This will conclude my walk-through of the Preface to Hegel’s Phenomenology. Here he gives an explicit anticipation of what he calls “the concept”, which will be a key term in the Phenomenology‘s successor work, the Science of Logic. Along with “idea”, “concept” for Hegel represents something that is already beyond the naive opposition of subject and object.
If we imagine the naive view of subject and object as a pair of distinct points, a preliminary analogy for Hegelian concept and idea would be a line between the subject and object points. This can be understood as including all the meaningful content of experience, and can be taken as close as you like to either or both endpoints, but does not include either endpoint. Then the inversion of point of view that Hegel speaks of between ordinary consciousness and the standpoint of his logic would correspond to the relation between seeing experience in terms of the static duality of subject and object, and seeing it in terms of “living” concept and idea.
He begins this part with some remarks about mathematics that are overall very negative-sounding. This is setting up for a contrast between mathematics as the paradigm of static “formal” reasoning, and the meaning-oriented, becoming-oriented “dialectical” reasoning he wants to promote. To put the negative remarks in proper perspective, it is worth knowing that he will devote nearly 200 pages in the early part of the Science of Logic to a serious and sympathetic discussion of mathematics that shows good familiarity with the leading mathematical writers of his day.
“As for mathematical truths, one would hardly count as a geometer if one only knew Euclid’s theorems by heart without knowing the proofs” (p. 25).
Here he repeats the important point that knowledge does not consist in bare conclusions or propositions.
However, I think he goes astray when adds that really, “The movement of mathematical proof does not belong to the object but is a doing that is external to the item at hand” (ibid). I would say almost the opposite: the appearance of externality between theorem and proof — the idea that theorems have a status of simple truth independent of their proofs — reflects the very same kind of error that he pointed out before in the separation of results from the development that produced them.
It is true that a mathematical proof viewed as an object does not consist in the kind of becoming of knowing that Hegel attributes to good philosophical thinking. To mix terminology from computer science and Aristotle, mathematical proofs are in principle “statically” evaluable; this means they do not depend on any runtime accidents. In Platonic terms, mathematical objects are “eternal”, and proof is a kind of strict unfolding of their essence that we can imagine after the fact to have been predetermined, even though we don’t see the full predetermination in advance.
Earlier in the Preface, Hegel has argued that in the genuine becoming of knowing, “accidents” play an essential role, just as I would say they do in any actual working out of Aristotelian teleology. The means is not irrelevant to the end to the extent that we care about the end’s actualization. Like Aristotle, Hegel treats the process of actualization as primary.
Thus he is right that the becoming of knowing that philosophy ought to aim at does not — and ought not to — follow the canons of mathematical proof. In philosophy, we learn as much from our mistakes as from our successes, but errors in mathematics do not present the same kind of opportunities for improving our wisdom. Mathematics is not philosophy but something else. It is not “conceptual” in Hegel’s sense that involves a kind of “life” and “self-movement” of the concept.
However, he goes on to say that “In mathematical cognition, insight is an external doing vis-à-vis the item at issue” (p. 26, emphasis added). I don’t find this to be true today, and think it was, if anything, further from true in Hegel’s day.
Surely the maximal externalization of human insight from proof would be today’s computer-based proofs. While it is now possible to produce purely symbolic proofs whose validity depends only on the syntactic rules of a functional programming language, and sometimes even to produce proofs in a fully automated way, the really big successes of computer-based mathematical proof in recent decades have involved automated proof checkers that eschew fully automated proof development in favor of “dialogue” with an insightful human. At least in the current and foreseeable state of the art, human insight is not at all external to the development of mathematical proofs, even though the checking of completed or partial proofs for errors can be fully automated.
I say that mathematics is not philosophy, but its practice is far from being the mindlessly formal “defective cognition” he makes it out to be here in the Preface. Mathematical objects including completed proofs are static, but I say that the doing of mathematics essentially involves the activity of human intelligence.
“[W]hat is formal in mathematical convincingness consists in this — that knowing advances along the line of equality. Precisely because it does not move itself, what is lifeless does not make it all the way to the differences of essence…. For it is magnitude alone, the inessential difference, that mathematics deals with” (p. 27).
Mathematics only deals with things that are in principle strictly univocal. Strictly univocal things lack “life” for Hegel, and are therefore inessential.
“In contrast, philosophy does not study inessential determinations but only those that are essential. The abstract or the non-actual is not its element and content; rather, its element and content is the actual, what is self-positing, what is alive within itself, or existence in its concept. It is the process which creates its own moments and passes through them all; it is the whole movement that constitutes the positive and its truth. This movement just as much includes within itself the negative ” (p. 28).
Philosophy for Hegel is especially concerned with actuality, and as with Aristotle, what is actual is not simply to be identified with what is factual.
“Appearance is both an emergence and a passing away which does not itself emerge and pass away… which constitutes the actuality and the living moment of truth…. Judged in the court of that movement, the individual shapes of spirit do not stably exist any more than do determinate thoughts, but they are also equally positive, necessary moments just as much as they are negative, disappearing moments” (pp. 28-29).
Here he is using “appearance” in a very different way from what Plato called mere appearance. It seems to be something like the concrete manifestation that is necessarily implicit in actuality.
“In the whole of the movement… what distinguishes itself in it and what gives itself existence is preserved as the kind that remembers, as that whose existence is its knowing of itself” (p. 29).
Previously, he said that the true is the whole. In this movement of self-knowing, which is quite different from being an object for oneself, the subject and object that are quite distinct for ordinary consciousness become interwoven.
“It might seem necessary to state at the outset the principal points concerning the method of this movement…. However, its concept lies in what has already been said, and its genuine exposition belongs to logic, or is instead even logic itself, for the method is nothing but the structure of the whole in its pure essentiality” (ibid).
The entry point for what Hegel calls “logic” is what I have glossed as being at home in otherness. For Hegel, logic is not about formal manipulations. It is a very non-ordinary way of looking at things that leaves distinctions of subject and object behind. The Phenomenology is supposed to provide a way into this perspective, starting out from what Aristotle would call the way things (ordinarily) are “for us” (see Otherness; At Home in Otherness).
“In everyday life, consciousness has for its content little bits of knowledge, experiences, sensuous concretions, as well as thoughts, principles, and, in general, it it has its content in whatever is present, or in what counts as a fixed, stable entity or essence…. [I]t conducts itself as if it were an external determining and manipulation of that content” (p. 30).
Ordinary consciousness regards things in the world as fixed, pre-known, and manipulable. It regards itself as somehow standing off to the side from the order of the world, and implicitly as able to act in complete independence from that order. It is “Cartesian”. The weakness of this point of view is progressively exhibited in the Phenomenology.
“Science may organize itself only through the proper life of the concept…. [D]eterminateness… is in science the self-moving soul of the content which has been brought to fulfillment. On the one hand, the movement of ‘what is’ consists in becoming an other to itself and thus in coming to be its own immanent content; on the other hand, it takes this unfolding back into itself, or it takes its existence back into itself, which is to say, it makes itself into a moment, and it simplifies itself into determinateness” (p. 33).
Hegelian rational “science”, sustained in otherness, examines a movement of “logical” unfolding and return that (unlike the unfolding and return in neoplatonism) occurs not in eternity but in worldly coming-to-be. The fact that the return occurs in becoming and in time gives it the form not of a simple circle but of an open-ended spiral that never literally returns to its origin.
“[S]cientific cognition requires… that it give itself over to the life of the object” (ibid, emphasis added).
In the main body of the Phenomenology, the Consciousness chapter shows the limitations of the ordinary view that we are wholly separate from the object, and the Self-Consciousness chapter develops a sharp critique of the attitude of the master who attempts to claim unilateral control over both objects and other people.
“[T]he stable being of existence… is itself its own inequality with itself and its own dissolution — its own inwardness and withdrawal into itself — its coming-to-be. — Since this is the nature of what exists, and to the extent that what exists has this nature for knowing, this knowing is not an activity which treats the content as alien. It is not a reflective turn into itself out of the content… [W]hile knowing sees the content return into its own inwardness, its activity is instead sunken into that content, for the activity is the immanent self of the content as having at the same time returned into itself, since this activity is pure self-equality in otherness” (p. 34).
Here we have a direct statement about what overcoming alienation ought to look like.
“Its determinateness at first seems to be only through its relating itself to an other, and its movement seems imposed on it by an alien power. However, … it has its otherness in itself…, for this is the self-moving and self-distinguishing thought, the thought which is its own inwardness, which is the pure concept. In that way, the intelligibility of the understanding is a coming-to-be, and as this coming-to-be, it is rationality” (p. 35).
Overcoming alienation is anything but the suppression of what is other. Neither is it a return to an original perfection. Rather, it consists in a non-ordinary sense of self that is not opposed to the other or to the field of otherness.
“Logical necessity in general consists in the nature of what it is [for something] to be its concept in its being. This alone is the rational, the rhythm of the organic whole, and it is just as much the knowing of the content as that content itself is the concept and the essence…. The concrete shape which sets itself into movement… is only this movement, and [its concrete existence] is immediately logical existence. It is therefore unnecessary to apply externally a formalism to the concrete content. That content is in its own self a transition into this formalism, but it ceases to be the latter external formalism because the form is the indigenous coming-to-be of the concrete content itself” (ibid).
In emphasizing the contentfulness of the concept rather than formal syntax as the true driver of logical necessity, he seems to be talking about something like what Sellars and Brandom call material inference.
“Although what is stated here expresses the concept, it cannot count as more than an anticipatory affirmation. Its truth does not lie in this narrative exposition” (p. 36, emphasis added).
Truth, once again, must lie in an extensive development that is never truly finished by us humans. This remark could reasonably apply to the whole Preface, but I am struck by the reference to the concept and by the place in which it occurs, just after an explicit reference to logic. Here he is looking forward not only to the main body of the Phenomenology, but even more so to what will become the Science of Logic.
He goes on to criticize “clever argumentative thinking” at length, and to contrast it with “comprehending thinking”.
“[C]lever argumentation amounts to freedom from content and to the vanity that stands above all content” (p. 36).
By Hegel’s high standards, any argument that assumes meanings are determined in advance at least tends toward the vanity and irresponsibility of what Plato and Aristotle denounced as sophistry.
Hegel wants to recommend instead that “This vanity is expected to give up this freedom, and, instead of being the arbitrary principle moving the content, it is supposed to let this freedom descend into the content and move itself by its own nature…. This refusal both to insert one’s own views into the immanent rhythm of the concept and to interfere arbitrarily with that rhythm by means of wisdom acquired elsewhere, or this abstinence, are all themselves an essential moment of attentiveness to the concept” (pp. 36-37).
Moreover, what plays the role of the subject of thought is not at all the same for comprehending thinking as it is for clever argumentation.
“[C]lever argumentative thinking is itself the self into which the content returns, and so too, the self in its positive cognition is a represented subject to which the content is related as accident or predicate. This subject constitutes the basis in which the content is bound and on the basis of which the movement runs back and forth” (p. 37).
He continues, “Comprehending thinking conducts itself in quite a different way. While the concept is the object’s own self, or the self which exhibits itself as the object’s coming-to-be, it is not a motionless subject tranquilly supporting the accidents; rather, it is the self-moving concept which takes its determinations back into itself. In this movement, the motionless subject itself breaks down; it enters into the differences and the content and constitutes the determinateness, which is to say, the distinguished content as well as the content’s movement, instead of continuing simply to confront that movement” (pp. 37-38).
Comprehending thinking “enters into the differences and the content”.
“[T]here is an obstacle based in the habit of grasping the speculative predicate according to the form of a proposition instead of grasping it as concept and essence” (p. 41).”
The form of a proposition is simply to be true or false. He may also have in mind the form of predication. Grasping something as concept and essence is treating it as articulable meaning to be interpreted, rather than as a mere thing to be pointed at.
“True thoughts and scientific insight can be won only by the labor of the concept. Concepts alone can produce the universality of knowing” (p. 44).