Einführung in den Begriff
Preliminary remarks 1
a) It is sometimes said that (mathematical / theoretical) physics is pure mathematics, but that is not true — it explains concepts like mass, force, motion, and the like, which do not occur in mathematics. That is why not every equation that would be permitted by mathematical laws makes sense in mathematical mechanics. Conversely, it is often the existing equations that first need to be explained, given a meaning (who would know, without prior explanation, what the famous equation e=mc² implies?).
b) Likewise, one can say of mathematics that it too concerns itself with specific mathematical concepts; even in mathematics, when constructing a proof, one does not transform arbitrarily but selects, from the zillions of possibilities, the one that makes sense within the aim of the proof.
These considerations, however, do not emerge from the proof itself, which is why it is often said that reading a proof, understanding it, or even arriving at it oneself are quite different things. (Many further reflections on this can be found, incidentally, in Ludwig Wittgenstein’s “Remarks on the Foundations of Mathematics,” stw 506).
c) Formal logicians finally claim that scientific systems can be divided into unproven and unprovable axioms and the “derived” propositions obtained from them through tautological transformations. In doing so, the transformation rules of formal logic applied here are themselves consistently regarded again as unproven and unprovable axioms.
Although thoughts of this kind can be found in books on formal logic and philosophy of science, and indeed find their way from philosophy into the feature pages and into the justification of all sorts of skeptical and relativistic currents of the zeitgeist, the “normal” business of the sciences is not particularly affected by them.
For the work itself of even the dumbest and most narrow-minded scientist does not consist (as far as I know) in simply inventing arbitrary axioms and then transforming them arbitrarily.
So what does one actually do when, as a scientist, one builds a scientific theory? What is one looking for when seeking an explanation? What is a good concept, a satisfying axiom? Clarifying this was once one of the main concerns of classical philosophy from Aristotle to Hegel.
Preliminary remarks 2
Science ideal-typically passes through the following phases (I here disregard, among other things, any pre-scientific phases); this can be traced within an individual scientist’s theory-building and can likewise be traced similarly in the history of the individual sciences themselves.
The elements of each earlier phase are always also contained, transformed by the elements added in the later phases, within the later phases:
At the beginning, as much information as possible is simply gathered — think here, for instance, of travelers’ reports in geography and ethnology, or the collection of various plants and animals in zoology and botany, and the like.
Once enough material is available, work begins on ordering the material. Here it can be observed that, as knowledge increases, the ordering advances from very external criteria (color, smell, number of individual parts, and the like) toward ever more fitting/immanent criteria (today, for instance, biology divides the plant and animal kingdoms according to DNA relatedness).
This progress toward ever more appropriate classification is prompted by the third step: a theoretical penetration of the field of study. As theoretical penetration increases, ever more appropriate classifications can be carried out. In theoretical penetration, the goal is often seen as advancing to those concepts, axioms, and laws from which everything else can be derived (mathematics is usually regarded here as the ideal, and correspondingly, among the natural sciences, mechanics).
What matters here, then, is ordering the material found in such a way that as many phenomena as possible can be explained with as few assumptions/axioms/laws as possible (used here in the sense of “not further derivable”).
The initial propositions of the respective science are therefore not chosen arbitrarily but are meant to contain, as concentrated as possible within themselves, the wealth of the object they treat (the “topic”). Only in this way can the edifice of science later be drawn back out of them again through the apparent conjuring trick. Axioms and laws are therefore also the end product of scientific activity and not its beginning.
Why, then, does Hegel speak of concepts rather than of initial propositions (axioms)?
Very simply: the initial propositions, after all, deal (at least) with subjects to which predicates are attributed. So these initial propositions are themselves composite.
The true beginning is therefore the subjects of the proposition (or is that again merely our narrow-minded European thinking, and would a Navajo Indian (Sapir/Whorf) say instead: the predicates? No matter — it plays no role for the following consideration in any case).
The subject of the proposition has the properties that are then attributed to it in the proposition; indeed, it probably has still further properties. The proposition should express the properties essential to it, from which the others can as far as possible be derived, and thus takes the concept as its measure (more on the relation between the concept and the proposition can be found in Hegel’s doctrine of judgment and in the good commentary on it by Heinrich Güßbacher, “Hegel’s Psychology of Intelligence”).
If it turns out that one proposition does not suffice for this (which is generally — I know of no exceptions — the case), then several propositions are needed. These propositions should be arranged into a system according to their logical relation (this is Hegel’s transition from the doctrine of judgment to the doctrine of the syllogism).
Purely phenomenologically, too, when one looks at the individual sciences, each presents itself as a respective explanation of its objects (used in what follows always in the broader sense, i.e., as concepts), in which, in turn, the individual concepts belonging to the subject matter are arranged into a system.
The main question, therefore, consists initially in finding the appropriate concepts and their determinations (that is, the proposition or propositions that state what is essential about the object), which naturally hang together, as we shall see.
So what is a concept, and how do I determine it?
From what has been said so far it should already be evident that what is meant here is not
a) an (arbitrary) definition/demarcation,
that is, not something like this:
“Man is a featherless biped” (as an old would-be Greek philosopher once put it, whereupon Diogenes is said to have presented him with a plucked chicken)
and therefore
b) the notion of universality as one knows it from formal logic and set theory, where a universal is simply obtained through (arbitrary!) abstraction (abstrahere = Latin “to draw off,” i.e., to leave out), is of little help either.
Although one can certainly find both of these again within the concept if one wishes, it is the arbitrariness that is troubling here. A scientist does not want simply, like an artist (and even whether the artist really works so arbitrarily is very much a question — if he does, presumably still with a reason), to work out some arbitrary aspect that is important to him, but rather to find the determination that is appropriate to the object.
The measure of the correctness of a scientific determination/theory still remains its agreement with its object — it is meant to be adequate to it (this is normally what distinguishes a scientific theory from science fiction).
If you look at the notions of the concept presented so far, they all have this in common: that a boundary belongs to the concept, one that determines what belongs to the concept and what remains outside, thus “determining” it (I use the word “determine” in what follows in this sense).
Already Spinoza says “omnis determinatio est negatio” (to determine is to negate) — that is, to exclude, to specify what the thing being determined is not.
The first step in concept formation, then, is to concern oneself with the boundary of the concept — that is, with borderline cases.
What still just fits inside? What just barely no longer fits? Where am I unsure?
Example: chair
Does the one-legged bar stool still belong to the concept? A three-legged stool? The armchair? The salesclerk’s leaning aid? The bench? The table? The sitting posture? (methodological note: try to find as great a variety as possible of qualitatively different, productive variants)
Example: shoe
Does a boot still belong to the concept? A sock? A sandal? Bare feet (= no shoe)? Calluses?
The neat disjunctive (in the sense of “mutually exclusive”) division into A and non-A of formal logic only takes hold once I have this boundary. And, incidentally, it does not help me at this point to know that A = non-non-A — that the shoe is not the non-shoe — because here I am concerned with the determinate negation, the determinate boundary, which is precisely not formal but determined in content (it does me little good to know of the shoe that it is not a non-shoe, but correspondingly little good, in concrete terms, that it is not a bird, not a color, not a state, not love, not a computer, and so on, as arbitrary examples of a non-shoe).
In the second step (the order of step 1 and step 2 is, in my experience, immaterial, as long as one does both over time. In practice there are fluid transitions anyway; they hang together, as will soon become apparent):
One should seek out as many qualitatively different manifestations of the concept as possible. For this I need the boundary from step 1; conversely, I find boundary material for step 1 here — so in practice the two steps constitute an approximation procedure, similar, for instance, to the approach of Gerhard Kleining (the founder of “Qualitative Social Research” in Hamburg, who incidentally invoked Hegel; see his foundational paper online: [external link] — this step in any case resembles one of Kleining’s methodological recommendations):
Example: chair
Office chair, kitchen chair, seating arrangements from other times / other peoples, etc.
Example: shoe
Ballet shoes, curled-toe shoes, mountaineering boots, anti-snakebite boots, safety shoes from industry / construction, low shoes, beggars’ shoes, fine leather dress shoes, paper shoes, baby shoes, and of course again shoes from other times and other peoples.
It is probably clear to everyone that the concept should, on the one hand, determine the boundary to the other clearly (?) (step 1), while, on the other hand, it should fit all the manifestations that fall under it (step 2).
The fine details are what matter here, but more on that later.
Let it at least already be said that in step 2 what matters is explaining as many of the different manifestations as possible from the concept. Conversely, the different manifestations thus provide for a “fuller” concept.
The concept is meant to be, so to speak, the seed from which the manifestations are to sprout. Those manifestations that we can still explain from the concept we call “ particulars” , those that can no longer be derived, “singulars.” It is clear that as many “particulars” as possible should be derivable from the concept.
This is an important difference from the notion of simple “abstract” universality, where one can never step back from an abstraction to something more concrete. (In set theory, therefore, the distinction between universal and particular makes no sense — there is only set and elements (and any number of subsets in between).
In a third step, it is then a matter of examining the parts belonging to the object, and likewise finding their significance for the object, their relation to the concept.
Example, shoe: sole, upper, lace
Example, chair: backrest, seat, legs
This part, too, actually happens organically together with the other steps — for instance, the reference to the parts often belongs to the drawing of the boundary (thus a chair is, among other things, distinguished from a stool by its backrest).
If the object has a history (individually and/or as a type) (and that is practically always the case), then this too must, in a final step, be related to the concept, and an attempt should be made to derive it likewise from the concept.
(I will show this in more detail later using the examples)
Okay, after the general overview, let us now go deeper:
On the first step, the drawing of the boundary:
in our investigation we find the relative justification of the drawing of the boundary. Truth/certainty is always relative to its grounds. What grounds do I have for drawing the boundary?
Let us take the example of the chair:
It is evidently a seating device. That is already the rough distinction, which we can make ever finer. In the simple cases we already have, through our language, a rough idea of what a word means, though we often cannot articulate it explicitly. In drawing the boundary, we first draw very wide boundaries, within which we are confident our object is contained (though perhaps other things are too), and from there we narrow the circle round by round until we have before us a perfectly fitting “tailored suit.”
The chair, then, serves sitting (in general it is a simple trick, with things produced by human beings, to think of their purpose, which almost always has something to do with their concept. This is why such things are especially well suited as examples, because concept formation, at least for simple, well-familiar objects, is so easy here).
With this we have determined the chair, in a first approximation, by its purpose as a “seating device,” and thereby already delimited it against other things.
Naturally this determination is still quite broad and must later be drawn more narrowly. At the beginning it is always advisable to draw the boundaries wide enough that the doubtful cases are still included (but, on the other hand, not cases that are clearly excludable — a state, a bird, etc.). One can always narrow it later; indeed, the narrowing occurs almost by itself in the course of further investigation.
To show here how steps 2 and 3 come into play: we now ask, for each intermediate result found, how it can be applied to the respective other questions — in this case, what does the determination of a chair as a “seating device” have to do with the many different types of chairs (how can these be explained from the concept), and what do the parts of the chair have to do with the concept?
Let us see what already follows from our determination “seating device”:
The chair is, as a (human) seating device, co-determined by the human body (length of the legs, position of the knees, size of the backside, and so on) (I disregard gravity here, since we are considering only earthly chairs — in space it might perhaps be different). Hence children’s chairs, baby chairs, and (limited only in regard to size) doll chairs.
On the other hand, it depends on the sitting posture/habit — peoples other than Europeans sit differently, for example much lower (and correspondingly they either have no chairs or much lower chairs).
Let us now examine more closely the act of sitting, for which the chair is thus meant to give us an opportunity (we could of course also switch over into logic and examine “opportunity” itself, which, however, seems less promising within the scope of our aim).
So sitting appears to be a bodily posture between lying and standing. What the stated postures have in common in this determination of sitting (! as you see, ever new determinations keep appearing) is that they are all stationary (in contrast to walking, running, and so on).
Sitting thereby occupies an intermediate position between relaxed lying (all activities that spontaneously occur to me in connection with lying have to do with this) and standing, which is closer to the border of (imminent) locomotion (e.g., “standing in line” or on the bus/train: “would you like to sit down?” — “No, I’m getting off in a moment,” and so on).
The weight of the body thus rests on the seat, and the legs are relieved. This explains the seat of the chair.
From the additional need to relieve the upper body as well, the backrest of the chair is explained, serving to support the upper body; from the need to relieve the arms, any armrests are explained.
[Here, then, the individual parts were explained from the concept]
Since the legs have the most work to do (they carry the entire weight), the need for relief is greatest in their case, second greatest in the case of the upper body — chair backs are therefore not always present, and armrests are found even more rarely.
[Even the absence of unimportant parts could thus be explained]
Why does the human being sit? In its intermediate position, sitting is a form of resting (similar to lying) that nevertheless leaves the upper body its full mobility (and the lower legs and feet, too, are at least to a limited extent mobile) and does not make concentration impossible (the latter more so in the direction of standing).
I think I am already going far too much into detail here; let me get back to what is important: from the different purposes pursued in sitting, a large part of the different kinds of seating devices can now be explained:
Thus there is the lookout post on the ship’s mast, the salesclerk’s leaning aid, the driver’s seat, the office chair, the television armchair, and the throne, to name just a few especially fine examples.
I come to the last, temporal aspect. It already follows from what has been said before that the more the activities that exist become differentiated, the more different seating devices there can (at least potentially) be.
Depending on the needs of society and its members, these different purposes are fulfilled by different means (in this case: chairs).
If I compare what has been said so far about the chair with Aristotle’s four causes, I have mainly addressed the final cause, or cause of purpose, to which Aristotle too attaches particular importance (which is no wonder, since Hegel draws very heavily on Aristotle).
Aristotle’s formal cause likewise appeared, but justified/mediated through the purpose (the form of the chair is mediated, via the purpose “seating device,” through the human body, the posture in sitting).
What is still missing are the material cause and the efficient cause.
Indeed, in the case of things produced by human beings, these two necessarily come in as well: which purpose is realized depends on the needs of society; how the purpose is realized depends further on the possibilities available to society: what materials (material cause), techniques, tools, experience/skills (the latter all belong to the efficient cause) are available?
The various chair forms are also explained from this.
A few more remarks:
The Asian cultures have, instead of the chair (or in addition to it), above all produced techniques of sitting. This too is a possibility that may not immediately occur to us Europeans, accustomed as we are to technology, but that can be derived without difficulty from the concept (seating device).
What would the next round of concept determination look like?
The objection concerning sitting techniques shows that we still have not clarified why we do not simply sit on the ground, or on a rocky ledge. Thus, so far, even the four legs of the chair have not been explained.
I do not want to overtax you here, but a new round could, for instance, turn the seating device into a piece of seating furniture.
It would then be the concept of furniture, as the apparently resulting broader concept, that needs to be clarified; here surely the investigation of the emergence of furniture as against, say, built-in fixtures would be relevant (here we would be seeking the boundary of furniture, and one of its boundaries, often very helpful because at least usually findable in books, is its boundary= emergence in time — compare the beginning of Hegel’s Logic).
Thinking back to the starting point, one might feel a certain disappointment: the question still remains, “is an armchair / a stool a chair or not?” The amusing answer is: it is a matter of definition.
By way of justification, once more a recourse to Aristotle:
As is well known, Aristotle gave as the rule for forming a concept that one must find the genus and, in addition, the “differentia specifica” (the specific/determinate/characteristic distinguishing mark).
This sentence has often been quoted, but how it should be handled (not arbitrarily) is often forgotten. What is meant, I have tried to show:
Concept formation proceeds by way of the boundary itself onward to its genera (with which we begin) and their subdivisions. What matters is that one develops a feeling for the relevance/importance/ justifiability/grounding of the subdivisions.
Once one knows this, it is in the end almost immaterial whether one decides to call the general seating furniture (including stool and sofa) a chair, or only the classical seating furniture for one person, made of wood under economical use of material.
What seems important to me here is only that the determination not contradict ordinary usage (one will therefore tend not to call an armchair or sofa a chair) unless one has important reasons for doing so (thus the whale, contrary to ordinary usage, is not counted among the fish by biologists).
A few small closing remarks, early in the morning:
I have already indicated that a good way to find the boundary consists in looking, in history, at the emergence of the object (if it has a history, of course).
Another, naturally related, method for step 1 consists in looking up the history of the concept in etymological dictionaries (Duden vol. 7, “Herkunftswörterbuch” [dictionary of origins], Grimm’s dictionary of the German language, Adelung).
The concept should, with qualifications, also explain its history. In any case, especially with everyday words and abstract words, good material for the initial drawing of the boundary/concept formation is found here (precisely for these words, the material in etymological dictionaries is usually better than that in modern encyclopedias, which unfortunately are made entirely without knowledge of the concept).
For step 2, especially with non-trivial objects, one will often also collect the different theories about an object and then (see the elephant image in the pluralism article) try to explain them all.
In any case these also provide good material (though the collection of existing theories should not replace the collection of the different manifestations.
Such a collection should perhaps be made a first time before the collection of theories, and then repeated after as qualitatively varied a reading of theory as possible).
Finally, I would like to note in passing that I have made an effort to include what I find rational/sensible in Marx in this connection; in this form it is quite compatible with Hegel.
By the way, this was not meant as a “systematic overview” of Hegel’s concept of the concept; rather, I wanted to give an idea/intuition of the concept, which usually works best with examples and application for practice.
The natural next step now would be to apply what has been described in this article to the concept of the concept itself — that is, to form as many different concepts as possible, for instance, and examine their particulars. Some of what I have described in this article does not hold, or holds only in modified form, for concepts from other fields (Hegel distinguishes, for instance in the greater Logic, between logic, nature, and the sciences of spirit (including society)).
The variety thus found would then not only offer a further and more differentiated concept of the concept, but the concept formation presented would thereby itself be grounded.
The concept formation presented can thus be applied to itself (which, oddly, is not at all a matter of course with concepts on this topic) and proves to be extraordinarily flexible and undogmatic.
Hegel’s work claims to be such a systematic presentation (for the concept, this is provided, for instance, by the logic part of his work).
He is often accused of being “dogmatic” for this.
In reality, IMHO, it is exactly the reverse:
Because everything is placed and grounded in its proper place, the freedom arises to examine the grounds in each case and judge them. One can read the whole of Hegel’s work against the grain and see, at every determination, every transition, the quality (in the everyday sense) of the grounding. In each case Hegel shows: this is as much as I know how to say about it.
It is therefore precisely not an affirmative work (even though one can read it that way, this way of reading contributes nothing to the interest in knowledge, and I would maintain that a purely affirmative reading also contradicts some of Hegel’s own basic intentions); rather, it precisely requires rethinking the thoughts each time. If one does this (instead of simply taking his system as external assurances), then one also knows where the problems lie, the strengths and weaknesses, etc.
For our present time, which apparently is no longer so accustomed to such a culture, an explicit presentation of the problems would certainly be desirable — which also generally lies in Hegel’s own tendency, to make everything implicit explicit.
See also: