I know people with an actual fear of olives. Is there a name in English for this phobia?
I have not been able to find anything in the usual websites.
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Phobias are productive in English, by which I mean that in English when one wants to describe a speciﬁc phobia, one simply identiﬁes the Ancient Greek word corresponding to the thing feared, adjusting as needed to serve as a preﬁx, and then sufﬁxes ‑phobia to it. This is an open set because people’s fears are unbounded. So all you need to do is ﬁgure out what the Greek word for olive is, and there you go.
According to the OED, there indeed exists a preﬁx variously transliterated elæo‑, elaeo‑, or eleo‑ which is derived from Greek ἕλαιο‑ν meaning olive oil, and can be used in technical words. Both English and Italian use it in this way, although English is more apt to use the Latin cognate oleo‑. Italian sometimes spells it elaio‑, but English does not appear to do that.
For Greeks and indeed other Mediterranean peoples, olive oil is the default oil they use for everything, and therefore the speciﬁc word gets used in a generic way. So just as a water-resistant substance is hydrophobic, an oil-resistant one is eleophobic (apparently the preferred spelling).
Normally then eleo‑ is a preﬁx meaning oil in general, but drawing on its origin in Greek there is no reason that one cannot also use this word for the specific thing if that’s the sense one wants. Of the three possible spelling variants, the last one is now the most common:
However, you might elect the second spelling to help folks think back to the more restricted sense instead of the general one.
The English words for the various "phobias" are simply constructed from Greek roots. This is done as-needed by the psychiatric community.
So the answer to any question of the form "Is there an English word for fear of X", where X has a word for it in Greek is "Yes". The word for it is "Yphobia", where Y is the Greek word for X.
In other words, asking any such question just devolves into asking "What is the Greek word for X?'