Is there such a thing as *conscious* inference?

...at least as I think we are accustomed to think about it. What I mean is that in cases of what is usually called "conscious inference" when I look closely I don't find that I'm really *doing* anything, which is how I think I've been led to believe about conscious inference whereas in "unconscious inference" it "just happens".

I just can't see what I'm *doing* other than perhaps wondering, sending a query to my cognitive system, a request for a result. And then I just wait for the result to pop up on the screen. That's not doing much. On this model conscious inference is little more than being conscious *of* an inference, of a process--the exact same process--that occurs when I'm not "looking".

Often it seems I don't even have to send the query. So when I display this:

(A v B) & ~A

You just had "therefore B" pop into your head whether you liked it or not. In this case *I* initiated the cognitive module for inference in your mind. Was that a "conscious inference"? You were conscious of the premise and conscious of the conclusion popping up on your screen (maybe you want a pop-up blocker for your mind (I know I would)), but you didn't really *do* anything, not even send a query regarding whether something followed from that WFF.

In a paper I'm working on, I argue that this more accurate understanding could save internalist foundationalism from skeptical worries about it.