Computing Theory Question

gistfile1.txt

The following is an interesting problem I found in the book Introduction to Computer Theory (2nd edition),
by Daniel Cohen, Wiley, 1997. See what you think ...

“ In the English language, we can observe that some adjectives apply to themselves. For example, the word
“short” is a fairly short word. We mighy say, “short” is short. Also, the adjective “polysyllabic” is indeed
polysyllabic. Some other possible adjectives of this type are “unfrequent”, “melodious”, “arcane”,
“unhyphenated”, “English”, “non-palindromic”, and “harmless”. Let us call all these adjectives that describe
themselves homothetic. Let us call all other adjectives (those that do not decribe themselves) heterothetic.
For example, the words “gymnastic”, “myopic”, and “recursive” are all heterothetic adjectives The word
“heterothetic” is an adjective, and therefore like all adjectives it is either homothetic or heterothetic.
Which is it?”