I recently had this problem as extra credit on one of my finals. Let's see whether /sci/ can figure it out.
In the English language, we can observe that some adjectives apply to themselves. For example, the word “short” is a fairly short word. We might 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?
Bonus points: if you know how Turing Machines work, how does this statement relate to Turing Machines?
In the English language, we can observe that some adjectives apply to themselves. For example, the word “short” is a fairly short word. We might 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?
Bonus points: if you know how Turing Machines work, how does this statement relate to Turing Machines?
