The besetting difficulty of the intuitionist
Deriving an is from an ought.
By "intuitionist," I mean someone who habitually claims to derive certain knowledge from data that are, objectively, insufficient to supply that knowledge. (And I call it "intuition" to emphasize how little it has to do with reasoning.)
Once you start on the intuitionist road, your mind begins to fill up with things you know that aren't so. False intuitions combine to derive -- in valid but unsound ways -- further false intuitions, and that's where you get into trouble.
If P implies Q, and P, then Q. If P is a false intuition, the intuitionist may see that Q ought to be true, and therefore assert that Q is true, even in the face of empirical proof that Q is not true.
Obviously, that can happen whenever someone holds as certain a false proposition. But the intuitionist is particularly susceptible to this, for two reasons: He is more likely to hold as certain a good number of false intuitions, and he lacks the habit of reviewing the validity of his conclusions.