One morning a man shaved his full beard into a goatee beard and then sat down for breakfast. His wife took one look at her husband's new appearance and was not best pleased.
"That's not a proper beard!"
"I think you will find that it is!"
And breakfast continued in frosty silence. Then, in the interest of marital harmony, the man asked his wife "Before I shaved my beard, how many hairs were in it - about 10,000?", and she allowed that 10,000 was a reasonable estimate.
He went on "And you must agree that removing a single hair from a beard does not stop it being a beard - 9,999 hairs would still be a beard?", and again she agreed with her husband.
"And removing another hair?" he asked. "Yes, yes, still a beard!" she replied, seeing where the argument was going.
And then his coup de grâce "So if removing a single hair from a beard never makes it 'not a beard' then no matter how many I have shaved off I still have a beard".
But as she flounced from the room she responded "That's a ridiculous argument - at some point it stops being a beard, and your is not a beard".
So who is right?
This is an example of Sorites paradox. Clearly, after removing one hair from a beard it is still a beard, but equally clearly, removing every hair from a beard means you are clean shaven.
This manifests itself when something can be viewed as a number of discrete states and as something continuous.
So is a goatee a beard - we think that's a matter of taste :-)