Neologisms, Paleologisms, and Grelling's Paradox

'Neologism' is not a new word, but an old word. Hence, 'neologism' is not a neologism. 'Paleologism' is not a word at all; or at least it is not listed in the Oxford English Dictionary. But it ought to be a word, so I hereby introduce it. Who is going to stop me? Having read it and understood it, you have willy-nilly validated its introduction and are complicit with me.

Now that we have 'paleologism' on the table, and an unvast conspiracy going, we are in a position to see that 'neologism' is a paleologism, while 'paleologism' is a neologism. Since the neologism/paleologism classification is both exclusive (every word is either one or the other )and exhaustive (no word is neither), it follows that 'neologism' is not a neologism, and 'paleologism' is not a paleologism.

Such words are called heterological: they are not instances of the properties they express. 'Useless' and 'monosyllabic' are other examples of  heterological expressions in that 'useless' is not useless and 'monosyllabic' is not monosyllabic. A term that is not heterological is called autological. Examples include 'short' and 'polysyllabic.'  'Short' is short and 'polysyllabic' is polysyllabic. Autological terms are instances of the properties they express.

Now ask yourself this question: Is 'heterological' heterological? Given that the heterological/autological classification is exhaustive, 'heterological' must be either heterological or else autological. Now if the former, then 'heterological' is not an instance of the property it expresses, namely, the property of not being an instance of the property it expresses. But this implies that 'heterological' is autological. On the other hand, if 'heterological' is autological, then it is an instance of the property it expresses, namely the property of not being an instance of the property it expresses. But this implies that 'heterological' is heterological.

Therefore, 'heterological' is heterological if and only if it is not. This contradiction is known in the trade as Grelling's Paradox. It is named after Kurt Grelling, who presented it in 1908.