The barber paradox as bad technical writing

[kpreid]

In the unlikely event that you haven't heard of it already, the barber paradox is:

The barber [who is the only barber in town] shaves every man who does not shave himself. Does the barber shave himself?

Now, this can be considered just logically contradictory, or a gotcha (“the barber is a woman”). But how about considering it as a poorly-written specification? Under this principle I propose a correction:

The barber shaves every man who would not otherwise be shaved.

Comments

Re: Interpreting specifications

[kpreid.livejournal.com]

Still, there are two issues: First, what if Alice and Bob (neither the barber) shave each other? Your specification seems to allow the barber to shave neither then.

And I'm sure Alice and Bob are perfectly happy with that.

Second, in an ordinary logic we would expect phi&phi to be equivalent to phi, but repeating your specification seems to change its meaning or even turn it into a paradox.

One of my prior versions was “The barber shaves everyone who is as yet unshaven”, which is essentially another form of that but timeful (and therefore explicitly transitioning from one world state to another). In this case, there is no paradox from doubling; the barber's second round (or the second barber; it doesn't matter) just shaves nobody. But some may be shaved that would prefer to have shaved themselves later.

BTW, when commenting, you're writing in HTML-plus-line-breaks; that's why your "phi&phi" turned into "phiφ".