Thinking-of, Thinking-for, Thinking-with. Never responded to this thread, but I'd like to now. I like the three categories and have found them useful recently. This will be scattered, because my thoughts are.
I think we'd probably both agree that thinking-for is nested. I've tried to suggest recently that philosophy is, at base, a thinking-for explanation. By that I mean that the broadest philosophical circle, the outer (or inner) matryoshka, is explanation. To explain is to find something static that underlies flux. This (static idea) explains that. Novalis said, and Heidegger requoted: 'Philosophy is really homesickness, an urge to be at home everywhere." That sounds right to me : wherever you are, and whatever is happening, you can bring it back into explanation, you can re-domesticate it. Now, of course, this is just what a lot of contemporary philosophers militate against - Derrida's differance is the obvious example. But this is still a concept one returns to in thought, which still effectively grounds no matter how many times you erase or strike-through a word. At the limit, the impossibility of final explanation takes the function of final explanation. Wittgenstein, decontextualized, but perfectly apt - 'You are sitting at a loom - even if it is empty -and going through the motions of weaving.'
I still think this is broadly right.
And I also think thinking-for (and -of and -with) are all handy tools outside of that context.
I think I've mixed up two things in the past. One is philosophy, in the sense outlined above, and the other is academic discourse. For the purposes of this post, I'm going to talk about the intersection of academic discourse and philosophy. Obviously, most of academic discourse is not discourse about philosophy, but that's what I'm going to talk about here.
Academic Discourse isn't necessarily trying to find an ultimate explanation, as with philosophy. The explanation has already been effectively decided upon. A shared methodology has determined in advance the kind of thing which will be accepted as an explanation.
From this, a family of thinking-fors crop up. One is thinking-for the massaging of inconsistencies latent in the current discourse, to be the one who does the personal labor of working them out. You develop what's there. Another is thinking-for the application of the discourse to fields as-yet untouched by it. Another is thinking-for Iconoclasm, trying to tear the whole thing down by finding a fatal flaw.
Most of these are, of course, nested in a broader thinking-for-recognition -- which of course, that's a primal human need.
At the end of the day, everything I'm saying breaks down into something middle school english simple - man versus society. Thinking-for always has to involve the social whole. But there's also a thinking-because-you-have-to which is just the mind and body (of the individual or a sub-societal group)working itself out, as one composes a song because one knows what note comes next, or as a group spontaneously creates what they need to.
But There's something about the intersection of philosophy and academic discourse which seems to take the social aspects of academic discourse and the inherent self-tail-biting aspect of philosophy and fuse them into a self-perpetuating machine. What is the thinking-for here? It seems like it has to do with a certain enclosed and ambivalent relationship toward recognition.