We are all familiar with optical illusions. These are situations where your eyes misperceive the nature of some image or physical object.
For some time now psychologists and cognitive scientists have been discussing the reality of cognitive illusions. These are situations where people just don’t reason properly about some readily described situation. The Monty Hall problem is sometimes described as an example of such an illusion, which, indeed, is why I have been thinking about this recently.
Below the fold is an interesting example drawn from elemenatry logic. I found it in the book Inevitable Illusions by Massimo Piatteli-Palmarini.
We begin with a warm-up. Suppose I tell you that:
(1) All Ruritanians are rich; and (2) John is a Ruritanian.
What follows from this? Plainly, that John is rich. Agreed?
Now suppose I tell you that
(1) No fruit-picker is a sailor; and (2) All Ruritanians are fruit-pickers.
It follows that no Ruritanian is a sailor.
Very good. Now suppose I tell you that
(1) All politicians are thieves; and (2) No composer is a politician.
What, if anything, follows?