite thinking that he employed in his genuine philosophical investigations (see the note to § 189).

 Addition. As little as in the daily course of life one tends even to think of inference at the level of understanding, it nonetheless plays its role incessantly there. Thus, for example, in the civil dispute of law, it is the business of the advocates to make the most favourable claim to a right [Rechtstitel] for their parties. In a logical respect, however, such a claim to a right is nothing other than a medius terminus. The same also takes place in diplomatic negotiations if, for example, diverse powers lay claim to one and the same land. In this connection, the right of inheritance, the geographical location of the land, the descendancy and language of its inhabitants, or any sort of other ground can be taken up as medius terminus.

 Addition. The objective sense of the figures of the syllogism is in general this, that everything rational demonstrates itself in the form of a threefold syllogism and, to be sure, in such a way that each of its members occupies equally the position of an extreme and that of the mediating middle. This is expressly the case with the three members of philosophical science, i.e. the logical idea, nature, and spirit. First, nature here is the middle member that joins the others together. Nature, this immediate totality, unfolds into the two extremes of the logical idea and spirit. The spirit, however, is spirit only by being mediated by nature. Second, then, the spirit, which we know [wissen] as individual and active, is the middle, and nature and the logical idea are the extremes. It is the spirit that recognizes in nature the logical idea and elevates it to its essence. Third, the logical idea is similarly the middle; it is the absolute substance of the spirit as of nature, the universal, what pervades everything. These are the members of the absolute syllogism.

 Addition. The quantitative syllogism mentioned here surfaces familiarly in mathematics as an axiom. It is customarily said of it, as of the other axioms, that its content cannot be proven, but also that this proof is not needed since it is immediately evident. Nevertheless, these mathematical axioms are in fact nothing other than logical sentences that are to be derived, insofar as particular and determinate thoughts can be articulated in them, from universal and self-determining thinking, a derivation which has to be considered then as their proof. This is the case here with the quantitative syllogism, set up in mathematics as an axiom that demonstrates itself to be the next result of the qualitative or immediate syllogism. – The quantitative syllogism, moreover, is the completely formless inference since in it the difference between the members, a difference determined by the concept, is sublated. Which sentences here are supposed to be premises depends upon external circumstances and, for this reason, in the application of this syllogism one presupposes what already stands fast and is proven elsewhere.

 Addition. The syllogism with respect to the set of all refers to the syllogism of induction in which the individuals form the middle that joins together the extremes. If we say 'all metals are electric conductors', this is an empirical sentence that results from testing undertaken with all individual metals. By this means, we get the inference of induction, which has the following form:
P – I – U
I
I
.
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Gold is metal, silver is metal; similarly, copper, lead, and so forth. This is the major premise. Then comes the minor premise 'all these bodies are electric conductors', and from this results the conclusion that all metals are electric conductors. Hence, here the individuality in the sense of the set of all is the binding factor. This syllogism then likewise sends us on to another syllogism in turn. It has, as its middle, the complete set of individuals. This presupposes that the observation and experience be completed in a certain domain. But because it is a matter of individualities here, this yields in turn the progression [Progreß] into infinity (I, I, I…). In an induction the individuals can never be exhausted. If one says 'all metals', 'all plants', and so forth, this only means as much as 'all metals, all plants with which one is familiar up to now'. Each induction is, therefore, imperfect. One has, indeed, made this and that observation, one has made many observations, but not all cases, not all individuals have been observed. It is this deficiency of induction that leads to analogy. From the fact that things of a certain genus have a certain property, it is inferred in the syllogism of analogy that other things of the same genus have the same property. Thus, for example, it is a syllogism of analogy if it is said: this law of motion has been found previously to hold for all planets; hence, a newly discovered planet will probably move according to the same law. In empirical sciences, analogy is rightly held in high regard and very important results have been attained on this path. It is the instinct of reason that has the presentiment that this or that empirically uncovered determination is grounded in the inner nature or the genus of an object and which is further based on this. Incidentally, analogy can be more superficial or more rigorous [gründlich]. Suppose, for example, it is said: 'Gaius, a human being, is a learned individual; Titus is also a human being; hence, he is also likely to be learned.' This is in any case a very bad analogy and, indeed, for this reason, that for a human being to be learned is not grounded without further ado in this, his genus. Nonetheless, the same sort of superficial analogies occur very frequently. Thus, for example, it is customarily said: 'the Earth is a heavenly body and has inhabitants; the Moon is also a heavenly body; hence, it is probably also inhabited'. This analogy is not a bit better than the previously mentioned one. That the Earth has inhabitants does not rest merely on the fact that it is a heavenly body; in addition, further conditions are also required, such as, first and foremost, the fact that it is surrounded by an atmosphere, that there is water on hand (something connected to that atmosphere), and so forth – conditions that, as far as we know, are lacking in the case of the Moon. What is called 'philosophy of nature' in the modern era consists to a great extent in a vapid play with empty, external analogies, which are nonetheless supposed to count as profound results. On account of this, philosophical consideration of nature has fallen into a deserved disrepute [Mißkredit].

 Addition. In ordinary logic, the first part, forming the so-called 'doctrine of elements', tends to come to a close with the treatment of the doctrine of the syllogism. Following upon this is the so-called 'doctrine of method', as the second part, in which it is supposed to be demonstrated how an entire body of scientific knowledge is to be brought about, through application of the forms of thinking, treated in the doctrine of elements, to the objects²⁷ at hand. Logic at the level of the understanding provides no further information about where these objects come from and what sort of a connection it has in general with the thought of objectivity. Thinking counts here as a merely subjective and formal activity, while what is objective, in contrast to thinking, counts as something firm and on hand for itself. This dualism, however, is not the true state of things [das Wahre] and it is a thoughtless procedure to take up the determinations of subjectivity and objectivity without further ado and to refrain from inquiring into their origin. Both, subjectivity as well as objectivity, are in any case thoughts and, to be sure, determinate thoughts which have to demonstrate themselves in universal and self-determining thinking. This has happened here first with respect to subjectivity. We have come to recognize this, or the subjective concept, which contains in itself the concept as such, the judgment, and the syllogism as the dialectical result of the first two major stages of the logical idea, namely, the stages of being and of essence. If it is said of the concept, 'it is subjective and only subjective', then this is completely correct insofar as it is, to be sure, subjectivity itself. But then, in addition, no less subjective than the concept as such are the judgment and the syllogism, determinations that in ordinary logic, next to the so-called 'laws of thought' (the principles of identity, difference, and sufficient reason), form the content of the so-called 'doctrine of elements'. Furthermore, this subjectivity with the determinations of it mentioned here (the concept, the judgment, and the syllogism) is not to be considered an empty framework which first has to acquire its filling from without, through objects on hand for themselves. Instead it is the subjectivity itself that, as dialectical, breaks through its limitation and by means of the syllogism discloses itself to be objectivity.