# Contradiction and Nonmonotonicity

In standard formal logic, even one pair of contradictory assertions is traditionally deemed to make any possible conclusion vacuously derivable. Ex falso quodlibet, as the scholastics used to say — from a contradiction, anything at all follows. Meaning is thus destroyed.

As an alternative to this, Hegel in the 19th century anticipated what 20th and 21st century logicians and artificial intelligence researchers have called “nonmonotonic” reasoning. In a nonmonotonic setting, a contradiction only invalidates what is contradictorily asserted. Something must still be wrong with one of the contradictory assertions, but the damage does not spread arbitrarily.

“[W]hat is self-contradictory does not resolve itself into a nullity, into abstract nothingness, but essentially only into the negation of its particular content” (Science of Logic, di Giovanni trans., introduction, p. 33).

Robert Brandom has pointed out that material inference — the kind of reasoning based on meaning that most humans really rely on most of the time — has this nonmonotonic character:

“Gil Harman sharpens the point in his argument that there is no such thing as rules of deductive reasoning. If there were, presumably a paradigmatic one would be: If you believe p and you believe if p then q, then you should believe q. But that would be a terrible rule. You might have much better reasons against q than you have for either of the premises. In that case, you should give up one of them. He concludes that we should distinguish relations of implication, from activities of inferring. The fact that p, if p then q, and not-q are incompatible, because p and if p then q stand in the implication relation to q, normatively constrains our reasoning activity, but does not by itself determine what it is correct or incorrect to do” (Brandom, Reasons: Three Essays on their Logic, Pragmatics, and Semantics, pp. 4-5).

“Monotonicity… is not a plausible constraint on material consequence relations. It requires that if an implication (or incompatibility) holds, then it holds no matter what additional auxiliary hypotheses are added to the premise-set. But outside of mathematics, almost all our actual reasoning is defeasible. This is true in everyday reasoning by auto mechanics and on computer help lines, in courts of law, and in medical diagnosis. (Indeed, the defeasibility of medical diagnoses forms the basis of the plots of every episode of House you have ever seen — besides all those you haven’t.) It is true of subjunctive reasoning generally. If I were to strike this dry, well-made match, it would light. But not if it is in a very strong magnetic field. Unless, additionally, it were in a Faraday cage, in which case it would light. But not if the room were evacuated of oxygen. And so on” (p. 6).

# Intangible Truth

Hegel wants to teach us to put aside the prejudice that a truth must be something “tangible” or discrete in itself, and thus capable of being viewed in isolation, in the way that a Platonic form is commonly supposed to be. He says that ordinary logic already gives us a clue to an alternate view of truth. Indeed, Plato’s own literary depictions of Socratic inquiry and dialogue already suggest a deeper notion of essence and truth than is promoted by standard accounts of Platonic forms.

“The Platonic idea is nothing else than the universal, or, more precisely, it is the concept of the subject matter; it is only in the concept that something has actuality, and to the extent that it is different from its concept, it ceases to be actual and is a nullity; the side of tangibility and of sensuous self-externality belongs to this null side. — But on the other side one can appeal to the representations typical of ordinary logic; for it is assumed that in definitions, for example, the determinations are not just of the knowing subject but are rather determinations of the subject matter, such that constitute its innermost essential nature. Or in an inference drawn from given determinations to others, the assumption is that the inferred is not something external to the subject matter and alien to it, but that it belongs to it instead, that to the thought there corresponds being” (Science of Logic, di Giovanni trans., introduction, p. 30).

There is a glimmer of a deeper truth even in the naive belief that ordinary logic can tell us about how the world really is (not of course how the world is, full stop, just some important things “about” how it is). What we infer by a good inference is at least as real as whatever is intuitively present to us. Neither of these is an infallible source of knowledge. Hegel’s main point, though, is that being immediately present to us is not a criterion of deeper truth.

He continues, “Everywhere presupposed by the use of the forms of the concept, of judgment, inference, definition, division, etc., is that they are not mere forms of self-conscious thinking but also of objective understanding” (ibid).

This leads to a criticism of Kant, which implies that Kant’s famous critique of dogmatism remains incomplete.

“Critical philosophy… gave to the logical determinations an essentially subjective significance out of fear of the object…. But the liberation from the opposition of consciousness that science must be able to presuppose elevates the determination of thought above this anxious, incomplete standpoint” (ibid).

The “opposition of consciousness” Hegel speaks of is its division into subject and object. For Kant, this distinction is interwoven with what Kant takes to be an uncrossable gap between knowledge on the side of the subject, and being on the side of the object. Hegel argues that we can avoid the dogmatism Kant means to criticize, without positing an uncrossable gap between knowledge and being. For him, the works of Aristotle are decisive proof of this.

Kant seeks to ensure the avoidance of dogmatism by treating logical determinations exclusively as attitudes actively taken up by a thinking being. Hegel points out that this leads inevitably to the unknowability of the Kantian thing-in-itself. In Kant, these are two sides of one coin. Thus cut off from logical determination, the thing-in-itself can only be unknowable, just as Kant says it is. According to Hegel’s analysis yet to come, meaning is grounded in judgments of determination, and so to be cut off from determination is to be devoid of meaning.

In criticizing Kant on this score, Hegel speaks of a Kantian “fear of the object”. Elsewhere he specifies that what is wrong with the Kantian thing-in-itself has nothing to do with its resemblance to a kind of essence, but rather with the putative self-containedness of that essence, and with the fact that for Kant the true essence is unknowable as a matter of principle.

Leibniz had earlier concluded that in order for the world to be intelligible in terms of self-contained essences or monads, each monad had to include within itself a microcosmic mirror of the entire universe and all the other monads, each of which also includes all the others, and so on to infinity. For Leibniz, things in the world are really only related to one another indirectly, via their individual immediate relations to God. God is ultimately the entire source of the world’s coherence.

At the very beginning of his career, Kant had argued against Leibniz that interactions and inter-relations between things are real and not just an appearance. The world therefore has a kind of objective coherence in its own right. This is a stance that Aristotle clearly would endorse.

Hegel strongly agrees with Kant on this, but thinks that Kant did not take his critique of Leibniz far enough. (I don’t mean to identify Kant’s critique of dogmatism with his earlier critique of Leibniz, only to suggest that there is a connection between the two.) Hegel in effect argues that no essence is ever really self-contained, and that once we also drop the Leibnizian notion that essences are each supposed to be self-contained in splendid Hermetic isolation, there is nothing left in Kant’s philosophy that would require them to be unknowable as a matter of principle.

Dogmatism for Hegel refers — as it also implicitly would for Plato and Aristotle — to any claim that we somehow know the things we believe to be true, when in reality the basis of our belief is potentially refutable. Dogmatism is claiming the necessity characteristic of knowledge for conclusions that Aristotle would at best call merely probable.

(For Aristotle, “necessary” is just a name for whatever always follows from certain premises; “probable” is the corresponding name for what follows most of the time. Whether or not something always follows is a disputable question. New information might require that we re-classify what previously seemed to be a necessary conclusion as a merely probable one. I would add that what therefore seemed to be knowledge — because it seemed to follow necessarily — may turn out to be only a relatively well-founded belief. Individual humans do have genuine knowledge, but no individual knower can legitimately certify herself as a knower in any specific case.)

(Beyond this, even the historic mutual recognition of any individual concrete community can also turn out to be seriously wrong on particular matters. Widespread and longstanding social acceptance does not guarantee that certain things that are believed to be known are not just shared prejudice. Just consider the history of inferences from race, sex, religion, etc., to characteristics claimed to hold for all or most individuals subject to those classifications.)

(This does not mean we should indiscriminately throw out all claims that are based on social acceptance. That would result in paralyzing skepticism. To avoid dogmatism, we just have to be open in a Socratic way to honestly, fairly examining the basis of our beliefs about what meaning follows from what other meaning, in light of new perspectives. For what it’s worth, I say that once exposed to the light, prejudice against people based on shallow classification of their “kinds” can only be perpetuated through — among other things — an implicit repudiation of fairness and intellectual honesty in these cases.)

(Hegel the man was not immune to the various social prejudices of his time and place. According to his own philosophy, we would not expect him to have been. Outside the context of his main philosophical works, he is recorded to have made a few utterly terrible prejudiced remarks, and a number of other bad ones. In cases like this, we should give heed to the philosopher’s carefully developed philosophical views, and blame the time and place for the philosopher’s spontaneous expression of other particular views that seem out of synch with these. Every empirical community’s views are subject to adjudication in light of the ethical ideal of the truly universal community of all talking animals. The core of Hegel’s philosophy provides unprecedented resources for this.)

Kant’s own response to the issue of dogmatism is to maintain that strictly speaking, certainty and necessity apply only to appearances, which he does understand in a relational manner, but not to the things-in-themselves, which — following Leibniz — he still regards as self-contained and therefore non-relational.

Kant and Hegel seem to share the view that the very nature of necessity is such that it applies to things only insofar as they are involved in relations, and is only expressible in terms of relations. Where they differ is that Hegel sees not only appearances but also reality itself fundamentally in terms of relations.

For Hegel, there is no self-contained “thing in itself”, because the world is made up of what things are “in and for themselves”. Hegel introduces the notion of what something (relationally) is “for itself”, in the context of a reflective concept, and precisely as an alternative to the still-Leibnizian self-containedness of the Kantian “in itself”. What things really are “for themselves” turns out to undo the assumption of their essences’ self-containedness.

# For Itself

Hegel’s distinctive phrase “for itself” (für sich, literally “for self”) always seemed a little mysterious to me. It seems to refer to a self-aware being’s taking itself to be this or that, following a more or less Kantian model of judgment. That part is clear enough. But what in the world is something like “the concept in and for itself”?

Once again, the simple Kantian/Hegelian notion of reflection sheds a great deal of light on this. It applies on two levels.

First, there is a purely relational one that applies to anything that may be conceived as having characteristics that are mutually related to one another. These in turn may be construed in terms of a kind of self-relatedness of the underlying thing. In this sense, “for itself” would apply to things that have self-relatedness. This means practically everything, except perhaps some abstractly simple things like points in geometry.

Second, there is the level of self-relatedness that is internal to a reflective judgment or unity of apperception, and to the value-oriented self-consciousness arising from mutual recognition. Self-consciousness is not a detached spectator beholding multifarious relations, but has its very being within and amidst all those relations. We might say, then, that in this context the relations themselves are “self-conscious”. Similarly, concepts involved in reflective judgment are in a way necessarily “self-conscious” concepts.

In a way, our essence as human beings is the integral whole that results from — or is teleologically aimed at by — the self-consciousness of our concepts. This whole would be the totality of our commitments — everything we hold to be good, true, or beautiful.

For Hegel as for Aristotle, what count as “our” commitments and “our” concepts are not just whatever we assert are ours. The measure of what commitments and concepts are truly ours lies in what we do in life. And what we really did in any particular case is not just what we say we did or meant to do, but also what others can observe and evaluate.

In this way, to be “for oneself” is simultaneously to be for others, because what counts as one’s deed — and ultimately as oneself — is partly up to all those others who experience us. This doesn’t mean we are not entitled to make contrary assertions of our own that may be right; maybe in some particular case, the others affected by our deeds are prejudiced. For Hegel, the bottom line is that everyone affected gets a hearing in such cases, and the outcome — what is ultimately right — is not subject to a predetermined formula, but rather follows from all the fine details of each case. This is characteristic of the openness by which Kant first distinguished reflective judgment. It is also characteristic of Aristotelian practical judgment.

To be “for itself” or “for oneself” is to be a subject of reflective judgment. For humans, it is also to be a subject of mutual recognition.

At least in the first instance, “subject” here need not imply a self-conscious subject, just a thing with properties with which the judgment is concerned. But perhaps the human case suggests something about how a self-conscious subject could be thought of as a special case or elaboration of a simple Aristotelian “subject” or underlying thing.

What distinguishes Aristotle’s view of the higher levels of subjectivity (and, I think, Hegel’s too) from typical modern ones is that self-consciousness inheres not in the subject per se as a special kind of entity, but rather in the activity of reflection (contemplation, thought thinking itself, deliberation) in which the subject is involved.

# Pure Reason?

Hegel’s “logic” takes what Kant calls pure reason as its subject matter. Hegel regards Kantian pure reason as a world-changing revolution, because in contrast to early modern views, it seeks not to imitate the formal character of mathematical reasoning, but rather to achieve the discipline of a kind of self-sufficiency that does not appeal to anything external to it. Kant and Hegel differ on the scope of this self-sufficiency, but that is a different matter.

Early modern views of the world generally rely on many substantive assumptions. There is strong motivation for them to do so, because in order to yield any substantive conclusions, reasoning of a broadly formal kind requires substantive assumptions. The assumptions are typically of a sort analogous to those that Aquinas regards as grounded in the natural light of reason, which is not itself reason, but a kind of originating intuition of truth given to us by God. Descartes, for example, explicitly appeals to a variant of the Thomistic doctrine of natural light.

(The strong Thomistic notion of the natural light of reason and of reason’s relative autonomy from the simple dictates of authority is itself a development of almost inestimable importance, compared to completely authority-bound views of religion such as present-day fundamentalism. Indeed, something like the natural light of reason was never completely absent from the earlier medieval tradition either.)

But for Kant, reason is purely discursive, and cannot appeal to any intuitive source of truth like a natural light. Pure reason is nonetheless supposed to be able to stand on its own. In Kant’s language, it is “autonomous” (see also Kant’s Groundwork; Self-Legislation?). Kant’s critique of dogmatism especially targets assumptions that are naively realistic in the sense of claiming direct knowledge of external or inner objects, but it is broader than that.

Kant in the Critique of Pure Reason is most directly responding to empiricist views broadly associated with Locke, which were dominant in England and France, and popular in Germany in his day; but even more so to the rationalist system of Christian Wolff (1679-1754), which then dominated German academic teaching. (Wolff was an accomplished mathematician who had corresponded with Leibniz, and greatly contributed to popularizing the part of Leibniz’s philosophy that Leibniz had published in his own lifetime. Like Leibniz, he is associated with moderate Enlightenment, while at the same time showing a degree of sympathy for scholastic philosophy.)

Kantian pure reason effectively aims to be free of unnecessary assumptions, especially those of the Wolffian system, but also those of the empiricists. Kant also criticizes Wolff’s and Spinoza’s idea that philosophical reasoning should as much as possible resemble mathematical reasoning. What makes it possible for Kant to avoid assumptions beyond the famous “God, freedom, and immortality” (and for Hegel to avoid any assumptions at all) is a move away from the early modern ideal of reason as formal.

Without ever explicitly saying so, Kant in fact takes up and works with a notion of reason that is close to aspects of Plato and Aristotle that were generally neglected in the intervening tradition. Reason in Plato, Aristotle, Kant, and Hegel is not limited to formal reasoning. It includes what in more recent times Sellars and Brandom have elaborated under the name of material inference.

Formal reasoning is called formal because it is supposed to apply to all things, independent of any analysis of meaning. But this makes it dependent on assumptions in order to yield conclusions. Material inference — which was also present as a minor theme in scholastic logic — is on the contrary grounded in the interpretation of meaning. It is this reflective grounding that can enable reason to be autonomous and “pure”, with no reliance on anything external to it.

Sellars illustrates material inference with examples like “there are dark rain clouds in the sky, so I should take my umbrella when I go out”. Brandom elaborates with an account of how such judgments may be successively refined based on additional information. In general, if I strike a match correctly, it will light. But under certain conditions, it will not light. But under yet more specific additional conditions, it will in fact still light.

Both Sellars and Brandom — working within the tradition of contemporary analytic philosophy — tend to reach for examples that involve empirical facts, and relations of cause and effect in the broad modern sense. But material inference is more general than that. It is grounded in meaning as we encounter it in real life. Its scope is not limited to any particular kind of meaning, nor does it assume any particular theory of meaning.

Pure reason, then — far from excluding meaning, as formal logic does — is concerned with the progressive self-clarification of meaning — or Kantian “taking as”, or judgment — in a reflective context.

For Hegel, “logic is to be understood as the system of pure reason, as the realm of pure thought” (Science of Logic, di Giovanni trans., introduction, p. 29). This is what he calls the “concept of science”, and also “absolute knowledge” (p. 28). As I’ve pointed out before, in Hegel these terms have specialized meanings that are far from their ordinary connotations in English. Science need not be empirical, and “absolute” in this context just means the same thing as “pure” or “autonomous” — that reflective judgment need presuppose nothing outside itself.

For Hegel, the standpoint of pure reason (or “science”, or “absolute” knowing) is that of reflective judgment. The whole effort of the Phenomenology of Spirit is required to reach this point, which he then uses as a starting point in the Logic.

“Pure science thus presupposes the liberation from the opposition of consciousness [between itself and its object]…. As science, truth is pure self-consciousness as it develops itself and has the shape of a 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” (p. 29, emphasis in original).

The reflective concept has the shape of a “self” — a reflexivity — that is not to be identified with our empirical self, but rather is related to the reflective character of self-consciousness, which overcomes the simple opposition between consciousness and its object.

“This objective thinking is thus the content of pure science. Consequently, far from being formal, far from lacking the matter for an actual and true cognition, it is the content which alone has absolute truth” (ibid).

He calls reflective judgment objective thinking, precisely because it begins only after the separation of consciousness from its object ends. Reflective judgment and self-consciousness will not be separated from “the concept” in which they are embodied. Rather, we have here a case of the Aristotelian identity of pure thinking with what it thinks.

“Logic has nothing to do with a thought about something which stands outside by itself as the base of thought; nor does it have to do with forms meant to provide mere markings of the truth; rather, the necessary forms of thinking, and its specific determinations, are the content and the ultimate forms of truth itself.”

“To get at least some inkling of this, one must put aside the notion that truth must be something tangible. Such tangibility, for example, is carried over even into the ideas of Plato which are in God’s thought, as if they were, so to speak, things that exist but in another world or region, and a world of actuality were to be found outside them which has a substantiality distinct from those ideas and is real only because of this distinctness” (pp. 29-30).

Truths are not objects, and they are not given to us in the way that ordinary consciousness takes objects to be. For Hegel, moreover, spiritual values do not have to do with turning away from this world in favor of another one. They are intended to guide us in life.

“There will always be the possibility that someone else will adduce a case, an instance, in which something more and different must be understood by some term or other” (p. 28).

Reflection and interpretation are inherently open-ended.

“How could I possibly pretend that the method that I follow in this system of logic, or rather the method that the system itself follows within, would not be capable of greater perfection, of greater elaboration of detail? Yet I know that it is the one true method. This is made obvious by the fact that this 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. It is clear that no expositions can be accepted as scientifically valid that do not follow the progression of this method and are not in tune with its simple rhythm, for it is the course of the fact [Sache] itself” (p. 33).

Translator di Giovanni comments in his glossary, “In non-technical contexts, [Sache] can and should be translated in a variety of ways, such as ‘substance’, or even ‘thing’. As category, however, ‘fact’ seems to be the best rendering. Sache, like ‘fact’, denotes a thing or a situation which we understand to implicitly contain all the factors required for an explanation of its existence. Its presence therefore cannot be doubted even when those factors have yet to be made explicit. The related word, Tatsache, was first coined… in order to translate the English term ‘matter of fact'” (pp. lxxi-lxxii).

To me, these sound like reasons for calling Hegel’s Sache something other than “fact”. Especially in a work of “logic” that invokes “science”, the English word “fact” would most commonly be taken taken to mean an unambiguous empirical truth. Both what I think Hegel means and the explanation di Giovanni gives of it seem better suited by the more open connotations of an English phrase like “the concrete case” or “the matter at hand”. The Sache is something objective, but it is objective in the indefinite sense of a Gegenstand [“object” in the sense of something standing over and against us, but whose nature has yet to be determined].

I used to think that reason that would be applicable to life (or to anything like Hegel’s Sache) could not possibly be pure. I now think that with the inclusive character of reflective judgment and material inference, it can be pure.

# Shallow vs Deep Reflection

“Logic… cannot say what it is in advance, rather does this knowledge of itself only emerge as the final result and completion of its whole movement” (Hegel, Science of Logic, di Giovanni trans., introduction, p. 23).

From either an Aristotelian or a Kantian perspective, it seems to me this is true of any sort of “self-knowledge”. We don’t just look within and see the truth; it takes a long detour to get there.

Hegel here stresses the radically presuppositionless character of this thing that he calls “logic”. This results in a far more ambitious project than Aristotle’s “tool rather than knowledge” approach to logic, which is also primarily geared toward more ordinary contexts, in which we do not aim to be radically presuppositionless.

I’m still inclined toward a middle position that what is at stake here is better called a kind of hermeneutic wisdom than knowledge. I agree with Pippin that Hegel is engaging in a kind of what Aristotle would call first philosophy here, but I take first philosophy itself to be a kind of meta-level interpretation, and thus again to be wisdom more than knowledge.

“The concept of logic has hitherto rested on a separation, presupposed once and for all in ordinary consciousness, of the content of knowledge from its form, or of truth and certainty. 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 from outside” (p. 24).

Here he is both saying that the more ordinary concept of logic has not yet learned the lessons of Kant’s Critique of Pure Reason, and implicitly criticizing the dualistic appearance of some of Kant’s formulations.

“These views on the relation of subject and object to each other express the determinations that constitute the nature of our ordinary, phenomenal consciousness. However, 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” (p. 25).

This is a very strong statement. Hegel has a very positive view of life in the world, but he strongly distrusts our ordinary consciousness of it. Philosophy is what teaches us to move beyond common sense, toward something higher.

“The older metaphysics had in this respect a higher concept of thinking than now passes as the accepted opinion. For it presupposed as its principle that only what is known of things and in things by thought is really true in them, that is, what is known in them not in their immediacy but as first elevated to the form of thinking, as things of thought. This metaphysics thus held that thinking and the determination of thinking are not something alien to the subject matters, but rather are their essence, or that things and the thinking of them agree in and for themselves (also our language expresses a kinship between them); that thinking in its immanent determinations, and the true nature of things, are one and the same content” (ibid).

Here he is clearly referring to Aristotle, and endorsing Aristotle’s point of view as in a way even superior to that of Kant. For Aristotle, thought and things meet on the middle ground of the “what-it-is” or essence of things, which is what allows the ultimate identification of thought with what it thinks.

He mentions the shallow “external” reflection he associates with Locke’s notion of human understanding, then the much more substantive kind of reflection discussed by Kant in the Critique of Judgment, which will be a major theme of this whole work.

“The [Kantian] 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 and attain insight into their discord is the great negative step on the way to the true concept of reason. But, when not carried through, this insight runs into the misconception that reason is the one that contradicts itself” (p. 26).

Contrary to Kant’s pessimistic conclusion in the antinomies of the first Critique, reason does not contradict itself; it is rather the determinations in things and situations that are subject to conflicting objective evaluations. Hegel’s more optimistic view of reason is accompanied by a very honest recognition of the existence of genuinely hard problems for thought about life in the world.

# Hegel on Hegel’s Logic

By his own account, Hegel makes a “completely fresh start” in what he calls logic (Science of Logic, di Giovanni trans., 1st preface, p. 9). Robert Pippin points out that insofar as it has precursors, the principal debts of Hegel’s effort are to Kant’s Critique of Pure Reason and Critique of Judgment and to Aristotle’s Metaphysics, none of which are ordinarily viewed as works of “logic”. Translator George di Giovanni calls it a “discourse about discourse” (p. xxxv). Fundamentally, it is about meaning, and the conditions for anything to be intelligible.

“[A]n altogether new concept… is at work here…. [Philosophy] cannot borrow its method from a subordinate science, such as mathematics, any more than it can remain satisfied with categorical assurances of inner intuition, or can make use of argumentation based on external reflection. On the contrary, it can only be the nature of the content which is responsible for movement in scientific knowledge, for it is the content’s own reflection that first posits and generates what that content is” (pp. 9-10).

He emphasizes “the nature of the content” (which is to say meaning), and “content’s own reflection”. That reflection, moreover, “first posits and generates what that content is“. Meaning’s own reflection “posits and generates” what it means. We are not far from Aristotle’s thought thinking itself that is the cause of the what-it-is of things. Hegel shares with Kant and Aristotle a discursively reflective view of thought and meaning.

I still prefer to speak of “knowledge” rather than “science” in a philosophical context. But Hegel just means a disciplined form of knowledge. The German word for science (Wissenschaft) literally means something like the art of knowing (wissen). Our word “science” comes from Latin scientia (knowledge in a strong sense). According to di Giovanni, wissen for Hegel “signifies the product or the origin, rather than the process, of reason” (p. lxx). It is distinguished from Erkenntnis (confusingly also rendered by some translators as “knowledge”), which starts from a root meaning of acquaintance or recognition, and comes to refer to the process of reason.

“The forms of thought are first set out and stored in human language…. In everything that the human being has interiorized, in everything that in some way or another has become for him a representation, in whatever he has made his own, there has language penetrated, and everything that he transforms into language and expresses in it contains a category, whether concealed, mixed, or well defined. So much is logic natural to the human being, [it] is indeed his very nature. If we however contrast nature as such, as the realm of the physical, with the realm of the spiritual, then we must say that logic is the supernatural element that permeates all his natural behavior, his ways of sensing, intuiting, desiring, his needs and impulses; and it thereby makes them into something truly human, even though only formally human — makes them into representations and purposes” (2nd preface, p. 12).

Our involvement with linguistic meaning is “our very nature”, or is the “supernatural” element in our natural behavior that makes us truly human. As one reading of Aristotle puts it, what makes us human is that we are talking animals.

“But even when logical matters and their expressions are common coin in a culture, still, as I have said elsewhere, what is familiar is for that reason not known…. To indicate the general features of the course that cognition goes through as it leaves familiar acquaintance behind, the essential moments in the relationship of scientific thought to this natural thought, this is the purpose of the present preface” (p. 13).

“First of all, it must be regarded as an infinite step forward that the forms of thought have been freed from the material in which they are submerged in self-conscious intuition, in representation, as well as in our desires and volitions or, more accurately, in ideational desiring and willing (and there is no human desire or volition without ideation); a step forward that these universalities have been brought to light and made the subject of study on their own, as was done by Plato, and after him by Aristotle especially” (pp. 13-14).

He credits Plato and Aristotle with first clearly articulating notions of thought and meaning in a way that is independent of particular subjectivity. Next he cautions against the illusion of mastery.

“We do not indeed say of our feelings, impulses, interests, that they serve us; on the contrary, they count as independent forces and powers, so that to have this particular feeling, to desire and to will this particular thing, to make this our interest — just this, is what we are. And it is more likely that we become conscious of obeying our feelings, impulses, passions, interests, not to mention our habits, than of having them in our possession, still less, in view of our intimate union with them, of their being means at our disposal. Such determinations of mind and spirit, when contrasted with the universality which we are conscious of being and in which we have our freedom, quickly show themselves to be particulars, and we rather regard ourselves to be caught up in their particularities and to be dominated by them. It is all the less plausible, therefore, to believe that the thought determinations that pervade all our representations — whether these are purely theoretical or hold a material belonging to sensation, impulse, will — that such thought determinations are at our service; that it is we who have them in our possession and not they who have us in theirs” (p. 15).

We are masters neither of our feelings nor of our thought.

“[W]hen the content that motivates a subject to action is drawn out of its immediate unity with the subject and is made to stand before it as an object, then it is that the freedom of spirit begins” (p. 17).

True freedom of spirit is the very opposite of following one’s arbitrary will or impulse.

“The most important point for the nature of spirit is the relation, not only of what it implicitly is in itself to what it actually is, but of what it knows itself to be to what it actually is” (ibid).

Here he already raises the Aristotelian theme of the priority of actuality.

“As impulses the categories do their work only instinctively; they are brought to consciousness one by one and so are variable and mutually confusing, thus affording to spirit only fragmentary and uncertain actuality. To purify these categories and in them to elevate spirit to truth and freedom, this is therefore the loftier business of logic” (ibid).

Hegel’s logic thus serves a profound ethical purpose.

“It is soon evident that what in ordinary reflection is, as content, at first separated from the form cannot in fact be formless, … that it rather possesses form in it; indeed that it receives soul and substance from the form alone and that it is this form itself which is transformed into only the semblance of a content…. By thus introducing content into logical consideration, it is not the things, but rather the fact [Sache], the concept of the things, that becomes the subject matter” (pp. 18-19).

What the moderns call “content” is a special case of what Plato and Aristotle call form. Hegel calls it a “semblance” of content. But its role in his logic is pivotal. Logic is concerned not with things as such but with meanings, Aristotelian forms, the what-it-is of things. What the translator calls “fact” seems rather different from ordinary English usage.

# Reflection, Judgment, Process

Reflection is a key concept both for later Kant and for Hegel (see, e.g., Reflection, Apperception, Narrative Identity; More on Contemplation). We have seen that it led Kant to deepen the notion of judgment he had already used in the Critique of Pure Reason, giving more explicit attention to what I have called the process of interpretation, in contrast to the eventual conclusions that had been the exclusive preoccupation of early modern logic. He had already criticized the latter for confusing judgment with predication.

When judgment is identified with simple predication, the process of interpretation entirely disappears. Indeed, both early modern and contemporary formal logic are explicitly concerned with mechanical syntactic manipulation of uninterpreted terms.

Kant’s narrower point in the first Critique had been that only categorical judgments (those having the simple form A is B) can be analyzed as linguistic predications. Against the early modern tradition, Kant pointed out that neither hypothetical judgments (if A then B) nor disjunctive judgments (if A then not-B) can be understood in this way.

Whereas the early modern tradition strongly privileged categorical judgments, taking simple predications straightforwardly as simple assertions, Kant argues that hypothetical and disjunctive judgments have at least equal significance for thought, if not more. Hypothetical and disjunctive judgments are irreducibly inferential, as can be seen from the presence of “if” and “then” in their forms. What Kant suggests about this in the first Critique is that the inferential aspect of judgment is more fundamental than its assertive aspect. Brandom makes the further suggestion that the kinds of inferences Kant is primarily concerned with in this context are informal “material” inferences, which are grounded in the meanings of terms rather than in formal syntax.

With the enhanced concept of reflective judgment developed in the Critique of Judgment, Kant begins to take an even wider range of interpretive processes into account in his view of judgment overall. Reflective judgment is primarily focused on the process of interpretation, though it also reaches conclusions. This makes the contrast between Kantian judgment and judgment in early modern logic even more profound. Early modern logic codifies a “conclusory” notion of judgment grounded in simple assertion, and makes the formal manipulation of such assertions the paradigm for all reasoning. Kantian judgment on the other hand begins as primarily inferential, and comes to emphasize the wider, open-ended, reflective process of interpretation.

The “logic of being” that Hegel presents as a kind of necessary preliminary failure in his Logic is precisely the logic of simple assertion. From any arbitrary assertions, we can deductively generate more assertions that will be consistent with these, and we can classify other assertions according to whether they are consistent with the accepted ones or not. But Hegel is concerned with the possibility of genuine intelligibility and knowledge. Starting only from mere assertions, we can never reach these. The most we can achieve is some kind of relational discrimination between the implications of different assertions, whose meaning is merely assumed.

Kantian reflection is the main theme of Hegel’s “logic of essence”. Hegel’s conclusion is that the ultimate ground of essence is none other than pure reflection, which embodies a kind of reflective infinity of mutually referencing relations, that presupposes no fixed terms. Essence, as a kind of deeper truth of things than the shallow one of logical consistency alone, is not based on “fixed” concepts of the sort that are always assumed in formal logic. Rather, essence for Hegel is grounded in reflection all the way down, which we can pursue as deeply as we like. Socratic inquiry can be seen as a foreshadowing of this.

I see an important parallel to book Lambda of Aristotle’s Metaphysics here. There, the ground of the what-it-is of things is the pure contemplation of thought thinking itself. In other words, the ground of essence is pure reflection, just as Hegel says. The pure actuality or pure entelechy of Aristotle’s first cause is an actuality or entelechy of what Hegel calls pure reflection.

A major difference between Aristotle’s first cause and ourselves, as I read it, is that the purity of the first cause makes it only concerned with essence or deep truth, whereas we rational animals also live in a world of appearances, and therefore also have to deal with these. Because we live in a world of appearances, we humans have a need for judgment that Aristotle’s first cause does not share.

In the “logic of the concept” with which he concludes his Logic, Hegel gives a thoroughly Kantian treatment of judgment, effectively identifying all judgment with reflective judgment in Kant’s sense. If the logic of essence was concerned with the objective determination of essence from pure reflection, the “subjective” logic of the concept is concerned with applying reflection to particular appearances that we encounter in life. This is something we rational animals have to do that Aristotle’s first cause does not.

Pure reflection is a kind of ideal thing that is analytically separable from process, but the kind of reflection that we embodied beings engage in only occurs as part of a concrete process that involves particular appearances and development in time.

# Is and Ought in Actuality

Aristotle regards the priority of actuality over potentiality to be one of his most important innovations. He regards it as a necessary condition for anything being intelligible. Along with the primacy of the good and that-for-the-sake-of-which in explanation, it is also central to his way of arguing for a first cause.

The Western tradition generally did not follow Aristotle on these points. Arabic, Hebrew, and Latin monotheisms have most often treated God as an absolute power, seeking to put unlimited omnipotence first in the order of explanation, before goodness. Christians were happy to criticize occasionalism in Islam, but theologians like Duns Scotus and William of Ockham defended an extreme sort of theological voluntarism, which was taken up again by Descartes. In the 19th century, Kierkegaard valorized Abraham’s willingness to sacrifice his son as unconditional obedience to God, claiming that faith should take precedence over ethics generally. In the 20th century, Sartre defended unconditional free will for humans, while asserting a militant atheism and the absurdity of existence. His currently influential follower Alain Badiou goes even further. He bluntly says that concern for ethics is a waste of time, and that dialogue and democracy are a scam — not just in particular cases, but in general.

Mainstream views of religion have always insisted that the absolute power is also absolutely good, but have been unable to show why or how this is the case. This has opened the door to simplistic but unanswerable arguments that the facts of the world cannot be reconciled with claims that it is governed by a good absolute power.

Instead of sacrificing ethics and the good on either religious or secular grounds, we should put them first. Leibniz argues that an emphasis on the absolute power or arbitrary will of God is bad theology, and effectively makes God into the kind of tyrant that Plato denounced (see also Euthyphro; Arbitrariness, Inflation).

Aristotle’s first cause doesn’t govern the facts of the world. It is the world’s normative compass. It is the pure good and pure fulfillment that all things seek, according to their natures and insofar as they are capable. Or as Hegel might say, it is pure Idea.

The priority of actuality is a priority of the good and of normativity. For Aristotle, we shouldn’t call something “actual” just because it exists or is the case. Rather, something is actual when it is the case that it is fulfilling its potential, as it “ought” to do.

It is not a matter of pure moralism either though. Actuality does involve an element of being the case; it is just not reducible to that. What is true also matters quite a lot in the determination of what is right, even though it is not all that matters. Every particular good is interdependent with particular truth. That is why Aristotle seems to make the understanding of causes into one of the most important elements of virtue, while at the same time cautioning us that ethics is not a matter of exact knowledge.

We are looking for a kind of mean here. What is true matters for what is right, but what is right also matters for what is true. Truth is not reducible to a matter of neutral fact. There can be no truth without intelligibility, and there can be no intelligibility without taking normative considerations into account in interpretation.

# More on Contemplation

I’m still, as it were, contemplating Aristotelian contemplation or theoria (see also But What Is Contemplation?; Kantian “Contemplation”?).

The two main English meanings of theoria — “contemplation” and “theory” — have a rather different connotative feel. What is tricky is that by all accounts, contemplation is also an activity. But it is not grammatically obvious that the English “theory” is an activity. Indeed, a theory is commonly taken to be a kind of inert representation, and not an activity.

Nonetheless, it seems reasonable to say that “theory” by itself can also refer to a corresponding activity. Theory’s activity would be contemplative, and would not in itself aim at any external result. At least on a relative scale applicable to humans, it would be pure thinking. Meanwhile, contemplation for Aristotle is a kind of activity that does not in itself have an external result.

In the contemporary revival of American pragmatist philosophy, figures like Brandom and Pippin insist that thinking is a kind of doing. Rather than a distinction between theory and practice, this leads to a distinction between specifically “contemplative” or “theoretical” practice, and practice in general. Doing and practice in English can thus have the full generality that activity has in Aristotle. Not all doing is “external” doing; not all practice is “external” practice.

Human pure thinking may implicitly issue in a kind of result — a relatively coherent representation, or broadly speaking a “theory” of what it holds to be the case — but it may still be said that this implicit result is “internal”, until some additional external action gives the representation some kind of embodiment.

However, Hegel might remind us that the very distinction between “internal” and “external” is problematic. He argues that it is not really possible to draw an unambiguous line between them, and that internal and external are instead related by a kind of continuity.

(Hegel confusingly calls this a speculative “identity”, though he is very clear that a speculative identity is not a formal, exact identity. Having come to see the value in what Paul Ricoeur calls narrative identity — another “identity” that is not a formal, exact identity — I don’t object as strenuously to Hegel’s nonstandard uses of “identity” as I once did, though I still prefer to use some other word when what is meant is anything weaker than exact isomorphism or substitutional equivalence.)

The continuity of internal and external seems to me like a very Aristotelian point, albeit one that Aristotle does not himself make. But unlike Hegel, Aristotle has no need to respond to a sharp Cartesian or Lockean dualism between consciousness and its representations on the one hand, and everything else on the other.

I think most people would allow that contemplation may involve representations, but contemplation itself is neither an activity of representing, nor a simple consciousness of static representations.

The English connotations of contemplation and reflection are closely aligned. Connotations of words do not count as a philosophical argument for identifying terms that might be claimed to stand for different concepts, but such alignment is nonetheless helpful, because in doing philosophy we are also concerned with communicating clearly, and there are always issues with translated terms not meaning quite the same thing on the two sides of a translation.

Aristotle identifies contemplation with thought thinking itself. I am suggesting that thought thinking itself can be strongly identified with reflection in the sense discussed by Kant, Hegel, Ricoeur, and Pippin, which builds on the common one. That would mean that contemplation can be identified with reflection.

Though the precise meanings of reflection and apperception in Kant are debated by scholars, there seems to be broad agreement that Kant strongly connects pure reflection with pure or transcendental apperception, and a more empirical reflection with a more empirical apperception. (See also Reflection, Apperception, Narrative Identity).

These same concepts are fundamental to Hegel’s Logic. The three “logics” he develops there concern mere assertion; reflection or reflective constitution; and reflective or apperceptive judgment. Hegel innovatively explains the constitution of essence in terms of a pure reflective determination that presupposes no fixed terms, but builds determination from relations between terms. Then he explains judgment as normatively applying reflective determination to appearances.

I want to suggest that Hegelian reflective or apperceptive judgment should be considered as a more detailed elaboration of Aristotelian deliberation and practical judgment.

All of this leads to the conclusion that Aristotelian contemplation — at least the contemplation that he explicitly makes the goal of human life — can be explained as the exercise of reflective or apperceptive judgment. It is not clear to me that the contemplation attributed to the first cause also issues in judgment, but it certainly does seem to be a kind of pure reflection such as Hegel associates with the determination of essence, and this tracks with Aristotle’s claim that the what-it-is of things depends on the first cause.

# Reflection, Apperception, Narrative Identity

Robert Pippin recounts how in writing what became the Critique of Judgment, Kant developed a new notion of reflection, which transformed his whole philosophy from the inside:

“In early 1789 Kant began to formulate the new problem of reflective judgment, as well as a new a priori principle for such a faculty, the purposiveness of nature. What is important to notice for our purposes is that with that development, the shape of the entire critical project began to change dramatically” (Hegel’s Realm of Shadows, p. 290).

“Kant had realized that something like the deep structure of judgments like ‘this rose is beautiful’ actually contravened its own surface structure, that the predicate ‘beautiful’ was not really functioning as a standard predicate, as it appeared to. It referred to no objective property or mere secondary quality. Instead, he concluded, it involved a nonconceptually guided reflective activity on the part of the subject of the experience, whose novel logic required notions like a free play of the faculties, purposiveness without a purpose, disinterested pleasure, a commonsense and universal subjective validity” (pp. 290-291).

“The realization of the distinct features of this reflective activity was only the beginning of a series of more strikingly novel claims of interest to us…. [T]he reflective judging that resulted in aesthetic judgments, also constituted the basic structure of teleological judgments, and so could account for the unique intelligibility of organic beings” (p. 291).

“And then a number of other issues seem to be thrown into the same reflective judgment pot. The formulation of scientific theories not fixed or determined by empirical generalizations involved this activity and its logic, as did the systematizing of empirical laws necessary for genuine scientific knowledge. Finally, even the determination of ordinary empirical concepts now seemed to require this newly formulated reflective capacity…. So reflective judging and its a priori principle were now necessary not only for explaining the possibility and validity of aesthetic judgments, but in accounting for the necessary distinction between organic and nonorganic nature, the formation of empirical concepts, the proper integration of genera and species, the general unification of empirical laws into systems of scientific law, theory formation itself, and the right way to understand the attribution of a kind of necessity to all such principles, judgments, concepts, laws, and systems” (ibid).

Much of the discussion of judgment in the Critique of Pure Reason sounds like it is a simple matter of “applying” pre-existing concepts to things. But in reality, applying even pre-existing concepts is not a simple matter at all, if we care about the soundness of the application (as Kant certainly did), or about how anyone preliminarily judges what concepts might be applicable in a given case. This is what Kant began to consider in more detail with his new notions of reflection and reflective judgment.

Reflection is characterized above by Pippin as “nonconceptually guided”. I don’t think this means at all that reflection is nonconceptual, but rather only that it is fundamentally guided by something other than the kind of pre-existing concepts that Hegel would call “fixed”. Reflection involves the formation and interpretation of concepts that are not treated as already fixed. That is why it does not presuppose particular fixed concepts.

I want to relate this back to the Aristotelian deliberation and practical judgment (phronesis) that are concerned with particulars as such. The significance of addressing particulars as such is that we do not assume in advance what universals (i.e., Kantian concepts) apply to them, but rather let the particulars “speak” for themselves, and thoughtfully consider what they might mean or be in their own right. By particulars I mean in an Aristotelian way independent or non-independent “things”, not putative raw phenomena.

Aristotelian deliberation and practical judgment, I want to say, involve a “free play of the faculties” of the sort that Kant associates with reflection. Aristotle’s commonly cited conclusion that practical judgment is inferior to contemplative wisdom is entirely tied to the fact that he considers practical judgment’s outcome to be an action. I think the term practical judgment ought to apply just as much or more to the activity of interpreting particulars, without prejudice as to how the interpretation is used.

Kantian reflection seems to me to have the great virtue of uniting Aristotelian theoria (contemplation) and sophia (contemplative wisdom) with deliberation, thinking things through (dianoia), and practical judgment (phronesis). Kant also explicitly argues for the primacy of practical reason, which ultimately involves the reflective normative evaluation of particulars, even though he foregrounds a separate effort to articulate ethical universals. An Aristotelian sense for the Kantian primacy of practical reason would start from the interpretation of particulars mentioned above.

Kantian reflection also has an important relation to the Critique of Pure Reason‘s key term of apperception. The term “apperception” was coined by Leibniz, originally to imply a kind of “higher order” perception — a perception of perception. Kant gives it a more explicitly discursive character. If we add a Hegelian dimension, the dialectical character of discourse makes discourse inherently reflective in Kant’s sense. By virtue of their common reflective, discursive character, apperception in Kant is closely related to what is called “self-consciousness” in Hegel.

Kant famously speaks of the effort to maintain a unity of apperception. Here is where I think phronesis comes to the aid of theoria and sophia. Contrary to what both Kant and Aristotle sometimes suggest, it seems to me that the interpretation of particulars is actually prior to and more governing than the articulation of universals, although there is much interplay between the two. It is the interpretation of particulars that mainly provides occasions for the articulation of pertinent universals. This comes back to Aristotle’s other point that universals do not have independent reality in their own right, and to Kant’s other point about the primacy of practical reason.

The effort to maintain a unity of apperception is the effort to maintain a unity of self-consciousness. Self-consciousness is not simple “consciousness” of a pre-existing “self”, as if the latter were a discrete, pre-existing object. Rather, self-consciousness is grounded in reflection that has potentially indefinite extent. I think a similar grounding in reflection is what makes intellect “something divine in us” — and more than just a part of the soul — in Aristotle.

Aristotle speaks of thought thinking itself as contemplation. He tends to emphasize that thought thinking itself is an identity. But with any kind of identity, we must consider the way in which it is said.

What then could constitute any persistent identity for a unity of apperception? Here we come to the problems that Paul Ricoeur discussed under the more general rubric of narrative identity. Strictly speaking, any particular unity of apperception is a concrete constellation of what Aristotle would call particular relations that hold at a given moment. It is something like the totality of what we are currently committed to. Insofar as we speak of it as existing in fact, its unity and coherence are relative. Only as a kind of ideal or ethical goal can its unity be considered to be unqualified.

Insofar as we want to speak of the relative persistent identity of a unity of apperception — or anything like the unity of a person — we also need the Aristotelian concept of entelechy. The narrative identity of a unity of apperception is a kind of entelechy in which the thing whose identity is maintained is itself a work in progress, as all living beings are. We only have the final form of a life when it is over (see Happiness).

The narrative identity of a unity of apperception, then, is a kind of entelechy of apperception. More generally, Aristotelian entelechy is the narrative identity of a unity, or just is a kind of narrative identity. An entelechy of apperception is the entelechy of a process of reflection. (See also More on Contemplation; Hegel on Reflection; Apperceptive Judgment.)