Antiprocess
So far we've covered multiple mental processes (multitasking), filtering (both positive and negative), stop-thought and recursive filtering. Now let's look at several increasingly elaborate ways that people hold on to beliefs even in the face of overwhelming evidence to the contrary.
Selective Antiprocess
When Bob has a choice, he tends to read, watch and listen to things that confirm what he already believes. They may not reflect his thinking precisely, but they are close enough that they do not cause him undue discomfort.

Here Bob is watching a TV show that is at odds with his opinions about the way things are. His solution to the problem is as close as the television remote (if he can remember where he put it).
Passive Antiprocess
In the next illustration, the person on the left is giving Bob some information that, at the very core of his being, he doesn't want. Bob has certain beliefs that make life tolerable for him. So how does he deal with unwanted information? By using his stop-thought ability. However, since Bob's in a conversation, he can't just stop thinking about it; his mind has to come up with a defensive strategy, such as giving the impression that he is paying attention when in fact he has tuned out.

This brings us to a key feature of Bob's antiprocess: he comes up with the defensive strategy without being fully aware of why he's doing it.
Bob has to do it that way. The whole purpose of the defensive strategy is to prevent the information from compromising his belief system. If he allows the information to fully enter his awareness, he's in trouble. The belief system that has worked so well for him in the past — a belief system he has worked on for years — is threatened. So his mind has to compartmentalize the work of coming up with the strategy in order to avoid cognitive dissonance.
The reason I call this "antiprocess" is because his mind is coming up with a way of defending against information without ever processing it consciously.
To put this in different words: at a subconscious level Bob understands the information perfectly well, but that complete understanding never fully enters his awareness.
Rote Antiprocess
Sometimes it is not sufficient for Bob to simply smile and nod. The other person may require some sign that Bob is actually listening...

Bob's filters recognize the argument being presented and categorize it sufficiently for him to select a stock response. He then repeats something he has read or been told — typically some kind of counter-example that Bob had no compelling reason to analyze when he first learned it. Bob may introduce some minor variations on the reply to make it his own, but thematically it is still the same one he learned previously.
Bob's antiprocess can toss out rote responses one after the other such that they act like a series of roadblocks. If he can impede the other person for long enough, the debate will grind to a halt and Bob's world-view will be safe for another day.
Active Antiprocess
Active antiprocess happens when for some reason a person feels they must continue to debate the topic at hand. There are many reasons somebody might do this, but I'll just give one example here.
In what I call "quasi-perilous validation", a person engages in what appears to be a belief-threatening activity, but does it in such a way that there is, in fact, no risk. This victory is the reason for the risk: it "proves" the belief in proportion to the apparent danger.

What you see here is that Bob is tapping into his understanding in order to formulate a rebuttal. But that rebuttal probably won't be very good, because he has not allowed himself to be fully aware of that understanding. The "understanding" is locked up in a mental cage so it can't hurt him.
There are many warning signs that this is taking place. One you may recognize is "Yes-butting", where the person replies, "Yes, but" to every challenging statement they hear, then makes a fairly lame rebuttal.
Antiprocess doesn't help Bob get any closer to truth, but his mind has already assessed the information in advance and perceived a threat. Thus, the last thing it wants is understanding, even if that means turning away from truth. That's because at a level below Bob's awareness, his mind has decided that there is a threat to his mental equilibrium.
To state the key point once again: he is not aware that this is happening. As far as he can tell, he really is debating in good faith.
Of course, as far as the other person is concerned, Bob seems incredibly dense.