I think that the difference here might have to do with the way that we each think of “content of thought”, or “object of thought”. I believe that the "particular matter-at-hand is already inherent within the thinking process of the subject, as the object of thought. It is not the independent, in-itself, the thing referred to by “the table”, or “the Roman empire”'. This is the Kantian principle, the in-itself cannot be the object of thought, nor could it be the “matter-at-hand”. Even Heidegger’s use of “at-hand” refers to a way of relating to things, not to the things themselves.
This is why I say that “object of thought” is best interpreted when “object” has the meaning of “goal”. Let’s say the matter-at-hand is problem X, and resolution of X is the object of the thinking. What is presupposed is that there is a resolution to X, otherwise the thinking would not be seeking it. I find Adorno was a little misleading, when he said “the explanatory attempt presupposes the explanation”, because it’s not the actual explanation which is presupposed, but that there is an explanation. When we seek to satisfy a desire, we assume that the desire can be satisfied.
So the matter-at-hand which Adorno refers to now is “simple logical contradiction”. And what I believe he says, is that if we call in an external ordering schemata from what he calls “objective cognition”, “the factical, especially by society”, then non-contradictoriness will already be presupposed. And this is where we see the other meaning of “object” which is distinctly different from “object of thought”. The “object” here is society, the factical of objective cognition. So Adorno says that the subjective thought-principle is inherent with the “object”, in this sense of “object”.
But if the matter-at-hand, problem X, the question of non-contradictoriness, is also understood as an “object”, the object of thought, then this object inheres within the subjective thinking. And within the subject alone, without reference to the outside ordering schemata of objective cognition, it may remain without judgement, without being ordered.
What I notice though, is that if problem X is my own problem as an individual subject, it is a particular. But if I express the problem to you, that is already to formulate it within such an outside ordering system, so it’s not a particular problem anymore, but a specific problem, and this takes it across the boundary from particular to universal. This is the issue of Wittgenstein’s private language.
Adorno then continues with an examination of how the subject can remove oneself from the outside ordering, the rule of objective logic. This is when thinking thinks against itself. And, he suggests it might be a good definition of “dialectics”. But here we may find expressed more clearly the two distinct senses of object. The “rules of thought” are proper to objective cognition, but he also says that thought is the object of thought, and that’s the other sense of “object”.
In certain respects, dialectical logic is more positivistic than the positivism which condemns it: it respects the object which is to be thought as thought, even there, where it does not follow the rules of thought.
I’d say yes and no here. The general principle refers to a method external to the matter-at-hand. But at the beginning of the chapter, the matter-at-hand is the possibility of a reciprocal relation of interdependence between subject and object. Therefore in this case we are talking about a method external to that relation.
What I think the issue is, is that we might take a specific matter-at-hand, and treat it as an object, the object of thought, problem X. X might be non-contradictoriness. Then we desire to understand how any particular subject might pass judgement concerning the applicability of X. If the subject turns to an external system, a part of the objective cognition of society, facticity, then the solution to X is already presupposed by the principles of that system which provides the solution. This doesn’t really tell us anything about the actual relation between the thinking subject at the object of thought, it merely tells us something about the thinking subject and the objective system of rules which the subject might apply in judgement. So the dialectical process is to reject all those systematized rules, and think against thinking, by making thought itself, the object of thought.
Yes, it’s a very interesting, and difficult section. I looked ahead at the next section, and it looks extremely difficult as well.