# How do you talk about set theory in Latin? Specifically, how do you say "set" as opposed to "union"?

Hodie in universitate (ego studeo scientiam computorum) docebamur de theoria unionum. Professor nobis explicabat, cur numerus cardinalis unionis unionum non semper sit summa (additio) cardinalum numerorum unionum: "Si hoc veritas esset, canis debet octo crura habere. Canis enim habet duo crura antica, duo crura posteriora, duo crura laeva, et duo crura dextera. Summa (additio) numerorum cardinalium earum unionum octo (quater bini) est, sed numerus cardinalis unionis earum unionum, sane, quattuor est.".

I was using the same word, "unio", for both the union and the set. That caused some people to not be able to understand my joke. So, how could I have done better? Which word should I use for "set" and which for "union"?

By "set" I mean a group of things with some common property. And by "union" I mean the operation on two sets that gives another set that contains all the elements that were contained in the first set or the second set or both.

• It would help your question if you edited it to include a strict definition of "set" and contrast it with the definition for "union" Commented Jul 5, 2023 at 0:20
• Latin Wikipedia uses theoria copiarum for 'set theory'. Commented Jul 5, 2023 at 4:11

## 1 Answer

I am an assistant professor of mathematics, and I am quite familiar with the issues of translating mathematical concepts between languages.

A main difficulty is that there are so many concepts of a set with additional endowed structure: set, group, space, ring, field, universe, collection, family, manifold, category, bundle, sheaf, scheme… Different languages come with different sets of available words to draw from, and some of the translations are surprising.

The key observation is that translation of such terms is not based on reason but on tradition. The mathematical communities of different regions have settled on their terminologies, and translations must adhere to those conventions.

Therefore, when it comes to Latin, the first question is whether there is an established term. Someone's translation on Wikipedia doesn't quite count as established, and mathematics isn't really published in Latin anymore so there is no natural force to produce established modern mathematical terminology in Latin.

If a concept is old enough to originate from the time when Latin was still in broad scientific use, then the Latin term used then is the way to go. But set theory as the foundation of mathematics is younger, so I would opt for the same solution I would use for any modern concept: Pick something that makes sense to you in that context and explain as necessary (maybe with a translation to a language with more established terminology) and treat it as an ad hoc translation. Nothing is official so don't worry about getting it officially correct.

It's also not unusual that a Latin term centuries old is inconvenient for modern scientific usage. I think Newton uses motus for momentum, and it gets confused with movement.

Finally, to answer your question: A comment suggested the term theoria copiarum as used on Wikipedia, and it makes sense for "set theory". With that, a "set" would be copia. Feel free to use it, but don't treat it as the one and only truth.

• Set theory was almost single-handedly invented by one man, Georg Cantor. He did write a few papers in Latin, but unfortunately none of them on set theory, it seems. Interestingly he vacillated on what to call sets in German, using the term Mannigfaltigkeit (varietas) for quite some time, but changing to Menge later. Copia seems like a pretty literal translation of Menge. Commented Jul 6, 2023 at 16:56
• @SebastianKoppehel Interestingly, the other word seems to have found another technical meaning in modern usage, one that I get to play with every day. Commented Jul 6, 2023 at 21:16
• I wonder who came up for the words for "set" in the various Romance languages. I know in Spanish it is "conjunto", which looks like it could be "back-ported" to Latin...? Not sure what the benefits would be if copia is a better map of Menge. Commented Jul 8, 2023 at 13:09
• @NicolasMiari The words in different Romance languages point to different Latin choices. In addition to those, German points to copia and Finnish points to grex and there are probably many other Latin translations suggested by the established term in various languages. My whole point here is that there is no good reason for preference among the various translation options. The translations between languages with established mathematical terminology appear quite illogical, so applying logic to Latin isn't useful. There is no official translation but there are many sound translations. Commented Jul 10, 2023 at 23:38