Editorial remarks from 2020

The following text was written by me (Kai Froeb) first in the XCSA mailing list around 1997. The “concept” (“Begriff”) I am descibing here in my mind belongs to classical philosophy and classical logic¹ and so both to Aristotle and to Hegel. As it has been forgotten or is at least not taught so much in modern time, it seems well worth to explain it. In reading patiently the following remarks, I hope that you will get some helpful remarks on how to do science, and especially how to come up with meaningful determinations, which should complement well the usual training in formal logics. At the same time, it should help to understand what Aristotle really means when he talks about the “Differentia Specifica”². Last but not least, it will help you to understand a central concept of Hegel, the “concept” (“Begriff”), which is misunderstood when you think of it in the terms of “Notion” and modern formal logic.

In the text below, my “prelimnary remarks 1” are a little bit polemic against some modern claims (I am especially thinking of the logical positivism/logical empirism of the “Vienna Circle” etc.) and just wants to make you think so that you might be interesting in following the rest of the text. If you are motivated enough, you can skip it.

The second prelimnary remarks are meant to observe your own experience what you / science does when you try to understand a given subjec and to find appropriate definitions. Thinking further about this gives us a common ground as starting point.

Starting from there, I just take you down the road how to find an appropriate definition, a “concept”. In my tutorial, I use the sample of a chair to make sure that everyone can easily follow.

Kai

Preliminary remarks 1

1. It is sometimes said that (mathematical / theoretical) physics is pure mathematics, but this is not true, it explains concepts such as mass, force, motion, etc., which do not occur in mathematics. That is why not every equation that would be allowed according to mathematical laws is useful in mathematical mechanics. Conversely, it is often necessary to explain existing equations first, to give them a meaning (who would know, for example, without prior explanation what the famous equation e=mc^2 implies for a meaning?)

2. In the same way, it can be said that mathematics is about mathematical concepts. In mathematics, a proof is not arbitrarily transformed, but from the zillions of possibilities, the one that is meaningful within the framework of the objective of the proof is selected.

However, these considerations are not apparent from the proof itself, which is why it is often said that it is something else to read a proof, to understand it or even to come up with it oneself³.

3. Some philosophers, inspired by formal logic, finally claim that scientific systems can be divided into the unproven & unprovable axioms and the “derived” propositions, derived from the axioms by tautological transformations. In doing so, the rules of transformation of formal logic used in this process itself are also consistently regarded as unproven & unprovable axioms.

Even if thoughts of this kind can be found in books on formal logic and philosophy and by all means also find their way from philosophy into the feuilletons and the foundation of all kinds of sceptical and relativistic zeitgeist, the “normal” operation of the sciences is not particularly affected by them.

For the work of even the stupidest and most narrow-minded scientist does not consist (to my knowledge) in inventing arbitrary axioms and then to transform them at will.

So what do you actually do when you build a scientific theory as a scientist? What do you look for when you are looking for an explanation? What is a good concept, a satisfying axiom? To clarify this was once one of the main concerns of classical philosophy from Aristotle to Hegel.

Preliminary remarks 2

Simplified, science goes through the following phases, this can be traced within the theory formation of a scientist and can also be similarly traced in the history of the individual sciences themselves.

The elements of each earlier phase are always included in the later phases, modified by the added elements of the later phases:

In the beginning, as much information as possible is simply collected. Think here of the reports of travellers in geography, ethnology, the collection of various minerals, plants and animals, etc.

If there is enough material available, then we start to sort the material. It can be observed that with increased knowledge the ordering advances from very external criteria (colour, smell, number of individual parts, etc.) to more and more suitable/immanent criteria (for example, in biology today the plant and animal kingdom is divided according to the relationship of DNA).

This progress in the ever more appropriate classification is prompted by the 3rd step, a theoretical penetration of the field of science. With the increasing theoretical penetration, more and more appropriate classifications can be made. In the theoretical penetration, it is often seen as a goal to advance to those concepts, axioms and laws from which one can derive the rest (mathematics is usually regarded as the ideal here, and mechanics accordingly by the natural sciences).

It is therefore important to arrange the material found in such a way that as many phenomena as possible can be explained with as few assumptions / axioms / laws as possible (here used in the sense of “not further derivable”).

The first sentences / axioms of the respective science are not chosen arbitrarily, but should contain the fullness of their topics as concentrated as possible. Only in this way can the science building be pulled out of them again later by the supposed magic trick. Axioms and laws are therefore also the end product of a scientific activity and not its beginning.

Why concepts instead of axioms as a starting point?

Why does Hegel now speak of concepts instead of initial propositions (axioms)? Very simple, the initial propositions deal (at least) with subjects to which predicates are attributed. These initial clauses are also composed.

In an elementary proposition of the form “S (subject) is P (predicate)”, which P is contained in S, one must therefore look at the subject of the proposition (the concept of which something is said) in a content-related logic.

The real beginning are therefore the subjects of the sentence.

The subject of the proposition has the qualities that are then attributed to it in the proposition, indeed it probably has other qualities as well. The proposition is supposed to pronounce the properties essential to it, from which, if possible, the others can be derived, and thus has the concept to measure (for more details on the relationship of concept to proposition see Hegel’s doctrine of the judgement (“Urteil”). There are several good commentaries available to it too).

If it turns out that one sentence is not sufficient for this (and this is usually - I do not know any deviations - the case) then just in several sentences. The sentences should be ordered according to their logical relationship to a system (this is Hegel’s transition from the doctrine of judgement to the doctrine of conclusion/sylogism).

Also purely phenomenologically, if one looks at the individual sciences, these are presented as respective explanations of their subjects (in the following always used in the broader sense, i.e. “conceots”), in which again the individual “concepts” belonging to the subject are arranged in a system.

The main question is therefore first of all to find the appropriate “concepts” and their definitions (i.e. the sentence(s) that say the essential things about the subject), which are naturally related, as we shall see later.

What is a concept ?

So what is a concept and how do I define it?

Delimitations

From what has been said so far, it is clear that this is not intended to be

1. an (arbitrary) definition / delimitation

So nothing like this:

“Man is a two-legged creature without feathers” (according to an old Greek wannabe philosopher, on which Diogenes is said to have presented him with a plucked chicken)

and therefore

2. the idea of the general, as known from formal logic and set theory, where simply a general is obtained by (arbitrary!) abstraction (abstract = lat. subtract, i.e. leave out) is of little help.

Both can be found in the concept if you like, but it is the arbitrariness that is disturbing here. A scientist does not want to simply work out an arbitrary aspect, but wants to find the determination which is appropriate for the object.

The measure of correctness of a scientific determination / theory is still the agreement with its object, which should be appropriate for it (this is usually what distinguishes a scientific theory from science fiction ).

Boundaries

If one looks at what has been said of the concept presented so far, all have one thing in common, which is that there is a boundary to the concept, which determines what belongs to the concept and what remains outside, i.e. “determines” it (I will use the word determine in the following in this sense).

Spinoza already says “Omnis determinatio est negatio” (all determining is negating), i.e. excluding, indicating what the thing to be determined is not.

The first step in the formation of a concept is therefore to deal with the limit of the concept. So with borderline cases. What just fits in ? What just doesn’t fit in anymore ? At which points am I unsure ?

Example: chair: Does the one-legged bar stool still belong to the concept ? A three-legged stool? The armchair? The sales assistant’s standing aid ? The bench ? The table ? The sitting posture ? (methodical hint: find the greatest possible variety of qualitatively different, productive variants)

Example shoe: Is a boot still part of the concept? A stocking? A sandal? Barefoot (= no shoe)? The cornea ?

The beautiful disjunctive (in the sense of “mutually exclusive”) divorce in A and NON-A of formal logic only takes effect when I have this boundary. And, by the way, it does not help me at this point to know that A = NON NON-A, that the shoe is therefore not the non-shoe, because I am concerned here with the certain negation, the certain boundary, which is not determined formally but in terms of content (it is of little use to me if I know about the shoe that it is not a non-shoe, but correspondingly also of little use in concrete terms, that it is not a bird, a color, a state, love, a computer, etc. as arbitrary examples of a non-shoe).

Second Step

In the second step (in my experience, the order of step 1 and step 2 does not matter as long as you do both. In practice, there are smooth transitions anyway, they are connected to each other, as you will see in a moment):

Look for 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, so in practice the two steps are an approximation procedure. ⁴

Example chair: office chair, kitchen chair, seating from other times / other peoples, etc.

Example shoe: ballet shoes, beak shoes, mountaineering shoes, anti-snake bite shoes, safety shoes from industry / construction, low shoes, beggar shoes, fine leather shoes, paper shoes, baby shoes, and of course shoes from other times and other peoples.

It is clear to everyone that the concept should clearly define the boundary to the other (step 1), but it should also be appropriate for all forms of appearance that fall under it (step 2).

It depends here on the subtleties, but more about that later.

In any case, so much should already be said now that in step 2 it is important to explain as many of the different phenomena as possible from the concept. On the other hand, the different phenomena provide a more “full” concept.

The concept here should be the seed, so to speak, from which the manifestations should sprout. Those manifestations which we can still explain from the concept are called “particularities” (From the division Universal - Particular - Singular/Individual. In German “Besonderheiten”), or “special features”, those which can no longer be derived “details”. It is clear that as many “particularities” as possible should be derived from the concept.

This is an important difference to the idea of the simple “abstract” generality, where it is never possible to go back from an abstraction to something more concrete. (In set theory, therefore, the distinction between generality and particularity makes no sense, there are only set and elements (and any number of subsets in between). Third Step

In a third step it is then necessary to examine the parts that belong to the object, and also their meaning for the object, to find their relationship to the concept.

Example shoe: sole, upper, lace

Example chair: backrest, seat, legs

In reality, this part also happens organically together with the other steps, so the reference to the parts is often part of the boundary (for example, a chair is distinguished from a stool by its backrest, among other things).

If the object has a history (individual and / or as a type/kind) (and this is practically always the case), then in a last step this history should also be related to the concept and an attempt should be made to derive it from the concept as well.

(I will show this later in more detail with the examples)

Consolidation

After the general overview, let us now go into more depth: To the 1st step, the drawing of boundaries: in our investigation we find the relative justification of the drawing of boundaries. Truth is relative to its reasons. What reasons do I have for the drawing of boundaries?

Take the example of the chair:

It is obviously a seating arrangement. This is the rough distinction that we can always refine. We have, in the simple cases already through our language, a rough idea of what a word means, we just often cannot pronounce it explicitly. When drawing boundaries, we first draw very broad boundaries where we are sure that our object is contained in it (but maybe other things as well) and from there we draw the circles narrower with each round until we have a tailor-made suit in front of us.

So the chair is used for sitting (in general it is a simple trick to think about the purpose of man-made things, it almost always has something to do with their concept. That’s why these things are particularly well suited as examples, because the concept formation, at least with simple, familiar objects, is so easy here).

Thus we have defined chair according to its purpose as “seat” in the first approach and thus already distinguished it from other things.

Of course, this definition is still quite wide and must be tightened later. At the beginning it is always advisable to draw the borders so far that also the cases of doubt are still in it (But on the other hand clearly excludable cases, (state, bird etc. ), are not). One can still draw narrower ones later on. Above all, the narrower drawing results almost by itself in the course of the further investigation.

To show how the 2nd and 3rd steps play a role here: we now ask ourselves with each intermediate result found how we can apply it to the other questions, so in this case what does the definition of a chair as a “seat” 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’s see what follows from our definition of seating:

The chair as a (human) seat is co-determined by the human body (length of legs, position of knees, size of the buttocks etc.) (I will leave gravity aside here, as we are only looking at earthly chairs, in space it might be different). Therefore, for example, children’s chairs, baby chairs, (limited, only regarding the size:) doll’s chairs.

On the other hand, it depends on the sitting posture/habit, e.g. other peoples than Europeans sit differently, for example much lower (and accordingly they either have no chairs or much lower chairs).

Now let’s examine the purpose of sitting more closely.

Thus, sitting seems to be a posture between lying down and standing. What the mentioned postures have in common in this determination of sitting (! as you can see, new determinations keep coming up) is that they are all location-bound (in contrast to walking, running etc.).

Sitting has an intermediate position between lying relaxed (all activities that come to my mind spontaneously while lying down have to do with it) and standing, which is more on the borderline to (immediately) moving (for example “standing in line” or in the bus / train: “do you want to sit down?”). - “No, I have to get off right away” etc.).

The weight of the body rests on the seat, the legs are relieved. This explains the seat of the chair.

The need to also support the upper body explains the chair back to support the upper body, the need to support the arms, possible armrests.

[So here the individual parts were explained from the concept]

As the legs have to do most of the work (they carry all the weight), their need for relief is greatest for the legs, second for the upper body, so chair backs are not always available, and armrests are even rarer.

[So even the absence of unimportant parts could be explained]

Why is the human being sitting? In its middle position it is a resting (similar to lying down), which however allows the upper body its full mobility (and also the lower legs and feet, are at least restricted in their movement) and at least does not make a concentration impossible (the latter rather towards standing).

I think I am already going into too much detail here, I will come to the important thing: from the different purposes pursued while sitting, a large part of the different sitting positions can now be explained:

There is the lookout on the ship’s mast, the saleswoman’s standing aid, the driver’s seat, the office chair, the television armchair and the throne, to name but a few particularly 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 are differentiated, the more different seats there can be (at least potentially).

Depending on the needs of the society and its members, these different purposes are fulfilled by different means (in this case: chairs).

Comparison with Aristotle

If I compare what I have said so far about the chair with the famous four causes of Aristotle, I have mainly mentioned the final/purpose cause, to which Hegel also attaches great importance (which is not surprising, since Hegel refers very much to Aristotle).

Aristotle’s formal cause also occurred, but justified / mediated by the purpose (the shape of the chair is mediated by the purpose “sitting” mediated by the human body, the posture while sitting).

What is still missing is the material cause and the cause of action.

In fact, it is precisely in the case of man-made things that these two are necessarily added: which purpose is realized depends on the needs of society, how the purpose is realized depends also on the possibilities of society: which materials (material cause), techniques, tools, experiences / skills (the latter all belong to the cause of action) are present?

This also explains the different chair forms.

A few more remarks: The Asian cultures have produced mainly sitting techniques instead of the chair (or in addition). This is another possibility that may not immediately come to mind for Europeans who are accustomed to technology, but it can be casually derived from the concept (seating).

What would the next round of definitions look like?

The interjection to the sitting techniques shows that we still haven’t clarified why we don’t just sit on the floor, or on a ledge. For example, the 4 legs of the chair have not been clarified yet.

I don’t want to overstrain you here, but a new round could, for example, refine the seat into a piece of seating furniture.

It would then be the concept of furniture, as an apparently resulting generic concept to clarify, here would certainly come the investigation of the formation of the furniture against, for example, the built-in parts (we would look here for the limit of the furniture and one of its limits, often very helpful, since usually at least from books can be found, is their limit = arising in time, compare the beginning of Hegel’s logic).

Relating what has been achieved back to the starting point

If one thinks back to the starting point, perhaps a disappointment remains, the question still arises: “Is an armchair / a stool a chair or not? Funnily enough, the answer is this: it is a matter of definition.

As justification once again a recourse to Aristotle:

Aristotle, as is well known, gave as a rule for the formation of a concept, one would have to find the generic concept and in addition the “Differentia Specifica” (the specific / certain / characteristic distinction).

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:

The concept formation goes beyond the border itself to its generic concept (we start with them) and its subdivisions. It is important to get a feeling for the relevance / importance / justification / justification of the subdivisions.

Knowing this, in the end it is almost irrelevant whether one decides to call the general seating furniture (i.e. including a stool and sofa) a chair, or just the classic seating furniture for one person made of wood, manufactured under material economy.

It seems important to me that the provision does not contradict the general use of language (so the chair and sofa are not likely to be called chairs), unless there are important reasons for this (for example, contrary to what biologists say, the whale is not considered a fish).