HEGEL ON FORMAL LOGIC

Abstract

The paper refers to the meaning of formal logic within Hegel's philosophical systems starting from the twofold meaning of the forms of classical logic: notion or concept, judgment and syllogism. The main point is that a formal approach of these forms is an unavoidable step of the construction of the speculative idea. In order to clarify the significance of these forms Hegel undertakes a speculative interpretation of these forms of logic, mixing their classical meaning with their speculative one.

Headnote

Abstract: The paper refers to the meaning of formal logic within Hegel's philosophical systems starting from the twofold meaning of the forms of classical logic: notion or concept, judgment and syllogism. The main point is that a formal approach of these forms is an unavoidable step of the construction of the speculative idea. In order to clarify the significance of these forms Hegel undertakes a speculative interpretation of these forms of logic, mixing their classical meaning with their speculative one.

Keywords: speculative logic, classical logic, concept, judgment, syllogism.

Throughout his Science of Logic, but also in the Logic of the Encyclopedia, Hegel associates the idea of the formal with subjectivity and abstraction. Formal logic, the theory of notion, judgment, and syllogism is a subjective logic or, following Kant, an approach onto the forms of thinking as opposed to the object, or of logic as separated from ontology. Thought thinking upon itself, leaving aside all objects - the definition of formal logic offered by Kant - is the very theory of these forms. From a Hegelian viewpoint, there are two distinct moments: the concept in its metaphysical interpretation, where being and essence are moments of the concept; the categories, in this case, belong to thinking, but subjectivity is withdrawn, thus the concept "is not aware" of the fact that these determinations ar of its own and credits them as belonging to the object; the second one is related to the concept in its logical interpretation; in this case, the concept considers all determinations as its own, in a subjective manner, first of all as forms of thought as separated from the object of thinking and then as objective - the concept "being aware" of the fact that the objectis linked to the subjectivity; finally, the unity of the two moments, within the idea, where the objective and subjective determination coincide. At this level the concept reaches its most suitable form, which is also the form of its object.

The concept is, in fact, the object in its most adequate meaning, at the peak of its authenticity. The concept is the substance of the object, the nature of the object as such. Thus, the forms of the concept are, at the same time, forms of the object or modes in which the object manifests its nature. The identification of the object and the concept is, effectively, produced at the level of the determinations of the idea, thus throughout the third part of subjective logic. These determinations of the object are taken as becoming to the object alone, throughout the section regarding objectivity. Within the first section, dealing with subjectivity, thought reclaims them for itself and takes them as forms of its own, as independent from the object, but still pertaining to the object, since they are forms by means of which thought grasps its object. Therefore, formal logic deals with the forms of subjective thinking as forms that belong to this type of thinking, but are, at the same time, forms by means of which subjective thinking grasps its object, or, to be more precise, forms that render the object with its structure. Now, since the concept is the object in its authentic nature, this means that the forms of subjective thinking, that are discovered by the turning of thought onto itself, are, in fact, forms that belong to the object, since they express its very nature. Therefore, in Hegel's formal logic, the forms express the nature of the object, but belong to thought; their separate approach - meaning formal logic - is an approach that takes them as structures of subjective thinking that have an objective value, meaning that they express the nature of the object (because the nature of the object can be expressed only by thinking and, as a consequence, by the use of its forms). This type of forms can be displayed only by a research upon thught as such, and not by means of dissecting the object, as Hegel did throughout the objective logic, precisely because in this case all determinations belonged to the object as indifferent to the subject, thus one could never say that the concept is the very nature of the object. Thus, formal logic is also a type of research that aims to displaying the fundamental forms under which thought grasps its object. Naturally, as it is subjective, this logic implies also an objective application, and this really happens within Hegel's subjective logic, throughout the chapter regarding the idea. Within the section on objectivity, thought grasps its object starting from its structures, but these structures are taken as belonging to thinking only, while the object is considered as having its own structures (mechanism, chemism, teleology). At the level of this relation between objectivity and subjectivity one finds the philosophical formalism (not of a Kantian type), that states differences between the forms of thinking and those of reality; this is passed over by Hegel's idea, where the forms of subjective thinking and objective reality coincide. At this level, thought grasp its object without fear of not being able to do so.

This short account of the importance of formal logic in Hegel's view raises the problem of the relation among these moments of the concept. Thus, the subjective concept is, in fact, the Cartesian, empiricist, Kantian and Fichtean concept. It is, in fact, about cogito, ergo sum1, thus about the primal form of the concept taken, within the history of philosophy, as a reality appearing outside objects2. Now, the subjective concept is, in fact, the concept as being. This means that the forms of classical logic are forms of being or of thought (following Parmenides' tradition). This makes formal logic - as Hegel understands it - a theory of being from the perspective of the concept, or a theory of subjective being, i. e. of subjectivity as being.

If all these are accepted, then the Hegelian concept of formal logic receives new meanings. Firstly, this is a logic of understanding3. Hegel did not reach the precise distinction between understanding as a faculty of functions and operations and reason as a faculty of forms of reflection4. Hegel reunites the understanding and reason within a faculty he names understanding and credits it with the ability to function formally and subjectively. Now, the forms of this Hegelian understanding are the concept as such, the judgment, and syllogism. They are forms of the concept in a general meaning. Thus, for instance, within the idea one reunites the unity of the concept as suct, the division of judgment and the mediation of syllogism. Now, the understanding, as Hegel conceives it, is functioning subjectively, meaning that it takes its forms as substance of things. Thus, for the understanding, the concept, the judgment, and syllogism are objective, but not because they really are, but because they as taken as such by the understanding. In fact, the forms of objectivity are the mechanism, the chemism, and teleology, but the understanding does not recognize them as such. Such a procedure of the understanding - placing is forma as substance - is also kept by the language. Thus, the English word is "understanding" and the German one is "Verstand". In both cases, they mean "what lies under". In other words, the fact that the forms of understanding are taken as a substance of things means that subjectivity is taken as objective. Therefore, the ultimate nature of objects is rendered to them by the very forms of understanding, the understanding becoming a strictly formal faculty of thought. Formal logic, as a theory of being, is a display of the forms of understanding as an authentic nature of objects.

Now, this formal logic of understanding can be integrated within Hegel's logic as a science of forms. Thus, what is classically called formal logic becomes formal approach on concept, judgment, and syllogism (here one must take into account the identification of understanding and reason, which leads Hegel to reuniting them under the name of understanding) and speculative logic becomes formal logic (science of the forms of thought). Since concepts are this way redefined, the science of logic is the science og pure logical idea, which is free from the nature's and spirit's determinations; the logical idea and all its determinations is, also, an internal structure of the whole philosophical system5. Classical logic - or, to be honest, Hegel's interpretation of it - is just subjective logic, therefore it is not the entire formal logic, but a part of it, i. e. that which displays the forms of subjectivity. Again, these forms can also be in an abstract manner dealt with, as separated from the logical process, this leading to the classical logic as such. Of course, subjectivity and its forms, concept, judgment, and syllogism, are the immediate form of the concept, which is characteristic for the understanding. But here the understanding is not a separated faculty of thought, but a moment of speculative thinking. Therefore, Hegelian interpretation is entirely different from other perspectives. Thus, usually, the theory of classical forms is the logic of reason, of the forms of reflection6. The logic of understanding is that of operations, relations, and functions, while speculative logic is that of the idea. All can be symbolically and formally approached upon, as they are sciences of form, but without reducing them to a mere calculus (as one has done, sometimes, with the syllogism). Hegel states understanding as comprising the understanding and reason in ordinary meaning and, for both, merely the formal approach of their concepts, since they are missing all content and one establishes some rules for them to be able to receive content from experience. Reason, on the other hand, is speculative reason, and its logic is the logic of the idea; the understanding is just a moment of reason that states the determinations and renders things with their thought-form; the forms of classical logic and those of the logic of understanding are not taken as such, but burdened with their speculative meaning (and modified at the extent at which one gets different logical forms - and Hegel is rarely aware of this). As a consequence, there are at least three possible meanings for formal logic: the logic of the forms of subjectivity as a moment of the concept (practically, the first chapter of subjective logic)l; logic formally approached, as a science of void forms (including the reduction of syllogism to a mere calculus); speculative logic as a whole, as a science of the forms of thought. Many times one can only circumstantially understand what Hegel means by "formal", and sometimes it could be any of the three. Anyway, one can clearly see that the meaning of "formal logic" is not univocally used by Hegel.

The main form stated by understanding an authentic nature of things is the concept7. This is the primal form of subjective thinking. In classical formal logic, the concept was merely a common feature of more individuals, which Hegel rejects8. Thus, the concept is an original unity and immediate unity with itself9. This entitled Errol E. Harris10 to say that the concept is, in fact, Fichte's and Schelling's transcendental ego, but logically considered11. This means, in fact, that the concept is the logical form of subjectivity, or the subjectivity reduced to its logical aspect. This is justified for Hegel, since the moment of complete determination of the concept is the individual, or the qualitative unity (this). Now, this qualitative unity is a form of subjectivity, closer to Kant's or Fichte's (the ego is a logical absolute). If so, the subjective concept is not merely the classical notion, but it has a role of organizing and unifying. This means, again, that it is subjectivity that renders the object with the form of the concept, since the concept is a unity and the object is conceived by means of this unity. Briefly, the concept unifies and renders objects systematic, being more than a common feature or a class of isolated objects12. Besides, as energeia, the concept also has some constructive potencies13, of course, according to its internal principle of unification. In fact, generally speaking, by form Hegel means a constructive principle that has a dynamic nature14. Besides, the subjective concept is the one that indicates the formal. As Hegel states,"Der Begriff ist zuerst der formelle, der Begriff im Anfang oder der als unmittelbarer ist."15. The meaning is that the concept is determined, at first, as being the formal (or what is only formal). The French translation is: "le concept est d'abord le [concept] formel, le concept au commencement ou qui est comme [concept] immédiat"16. One notices that the French translation is more prudent, using brackets for the term "concept". It is all about the fact that thinking, as understanding, is, at first, formally related to things, taking them as essentially concepts. Hegel often recognizes this for the understanding: elevating things at the form of the concept. Obviously, this is, at first, formal, meaning that the understanding sets the concept as a form of thing, a subjective form, by means of which understanding conceives all things. Thus firstly, understanding conceives thins by means of concept, but this concept is only the form of the understanding, and not the form of objectivity. Meaning that, by means of concept, the understanding formally determines all things at first or, in other words, conceptual approach is a formal approach. This is why he does not refer to the formal concept - since there is no other concept besides the formal one, given this meaning of it (leaving aside the general signification of the concept and the concept as an idea). Of course, the guilt for these misunderstandings belongs to Hegel, who often uses the term "concept" with different meanings. But, in the case of subjectivity, it is all about the precise meaning of this term, and it is identical with the meaning of the term "the formal" (taken as a noun). Now, the understanding deals with this. It differs from the power of judgment ad formal reason. The first one is the faculty of judgments (as Kant states it) and the second one it that of syllogisms. Formally conceived, understanding is the faculty of determined concepts (concepts like "man" or "friend"), and thus the faculty of the concepts taken as singularities. Still, the faculty of judgment and formal reason are, in a way, similar to understanding, as Hegel puts it17 . Then, he means the faculties of formal classical logic: the understanding (Verstand) settles down the determined concept of a thing; the faculty of judgment (Urteilskraft) establishes its features; the reason (Vernunft) looks for the middle term and, of course, the grounding of a determined judgment. Formal classical logic, in this context, is meant to approach onto these forms and to establish the regions they apply to, while speculative logic exposes their genesis as forms of the idea. Therefore, the understanding comprises the understanding as such, the faculty of judgment and formal reason. Its forms (which, usually, are the forms of reason) are the concept, the judgment and syllogism, taken as separated, just like the faculties that produce them, meaning the understanding as such, the faculty of judgment and formal reason. The understanding in general (comprising also the other two) is responsible for the setting up of the concept as authentic forma of subjectivity or of the setting up of subjectivity as concept. In fact, here one finds the most precise definition of the formal given by Hegel: the subjective concept or subjectivity stricto sensu (unrelated to objectivity) is the formal18. In this context, the concept as such, the judgment, and syllogism are the forma determinations of subjectivity (or of the concept in general) or, to be more precise, determinations of the abstract concept.

Now, unlike formal classical logic, Hegel no longer refers to judgment, but to the concept as judgment19. Meaning that the judicative form is deduced from the form of the concept, and it is not merely a joining of a subject and a predicate. The same goes for syllogism, which it the form mediated in itself of the concept. It is clear, then, that Hegel thinks that formal logic does not refer to the forms of logic as such, but to their genesis within the logical process, as determinations of the idea. Hegel is aware of the fact that one can give a formal approach onto concept, judgment, and syllogism; but he is interested in displaying these determinations as belonging to the idea, thus as they are developing (he could have written a treatise on classical logic, but this was not the goal of his logic). Thus, it is all about the way in which subjectivity - or the thinking subject in general - comes to express itself under the form of the concept, that of the judgment, and that of the syllogism. There is, of course, a connection with formal classical logic: the treatment of these forms as independent from the manner in which they are generated within the process of the idea is possible (this is classical logic), the role of speculative logic being to integrate these forms within this process. This in neither a reduction of formal classical logic to speculative logic, nor a hierarchy between them, but merely a completion or a reevaluation of formal classical logic. Especially because speculative logic deals with the manner in which these determinations of classical logic evolve from one to another, while classical logic deals with a former establishment of these forms and of rules of well-forming and use. This is what Hegel calls natural history of the forms of spirit, meaning a research upon the forms thought passes through, and not a deduction by necessity. Thus, to say that Hegel has a speculative understanding of the forms of traditional logic seems to be in order20.

There are, also, some other meanings of the formal in Hegel's logic. Formal means what is immediate and abstract. These concepts have a slightly clear meaning in Hegel's logic. Thus, by determining the formal concept (the meaning is that presented above) as immediate and abstract he means the concept as mere form, missing all content. One may see here a return to the Kantian formalism that Hegel repudiated21. This is not the case, since by formal concept Hegel means a concept whose content has not yet been exposed. This is not an external context, like in the case of formal concepts of understanding (or, to be more precise, like in the case of formal approach onto concept that understanding undertakes), but is the totality of the forms of the concept, meaning concept, judgment, and syllogism22. This is also a little unclear. Thus, the nature of the concept is, from a dialectical viewpoint, the mediation. Thus, the logical form of the concept is mediation as such. In other words, the meaning of the "concept" is "a logical form reflected in itself, as judgment, and mediated in itself, as syllogism". Thus, the content of the concept as such is the totality of its forms. The form that best expresses this content is the syllogism. The concept as such represents this abstract content, which is implicit, without mediation; the judgment expresses this content under the form of reflection, while the syllogism expresses it under the form of mediation or development. In other words, Hegel means by abstract that which has not yet passed through the process of developing all its determinations. This also goes for determinate concepts. There is an "emergency" of a concept to determine itself as judgment and then as syllogism. The concept of man determines itself as the judgment "the man has a body" and then as "the man is a living being / living beings have bodies // the man has a body" (this being just an example, regardless of the nature of the predicate, the syllogistic figure, etc.). The same way, immediate means that which has this form of identity with itself, and not the mediated form (that of the syllogism, in this case).

In the end, one needs a special remark about concept, judgment and syllogism. When dealing with them, Hegel refers to their speculative meaning. Thus, they must be taken as formal, as determinations or forms of subjectivity, but also as speculative, as concept, division and synthesis. Now, if one undertakes a genetic exposition of logic, these three forms must be taken as formal, as moments of subjectivity; this is because, within the construction of the idea, the formal moment of understanding cannot be avoided. If, instead, one means to elaborate a structural exposition that refers to the manner in which the idea and its structures are present within the logic, these three form are, in fact, particular cases of the forms of speculative logic - concept, division, and synthesis. This means that the concept as such is the subjectivity taken as a concept (as speculative thinking does); the judgment is the subjectivity as division; while the syllogism is the subjectivity as synthesis.

Footnote

1 This is about the reinstatement of Parmenides' principle of identity between being and thought, now from a conceptual perspective; Parmenides' perspective as such left aside the subjective determination, thus the Greek thinker was at the level of objective thinking, within the theory of being. See G. W. F. Hegel, Science of Logic, translated and edited by George di Giovanni, Cambridge University press, 2010, p. 60.

2 Errol E. Harris, An Interpretation of the Logic of Hegel, University Press of America, 1983, p. 222.

3 Loc. cit.

4 See Alexandru Surdu, Aristotelian Theory of Prejudicative Forms, translated into English by Stefan-Dominic Georgescu, Georg Olms Verlag, Hildesheim, Zürich, New York, 2006, p. 223-228.

5 André Lecrivain, Introduction à la lecture de la Science de la logique de Hegel, Aubier, Paris, 1983, p. 36-37.

6 The distinction we refer to was elaborated by Alexandru Surdu, in some of his papers.

7 Understanding is, according to Hegel, a "faculty of concepts in general". Science of Logic, ed. cit., p. 529. See also André Lecrivain, op.cit., 1983, p. 29.

8 G.W.F. Hegel, Science of Logic, ed.cit., p. 620.

9 Ibidem, p. 599.

10 Op.cit., p. 224.

11 See also André Lecrivain, op.cit., 1983, p. 25.

12 Errol E. Harris, op.cit., p. 227.

13 André Lecrivain, op.cit., p. 12.

14 John Grier Hibben, Hegel's Logic: An Essay in Interpretation, Batoche Books Limited, Ontario, Canada, 2000, p. 108.

15 G.W.F. Hegel, Werke in zwanzig Bänden. 6. Wissenschaft der Logik. II, Suhrkamp Verlag, Frankfurt am Main, 1969, p. 272.

16 Apud André Lecrivain, op.cit., p. 37

17 G.W.F. Hegel, Science of Logic, ed. cit., p. 597.

18 André Lecrivain, op.cit., p. 37.

19 G.W.F. Hegel, Science of Logic, ed. cit., p. 596.

20 André Lecrivain, op.cit., p. 39.

21 Ibidem, p. 41.

22 Loc. cit.

References

REFERENCES

Hibben J.G., (2000), Hegel's Logic: An Essay in Interpretation, Batoche Books Limited, Ontario, Canada.

Hegel G.W.F., (1969), Werke in zwanzig Bänden. 6. Wissenschaft der Logik. II, Suhrkamp Verlag, Frankfurt am Main.

Hegel G.W.F., (2010), Science of Logic, translated and edited by George di Giovanni, Cambridge University Press.

Lecrivain A., (1983), Introduction à la lecture de la Science de la logique de Hegel, Aubier, Paris.

Surdu Al., (2006), Aristotelian Theory of Prejudicative Forms, translated into English by Stefan-Dominic Georgescu, Georg Olms Verlag, Hildesheim, Zürich, New York.