I have been conducting a pleasant discussion concerning the philosophical credibility of intuition on a thread started by Helen De Cruz here which seemed to link thematically to an earlier thread started by myself here.
Today, by chance, I happened to catch an instructive exhibit on Surrealism in the Vancouver Art Gallery, where I came across an "unexpected quote" (cp. Schliesser) from André Breton. Breton defines surrealism as "pure psychic automatism, by which is intended to express . . . the true functioning of thought." It seems to me that "pure psychic automatism" is a good description of how intuition ought to work. Think of something interesting--the surrealists were good at this--and let your mind go where it might.
There are many sources of such automatism. If you are thinking about belief or knowledge, it might (as Jennifer Nagel argues) be founded on "mind-reading"--the human capacity to "perceive" the mental workings of other people by observing them talk and act. The idea here is that the sort of "mind-reading" abilities we exercise when we (for instance) observe somebody laugh in response to some pleasant and amusing social exchange can be deployed in hypothetical scenarios about action and knowledge.
The Twin Earth example discussed in comments on Helen's thread is different again. It neither relies on one's sense of what would happen in a case like Galileo's nor on one's innate human capacity to read the minds of other humans. Rather it relies on one's implicit knowledge of a concept such as WATER. You are offered the Twin Earth scenario and you let your mind do the rest unfettered. The experiment coaxes out the internalized, but implicit, content of the concept.
This said, I think there has been a certain move away from "psychic automatism" in some recent uses of the method of intuition. It sometimes seems to me that philosophers try to figure out where the unoccupied regions of logical space lie--a kind of philosophy by eliminating all hitherto occupied positions. (Very reminiscent of the method of Sudoku.) Having found such unoccupied regions, they dream up a "thought-experiment" designed to show that this region of logical space is "conceivable." A lot of intuitve philosophizing in "philosophical psychology" seems to fit this bill. Large conclusions about determinism and indeterminism and free will are arrived at by the construction of bizarre hypotheticals.
My claim is that the disciplined use of intuition is philosophically legitimate. But intuition can be overused. My message for the day: Surrealism yes, Sudoku no.
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