I. Self-consciousness

We may investigate all manner of things, seeking to understand and in the best case arrive at a science of them. One thing we may investigate, seeking to understand and in the best case arrive at a science of it, is what constitutes investigation and its end: thought, understanding, knowledge, insight. So there may be a science of thought, understanding, knowledge, insight.

These are different words: thought, understanding, knowledge, insight. We do not presume to know what each of them means and whether and how their meanings differ. They roughly indicate an object and thus a possible science. The science of that object will clarify those terms. It will mark any distinctions that need be marked. For now, for ease of exposition, we let ‘thought’ stand for all those terms.

It conforms to the meaning of the term and its traditional use to call the science of thought ‘logic’.Footnote ² The science of logic is the science of thought.Footnote ³ (Or knowledge, understanding, insight. The terms do not matter.) As a science, logic is understanding; it expounds an understanding of thought. That understanding and thus that science bear a distinctive character. For thought is self-conscious.

When we speak of self-consciousness, we do not specify a consciousness by its object, by that of which it is a consciousness: self-consciousness is not consciousness of a self, should there be such a thing. Rather, we specify a consciousness by the manner in which it is of its object: self-consciousness is a consciousness that is not separate from, but internal to, that of which it is a consciousness. So when we say that thought is self-conscious, we mean: she who thinks something is conscious of doing that; she is conscious of thinking what, therein, she thinks; she is conscious of thinking what she thinks in thinking it. It is not that, in one act, she thinks something and, in another act, understands herself to do so. Her thinking something and her thinking herself to think it are one act of the mind.

We used various words to indicate the object of logic: thought, knowledge, understanding, insight. Perhaps these terms, or some of them, have uses in which they signify something that is not self-conscious. We exclude from our consideration such uses. When the terms describe investigation and its end, what they signify is self-conscious: she who, seeking insight, finds it and now sees, understands that she does. Again, it does not matter what terms we use, and we shall continue to use ‘thought’ for all of them. In any case, that of which logic is the science is self-conscious.

In thinking something, I understand myself to think what I, thereby, think. Thus, in thinking, I understand what it is to think. This understanding of thought is internal to that of which it is the understanding. It is internal to thought. We may call it the self-understanding of thought, using the prefix ‘self-’ as in ‘self-consciousness’: to indicate not that the object understood is a self, but that the understanding in question is internal to that of which it is an understanding.

The science of thought says what it is to think; it expounds an understanding of thought. This understanding is not other than what it understands. So the science of thought is not other than that of which it is the science. It is the self-science, we may say, using ‘self-’, again, to indicate the internality of the science to its object.Footnote ⁴

II. The self-science

Any thought, as such, understands itself to be that: thought. Thus any thought is an understanding of thought; it is an understanding of what it is to think. One may want to contrast this understanding of thought, the understanding of it that is internal to thought, with another understanding of thought, an understanding from the outside, as one may want to put it. However, there is no such thing.Footnote ⁵

Let us call what it is to think the nature of thought. The concept of thought comprehends that nature. As any thought understands itself to be a thought, the concept of thought is inside any thought. Therefore this concept does not comprehend a nature that is as it is independently of being known to be so. A thought is a thought in and through its understanding of itself. Hence thought is nothing other than what it is understood to be in the concept that is inside any thought. The nature of thought is its own understanding.

If there is to be an understanding of thought from outside, then this understanding must be an understanding of the understanding that is internal to thought. For the nature of thought is that understanding. However, that internal understanding is an understanding of itself. It is already what we pretend to add to it. There is no space to add an understanding of thought to thought; the understanding that thought itself is has always already taken up the space that the added understanding would want to fill. So when we call the understanding of thought internal, we do not distinguish it from another manner of understanding thought. We distinguish it from the understanding of, for example, stuff: the nature of a certain stuff is not its own understanding. We do not contrast forms of understanding thought; we contrast thought to nature.

Logic articulates the understanding of thought that is inside thought; it articulates the self-understanding of thought. This explains why it is and what it means that logic is knowledge a priori. As it is not other than that of which it is the knowledge, the knowledge of what it is to think is not received through affection by its object. Thought supplies that knowledge from itself. The knowledge of logic is pure.Footnote ⁶

Logic therefore bears the traditional marks of a priori knowledge: it is necessary and indubitable. These marks reflect that logical knowledge lies beyond the possibility of error. It is absolute. Logic says, says only, what anyone always already knows, knows in any thought, knows in thinking anything at all. Therefore there is no such thing as denying what logic says. There is no denying what is known in any thought, no denying what is such that thinking anything at all is knowing it. She who pretends to deny it therein pretends to think (see, understand, know), and pretending to think is knowing what it is to think and thus knowing what one pretends to deny. Consequently, there is no such thing as doubting what logic says, calling it into question, arguing for or against it. Logical knowledge does not lie in a space of competing statements and positions. Someone who, presuming to speak to what thought is, proposes a theory, a view, a thesis, fails to do what she presents herself as doing.

III. The subject of thought

Logic articulates the self-understanding of thought. It is thought thinking itself. While this formula is familiar, it may raise opposition. It may be held to be obscure to speak of thought thinking. It is not thought that thinks, one may say, but you and I and John. The subject of thought is a particular human being.

When we speak of thought thinking, or understanding, we indicate its self-consciousness: that a thought comprehends itself to be a thought means that the act of thinking and the act of understanding it are one act of the mind. This does not introduce a subject of this understanding different from the subject of that thinking. So it does not give rise to difficulties regarding the subject of thought.

This explanation may put the objection to rest as long as we speak of particular acts of thought. But we said that thought understands its own nature and that its nature is its own understanding. Here we speak not of a particular act, but of the power of thought; we speak of reason or nous. Are we saying that thought, the power, is the same act of the mind as an understanding of what it is to think? What could that mean?

It means that the power of thought is an act of this power. This is contained in the idea of knowledge that is a priori, or pure. By nominal definition, pure knowledge is an act of knowledge that is nothing other than the power of thought. For pure knowledge originates in thought alone. As it has no condition not provided by the power of thought, the power is always already this act. We added the real definition of pure knowledge: it is the self-consciousness of thought. The power of thought is its own act—it is pure knowledge—because thought is self-conscious. As thought is self-conscious, every thought, as such, is an understanding of what it is to think. That understanding of the nature of thought is the same in every thought, and it is that by which it is a thought. So that understanding is the nature of thought. The nature of thought is the understanding of thought that every thought itself is. This understanding is an act of thought that is as general as the power of thought. The power is that act.

Thought understands itself, this means, the power of thought is the same act of the mind as the understanding of what it is to think. Again, this does not introduce a subject of understanding different from the subject of the power to think. So again, it does not give rise to difficulties regarding the subject of thought. The subject of the power of thought and therefore the subject of its self-understanding are you and I and John. When we say that thought knows things, we say that we know them and know them a priori: we know them being able to think at all. We do not speak of a ghostly subject called ‘reason’. We speak of a familiar subject—you, me, John—who is able to think and therewith possesses pure knowledge. Nothing spooky here, we think, relieved. But no.

When we think of powers in general, this is how we think: the subject is a particular substance; the power, being the same in everything that possesses it, is something general. When the power is exercised, the particular subject exercises it; she exercises the power as the conditions of its exercise are met in her circumstances. Therefore acts of the power in a subject are her acts. She, not the power, is their subject. The power on its own does nothing. After all, it is power, not act. This way of thinking fits when power and act stand to each other as general and particular. However, the power of thought is not mere power; it is itself act. Pure knowledge is the act that is nothing other than the power. This makes it difficult to see how we can assign pure knowledge to the particular human being as distinct from the power. Her particularity does not enter into this act at all. Thus we are led to say that the human being is not the subject of pure knowledge. Instead, reason is. The subject of logic is not you nor I nor any particular human being; it is thought itself.

Thus we see why one would say that the subject of logic is thought itself, which we must distinguish from the particular human being, from me and you and John. But it cannot be right to say this. For it makes incomprehensible how I can know what thought knows. However, from the fact that it makes no sense to attribute knowledge of logic to thought itself as opposed to me, you, and John, we cannot conclude that the subject of pure knowledge is the particular human being after all, as opposed to thought or reason. Rather, we must reject the opposition. We cannot conceive the human being through an opposition of particularity and universality that fits subjects of powers that are not their own understanding and therefore are mere powers. If human nature, the nature of the human being, is reason, intellect, thought, then a human being has an inner universality, which does not stand opposed to, but is the very form of her particularity.Footnote ⁷

If the human being is the life that thinks, then understanding what the human being is requires understanding what thought is, and understanding what thought is cannot fall short of providing knowledge of what it is to be a human being. Therefore the science of logic, it alone, provides the concept of the human being; it is the core of the science of man, according to an old-fashioned use of this term. That logic belongs to the science of man may seem an empiricist idea, for it was prominently advertised by David Hume.Footnote ⁸ But it is not that. It is empiricist only if one’s conception of man is. And the recognition that the science of man is, centrally, logic, must disabuse one of such a conception of man.Footnote ⁹

We must not distinguish reason or thought as the subject of the pure science from you and me and John. The distinction suggests itself if we assume an empiricist conception of what it is to be you or I or John. We do well to think that the subject of logic is you, I, John. But we must be clear that we do not thereby know anything about thought, knowing what kind of being it is who thinks. We do not presuppose that we can think the human being through the category of an object of experience, individuated by its location at a time according to a principle of spatial and temporal unity, or through the category of a living being or an animal. We know nothing of her who thinks other than this: she thinks. She who thinks is thought. Thought thinks. This is not to deny that you, I, John think. It is to say that I only know what I am by knowing what thought is. I am thought. The same for you and John.

IV. The object of thought

In thinking something, I understand myself to think what I, thereby, think. This is to say that I understand what I think to be something thought. I think what I think through the concept of something thought and thus through the concept of something that is such as to be thought. There is no thinking something without therein comprehending it to be thought and hence to be such as to be thought.

This is a mark of the act of thinking. Therefore it is a mark of what is thought: what is thought is such that thinking it is understanding it to be thought. One may think that the object of thought is there, to be apprehended either in thought, in which case its apprehension is conscious of itself, or in some other way, in which case its apprehension may fail to return to itself. Then the return to itself characterizes only the act of thought; it does not determine the object of thought. This fails to register that thinking something is being conscious of thinking it. As thought is self-conscious, one need be conscious of nothing over and above the object of one’s thought—which consciousness of it is one’s thought—in order to be conscious of thinking this object. The object of thought, on its own, provides for the consciousness of the thought of it. On its own because, again, thinking something is, itself, being conscious of thinking it. If we take the concept of an object of thought out of the object of thought, what is left is not the object of thought as it is in itself. What is left is nothing. There is no consciousness of an object of thought in which it is not comprehended to be an object of thought.Footnote ¹⁰

In thinking I understand what I think to be an object of thought; I think it through the concept of an object of thought. We may use various words to signify this concept: reality, the world, the objective world, the facts, or, simply, the object. The concept signified by these words is none other than the concept of thought. What I understand, understanding something to be such as to be thought, is nothing other than what I understand, understanding what it is to think. There is but one concept and one understanding.

People are fond of these words: world, reality, objectivity, and, if these are to mark a contrast and thus be located on the same plane: mind, thought, subjectivity. Indeed, these may be the most popular words of contemporary philosophy. They are used with confidence in their meaning. One uses them to put forth assertions, opposing competing assertions one portrays as whacky or irresponsible. These words are used specifically to express disapproval of idealism: the world is not mind-dependent; or, by means of perception, we have knowledge of objective reality, not merely of subjective representations. However, these words are empty unless their content is expounded. Their exposition is the articulation of the self-understanding of thought. It is the science of logic. Logic is the science that gives the meaning of these concepts. Conversely, any exposition of their meaning is logic.

V. Metaphysics

In thinking something, I understand myself to think what I, thereby, think. This is to say that I understand what I think to be such as to be thought. I think what I think through the concept of the object of thought. It follows that logic and metaphysics are the same. Logic is the science of thought. Metaphysics is the science that investigates what is in so far as it is.Footnote ¹¹ The term ‘what is’, here, signifies the object of thought. We mentioned various terms used to signify this object: world, reality, objectivity. ‘What is’ is one of these, less commonly used today, but popular through the ages. And indeed, when we consider how knowledge, understanding, insight express themselves in Indo-European languages, we find the term fitting: as I know something, understand something, have an insight, I say, ‘So it is’. It is so: as I understand it to be, as I know it to be, as I see it to be. That ‘is’ signifies the object of metaphysics.

Logic is metaphysics, metaphysics is logic. So what we said about logic holds of metaphysics. Metaphysics is the science a priori, the pure science; its knowledge is necessary and indubitable because it lies beyond the possibility of error. Metaphysical knowledge, being nothing other than the exposition of the concept of what is such as to be thought is knowledge that every thought as such is. Therefore there is no such thing as denying what metaphysics says. There is no such thing as doubting it, calling it into question, arguing for it. The notions of thesis, objection, justification do not apply in metaphysics. Metaphysical knowledge is absolute.

Knowledge of thought and knowledge of what is in so far as it is are the same. This is a consequence of the self-consciousness of thought. And since the self-consciousness of thought is known in the self-consciousness of thought, what we said about logic, and metaphysics, applies to the identity of logic and metaphysics: it is not something one could assert in order to mark out a position that would contrast with other positions, for example, the position holding that logic and metaphysics are distinct sciences. When we say logic is metaphysics, or, shorter, that thinking is being, we express absolute knowledge. It is not something one could undertake to defend or refute.

The knowledge of what it is to think and the knowledge of what it is to be such as to be thought are one knowledge. It may be called logic or metaphysics and be represented as self-knowledge of thought or as knowledge of what is as such.Footnote ¹² This identity is known in any thought and thus is something anyone always already knows in thinking anything at all. Therefore one may call it a truism. It is a special truism, though; the reason why it is one is the distinctive one just given. On account of its special character it is not, as other truisms are, common sense. What anyone always already knows is what is most difficult to think clearly; it is that with respect to which it is easiest and most common to fall into confusion. Any waking thought of any man, be he common or not, is nothing other than the self-knowledge of thought which is, and understands itself to be, knowledge of what is as such. Yet the common man is certain to find himself in the most horrid morass when he is called upon to pronounce on the theme of the identity of thinking and being.Footnote ¹³

VI. Kantian nihilism

Logic is the science of thought. It expounds the understanding of thought that is internal to thought. As such it articulates the knowledge of what is in so far as it is. In Kantian terms, thought relates to the object directly: the power of thought is knowledge of the object of thought. So it is because it is self-conscious. The nature of thought is its own concept, and this concept is nothing other than the concept of what is such as to be thought. This one concept is a priori knowledge. It depends on nothing’s being given. It depends on no facts, a fortiori not on facts about our constitution as sensory, natural beings.Footnote ¹⁴

It may seem that this knowledge must be incredibly thin, even nothing at all. What do we know about what is, knowing nothing more than this, that it is? What do we know about something, knowing of it only this, that it is such as to be thought? It may seem that the concept of thought, or equivalently the concept of what is such as to be thought, is empty; so it is, anyway, before something is thought. Thus Aristotle says that nous is nothing at all prior to its act (De Anima: 429a22–24).

It is true that the concept of thought is empty before something is thought. This follows from the self-consciousness of thought, which entails that the power of thought is its own act. And precisely this suggests that there is something that is thought in such a way that what is thought is nothing other than its being thought and thus is nothing given to thought. So what Aristotle says is fine. It is a different thing altogether to say what Kant says, namely, that the concept of thought, and thus the concept of the object überhaupt, is empty before something is given to thought, and be what is given a priori in the sense of being a character of our faculty of sensory representation.

The assertion that thought is empty before something is given to it makes no sense. Asserting this is saying that thought is nothing at all. And if it is nothing, then nothing can be given to it. Even Kant does not say that thought is nothing at all. Indeed, he gives an elaborate description of thought, describing the forms that thought exhibits as thought. However, since this is not to be a description of what is, since it is not to be a priori knowledge, there can be no comprehension why thought should exhibit these forms. These forms appear as a brute predicate of the subject, who happens to have them.Footnote ¹⁵ This perfect incomprehensibility is an immediate consequence of the notion that the self-consciousness of thought is not knowledge. We set this aside.

VII. The internality of the work of philosophy to the self-knowledge of thought

Whatever is thought is thought through the concept of thought, equivalently, through the concept of what is such as to be thought. Therefore this concept is not one concept among many. It is contained in any concept: whatever is thought in any concept is thought, therein, through the concept of thought, equivalently, through the concept of what is such as to be thought. We can mark this character of the concept of thought, or the concept of what is such as to be thought, by calling it the concept überhaupt, or, simply, the concept. Logic is the exposition of the concept. It is the science that expresses, that puts into words, the concept.Footnote ¹⁶

Putting words to the concept may be thought to be an act of describing a given reality: here is the concept, let me tell you what I find in it. What is in it is one thing, my saying that it is there is another. We need only so to state it in order to see that this is wrong. The concept of thought is the self-consciousness of thought; it is the understanding of thought that is internal to thought. This concept thus is nothing given at all; it is nothing other than what it is understood to be; it is its own understanding. When this understanding takes the form of its articulation in language, then this articulation, the work of writing and reading the logic, is nothing other than the concept itself.

The externalization or mediation of the concept—the activity of putting it into words, of writing and reading it—is the exposition of that which bears the character we described above: it is the exposition of what anyone always already knows, knows in any thought. Therefore it is not a claim, a thesis, a hypothesis; there is no such thing as asserting it, if this is to include the rejection of the opposite assertion, no such thing as doubting or challenging it. In so far as the word, as the sensory reality of thought, places itself in the space of claims and reasons, challenge and doubt, the word of the logic is one that, through itself, and immediately, vanishes.Footnote ¹⁷ What vanishes with it is the particularity of her who speaks or writes, who is particularized by the sensory character of the word. This is how Hegel describes the logic: as the word that vanishes through itself.

The science of logic expounds the concept. This is not a description of something given, a wonderful reality called ‘the concept’. The science of logic does not describe the self-articulation of the concept, an immaterial process witnessed by the logician who then reports his experience. Rather, logic is the self-articulation of the concept. This means that the reading or writing of the science of logic is itself the self-determination of the concept; in this activity, the opposition of the particularity and the universality of the subject of thought vanishes. This is how logic is the comprehension of the human being, who is that unity of universality and determinacy (cf. section III).

VIII. The beginning of Hegel’s Science of Logic

The concept, and therefore the articulation of it in language, is determinate through itself. Nothing determines it from outside as given to it. We have already seen that the concept is self-determining, when we saw that logic is metaphysics, self-knowledge of thought knowledge of what is, the world, reality. The concept is not empty. It contains within itself that opposition: the simple unity of the universal and the infinite differentiation of the totality. The beginning of the Science of Logic establishes the original determinacy of the concept as it reveals the first thought-determination to be becoming, the concrete unity of being and nothing.

It may be objected that, according to the Science of Logic, being is that first determination. But it is not, for outside its unity with nothing, being is nothing. Logic does not begin with being, the abstract unity, but with becoming, the concrete unity, the unity that is opposition. The concrete unity is the element of logic in the sense that any logical determination is a determination of that unity; the logical development unfolds within that concrete unity.

The second passage speaks of the difference of knowledge and what is known. Logic, or metaphysics, the passage says, is their concrete unity from the beginning: the difference is inside self-consciousness, or the concept, ‘at once’. This means it is in the first logical determination: the difference of knowledge and what is known, and their concrete unity, is, first and originally, the difference of being and nothing, and their unity. The thought of becoming is the first form of the unity of knowledge and what is known, of thought thinking itself and knowledge of what is as such, of logic and metaphysics. This is to say that it is the first form in which thought comprehends itself to be the source of its content. If being were the beginning, then there would be no logical progression and there would not even have been a beginning. We start with being in order to understand that it is not the beginning; the unity of being and nothing is.

IX. Being

Being is the first expression of the concept of thought or, equivalently, the object of thought; it is the first expression of the concept. As we noted above, thought says it is.Footnote ¹⁸ The Eleatics, Hegel says, specifically Parmenides, first enunciated the thought being, in which thought thinks nothing but itself.

Thinking pure being, thought embraces itself in its absolute abstraction. Parmenides enunciated this thought with excitement, Hegel says, the excitement of thought thinking itself. The Eleatic abstraction may strike one as strange. But to the analytic philosopher it is familiar. For there is a more recent expression of it, which is equally abstract, namely Frege’s judgement-stroke. While it would be helpful and possibly more exciting to read Parmenides’ poem in order to gain insight into Hegel’s meaning, the analytic philosopher may turn to Frege.Footnote ¹⁹

Hegel scholars may raise an objection. It cannot be right, they may say, to bring in the judgement stroke in order to read the section entitled ‘Being’ because that section does not treat of judgement. There is a later section in the Science of Logic on judgement. We must respect the order of the Logic and not import later notions into the interpretation of earlier ones. This objection is hung up on words. The object of logic is thought. Or judgement, knowledge, insight, etc. The science of logic will use these words to mark distinctions as it sees fit. Its table of contents reveals that the Science of Logic does use ‘judgement’ to signify a logical determination. While Frege speaks of judgement, it does not follow that what he says belongs with the section of the Science of Logic entitled ‘judgement’. It may be that Frege’s grasp of the self-consciousness of thought, as it is expressed in his logical notation, does not go beyond the articulation of it that Hegel gives in the chapter entitled ‘Being’. Indeed, that is the case.

In Frege’s Begriffsschrift, the sign of an assertion has two parts, a part that signifies what is asserted and a part that signifies the assertion of it. The latter is the judgement-stroke, placed leftmost, the former is everything to the right of it. As the judgement-stroke is outside the part of the sign that signifies the content of the judgement, it in no way determines what is judged, except in this way: it signifies that it is being judged. The meaning of the judgement stroke is the concept of judgement; equivalently, it is the concept of the object of judgement.

Frege’s sign of assertion is of interest to us in so far as the Begriffsschrift is to make visible in the form of the sign the form of the consciousness expressed by means of it. When Frege writes an assertion in the manner described, he does not mean to impose an articulation on it from the outside. He means to reveal a structure in the understanding of her who makes the assertion, the understanding with which she asserts what she, thereby, asserts. That the judgement-stroke signifies the self-consciousness of judgement can be seen in this way. The Begriffsschrift is a universal notation for all sciences. As the judgement-stroke is part of the expression of any judgement, it does not signify a concept that belongs to any particular science. The use of the concept signified by the judgement-stroke is internal to the use of any concept. It is not a concept, but the concept. If we were to express it in ordinary words, then ‘it is: …’ or ‘being: …’ would do fine.

The judgement-stroke embraces thought in its absolute abstraction. As it lies outside the sign of what is judged, the concept of judgement is sealed off from any determinacy of what is judged. Manifold, difference, opposition reside in the content. The force, the concept of assertion, or the concept, is untinged by manifold, difference, opposition. It is empty and pure.

One may think the judgement-stroke expresses affirmation: saying yes to what is placed to the right of it. But assertion as expressed by the judgement-stroke does not stand opposed to denial or saying no. Hence, not only is there no difference within assertion; assertion is not different from anything outside it. We can say of the concept expressed by the judgement-stroke:

Frege explains why assertion does not stand opposed to denial in this way: denying that such-and-such is the case is asserting that it is not the case (Frege Reference Frege1918–19: 153ff.). If we want to, we can say that asserting that snow is not white is denying something. And we can say that asserting that snow is white is affirming something. We can speak in this way. But when we do, we must beware that the difference of affirmation and denial is a difference in content. The force, assertion, is neither denial nor affirmation. It is indifferent to this difference.

The assertion that things are so differs from the assertion that things are not so in content, not in force; it is and it is not are different contents that are such as to be taken up in the single force of assertion. If we represent the force of judgement by it is the case, we can put the point by saying that there is no such thing as asserting what is not the case. When I assert that snow is not white, then I assert what is the case, namely, that snow is not white. John McDowell makes this point in the following passage:

The only way in which thought can be distanced from what is the case is by being false. True thought, as such, is of what is the case. True thought is of what is. McDowell chooses that spring has begun as an example of something that may be the case. That spring has not begun would do equally well: judging truly that spring has not begun is a case of judging what is the case. What is the case, in this case, is: that spring has not begun. In this way, force, or assertion, is unaffected by and unmixed with the difference of is from is not. The act of assertion, and that is, the understanding of it, is the same in these different contents. We may put this by saying that assertion is the abstract unity of these contents. It is a unity because it is the same in each: each is such as to be judged. It is abstract because it abstracts from their difference.

The concept of judgement abstracts from the opposition of is and is not. It follows that judging that things are so is not itself the recognition that it is wrong to judge that they are not so. And vice versa. If it were that, then the opposition of is and is not would be comprehended within the concept of judgement. Not would not be a part of a content, but would reside within the act of judging and be represented by the judgement-stroke.

Frege’s distinction of force from content excludes that the opposition of is and is not, being and nothing, be internal to what it is to judge. This is not to say that, on Frege’s conception, there is no opposition of the judgement that snow is white to the judgement that snow is not white. It is to say that this opposition is provided by the content judged, as opposed to by the act, and that is, the concept of the act, of judging it.

We may understand Frege to hold that a content that is such as to be asserted determines the conditions under which one would be right to assert it. And we may postulate that, in this respect, p and not-p are related as follows: having asserted p, one cannot rightly assert not-p. Someone who judges p, understanding what it is that he judges, understands this. The content not-p contains a rule prescribing that, having asserted p, I must not assert not-p, and vice versa. This is like a rule of chess: having moved my king, I cannot castle. The latter rule is part of what it is to castle; it may be called a constitutive rule of castling. In the same way, it is a constitutive rule of judging not-p that, judging p, I am not free to judge not-p. This is a rule of the game of asserting p and not-p. That game may contain further contents together with the rules that constitute them. If we call the game as a whole ‘rationality’, we can say that one cannot assert p and not-p on pain of irrationality. Like one cannot move the king and then castle on pain of unchessnality.

Robert Brandom claims that more fundamental than negation of a content is the incompatibility of contents.Footnote ²⁰ Contents are incompatible just in case their assertion is subject to a rule of this form: judging p, I cannot judge q. The negation of p, not-p, then is defined as the content entailed by everything materially incompatible with p. This is not a different conception of negation from Frege’s. On the contrary. It brings out the nature of this conception: it presents it is and it is not as different contents of judgement. Brandom diverges from Frege in that he postulates that for every content p there is a manifold of contents related to it by a rule of the relevant form. But it is a matter of indifference how many contents are related to a given content in this manner.

Judging that p is judging it is, namely, so that p. Judging that not-p, too, is judging it is, namely, so that not-p. The opposition of is and is not is not internal to judgement; judgement is indifferent to it. Judging is not as such opposing judging. It is true: judging that snow is white, I understand that I must not judge that snow is not white. But I understand this not knowing what it is to judge, but knowing what it is to judge that snow is white. Therefore we cannot say that she who judges p therein understands that she must not judge not-p. Her understanding does not exhibit the generality expressed by the variable p. This variable represents what is judged as such; it signifies the concept of judgement. Her understanding of the opposition of being and nothing, of it is and it is not, does not rise to this generality.

This is evident when negation is defined in terms of a prior notion of incompatibility. Someone’s understanding that something is incompatible with something else is not provided by the concept of judgement, but constitutes her understanding of what she understands to be incompatible. The same holds for the incompatibility of the Fregean contents p and not-p. So while there is opposition of the judgement snow is white to the judgement snow is not white, this opposition is provided by what is judged: snow is white. It is not provided by judgement. The opposition of being and nothing lies outside what it is to judge.

These ideas are equivalent: asserting that things are not so is asserting it is, namely, so that things are not so; true thought is of what is and in no way of what is not; judging not-p is judging something other than p; the principle by which it is opposes it is not is a rule of the relevant game. These are ways of saying that judgement is empty and pure, identical with itself, without difference either within or from something outside it. They are ways of saying ‘being is, not-being not’ (Parmenides, DK B 6, 1–2).

Yet Frege is not Parmenides, one will say. After all, while the act of assertion is empty and pure, there is a manifold of contents, signified by the manifold signs to the right of the judgement-stroke. This is right; Frege and Parmenides differ in this way. And this difference indicates a lack of rigour in Frege. As Frege attempts to comprehend judgement, the determinacy of the contents that are such as to be judged, their difference from each other, is not included within the concept of judgement. It cannot be comprehended through the concept of judgement. This concept contains no difference, neither within it nor from something outside it. So the determinacy of its content would have to be given to judgement. But difference cannot be given to judgement. Parmenides knew this. Frege did not. He did not realize that his manifold content is an illusion.

The opposition of is and is not lies outside the self-consciousness of judgement. It follows that there is no difference in judgement, not for judgement. In order for there to be difference, the difference must matter; it must matter to judgement. So it does as different judgements are related in such a way that judging one thing is excluding judging another. It may be thought that this is provided by the incompatibility of judgements. However, incompatibility is a relation of judgement to judgement that is not comprehended through the concept of judgement. It is a relation in which judgements stand in virtue of having the contents that they do. In order for there to be incompatibility, judgements must be many according to their content. Incompatibility does not explain this; it presupposes it.

One may stipulate that judgements have contents that stand in relations of incompatibility. This is to assume a set of rules that define a game of judgement. The rules are not provided by the concept of judgement. They are not known in the self-consciousness of judgement. It comes to the same to assume, as Frege does, that there are those things that he calls thoughts, things to be judged that are true or false. The opposition of truth and falsity provides for determinacy, for it underwrites incompatibility. P and not-p are incompatible, for not-p is defined as what is true just in case p is false. Since one ought to judge, and judge only, what is true (the prime rule of any game of judgement), one must not judge both p and not-p. The opposition of truth and falsity, and with it the idea of judgement as determinate, is not comprehended in the concept of judgement. Judgement is not known to be determinate in self-consciousness.

The self-consciousness of judgement, or the concept of judgement, or the concept of what is such as to be judged, does not represent an opposition in judgement and therefore no difference of judgements. The object of judgement, as it is understood in judgement, is it is, or being. Now we stipulate that the object of judgement is many. We stipulate this in order to ensure that there is opposition in judgement. This stipulation is incomprehensible. The understanding of judgement that the judgement-stroke expresses repels what we vainly attempt to stipulate.

This is the lack of consequence in Frege: on the one hand, he asserts that what is judged is what is, and in no way what is not. On the other hand, he postulates that there are many judgements, judgements opposing each other like light and night, etc. Parmenides is right to indict this as the error of those who do not attain to judgement, to the absolute abstraction in which judgement embraces itself (Parmenides, DK Fr. 8, 53–59).

X. Nothing

Fregean assertion is indifferent to the opposition of is and is not; it is the abstract unity of affirmation and denial. Thus the concept of assertion is empty and pure and the concept of its object is being, without difference, neither internal nor external. This may seem to show that the opposition of is and is not must be brought inside assertion and its self-consciousness: assertion is opposition; assertion opposes assertion.

It may seem that this means that we need to represent the assertoric force to be divided into affirmation and denial, saying yes and saying no. Then the judgement-stroke has two forms, one signifying affirmation, it is, the other rejection, it is not. However, the judgement it is so is just as much a denial of the judgement it is not so as the latter is a denial of the former. Asserting something is saying no to the opposing no.Footnote ²¹ So when we see that judgement cannot be above the opposition of is and is not, we do not conclude that it has two opposed forms, is and is not. Rather, we conclude that it is rejection, denial, no. Judgement is not the infinite power to embrace being, but the universal power to negate, to annihilate, to crush. The power of judgement to negate is universal because its idea of itself as denial is a priori, or pure. Judgement comprehends itself to be denial as it embraces itself in its absolute abstraction. Since this self-understanding does not depend on anything’s being given, it is absolute. Therefore the word that expresses the concept of the object of judgement, as it is understood in the self-consciousness of judgement, is ‘nothing’. While ‘not’ (nicht) awaits the specification of something that is negated, ‘nothing’ (nichts) captures the universality of denial that judgement understands itself to be.

The understanding of judgement as denial re-conceives the force of judgement; it leaves the externality of the content judged to the force of judging it intact. If we were to represent the act of denial by a sign, then that sign would be placed outside the sign signifying the content denied. Therefore, the universal no, or nothing, that judgement understands itself to be is empty and pure. The self-consciousness of judgement, its concept of itself, and that is, its concept of its object, is free of any determination or content. Nothing, judgement’s thought of itself, is ‘complete emptiness, complete determination- and contentlessness’ (SL: 59/21.69).

However, it is the content denied, and it alone, that provides for the opposition that denial is. A no says no to something, it is itself the thought of its distinction from that which it denies. As a content is given, the power of negation can apply itself to it. Again, this content may be a thought that is true or false or a set of normative rules by which judgements oppose each other. But the self-consciousness of judgement, its concept of itself, and that is, of its object, does not provide for the determinacy of these contents. Judgement, in its thought of its object, repels the notion that it should possess determinacy. As we embrace the denial in its absolute abstraction, prior to all determinacy and content, the opposition that it purports to be collapses. Indeed, there is no way to distinguish pure denial from pure assertion. We say the object of judgement is nothing, but this is nothing other than the thought that it is being. ‘Nothing thus is the same determination or rather determinationlessness, and thus altogether the same as what pure being is’ (SL: 59/21.69).

Assertion and denial are indistinguishable. Both what is asserted and what is denied is empty and without any determination. Therefore, their opposition is nothing. The one grand denial is not different from the one grand assertion. We might say that the contents denied are the converse of the contents asserted and therefore they are different. But the difference of contents is incomprehensible to judgement as it thinks itself in its absolute abstraction.

One may want to say, so much the worse for absolute abstraction. Sensory consciousness provides the determinate contents; their being given does not pass through the self-consciousness of judgement. Judgement is the performance of certain operations on these contents. This—empiricism—is to do away with judgement altogether. For it is to renounce the self-comprehension of judgement, which is nothing other than judgement. As judgement is self-conscious, there can be determinacy of judgement only if the determinacy is comprehended as such in judging. The self-consciousness of judgement, its concept of its object, must provide for this determinacy.

A more sophisticated rejection of the absolute abstraction—a more sophisticated rejection of judgement—is the suggestion that in the words in which the absolute abstraction expresses itself language has gone on holiday. This idea emerged from a reading of Wittgenstein, from whom this phrase is taken (cf. PI: § 38) and is associated with the notion that Wittgenstein has succeeded to transcend metaphysics, or philosophy, that his is a form of after-philosophy. The sophisticated rejection rejects as empty the universality of thought thinking itself. It is true, it explains, the opposition of judgement is not comprehended within the concept of what it is to judge. But this is so only because this concept is empty. When we try to put words to this concept, language is celebrating, it is holding a feast.Footnote ²² When we see that there is nothing to be thought at this level of generality, we regain our certainty in our particular concrete judgements and their oppositions. In each case, a judgement, for example, snow is white, opposes another judgement, for example, snow is not white; alternatively, it opposes many other judgements, for example, snow is green, or blue, or red. She who judges understands herself to oppose contrary judgements in understanding what it is that she judges, as the case may be, snow is white.

This reasoning rises to the very generality it denounces, saying ‘in each case’. If it did not say this, it would provide no satisfaction. Recognizing this, one may raise the sophistication and devise rhetorical strategies of self-effacement: the speech is to dissolve the illusion of its own meaningfulness. This is a futile effort to avoid philosophy, and that is, thought. It cannot but lead to despair, because in every effort to silence philosophy, philosophy will be found to have spoken up all the louder, just like, as Luther describes, every effort to shed sin will be found to be an ever more wicked work of sin. In fact, it is right to associate philosophy with the day of rest, the Sunday, the feast. It requires a cultural-psychological explanation why one might think that the observation that philosophy is language celebrating, language celebrating itself, would indicate that something is amiss with philosophy.

Instead of renouncing judgement, we may undertake to think it. We may undertake to comprehend judgement itself to be the thought of its determinacy. So it is, if what is judged, as such, contains the opposition of judgement. The opposition of is and is not neither determines the content judged nor the force of judging it. It dissolves this distinction. A proper Begriffsschrift makes the sign of this opposition neither a part of the sign of the content, nor does it make it a feature of the sign of force. Rather, it writes the opposition of is and is not into any sentence letter; it inscribes it within p, which for this reason no longer requires a sign of force outside it.

XI. Internal reflection of the unity of being and nothing

The force of judgement, isolated from its content, is empty. In consequence, this content is empty; the appearance of a manifold of contents is an illusion. Difference of contents cannot be brought to judgement from outside it. Unless judgement itself is difference, difference does not enter it. When an appeal is made to something outside judgement to provide for difference, as for example in Kant, it cannot be taken to be intended to provide an explanation of the manifold we know there is in judgement. It must be taken to assert the perfect incomprehensibility of it. This is how Kant understands his invocation of sensibility, as is indicated by the fact that he takes it to imply that we know only appearances.

Opposition in judgement, when it is separated from what is judged, collapses: being is nothing, nothing is being. Unless what is judged provides for opposition, the opposition of force is empty. Yet opposition in judgement cannot come from contents given to judgement. Within the separation of force and content, the result of the collapse of the opposition of being and nothing is the return of the empty assertion: being, is. Logic ends here.

This is an external reflection: it treats that which is thought in the absolute abstraction as though it were something given. It notes that what is so given, whether it be represented as being or as nothing, is the same. In this external reflection, we fail to notice that our reflection itself, in its entirety, lies within the self-consciousness of judgement. It is the self-consciousness of judgement. Hence the self-consciousness of judgement, its concept of itself and its object, is neither being nor nothing; it is the transition of being into nothing and nothing into being.

This is an internal reflection. It reveals the result of the collapse of being into nothing and nothing into being to be the concrete unity of being and nothing: becoming. Thought is this concrete unity, and therewith it is, through itself, determinate and its own content.

The unity of being and nothing in becoming is not the abstract unity of is and is not. It is concrete: it does not abstract from the difference of is and is not, but is their very opposition. Therewith it is determinate. Indeed, becoming, the concrete unity of being and nothing, is determinacy itself.

The judgement-stroke of Frege’s Begriffsschrift signifies the self-consciousness of thought; it signifies the thought in which thought embraces itself in its absolute abstraction. But Frege is not conscious that this is what it does. Therefore, we need to go through the thought that reveals that being is nothing and vice versa in a manner that presents it as self-consciousness. In this way, we turn what, in our discussion of Frege, appeared as an external reflection into an internal reflection.

The Science of Logic expounds the concept of thought, equivalently, the concept of what is such as to be thought. That concept is not a concept, but the concept, the concept überhaupt. It is not a universal, but the universal. In the first thought of it, the universal is universal immediately, that is, not by passing through difference. Thus it is abstract: its thought of itself as everything is not articulated. Indeed, for this reason it should not be represented as the thought of everything, for this implies a recognition of difference. Its true expression is not ‘everything’, but ‘being’.

A universal is what is the same in many. Being in this one and that one and that one, it is the same, or identical, in every one. It therein negates the difference of this one and that one and that one, and in so far as it negates their difference, it is itself a consciousness of their difference.Footnote ²³ The first universal, however, universality thinking itself for the first time, does not contain a consciousness of given difference. It is nothing but identity with itself: ‘it is equal only to itself’ (SL: 59/21.68), ‘it is simple equality with itself’ (SL: 59/21.69) As it contains no difference, it is abstract. And since it is abstract, it is empty. Thought thinking itself as being thinks nothing.

Thinking being is thinking nothing. This is no objection to pure thought. For, thinking nothing is not not thinking. This marks the difference of thought from sensory consciousness. Thinking nothing is not not thinking because the distinction of nothing from something is inside the thought of nothing: thinking nothing is the distinguishing of itself from thinking something. Thinking nothing is thinking, it is the thinking that excludes from itself any determination and therein embraces itself in its absolute abstraction. What it thus thinks is—being.

Being is nothing because the universal, as abstract, excludes all determination. It may seem that we thus represent the first universal as a result, the result of an abstraction and thus not as first. This is the empiricist objection we discussed above. It asserts that thought thinking itself abstracts from something that is prior to thought and its self-understanding. But no abstraction from objects of experience can yield the universality of being. The thought of being is abstract not in the manner of abstracting from given differences. The first universal is the thought not of everything, but of being; it excludes not all difference, but difference. It does not rest on anything given. The thought of being, the exclusion of difference that that thought is, understands itself to be original. It is original as it is self-consciousness. In this way, we reject the empiricist objection and say: pure thought is nothing, which is to say, it is being.

Nothing is being because it is thought itself. We discussed Aristotle’s dictum that thought is nothing before it thinks. Aristotle presents this as a corollary of the universality of the object of thought: thought has no given nature, for, if it did, then this nature would delimit the object of thought. It would delimit what is such as to be thought. Thought is nothing because it is everything. Better, its being nothing is its being everything. Hegel repeats this reasoning of Aristotle’s. Thought is universal, which means that it has no given nature, and thus is universal. In particular the universality of thought is not a given character of thought. The object of thought is universal in and through the thought of its being universal, and this is the thought of thought’s being nothing.

Being is the thought in which thought embraces itself in its absolute abstraction. The absolute abstraction of thought is its self-consciousness. In thinking itself, thought recognizes itself to be undetermined by anything. This emptiness of thought, its nothingness, is its own deed: we comprehend, in thought, the absolute abstractness of thought, which we, thereby, realize in this very thought. Annihilating any determination, we recognize thought to be the annihilation of any determination. The nothingness of thought is not noticed from the outside, in an external reflection, which could be taken to give a ground to dismiss thought. That is the path of empiricism. Rather, the absence of determination is the self-determination of thought. Therefore it does not depend on given determinations. On the contrary, it opens up the whole: being.

XII. Becoming

Hegel emphasizes that being does not transition into nothing. Being has transitioned into nothing, and nothing into being. In fact, being is its having transitioned into nothing, and nothing is its having transitioned into being. To think thought itself, recognizing it to be being, is to think nothing. And to exclude any determination from thought, recognizing it to be nothing, is to think being.

Thinking being is thinking nothing. As we recognize this we think the first determination of the concept. Becoming is ‘the first truth’ (SL: 60/21.72).Footnote ²⁴ There is no truth in being nor in nothing; being and nothing are the most perfect untruth. ‘Thus those determinations are no longer present therein in the perfect untruth in which they are as being and nothing’ (SL: 61/21.71) Hence, the logic does not begin with being. It begins with becoming. The logic is not the development of being. It is the development of becoming. Becoming is the element of all determinations of the concept. The thought of becoming is the recognition that the universality of thought is the same as its determinacy. The Science of Logic unfolds this thought.

It is helpful to approach the thought of becoming by thinking of ordinary becoming: something’s becoming so. For the consideration of ordinary becoming may suggest an objection. It may seem that ordinary becoming is not a unity of being and nothing, but holds them apart, locating them at different times: something that has become so first was not so and now is so. Becoming separates, and does not unite, being not so and being so. However, this is not right. It is true that the terms of something’s becoming so, its being not so and its being so, are not a unity of being and not being. But becoming, while it has terms, is not its terms. Thought of something’s becoming so, that is, thought expressed by the progressive aspect, ‘it is becoming so’, cannot be reduced to thought of something’s first being not so and then being so, thought expressed without a contrast of aspect: ‘x was not so’, ‘x is so’. Thought of ordinary becoming is described very precisely as holding together, in one thought, something’s being not so and its being so.Footnote ²⁵

Ordinary becoming has a terminus; something’s becoming so terminates in its being so. Moreover, what becomes so is of a certain kind and remains of that kind throughout. In these two ways, ordinary becoming involves being that is distinct from and untouched by becoming. But we can universalize the thought of becoming and extend it to these two moments of being that characterize ordinary becoming. Then there is no determination in which becoming comes to a close and there is no substance that remains through a change of its determinations. This is the becoming of which Hegel speaks.

Ordinary becoming occurs in time. By contrast, the becoming that is the first truth, the first logical determination, has no temporal meaning. We understand this when we see that this becoming is universal becoming. Universalizing ordinary becoming, we extinguish its temporality. For its temporality resides in its being a change of state of an underlying substance. This structure we delete as we universalize. It is no surprise that universalizing is logicizing. Logic is the science of the universal, or the concept.

One may argue that the thought of universal becoming destructs itself. If all is becoming, then there is not even becoming. For becoming requires the opposition of being and nothing. Becoming is a unity of being and nothing that does not abstract from their difference. This abstraction was the first determination, the abstract universal. Rather, it is the thought of their unity that is precisely the thought of their opposition. However, this very opposition disappears in universal becoming. Thus the thought of becoming turns out to think nothing.

However, while it is true that the thought of universal becoming collapses, it does not collapse into nothing. Precisely because the thought of becoming does not abstract from the difference of being and nothing, and thus is not the thought of being, the recognition of its collapse is not the thought of nothing. As everything flows, all being is lost, always already pushed out. We cannot hold on to anything, for as we try to do so, it has always already disappeared into nothing. But universal becoming is not only being passing away; it is also being arising; not only does being disappear into nothing, ‘ceasing to be’; nothing gives way to being, ‘coming to be’. In fact, becoming is the unity of these, the unity of Entstehen und Vergehen. Heraclitus’ flux does not simply stand opposed to Parmenidean being. It registers the negativity that being, and that is, the thought of it, is. Therefore the thought of becoming does not resolve into nothing. Rather, it is the recognition that being as such is negation: it is determinate being, being that is not what it is not, being that excludes, negates, what it is not. This is the first true universal.

We found that negation is not part of the content of judgement as distinct from the force. Nor is it an opposition of forces outside the content. One may wonder where negation may be, if it is neither in the content nor in the force. The answer is: nowhere. It is not possible to comprehend negation while holding to the distinction of force and content. That distinction holds us fettered in the most perfect untruth, the untruth of being and nothing. Rejecting the distinction, we comprehend the unity of being and nothing; we think becoming. Thinking the unity of being and nothing, we think what is asserted to be itself the opposition of is and is not. This content is Dasein, determinate being: thinking it, we think it to exclude what it is not. One step further we may introduce incompatibility, comprehending what is thought to be such that thinking something is understanding it to exclude something other. In the Science of Logic, this appears as Daseiendes (what is in the manner of determinate being).

Negation is inside what is thought in so far as it is such as to be thought. What is thought as such contains the thought of an opposition in judgement, of is and is not, being and nothing. A perfect Begriffsschrift would make the sign of this opposition the graphic matter of all sentence letters. Nor would the Begriffsschrift stop there. For now it is known, in the universal, that it is its own negation. The science of logic will make this inner negativity of the concept explicit and reveal the concept to be a contradiction. The science of logic embraces this contradiction and thus progresses in its articulation of the concept. Ultimately, the entire science of logic will be inscribed in each sentence letter. Indeed, we can consider it as being already inscribed in every sentence of every language.