Reasoning III (Fragmentation)
As Robbie Williams remarked in the comments, perhaps what we do when we reason is putting parts of our fragmented belief space together. However, I doubt that this will do as a general solution.
First, at least in the context of an interpretationist account of content, it doesn't suffice for fragmentation that the relevant beliefs are somehow stored in different parts of the brain. Rather, if my beliefs are fragmented, say, into a compartment in which I believe P and one in which I don't, this must show up in my behaviour, more or less as follows: 1) In some contexts, the best explanation of some of my actions involves the assumption that I take the world to be P; but also 2) in some contexts, the best explanation of some of my actions involves the assumption that I don't take the world to be P; Moreover, 3) the discrepancy can't be explained as a change of belief.
These conditions aren't trivial, in particular since interpretations that attribute simple, unfragmented content usually qualify as better explanations than fragmented ones. If you tell me that you're a vegetarian while eating a steak, I won't just conclude that this is a matter of fragmentation. That's only a last resort if all other attempts to make sense of your behaviour fail (such as that you didn't mean what you said, perhaps because you have some non-standard conception of "vegetarian").
So while sometimes there might be good reasons to postulate fragmentation -- e.g. when a split-brain patient correctly points at an object on being asked to do so while at the same time sincerely telling you that he has no idea where it is --, it is rather incredible that this happens all the time. If whenever I do a calculation I unify two parts of my belief space, my beliefs would have to be almost infinitely fragmented: virtually every single one of my mathematical beliefs would have to inhabit its own belief space. The only reason I can see to postulate all these fragmentations is to solve the problem of deduction.
Second, I find many applications of the fragmentation strategy quite unconvincing. Suppose I'm playing chess. I know the rules of chess, and I know the current position of the pieces on the board. Together, these entail that move M is better (for winning) than move N. Yet being a bad chess player, I choose move N. On the fragmentation account, it follows that in the compartment where I made my decision I was ignorant of (or mistaken about) either the rules or the current position of the pieces. But that seems false. In fact I took both the rules and the current positions into account when making my decision.
Finally, the fragmentation strategy only works if we can always find some real, non-trivial content in the conclusion. For if the conclusion is a necessary truth (like the conclusion that in such-and-such a state of a chess game, M is a better move than N), it will be contained in every belief set whatsoever, hence also in all the fragments I might or might not put together. That's why Stalnaker, in §5 of Inquiry, has to combine the fragmentation strategy with the "new information" strategy: in mathematics for example, he says we acquire new information about symbols (or classes of symbols) by combining fragments. But again, I'm afraid this won't account for the Martian reasoner who knows nothing about symbols.
"Second, I find many applications of the fragmentation strategy quite unconvincing. Suppose I'm playing chess. I know the rules of chess, and I know the current position of the pieces on the board. Together, these entail that move M is better (for winning) than move N. Yet being a bad chess player, I choose move N. On the fragmentation account, it follows that in the compartment where I made my decisiion I was ignorant of (or mistaken about) either the rules or the current position of pieces. But that seems false. In fact I took both the rules and the current positions into account when making my decision."
Consider Paul. Paul is a very good chess player. He knows the rules of chess (if we would ask him how to play chess, he would tell us the rules, and so on), he is able to anticipate
30 moves (or so), and he knows the current position of the pieces. If Paul would choose move N, we would say that he didn't anticipate enough moves to get the right strategy.
Consider Hanna. Hanna is a very bad chess player. She knows the rules of chess (if we would ask her how to play chess, she would tell us the rules, and so on) but can anticipate only three moves.(And she knows the current position of the pieces.)Now, if Hanna would chosse N, we would say the same as in Paul's case, I guess.
"In fact I took both the rules and the current positions into account when making my decision."
I think, you're right. But knowledge of the current positions and of the chess rules is not enough to tell the story right. Therefore, it just doesn't surprise me that you say
"But that seems false."
But I don't think, that this could be an argument against the fragmentation strategy.It's just because of your premisses, that a bad chess player is a bad chess player because of his ignorance of either the chess rules or the current position of the pieces.