Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The problem: If a man has a full head of hair, removing one hair will not make him bald. Therefore the act of removing one hair cannot make a man bald.

The Answer:
This is a well-known paradox by Eubulides, a greek philosopher.
However the standard answer is incorrect. The definition of bald is “possessing no hair on the scalp”. If hair still remains, the individual is balding – that is, in the process of going bald. Therefore if there is no more hair to remove, the individual is bald.

This type of problem is the sort of thing programmers have to solve all the time, and if it was a true paradox then most coding would be impossible. Viewed programmatically, the paradox fails very easily:

$h = 100,000; //total amount of hair on head
$bald = false; //person is not bald
for (h, h=0, h–) {
   //remove one hair at a time until none remain.
If h ==0 {
bald = true;// person is now bald.
}
}

 

You could even take this a stage further. “Balding” is described as in the process of going bald – having lost the majority of hair. Majority is defined as more than 50% – so…

$h = 100,000; //total amount of hair on head
$total-hair = //original amount of hair on head
$status = “not bald”; //person is not bald
for (h, h=0, h–) {
  //removes one hair at a time until none remain.
If (h ==0) {
$status = “bald”;// person is now bald.
}
elseif (h<=( ($total-hair/2)-1) ){
$status = “balding”; //person is balding
}
}

Ignoring my rather pedantic programming digression, the correct answer is simple.

When no further hair remains to be removed, the individual is bald.