Introduction to the Science of Logic

The Familiar Logic

Logic is the systematic study of valid reasoning, inference, and argumentation. It deals with principles and rules that govern correct and consistent reasoning. In essence, logic provides a framework for evaluating the validity of arguments and determining whether conclusions logically follow from premises. It encompasses various branches, including propositional logic, predicate logic, modal logic, and mathematical logic, each with its own set of rules and applications.

At its core, logic involves analyzing statements or propositions and their relationships to ascertain whether they lead to a sound and coherent conclusion. It helps in distinguishing between valid and invalid forms of reasoning, facilitating clear and rational thinking across different domains, such as mathematics, philosophy, computer science, and linguistics.

This is logic as it is commonly known to us. In this vein, logic is like following certain rules when dealing with ideas. Imagine an idea to be a certain "block" and logic the "rules" for playing with "blocks" in a good way. Just like how you need to follow certain rules to build a stable and cool structure with your blocks, logic helps us figure out how to put our ideas together in a way that makes sense. For example, if you have a red block and a blue block, and someone says, "All red blocks are big," and you know the red block you have is small, you can use logic to figure out that the statement is not true for all red blocks. Hence, logic is like a set of rules that helps us understand if the things we say or think fit together properly, just like how blocks can fit together to build something, or, equally, how blocks can be jumbled together into a pile with no innate consistency or structure.

These definitions of logic all fall short of the self-critical demand of philosophy.

While for most ordinary and pragmatic pursuits, these definitions of logic work perfectly fine; as soon as the self-critical lens of philosophy is applied, however, it becomes readily apparent that there are incoherent gaps or unwarranted dependencies. A cursory inquiry exposes this: What is valid reasoning and argumentation? What grounds the principles and rules that govern correct and consistent thinking? How does a framework that is external to the issue it looks into have any real authority over that issue if it is really external to it? What are the conditions for the possibility of rational thinking; is not all thinking, per definition, rational? Can a thought exist that is not rational? What even is rationality?

This is why Hegel begins, in the introduction to The Science of Logic (SL), with the following statement:

In no science is the need to begin with the fact [ Sache ] itself, without preliminary reflections, felt more strongly that in the science of logic (Hegel 2010, 23/21.27).

The hindrance being thrown ahead is not so much that the functional definitions of logic are false or bad, but they are, taken as a whole, lacking or insufficient. And this becomes readily apparent when one thinks carefully through the questions that the established forms of logic prompt. Said otherwise, when one turns to think philosophically, the context itself becomes unbounded and thought is absolutely free in its pursuits.

The Unfamiliar Logic

The philosophy of logic examines logic not merely in its parts and established definitions, but also as a whole and questions what has been established. To follow our toy example, in philosophy one is not only concerned with blocks and how they possibly fit together, but also "what is a block", what does it mean for blocks (or anything) "to fit together", how do blocks "emerge" or have they "always been there", or is it the pattern itself of how things fit that has always been there? When we apply this line of thinking to actual logic, our concern becomes, to use the example of syllogism (a pattern of inference): what is a syllogism, how are the major and minor premises constituted to create the conclusion, how do premises emerge or are they latent within one, is the syllogistic pattern mutable or immutable? Now apply this line of inquiry not to any particular logical rule, but to logic itself! Besides the intense inquiry into the nature of things, philosophy does not dismiss ordinary or familiar notions of logic (or any concept) but takes them seriously. Indeed, it is out of wonder and curiosity of how and why things work the way they work that first elicits one to investigate more closely.

The barrier that the familiar notion of logic had erected has begun to break down. It is understood inquiring into logic as a pre-established set of rules for reasoning, inference and argumentation induce questions of justification when examined under a philosophical, unbounded lens. But one may decide at this point to hold on to these established notions and instead work backwards to discover a common foundation. Notice how this leaves precisely the core issue unattended, namely, the established concepts themselves! In pinning a certain logical idea and then setting out to inquire into its presuppositions leaves that very idea as the presupposition. For example, if one decides to inquire into the nature of propositions (S is P) by looking at what is the subject, what is the predicate and what is their connection, one takes no less for granted that there is such a thing as the proposition. But then what grounds the proposition as such? Here one can continue to attempt to pursue the same track by looking at constituents or presuppositions, or one can short circuit the line of inquiry itself and see that no pre-established, familiar idea will adequately answer the demand of self-critical thought.

This is what Hegel has in mind when speaking of the need to begin with the fact itself, without preliminary reflections. In fully self-critical philosophy, where the context is unbounded (if it at all makes sense to speak of a context), one cannot take for granted any pre-established notion or logical set of rules such that one must make an absolute beginning. Indeed, taken to its extreme, this rigorous inquiry necessarily purges not only the typical associations of familiar logic (rules, propositions, syllogism, etc.) but also the less standard ones such as reality, world, negation, certainty, truth, infinity, finitude, form, content, matter, thing, property and a host of others. These categories are basically dropped, and, crucially, any sense of externality along with them.

In every other science, the matter that it treats, and the scientific method, are distinguished from each other; the content, moreover, does not make an absolute beginning but is dependent on other concepts and is connected on all sides with other material (Hegel 2010, 23/21.27).

This sense of absolute beginning requires one to think of logic not as relative to its subject matter, or as a certain form that merely structures some other content, but being both at once. At the outset of its inquiry, logic cannot be distinguished from its matter and it cannot be dependent on anything else but itself.

This finally crumbles the initial edifice established by the familiar notion. In this presuppositionless thinking about logic, the decision has been taken to suspend the customary meanings of rules and laws of thinking, and thus upend the usual procedures and methodologies. With no established idea, category, method or notion, one strictly cannot declare in advance of its thinking what logic is or will be. Strictly speaking then, as Hegel says: "Logic, therefore, cannot say what it is in advance, rather does this knowledge of itself only emerge as the final result and completion of its whole treatment. ...its concept is generated in the course of this elaboration and cannot therefore be given in advance" (Hegel 2010, 23/21.27). No idea or concept can be pinned, established or simply put before us. Our blocks and their patterns melt away. Indeed, the very sense of logic vanishes.

At the Beginning

One thus is, albeit in a highly expedited way, transported to the place of absolute beginning, the place where the inquiry into logic can begin in earnest. Yet, at this point a final hurdle remains that bars the deployment of thinking positively what logic is and that is the problem of beginnings. More technically, it is the issue concerning the nature of beginnings which surreptitiously seem to pre-determine their ends. We see that echoes of a distinction between form and content, logic and its subject matter, persist. Doing philosophy of logic then is less a set procedure with definite steps as it is a continual refinement of distilling the adequate conceptions according to the skill of one's craft. This is owing in no small measure to the fact that logic and its actual thinking are deeply intertwined. But this does not diminish the idea of clear resolutions and definite determinations, but it does diminish the idea that that is all there is to logic. As it will be seen, logic is far more strange and wondrous than is usually given credit, and that logic in its full scope both contains and transcends a living, self-correcting evolution and is the universally eternal touchstone of truth.

Only after a more profound acquaintance with the other sciences does logic rise for subjective spirit from a merely abstract universal to a universal that encompasses within itself the riches of the particular: in the same way a moral maxim does not possess in the mouth of a youngster who otherwise understands well the meaning and scope that it has in the spirit of a man with a lifetime of experience, to whom therefore the weight of its content is expressed in full force. Thus logic receives full appreciation of its value only when it comes as the result of the experience of the sciences; then it displays itself to spirit as the universal truth, not as a particular cognition alongside another material and other realities, but as the essence rather of this further content (Hegel 2010, 37/21.42).

Other Predispositions Considered

Hegel considers a number of other typical approaches to logic and its relation to thinking. These help to further specify the determination of logic that Hegel intends to work with. The following issues are explored in more technical detail, but they all revolve around the core issue of logic being merely something external to concrete reality and formally dependent on it instead of being the self-determining essence of reality.

Logic as Mere Form

When logic is considered as a science or knowledge of thinking, it is first understood that this thinking is "the mere form" of cognition that abstracts from all content (Hegel 2010, 24/21.28). This has two consequences: Firstly, logic or thinking as mere form is completely devoid of any internal truth and acts merely as the stepping stone to another's. Secondly, logic is wholly dependent on extraneous matter to be given to it, for it itself consists only for formal conditions and not of any real truth. Moreover, it can be seen here that logic is taken externally to its subject matter, which holds latent an unquestioned metaphysical assumption. As Hegel notes:

Presupposed from the start is that the material of knowledge is present in and for itself as a ready-made world outside thinking; that thinking is by itself empty, that it comes to this material as a form from outside, fills itself with it, and only then gains a content, thereby becoming real knowledge (Hegel 2010, 24/21.28).

Kantian undertones of blind intuitions and empty concepts can also be found in this assumption (although, to be fair to Kant, he was working from a different context)(Kant 1998, 194/A51). The idea being that logic or thought are devoid of any truth until material from the world (which itself is ready-made and complete unto itself) is given to it.

The further consequence of this assumption is that logic and its subject matter (here the world) are utterly different from each other; "each turns out to be a sphere divorced from the other" (Hegel 2010, 24/21.29). As Hegel notes, this leads exactly to the Kantian position of thing-in-itself, since logic or thought are utterly other to the world, the world is a complete thing unto itself logically prior it being given as material for cognition as intuitions. In other words, the world cannot be thought of with any certainty prior to its experience; or, put differently still, thought is incapable of coming to any resolution about its subject matter (be that the world, existence or anything).

If one pursues this line of thought further, then it effectively means that thought is incapable of coming to any conclusions about itself. Thought, as well as logic, are merely the formal instruments of experience that await reception of worldly material; prior to which thought is unable to think. Thought and logic in this view are externally determined, not self-determining. Put bluntly, then, according to this perspective thought cannot think. One does not make up one's own mind about something, but only ever reacts to certain sensuous data.

A further conclusion of this thread is that the world itself, or any subject matter of logic, is inherently illogical. This is the other side of that stark difference between logic and its subject matter. Since logic is mere form and this form requires material, the world cannot with any definitive resolution be understood to be logically prior to its reception as material for cognition. We cannot speak of a reality outside experience. Hence, one is firmly placed in the Kantian position that posits the world as such to be a thing-in-itself.¹

Hegel notes that the manner one here views logic and its subject matter, thought and the world, subject and object, is in phenomenal terms. But he calls it a prejudice to carry over this view into reason and logic. His argument is that it is incoherent from the start since the phenomenal attempts to make a metaphysical claim, but the former is exactly not the latter. That is, the scope of what one experiences sensuously is less than what can be thought, so it is wrong to apply the standard of the former upon the latter. The way one experiences things through the senses cannot be the standard for how everything is evaluated. Indeed, senses do not in the strict sense evaluate. This is not to say that experience is not real or important, but it is being misused if it is taken out of its scope. This miscarriage of logic is simply classed as an error and Hegel notes how it can be an impediment to philosophical thinking.

...when these prejudices are carried over to reason, as if in reason the same relation obtained, as if this relation had any truth in and for itself, then they are errors, and the refutation of them in every part of the spiritual and natural universe is what philosophy is; or rather,since they block the entrance to philosophy, they are the errors that must be removed before one can enter it (Hegel 2010, 25/21.29).

Curiously, the ancient thinkers, Hegel continues, had a higher conception of thinking since it was reasoned that only things known in thought, as opposed to known immediately, where understood to be the truth of the matter. It is, then, not what is first experienced that is considered true, but what is thought to be so. For example, in the distance an object may appear as a shipwreck but coming closer it becomes apparent that the object is actually a peculiar hut. Did the object itself morph between the two states? No, one reasons that perception gave a certain impression at one point and a different form another, but that the object had been what it was in both respects. One simply comes to realize what the thing really was. Here thought is not alien to the world but is immanent to it, "the things and the thinking of them agree in and for themselves (also our language expresses a kinship between them)" (Hegel 2010, 25/21.29).

The Conflict of Determinations

Hegel complains that the understanding has taken hold of philosophy, and that, what is worse, ordinary common sense is granted dominion over the evaluation of the the truth about all things. Ordinary common sense being rooted in sensuous reality with the notion that thoughts are only thoughts. Essentially, this view is uncritical and philosophically naive. Mention to Kant and his transcendental philosophy will be made here, as it is a prime example of this view. Kant's philosophy is rooted in the idea that thoughts are only thoughts and that real knowledge is the intertwining of thoughtful form and worldly impressions.

However, Hegel detects a more serious obstacle in this thinking when it is attempted to be philosophically applied. When, according to this naive position, thoughts are only thoughts and that real knowledge is the intertwining of thoughtful form and worldly impressions, it can be easily missed that what are assumed to be conflicts of the world are really conflicts of ideas. In Hegel's more technical vocabulary, it is the conflict of determinations (see also Kant 1998, 459/A405/B432).

The basis of the [conception of modern philosophy is] in the insight into the necessary conflict of the determinations of the understanding with themselves. - The reflection already mentioned consists in transcending the concrete immediate, in determining* and _parting* it. But this reflection must equally transcend its separating determinations and above all connect them. The conflict of determinations breaks out precisely at the point of connection. This reflective activity of connection belongs in itself to reason, and to rise above the determinations ad attain insight into their discord is the great negative step on the way to the true concept of reason (Hegel 2010, 26/21.30).

When logic is not considered on its own terms but merely in relation to sensuous existence, one fails to grasp that logic is in fact in conflict with itself. Discord and struggle are not exclusive to the domain of worldly reality but are also—perhaps more intensely—active in the domain of logic and reason. Philosophy disciplines the ability to distinguish what is proper to each domain and being able to understand when an apparent conflict belongs to worldly reality, the realm of pure logic or is an erroneous mismatch between the two.

Hegel notes a further error in the case where one is discouraged by a contradiction in the understanding and resolves to find accord and stability in sensuous reality. But, and here Hegel criticizes the Kantian transcendental standpoint once more, if one resolves to look to sensuous reality as the criterion of truth, in the same instance one cannot determine the thing in question to have any independent truth since the truth of the matter is settled only as it appears. "This is like attributing right insight to someone," Hegel writes, "with the stipulation, however, that he is not fit to see what is true but only what is false" (Hegel 2010, 26/21.30). To put this another way, if by truth one understands an independent standard, then this immediately clashes with the knowledge that one acquires through appearances, since knowing here is totally dependent on appearances and cannot make any independent claims about the matter at hand. To emphasize this point further, if the transcendental arrangement is actually granted, then one cannot truly speak of laws of nature or even state that the sky is there the moment one turns one's gaze towards the ground. This is why, if Hegel is right, this claim that sensuous reality is the sole arbiter of truth leads to absurdity.

Finally, Hegel then points out that as the understanding (according to transcendental idealism) cannot apply its determinations or concepts to things in themselves, it must therefore mean that these determinations are in themselves something untrue and consequently cannot be turned upon itself or anything else related to pure reason. The standard set for the understanding is based on experience and empirical objects, but the categories that define these empirical objects are not themselves empirical—they are precisely pure—and so the categories of the understanding cannot apply to anything other than sensuous reality. But this is incoherent, since the categories themselves are pure, their validity cannot come from sensuous reality. "If they cannot be determinations of the thing in itself, still less can they be determinations of the understanding, to which one ought to concede at least the dignity of a thing" (Hegel 2010, 27/21.31). In this Kantian regime, according to Hegel, one cannot consistently use the tools by which the understanding navigates the world to also navigate the realm of ideas and thoughts, with the result being that the understanding (or the mind) cannot be a thing, much less be said to exist.

The cause for this error, Hegel diagnoses, lies in the fact that the determinations or categories of the understanding were never given an independent examination and immanent deduction but were simply taken for granted.

On the Absurdity of Knowledge Based on Appearances (Niklas)

Further observations may be drawn regarding the absurdity of truth vis-à-vis appearances (what we can call the double-standard of knowledge) in inspecting its implicit elements. When it is posited that knowledge is split by way of subject matters, and that of certain subject matters one can know nothing about (such as things-in-themselves) but others one can have knowledge (such as what appears in experience), knowledge remains the common element in both. The incoherence may be traced to an unstated third element that orchestrates the mediation between knowledge based on appearances and knowledge as such. This third element can be either one of the two extremes (knowledge based on appearances or knowledge as such) or something else entirely. It seems that, according to Hegel, if transcendental idealism is taken at face value, one subscribes to the view that knowledge based on appearances grounds both itself and knowledge as such, yet Hegel's criticism is that this precisely leads to absurdity which subsequently must mean that Kant merely takes for granted either that knowledge as such grounds both itself and knowledge based on appearances or that there is another third, yet unknown, common denominator. The latter seems to align well with Kant's own thinking in the First Critique:

All that seems necessary for an introduction or a preliminary is that there are two stems of human cognition, which may perhaps arise from a common but to us unknown root, namely sensibility and understanding, through the first of which objects are given to us, but through the second of which they are thought (Kant 1998, 135/A15).

In fairness to Kant, however, more emphasis is placed on pure concepts as the argument of transcendental idealism develops. Kant, in contrast to Hume, places pure categories or pure concepts in the purview of reason such that these cannot have their validity or truth established by sensuous reality, but that, rather, they serve to establish the validity and truth of sensuous reality. There are also a number of other key concepts—called concepts of reason—that never directly interact with sensuous reality, such as ethical principles or the concept of world (Kant 1998, 394/A311). Indeed, concepts of reason are in this way genuinely unconditional. With these things in mind, the thrust of Hegel's criticism is somewhat blunted, since Kant's argumentation does not entirely rest on the intertwining of thoughtful form and sensuous impressions. Yet Hegel's real target is the fact that transcendental idealism has invalid or weak means to establish the truth of the very tools of cognition it purports to use to establish truth tout court.

The take-home message thus being that, if Hegel is right, philosophy cannot but begin with metaphysics or, if it deigns to begin elsewhere, such as the instrument of cognition or conscious experience, be forced to take for granted a bad one.

Logic as Non-Metaphysical

[W]hat is commonly understood by logic is considered with a total disregard of metaphysical significance.

(Hegel 2010, 27/21.31-2)

What is crucially omitted in typical discussions concerning logic is its state with regards to reality. Logic is not usually understood to exist in the same way a tree or a squirrel exists (i.e. a thing), and Hegel admits that logic does not have the kind of content that comes readily available unless one thinks about it carefully. However, this is not due to the nature of logic as much as it is with how it is being used. "Scattered in fixed determinations and thus not held together in organic unity, they are dead forms and the spirit which is their vital concrete unity does not reside in them" (Hegel 2010, 27/21.32). While the language here is somewhat lofty, the underlying point is clear: when logic is considered merely as a settled structure, it is not considered how its many forms and patterns hang together, and especially how they are understood vis-à-vis the thinking mind, which leaves logic immutable and insubstantial. These features of logic—when formally considered—become brittle and arbitrary when the full weight of the self-critical, demand of freedom is brought to bear.

This non-metaphysical, or formal, logic must continually seek a content outside of itself in order to become something meaningful. Formal logic must deal with objects of the world if it is to determine something substantial, such as how various natural things behave. But Hegel's claim is that logic does have a content of its own; it does have something internally meaningful—at a minimum it is the concrete unity that holds together all the fixed, pre-established structures, be they syllogisms, propositions or other categories. It is not the fault of logic, Hegel says, that it seems empty, but it is, rather, the way in which it is being understood which is empty (Hegel 2010, 28/21.32). If one begins to inspect how these various logical forms are connected, one has already begun to leave behind logic as fixed patterns with the implicit understanding that an integral unity exists. From there, the step to metaphysics is a small one—insofar as it is understood that metaphysics, generally speaking, is the philosophical inquiry into the nature of reality, existence and universe—since it is already given to understand that logic is something that forms part of reality.

On the Use of the Term Science

The term science (German: Wissenschaft) is often used by Hegel throughout his writings and signifies a larger context than what is commonly understood by the use of the term. Typically, science is understood to entail inquiries strictly into the natural world or what can be proven empirically. Science thus is therefore knowledge of empirical reality. Hegel, along with Kant, Fichte and others of his contemporaries, expand the notion to include also what can be proven logically. While science, for Hegel, still concerns empirical knowledge, it is also knowledge of non-empirical items such as logic, metaphysics, ethics, aesthetics, religion and even knowledge itself. It is perhaps best to think of knowledge whenever Hegel speaks about science, insofar as knowledge is a provable conception (logically or empirically) of something that is neither exclusively objective or subjective. The class of knowledge that is particularly concerned with logic, metaphysics or knowledge as such is frequently connoted as pure knowledge or pure science; "pure" because it is knowledge about knowledge, or science about science, or the subject matter of logic is strictly not intermingled with anything other than logic itself.

At the start of The Science of Logic, the term science is lightly presupposed. Hegel claims that the concept of science is established in The Phenomenology of Spirit (another major treatise by Hegel), but that he is cautious of providing any definitions of it at the outset. This is because any such definitions will at best be mere assurances. As with all pre-established forms of logic, at the start of presuppositionless thinking, science too must be emptied of any preconceived notions of what it is.

However, there is an important caveat to this. While nothing definitive can be said about science, its conception is presupposed at the start of the The Science of Logic. This conception is the minimal grasp that the fact of the matter (die Sache) is equally the thought of it. This is largely a negative conception, inasmuch as it serves to annul the opposite conception that the fact of the matter is different from the thought of it. That, according to Hegel, is an assumption made by consciousness which is ostensibly undermined in The Phenomenology and which undermining is taken for granted at the start of the Logic. Should it be held that the fact of the matter and its thought are fundamentally different, or that the difference between subject and object is unquestionably true, then The Phenomenology aims to prove that conception to undermine itself and derive a concept of science from that undermining. As Hegel writes:

Pure science thus presupposes the liberation (Befreiung)² fom the opposition of consciousness. It contains thought in so far as this thought is equally the fact as it is in itself; or the fact in itself in so far as this is equally pure thought. As science, truth is pure self-consciousness as it develops itself and has the shape of the self, so that that which exists in and for itself is the conscious concept and the concept as such is that which exists in and for itself (Hegel 2010, 29/21.33).

Pure science, or pure knowledge, cannot but follow from a freeing of consciousness in that thinking is able to consider an issue without being bound to a limited subject-object dichotomy. What Hegel describes here is simply the free movement of the knowing mind—an exercise human beings have engaged in since before history. However, it would be inadequate to regard pure science merely as any activity that resembles knowing. Hegel adds additional qualifiers that makes this conception something that is permanently explicit. Science, strictly speaking then, cannot be merely implicit, but must have itself as its own object and that object be itself. This is what minimally constitutes pure science. Furthermore, Hegel goes on to add that pure science or pure logic is not bereft of self-consciousness but is it in its purity. Still further, Hegel adds the key qualifier that this is not mere pure self-consciousness as was but as it develops itself. As it will be seen in the Logic itself, and indeed throughout Hegel's body of work, continuous development and integration are staple features of the concept.

This is a nexus of many important technical terms. Pure science, pure form, pure reason, pure knowledge, pure self-consciousness and pure thought. In a manner of speaking, at the zero level of presuppositionless thinking, all these terms collapse into the same. Or, they cannot afford any substantial difference that would set them apart from one another when taken to the extreme of their purity: pure thought is equally pure logic, and pure logic is equally pure knowledge and the purity of self-consciousness is pure thought.

One might be tempted to think that this purity makes it a mere formality, but according to Hegel it is the purity of thought as it is thinking that is the content. "This objective thinking is thus the content of pure science" (Hegel 2010, 29/21.34). A formality would precisely lack any content of its own—much like the familiar conception of logic—and would be unable to actually generate a thought. But Hegel points out that the pure form of thinking considers its own thinking as its content and that content just is the form of thinking. Put plainly, it is thinking about thinking, no more and no less.

Logic, then, becomes the system of pure thinking (Hegel 2010, 29/21.34). Here Hegel omits the connotation "pure" since a system puts into determinacy what pure thought turns out to be, and determinacy minimally qualifies between what is and is not. Likewise, this system of pure reason is no less a science of logic since logic becomes expounded determinately and what it expounds is the very evolution of logic. This is admittedly looking ahead, since at the start the very idea of determinacy cannot be left unquestioned. Indeed, if there is to be a system of logic (or logic as a system), then this too must develop immanently from pure thought, from the conception of pure science or, as Hegel wrote above, pure self-consciousness as it unfolds in its own shape.

The Evolution of Logic

[S]ince Aristotle, [logic] has taken no backward step, but also none forward, the latter because to all appearances it seems to be finished and complete (Hegel 2010, 30/21.35).

While Hegel gives a dismal appraisal of the history of logic since Aristotle, the issue is as much a philosophical as a social and historical one. The philosophical issue being that logic is regarded as something inherently complete and static. "Its determinations," Hegel writes, "are accepted in their undisturbed fixity and are brought together only in external connection" (Hegel 2010, 32/21.36). Logic, as it is typically known outside a philosophical context, amounts to something of an accounting of various logical forms which does not critically assess their immanent connections or attempt to derive a systematic deduction of the forms themselves. While Hegel speaks here from his own time about the state of logic, the underlying philosophical assumption is that the method of logic is itself constant and perfectly concluded.

Curiously, Hegel specifically complains that in his present situation there is no trace of the scientific method in the typical considerations of logic. While the scientific method has come to include notions like observations, question, hypothesis, prediction, experimentation, reproduction, conclusion from established observation and communication centered around empirical objects, these items constitute a general idea that is not far off from what Hegel has in mind here with regards to logic.Namely, that the form of logic itself is actively failing to live up to standards similar to those of scientific inquiry. Logic itself and its forms (propositions, inference, categories, etc.) are not being scientifically examined in accordance with rigorous questioning, experimentation, reproduction and communication.³ Indeed, Hegel points to empirical science and pure mathematics as having their own suitable methods whereas this is sorely lacking in the domain of logic. This has led to philosophy borrowing methods from these other domains and attempting to apply them to logic, but Hegel thinks that this is an error. It is an error because it is a method that is being externally applied. Yet, it is equally an error to crudely reject any method whatsoever.

The method must come from within the treatment logic itself. But how does that not entail that this method is already established and given? What are the claims that support that the method of logic is something that is indeed incomplete and in development? Hegel offers a quick but potent response by considering a few principles. The fixtures that act as the underlying support for the typical logical inquiries do not recognize that negation is equally positive or that contradiction does resolve to an abstract nullity of the matter at hand but only a negation of a particular form (Hegel 2010, 33/21.38). The proof of these claims are in The Phenomenology, but given these are at least entertained, then just the idea that the positive and negative overlap or that contradiction is constructive are enough to seriously upend the restful repose of logic's typical considerations. To embark on a scientific inquiry of logic proper, then, requires one to be open to—if not equipped with—the insight that there is more at work in its definitions than is nominally given and used. In other words, there is more to logic than meets the eye.

While the points Hegel makes with regards to the principles that could be said to underlie the typical approach to logic are themselves wanting of proof at this stage, the key takeaway is the fact that whether or not Hegel is right in undermining these principles, there appears to be some principles necessarily at work in the naive approach to logic. To just focus on one of these, namely, the idea that the positive is simply positive and the negative is simply negative and never the two shall meet, and it is granted that the naive consideration of logic must entail this, then that is a principle that is simply assumed to be the case. How is this principle proven? And by which method is this principle proven? What are the credentials, so to speak, of this method, if there is any? If Hegel is right, then in the standard considerations of logic, there are latent unproven assumptions which come to hold fast to an erroneous conclusion—such as the idea that logic is complete and finished simpliciter.

The method of logic must come from within the treatment of logic itself and this cannot entail that the method is pre-established and given a priori (before the fact). This is perhaps a radical idea of logic to think that its very method can take on not only such an evolutionary aspect but that this also occurs within its own inquiry of itself. But if Hegel is right about the self-critical demand of presuppositionless thinking, it must systematically follow.

Yet, Hegel does not pretend that the method developed in the course of the Logic is itself fully completed and perfected. This is perhaps surprising to some given that logic would include metaphysical claims, which would entail some sort of atemporal truth. It is a fertile discussion unto itself just how much of Hegel's logic is atemporal and historical and where the difference lies, but that is beyond the scope of this introduction. At this stage, and in keeping with the basic tenets of presuppositionless thinking, the method itself is—and Hegel claims remains—open to continuous revision. All that is necessary is that the "method is not something distinct from its subject matter and content - for it is the content in itself, the dialectic which it possesses within itself, which moves the subject matter forward" (Hegel 2010, 33/21.38).

Finally, one might point to the fact that there must be some pre-established idea in mind, at the very least since Hegel has written a book, which necessitates division into sections, headings, etc., that show that not everything about Hegel's logical project is presuppositionless. Hegel reminds the reader that these serve nothing else than "indications of content" and are of essentially historical value. These are the constructions of a compendium rather than the determinations of the content itself. Or, put more figuratively, they are the signposts erected after the journey of discovery has been completed. Once again, Hegel stresses the fact that such divisions do nothing to elucidate their method. The real deal is in the concepts that are thought in reading the text. As Hegel writes, "the necessity of the connectedness and the immediate emergence of distinctions must be found in the treatment of the fact itself, for it falls within the concept's own progressive determination" (Hegel 2010, 34/21.39). The reader is therefore invited to follow the content exactly as Hegel did and examine whether or not the various developments and resolutions indeed follow as Hegel describes.

Dialectic: The Engine of Logic

If the method of logic is something that emerges, develops and evolves, one is instinctively prompted by the question of what drives logic itself to progress in the first place? Keeping in mind everything said about indications of the content above, Hegel's simple reply to that question is:

What propels the concept onward is the already mentioned negative which it possesses in itself; it is this that constitutes the truly dialectical factor (Hegel 2010, 34/21.39).

Here there are two elements which, although often intertwined, are subtly distinct: the negative and the dialectic. The dialectic has a rich lineage in the history of philosophy and Hegel draws some key comparisons between his usage and that of Plato and Kant. Before turning to that discussion, it is worthwhile to keep in mind how the negative and the dialectic are distinct.

While no detailed examination can take place of these terms here, some cursory remarks and images can be helpful. When speaking of Hegel's dialectic, consider the negative as a moment of something that activates its transformation into something other. What makes this change particularly dialectical is the fact that the change is purely internal. The thing in question simply changes on its own account, like a piston engine that is able generate its own pressure to create motion, or, perhaps more appropriately, a heart that generates the pulse necessary for the support system of the heart to in turn keep beating. Now, in absolutely strict terms, one might determine that what the thing first is and then becomes are essentially two different things, such that there is really no change, much less dialectic, since the thing is no longer the same thing should there be any new anything. So it is required inasmuch as something is understood dialectically that the thing in question minimally retains an identity in spite of difference. Moreover, in thinking of dialectic as change, this change entails many categories working together: constitutive moments, spontaneous or self-determined negative moment, integration of that negative moment into a whole. One can see how this idea quickly reveals a wealth of determinations.

Like with all other terms and notions at the start of The Science of Logic, dialectic itself is unproven and Hegel must show something to develop dialectically before he is justified in using that term as well as making it meaningful. Indeed, even the important negative must develop immanently. As indicated above, dialectic might not exist since what appears as change is really two entirely different things, and this kind of challenge is something that Hegel's argument must be capable of responding to.

Turning now to the historical appreciation of the term dialectic, Hegel notes that, since the time of Plato and Socrates, that dialectic has signified an external activity concerned with rooting out what is misplaced or erroneously conceited about something. When the truth of the matter is settled, dialectic no longer plays any vital role and can be dismissed from the revised concept. It is in this way that dialectic is considered as something merely subjective and associated with dissolving shallow and brittle conceptions.

Hegel praises Kant for discovering that dialectic is not an external and arbitrary movement but is integral to the functioning of reason. Dialectic, with Kant, ceases to play a merely optional role but is necessary to the idea of reason as such. Whether for good or ill, then, conceit—or how something merely appears—surrounding the determinations of thought are vital to thought itself. Hegel goes on at length:

...the general idea to which [Kant] gave gave justification and credence is the objectivity of reflective shine and the necessity of the contradiction which belongs to the nature of thought determinations ... [that] such determinations are in reason, and with reference to what is in itself, this is precisely their nature. This result, grasped in its positive aspect, is nothing else but the inner negativity of the determinations which is their self-moving soul, the principle of all natural and spiritual life (Hegel 2010, 35/21.40).

By objectivity of reflective shine, Hegel means that how things appear, not only as they are in and for themselves, is understood to be objectively valid. That is to say, that appearances gain the status of forming part of reality and not merely obfuscating it as if they were only a veil that could be permanently pulled back. Hegel then adds the conclusion that, if appearances are integral to reality, then reality itself has an inner negativity whereby it is in opposition with itself between these two determinations, namely, what is the case and what seems to be case. Or, put differently, the thing is internally disjointed between how it appears and how it really is. Furthermore, this opposition or internal negativity is considered positive since it is through this divergence or conflict that difference (or movement) is engendered. As Hegel confirms: "It is in this dialectic as understood here, and hence in grasping opposites in their unity, or the positive in te negative, that the speculative consists" (Hegel 2010, 35/21.41).

The speculative here being nothing less than the name of the kind of self-critical philosophy Hegel, and others, engage in that are sensitive to the movement of the determinations of thought and understand this movement to be necessary to the content as it is in its truth.

Bibliography

Authors
Filip Niklas (2024)

Editors
Ahilleas Rokni (2024)

Notes

Footnotes

1. It can be seen that just as thought is downstream from pure concepts and sensuous intuitions, the whole logic of the argument is itself heteronomous. Just as thought must assume worldly material given to it, so the transcendental argument itself turns around the world as given, despite positing its source as irrational. (Niklas) ↩

2. Introduction of The Science of Logic in German at Zeno.org (opens in a new tab) ↩

3. It should be noted that while the common scientific method shares much with presuppositionless thinking, it cannot perfectly overlap with the method concerning pure logic, since a number of notable conditions cannot apply. Pure logic cannot be hypothesized about since there is no space between pure logic and its subject matter, or pure logic is always categorical and actual. Likewise, predictions cannot take place since time is not a factor in the development of logic. And while the scientific method is not always a linear process, the systematic development of logic must be. Observation must also be qualified since pure thought is not concerned with the light reflected off any empirical perceptions, but with seeing, as it were, through the lens of understanding and reason, into the light of concepts themselves. (Niklas) ↩