I read with interest your short text: “The two characteristics of an antinomy: self-reference and negation”.

It should be noted that logicians generally get nervous when Hegel’s logic is the topic.

Russell’s paradox maps quite nicely a typical dialectic in Hegel’s logic.

The difference, of course, is Hegel does not see inconsistency as a difficulty to be avoided. For Hegel, the actualization of self-thinking is an inconsistent thinking.

Or using your terminology, it is the self-referential characteristic of such thinking. The second characteristic – negation – gives the truth of this referentiality.

But I do not believe that the logic of this negation is well understood.

This would involve cashing out the third characteristic you mention: the negation has to be applied to the self-reference (and not to something else).

For Russell, this third characteristic is ad hoc or an arbitrary imposition upon the inconsistency of self-reference. With Russell, there is no logic to support this move. 

For Russell, it is a fudge introduced to paper over what Russell is unable to deal with. 

In contrast, with Hegel, understanding the logic of this move is crucial if one is to understand the Hegelian logic of self-thinking. 

It involves making sense of what you call “the negation of self-reference”. 

It involves clarifying the logic of this claim from your piece: “The negation as a negation of self-reference is a self-referencing negation.”

That is, it involves explaining the logic that necessitates this move. 

You note: 

“The reflection on the categories of identity and difference indeed shows that those cannot be determined in an isolated manner, i.e., _logically_ contain their other: '... the difference in itself is self-related difference; as such, it is the negativity of itself, the difference not of an other, but of itself from itself. [...] - This is to be considered as the _essential nature of reflection_ and as the _specific, original ground of all activity and self-movement_. - [...]'"

This is true of self-thinking. But the nugget in the middle of this quote from Hegel is precisely what has to be cashed out. Explain this Hegelian nugget and the speculative kingdom is yours.

Since formal logic is not a self-thinking. For such a logic there is no reason for such a thinking. Thus, Russell can get away with his ad hoc solution to his own paradox. 

Even though his paradox is not the result of self-thinking, the very fact that it manifests the form of self-thinking is all the reason Russell needs to rule it as in violation of his logic.

So, the response of the logician to your remark would be that you are confusing what we who think are doing so that we are able to think identity and difference with identity and difference thought apart from what we must do. What you need to establish is why self-thinking is relevant to the thinking of identity and difference. 

Another way to put this is that Russell would be ready and willing to apply his ad hoc solution at every point in Hegel’s Logic where the thought determinations manifest the form of a self-reference.

So, what the Hegelian must do is explain why Hegel is right and Russell if he attempted to make his ad hoc move would be wrong.

So, yes. The logic of reflection is the most difficult part. 

But the reason why it is so is because here more than anywhere else in Hegel’s Logic we see the thinking reflected back into the determinations that are being thought. 

-          Alan

I do not know Iber.

But no matter.

What he clearly states is one thing. I am interested in the argument in support of his statement.

Who has the authority to  prohibit the contradiction? And in what respect is the prohibition and imperative of the contradiction two sides of the same coin?

It is an interesting claim which is why I am interested in the argument.

As you go on in your next paragraph, you make the claim “that Hegel of course doesn’t allow the contradiction in the realm of formal logic and mathematics.”

I would put this differently. Hegel recognizes that in the realm of formal logic and mathematics contradiction is precluded. It has nothing to do with what Hegel does or does not allow.

But the point that should be at issue is why there is need for a second – speculative – species of logic where Hegel does allow contradiction?

Why is not formal logic sufficient?

And if there is a second species of logic what is the nature of this logic?

What is a logic of contradiction?

How do speculative logical moves differ from formal logical moves and why are such moves needed?

I raise these questions because I believe that these are the questions a formal logician or mathematician would raise upon hearing that Hegel “doesn’t allow the contradiction in the realm of formal logic and mathematics.”

The reason why I am raising these questions with you is that I believe that it is a common view among nonHegelians that Hegelians do not understand the logic of Hegel’s Logic.

The reason why Hegel is ignored is in part because his advocates have done a poor job of presenting the why and wherefore of Hegel’s speculative logic.

The American Hegelian, Terry Pinkard, has gone so far as to suggest that there is no such thing as a distinctive speculative logic. For Pinkard, there is only the one logic we have always shared. He hopes to gain a hearing for Hegel among nonHegelians by focusing on features of Hegel’s thought that for Pinkard appear to align with Sellars’ notion of the space of reasons.

I do not sense that you want to go this far. But I am not sure how you wish to make sense of the cryptic core of Hegel’s thought as represented by what I called the Hegelian nugget in the passage from your remarks that I quoted in my post.

Since you are new to this site I am interested in how you view these matters.

You do not have to do this right here, right now. It is just something you might want to consider and discuss at your leisure.  

• Alan