Commentary on the Logic, Chapter 15
What Have We Achieved?
| Chapter | Form | Structure | Function |
|---|---|---|---|
| Ch. 9 | The Concept | U-P-I | Self-determination |
| Ch. 10 | The Judgment | S is P | Explication |
| Ch. 11 | The Syllogism | I-P-U | Grounding |
The self-application: The doctrine of the syllogism concludes about syllogisms, the doctrine of judgment judges about judgments, the doctrine of the concept conceives the concept.
Science as System, Not Aggregate
Three negative determinations — what science is not: (1) Not an abstract principle (Everything is energy, Everything is dialectical — such principles say everything and therefore nothing). (2) Not mere enumeration of differences (data without connection is information, not knowledge). (3) Not a series of judgments without mediation (true individual judgments standing side by side without relation). Rather: science is the thinking reenactment of the unity of the matter that produces its differences — “a self-organizing whole.” Whoever has mastered the structures of Chapters 9–12 possesses the method of science — not as a recipe, but as a form of thinking itself.
Practical Tools from the Logic of the Concept
Three tools for the search for truth:
Tool 1 — Consciously Using the Three Forms of the Concept: For every problem: (a) The concept — move across all three levels: the universal (What is the principle?), the particular (How does it show itself concretely?), the individual (this case, here and now). (b) The judgment — formulate definite claims (not “X is somewhat like Y,” but “S is P”) and test the judgment form. © The syllogism — give grounds: which mediation connects the judgments? (d) The syllogism system — check: which dimensions of mediation are realized, which are missing?
Tool 2 — Distinguishing Levels (developed in Systematisches Denken, Kapitel 16): Are we talking about forms of thought (meta-level: “That is a categorical judgment”) or about states of affairs (object level: Gold conducts electricity)? Many discussions founder on this confusion. Particularly dangerous: confusing formal completeness (a syllogism system) with moral legitimacy.
Tool 2a — Distinguishing Anticipation from Result: If you want to understand someone else, ask yourself: Do I know this, or am I inferring it? What you infer from origin, schooling, camp, or milieu is an anticipation — useful for getting started, revisable at every step. What the other person actually thinks, you learn only by asking and letting the answer stand. Practical test: Can you formulate their position in a way they would recognize as their own? If not, you are criticizing an inference (9.4b, 9.7).
Tool 3 — Carrying Out the Transition to Objectivity: Thoughts become real when we act; theories become intersubjective when others adopt them; concepts structure our experience. Check: Does your thinking remain merely subjective — or does it prove itself against reality?
Why Four Judgment Forms, but Three Syllogism Forms?
A question that arises upon review: the judgment had four classes, the syllogism has three. Anyone looking for a scheme will be puzzled — and that is the point. Hegel follows no scheme, not even the schema of triadicity. [KF]
The judgment needs four because it is the first confrontation of the concept with itself. It runs through the three sides that belong to every logical determination — immediacy (the judgment of determinate being), reflection (the judgment of reflection), mediation (the judgment of necessity) — and with this it has not yet arrived at itself: it has explicated itself, but has not yet checked whether what has been explicated corresponds to the concept. Only the fourth, the judgment of the concept, does that.
The syllogism needs three because it no longer explicates but mediates. Its task is the middle term, and there are exactly three middle terms — universal, particular, individual. A fourth form would not be a new middle term; on this point, consider Hegel’s judgment on the scholastic tradition: Aristotle rightly recognized only three figures, “the fourth is a superfluous, indeed even tasteless, addition of the moderns” (§ 187 Remark).
The number thus follows in each case from the matter itself, not from a blueprint. Whoever takes the U-P-I structure or triadicity as a schema that Hegel applies will expect the wrong thing at this point.
What the Examples Reveal
A look back at the examples of these four chapters: “The rose is red,” “All men are mortal,” “Gold is a metal,” the state. None of these comes from logic. They are the classic examples of logic textbooks since Aristotle, and Hegel uses them just as everyone else does.
This is more remarkable than it looks. The logic in which the concept comprehends itself is the exception — the rule is its application to roses, human beings, states. The examples thus reveal what logic tacitly presupposes: that concepts relate to what is conceived, and above all to such things in a world that is not logic itself. [KF]
This is precisely the reason why the subjective concept does not suffice.
How Much of the Doctrine of the Syllogism Is Needed — Hegel’s Own Answer
The doctrine of the syllogism can be pursued to any degree of elaboration, and the tradition has done so. Hegel himself states where the limit lies, and his answer is decisive.
The three figures, he says, have “a very profound sense, resting on the necessity that each moment, as a determination of the concept, itself becomes the whole and the mediating ground” (Encyclopedia Vol. 1, § 187 Remark). With that the matter is stated, in a single sentence. What goes beyond this — which determinations the propositions must have, whether universal or negative, so that a correct syllogism results in the various figures — he calls “a mechanical investigation which, on account of its conceptless mechanism and inner meaninglessness, has rightly fallen into oblivion.”
His argument for this is historical, and it hits the mark: one can least of all appeal to Aristotle, who first described the figures. For Aristotle was “so far from wanting to make the form of the syllogism of the understanding the foundation and criterion that one could say not a single one of these concepts could have arisen or been retained, had it been required to submit to the laws of the understanding.” Whoever makes the syllogistic figures the standard cannot even form the concepts with which their inventor worked.
This commentary abides by that. The permutation has been developed (11.3–11.4), its usefulness shown by an example (11.9a), and its limit stated (0.4). That suffices — and it suffices precisely for what matters: from here on, Hegel uses the syllogistic form again and again in application to objects, without explaining it any further. The mechanism of the planetary system, life with its three processes, the state — everywhere three moments stand, each of which once forms the middle term. Whoever knows the figure reads these passages as application; whoever does not know it takes them for figurative language. [KF]
What Is Still Missing: The Question of Objectivity
The syllogism is still a construct of thought. It describes the form of reason. But does it also exist out there?
Hegel himself formulates the transition as though the concept objectifies itself — which sounds as though it wants something. This is the mystification that Marx criticizes (developed in Hegel und Marx). The underlying concern is correct and can be stated soberly; there are two arguments, and each carries independently of the other. [KF]
First argument: The disjunctive syllogism demands the particulars. It has the form “A is either B or C or D” — the universal breaks down into its particulars. It works only if one knows these particulars: “This triangle is either equilateral, isosceles, or scalene” carries weight because we know the three kinds. A universal without particulars would be empty, the syllogism without content.
Applied to what has been achieved: Chapters 9 through 11 developed the concept of the concept — the U-P-I structure, the judgment, the syllogism. Every concrete concept, whether tree, justice, or electron, has this structure. But this states how concepts are constructed, not which concepts there are. The concept of the concept is the universal and needs its particularizations — exactly what the disjunctive syllogism demands and what subjective logic does not supply.
Second argument: Thinking needs difference. In the subjective concept, thought comprehends itself. That is no small thing, but it cannot stop there, and for a reason already developed in the logic of essence: positing reflection (A = A) had to advance to external reflection (Non-A) and then to determining reflection. The judgment, too, explicates the concept only by distinguishing subject and predicate. Thinking is always also thinking of something else.
Without this difference, the concept would remain deficient in three respects: logically — the disjunctive syllogism would remain empty; in terms of the logic of essence — there would be only positing reflection, no determining reflection; practically — only self-relation, no relation to the world. The complete concept thus includes that to which it relates.
Hegel’s own argument, from the lecture course. In the 1825 lectures he gives a third reason, which supports both arguments and comes from the doctrine of the syllogism itself. The concept completes its determination in the syllogism by the fact “that each moment is itself the whole totality; in its completion, therefore, the concept makes itself into an object.”[1] This is exactly the result of the permutation: at the end, each of the three moments has once been the middle term and thereby itself the whole.
And now the step: as long as the moments are posited merely ideally — “in subjectivity, in me” — they are transparent and distinguishable. But if “each is developed into totality,” then “each moment is independence [Selbstständigkeit],” and thereby “their difference has vanished.” Independent moments, however, are no longer mere thought-determinations; what connects them is the object. Hegel concludes: “This is the true transition into the object.”[1:1]
He says this immediately after his critique of the ontological proof of God’s existence. Its error, he says, is that it makes a comparison between the concept of God and what we think as the most perfect — and in doing so presupposes “that the concept is objective.” What the proof presupposes, logic must first establish. The transition to objectivity is the place where it does so.
Thus the transition is not asserted but derived — and it needs no concept that wants something. The image of the architect with a perfect blueprint who has never set foot on a construction site captures the deficiency; the two arguments state where it shows itself.
The decisive distinction: Chapters 9–12 deal with the form of the concept (U-P-I, judgment, syllogism). From Chapter 13 onward, it is about the relation of form to content — how the structures of the concept are found again in the experience of objectivity. This still belongs to logic, because mechanism, chemism, and teleology are forms of thought — forms in which nature and spirit are thought. But they are more specific than the general categories.
Methodological self-criticism: What remains problematic? (1) Is the subjective concept really complete — are there still other forms? (2) How does this logic relate to formal logic (propositional logic), modal logic (the logic of the possible/necessary), dialogical logic (logic as disputation)? (3) Is the analysis of the syllogism system too formalistic? Honest answer: the four forms (concept, judgment, syllogism, syllogism system) follow necessarily from self-determination — but we cannot prove completeness, only show that no gap has been found.
Demystified — why the subjective concept does not suffice: Hegel’s formulation “the concept objectifies itself” sounds as though the concept were an acting subject. What is meant is something sober: (1) The disjunctive syllogism has the form “A is either B or C or D” — but it needs the particulars B, C, D in order not to remain empty. A universal without particulars is devoid of content. (2) Thinking needs difference — it cannot stop at A=A; it is always also thinking of something. Already in the judgment and the syllogism, the examples do not come from logic: “All men are mortal,” “The rose is red,” The state — the examples reveal what logic tacitly presupposes: that concepts relate to what is conceived, to a world that is not logic itself. Thinking is complete only as thinking of something.
But beware: the naive correspondence theory (concept in the head, reality out there, truth = correspondence) is not Hegel’s solution. For: if the two are separate, how could I ever know whether they correspond? To check the correspondence, I would have to stand outside my own thinking — and that I cannot do. Hegel’s solution: the categorial structures that we develop in thought are also found again in the experience of objectivity. Not because the concept creates the world, but because cognition is always conceptually structured — and the world proves itself to be knowable. This must be shown — and that is exactly what happens in Chapters 13–15.
Part 3.2: Objectivity — When the Concept Meets Resistance
What is this about? Thinking alone is not enough. At some point, our concepts must show whether they work in the world. The doctrine of objectivity examines three ways in which things hang together: as a mechanism, as a reciprocal relation, or as a purposive whole. Most problems arise where the wrong form is applied.