A redated post, since someone asked.
One fundamental issue between myself and Richard Carrier (and his is not alone in this by any stretch of the imagination) is the difference between arguments from reason, which people like Lewis, Hasker, and myself have developed, and arguments from consciousness, such as we find in people like Swinburne and R. M. Adams. Here is the central difference. Suppose we look at an anti-naturalist argument from, say, objective moral values. The argument goes like this:
1. Probably, if there are objective moral values, the naturalism is false.
2. There are objective moral values.
3. Therefore, (probably) naturalism is false.
In J. L. Mackie's the Miracle of Theism he pretty much agrees with 1, on grounds that objective moral values do not fit well within a naturalistic world view. But he rejects 2, and says that he thinks objective moral values do not exist. Now, I have here argued that rejecting 2 would be a prett y costly move. You would, for example, have to accept the idea that we don't have the kinds of inalienable rights that the Declaration of Independence says we have; and that statements like "It is wrong to inflict pain on little children for your own amusement' are not objectively true. But moral subjectivism isn't incoherent; it's not inconsistent with the possibility of science, or the possibility of argument.
Now let's try a plain vanilla argument from consciousness.
1. Probably, if naturalism is true, there is no consciousness.
2. There is consciousness.
3. Threfore (probably) naturalism is false.
Now, on the face of things, it looks as if the naturalist can respond by denying 2. Ah yes, what you think of as consciousness really doesn't exist. Or perhaps they will give you a definition of consciousness which eliminates salient features of what we common-sensically think of as concsiousness, while retaining the name. I take it that's what's going on in Dennett's Conscoiusness Explained, and that is why some have suggested the title should have been Consciousness Explained Away.
But we can make the AFC into a species of the AFR if we can use the following orgument:
1. If consciousness does not exist, then reason does not exist either.
2. Reason does exist.
3. Therefore, consciousness exists.
Now there is a "transcendental justification' for 2. The sciences, and the very process of argument that, say, Carrier and I are engaging in, presupposes that what we are really doing is supporting claims, instead of doing something that perhaps has the grammatical form of rational inference but is really not rational inference.
All arguments that block denial moves by using an argument like the above are arguments from reason. This is a strength that arguments from reason have that other arguments against naturalism do not have. Some things can't be eliminated without eliminating science and reasoning.
I wouldn't exactly call them transcendental arguments themselves; as I am thinking about it the various AFRs are straightforward arguments, but if the opponent wants to say that the object that I am claiming fails to fit in with a naturalistic view doesn't exist, then there is a transcendental argument saying that it does.