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A usual latin phrase is horror vacui, which in English can be rendered as fear of emptiness.

Question: what do you consider a correct Latin translation of the English fear of equality?

The question is mostly about the correct declension of a Latin word for equality of being identical.

I would propose:

horror aequalitatis

Do you agree with that?

Background to the question: here, equality is to be understood as in mathematics, abstractly. There are parts of mathematics where, with good reason, one tries to avoid speaking of objects being actually equal (whatever that means—in fact, the reason for avoiding the concept is that sometimes it is actually highly problematic what equality means), and rather develop useful precise notions of similarity.

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    Welcome to the site! I made some slight edits to your question (feel free to roll back or re-edit) and tried to provide an answer. I'm glad to see mathematically oriented questions here; in fact, you could consider adding the tag mathematics to the question. – Joonas Ilmavirta Jun 23 '17 at 20:02
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Your translation horror aequalitatis is great! When something is feared, the something is in genitive — an objective genitive. Therefore aequalitatis is correctly declined.

The hardest question is choosing the best translation for "equality". I support aequalitas, which also happens to be (rather obviously) etymologically connected to the English word. Take a look at the underlying adjective aequalis and that of aequalitas itself in L&S to see what they meant in antiquity. It fits your purpose well.

In addition, Gauss uses related words in similar meanings. The linked text contains words like aequatio and (in)aequalis. Although aequalitas itself is not used, he would have certainly understood the word in the right sense.

Thirdly, my intuition as a Latinist and a mathematician says that aequalitas is just the right word for this kind of thing.

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In linguistics there is a term horror aequi, referring to a tendency to word sentences so as to avoid repeating the same grammatical structure consecutively or nearly consecutively.

This term was coined fairly recently, in 1909, and the study usually cited to explain it is "Cognitive complexity and horror aequi as factors determining the use of interrogative clause linkers in English" by Günter Rohdenberg, in Determinants of Grammatical Variation in English (2003), p. 205. An example from that article:

(1) She was at a loss to know what to do.

(2) She was at a loss to know what could be done.

The horror aequi principle says that speakers will tend to favor (2) because it avoids the unseemly repetition of to <verb> in (1).

It sounds like horror aequi was coined in imitation of horror vacui, but I haven't tracked down the original article yet to be sure.

Both vacui and aequi are genitive forms of an adjective. I understand horror vacui to mean most literally "dread of empty space". That is, the adjective is used substantively (as a noun), so it means "something empty". Horror aequi thus means "dread of things that are equal".

Someone with a better feeling for Latin will have to confirm this (maybe in a comment), but it sounds like Joonas's answer might fit your meaning more precisely even though it doesn't parallel horror vacui as closely, because you mean not a dread of things that are equal, but of the abstraction of equality—aequalitas rather than aequa.

By the way, when writing that last sentence, I chose "precisely" to avoid repeating "closely".

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    Illuminating answer, many thanks. Will accept the one of Joonas Ilmavirta, for technical reasons. In particular, the fact that horror aequi is used as a technical term in liguistics for this particular avoidance seems rather a reason not to use it for the abstract avoidance of equality, like you already pointed out. – guest Jun 24 '17 at 4:38

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