Hegels Teachings
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I will first answer what I find to be the essence of Hegel's teaching (2), then explain what I think is objective (or, how Hegel calls it, absolute idealism and how this relates to the basic questions one might have towards such a position (3), I will then explain some ideas how to criticize it (4). This will make this article rather long but I hope it's worth it.

1.

The last 20-30 years have seen a fundamental advance in Hegel studies in that we now (At least in Germany) not only have great philological editions of most of Hegel's works and lectures (published at Meiner Verlag, Hamburg) but also very good and clear commentaries to most parts of Hegel's System, the most important being "Hegels System" from Vittorio Hösle (also at Meiner Verlag, Hamburg).

Let me state that the following statements are based on my understanding of the late Hegel, the Hegel of the "Encyclopedia", the Hegel of the Berlin years (about 1815-1831).

2.

So what are the basic teachings of Hegel in the context of science? 

2a) 

Truth is only relative to the arguments (in a wide sense, including "facts") you have for it to prove it. So try to explain as much as possible with arguments as strong as possible. This does not only include explaining as much known facts as possible, but also the category system used: your notions / concepts and their relation / system, both in the general sense and applied to the concrete situation / theory.

Don't presume anything.

But when you question everything, what happens if you apply this to questioning itself? What are the grounds / reasons for this critical position itself? So a consequently applied position a) will need on the one hand some kind of non-relativistic foundation, but not in a way of just postulating / assuming it, but, in accordance to a), in a way that it can be proved. That's where b) and c) come in:

2 b)

If we ask for proves to explain anything (all assumptions, axioms), how can we do this without falling in an endless regression (any explanation can itself be questioned)? In order to escape that endless regress, the most basic foundations have to be self reflective / self proving/self grounding in the sense that they can't be questioned themselves in a meaningful way (a kind of negative prove: we can show that the assumption that they are not valid leads to contradictions).

2c) 

2c-1)

 In order for a position (i.e. theory) to prove to be superior to another, it is not enough to show that the other position differs.

2c-2)

One has to show  that the other theory has self contradictions (using the categorical system / methods / assumptions of the other theory, not presupposing my categories) and 

2c-3) 

that the better position preserves or enhances everything meaningful in the other theory (Sublation).

Hegel's positions are of course much more sophisticated then I showed them in a) -c), but you will have a good understanding of them when you realize that most of the more complex stuff Hegel adds is due to the fact that he applies these 3 rules to these rules themselves (This itself is a consequence out of 2b)).

2d) 

Probably the most known aspect of Hegel is that he tries to overcome all dualism: Be it the dualism of Monism vs. Dualism itself or Nature vs. Spirit, Subject vs. Object, Egoism vs. Altruism, Genes vs. Environment, Individual vs. Society, Knowledge and will, feeling and thinking, Form vs. Content etc.

You can see Hegel's System in vast parts an attempt to overcome these contrapositions. This is a consequence out of 2c).

They have to be overcome in a way that their difference is not neglected (but acknowledged), but that you also look for what they have in common (otherwise, if they hadn't anything in common, they couldn't be contrapositions of each other), the implicit basic assumptions both contra positions share.

So it is very clear that based Hegel's own standards, whenever you can say something negative of his system/philosophy, it is either unjustified (probably based on lack of knowledge) because it is already sublated in / part of his system, or his system has to be changed, either because Hegel made an error or because he didn't know about that position (theory, fact). And yes, it should be clear by now, that indeed I find several things to change (See 4d and the mentioned book of Hösle for a start).

3.

3a)

So based on what I wrote in 2) it should become clear that Hegel doesn't mean idealism in the sense of a simple contraposition to "materialism" or "realism" (as this would immediately be against principle 2c / 2d).

3b)

For Hegel, the highest peak of his logic is the Ideal, where subject and object become the same (but of course this has to proved not just postulated and therefore is subject to criticism).

In a scientific context, speaking of science, I find it helpful to read Hegel's Idealism as a way of speaking of the scientific aim to have a theory that meets its topic (I know that one can read him in a other ways too).

There are two very good books on that subject:

Guessbacher, Heinrich: "Hegels Psychologie der Intelligenz",  Verlag Dr. Johannes Koenigshausen + Dr. Thomas Neumann, Wuerzburg 1988, ISBN 3-88479-346-2, 364 Pages, about 65 DM.

explains very detailed Hegel's concept of how we acquire knowledge, how we learn etc (And yes, of course Hegel accepts that we take our knowledge of facts from the outside world, but he doesn't stop there. Nor does, say, physical science).

There is also a very good book , which has the best discussion of Hegel's Kant critique I know of:

Schick, Friederike "Hegels Wissenschaft der Logik - metaphysische Letztbegründung oder Theorie logischer Formen ?", Alber Verlag, Reihe Symposium Nr. 100, Freiburg / München 1994, ISBN 3-495-47794-2, 336 pages, 98 DM.

Both books together will give you a decent idea on Hegel's "epistemology", if you like to call it that way.

You will see that Hegel's ideas are nearer to common sense and science, (which both are also based on the goal to meet with their topics by their concepts) then is commonly believed of Hegel.

3c)

As for "absolute", you can basically read this term as an abbreviation for the 4 principles mentioned above( 2a-d). It is a very big misunderstanding if one would think that this is mainly a proclamation, arrogance. Quite on the opposite, it means that Hegel tries to meet the highest possible standards with his theory, in that he wants to argue prove it in a way that it can't be questioned (especially think of 2b).

4.

Based on Hegel, one would see the development of the theories after Hegel as an expression that Hegel's theory in itself is incomplete, in a way or another and has to be sublated itself.

Two major areas come to my mind:

4d-1) 

Apel and Hösle see the philosophy of the 20th century basically under the aspect of intersubjectivity. Hösle goes to great length in his book "Hegels System" to show that some of the basic problems with Hegel's System are probably due to that fact / can be corrected one taking intersubjectivity into account.

4d-2) 

A trend I see in post Hegelian philosophy especially of the 19th century, but not limited to it, is the emphasis on the Non-Rational in it's widest sense. Hegel does include it in his philosophy, but people like Feuerbach, Marx, Nietzsche, Schopenhauer, Freud et all and many others provide a lot of material to be meaningful sublated.

I guess that most of the critique of Hegel comes from one of these two directions, where I personally assume that more arguments will come from position d-2).

Sublating these 2 trends may mean to change a lot even of basic stuff in Hegel, however I think that when one still can apply the 4 rules listened above, the outcome still can be called Hegelian (Especially as rule 3 will ask for sublating everything meaningful from Hegel himself into that new theory).


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