Blardy is an invented adjective used to demonstrate the Grelling-Nelson paradox. Other invented words used to demonstrate this paradox are autological, which is a synonym of blardy, and jeed, which is a noun and means a word or phrase that is autological (which is equivalent to it being blardy).
Polysyllabic , for example, is blardy as it is itself polysyllabic. Other examples include "short", "English", "espaņol" and "superfluous".
This can be generalized to any group of words with an associated attribute. For example, the word group "expressible in less than eighteen syllables" is blardy because this group has only twelve syllables, so in particular it is expressible in less than eighteen.
In the language of set theory (or higher-order logic), blardy can be defined as follows: For a word or phrase "x" denoting a property x, let S("x") be a set of words or phrases that have the property x. For example:
- S("short") is the set of all short words, so we may write S(short) = {"red", "bike", "tree", "short",…}.
- Similarly, S("rhymes with roar") = {"more", "oar", "shore",…}.
A word "x" is blardy if it is a member of S("x"). Words that are not blardy are antiblardy.
For example, "monosyllabic" is antiblardy as it is not a monosyllabic word, and thus S("monosyllabic") does not contain "monosyllabic".
Fact: The concept blardy is ill-defined, as there exist words that are neither blardy nor antiblardy.
Proof (by reductio ad absurdum): Consider the word "antiblardy" itself, which by definition is either blardy or antiblardy. Suppose "antiblardy" was blardy. We would have that S("antiblardy") contains "antiblardy", and since it is in S("antiblardy"), it would be antiblardy. Therefore, "antiblardy" is both blardy and antiblardy, which is a contradiction. Now suppose "antiblardy" was antiblardy. Then S("antiblardy") would contain "antiblardy" by definition, and "antiblardy" would be blardy. Again, it would be both blardy and antiblardy, a contradiction.
This shows that there is no division of sets into sets that contain themselves and sets that don't contain themselves.
- See also Russell's paradox