Are there languages which use the negation of 'odd' to denote 'even'?

Question

This question is influenced by another one I found on the German SE, "Warum nennt man in Deutsch die Zahlen 0, 2, 4 … “gerade” Zahlen?". It asks "Why call Germans the numbers 0, 2, 2 "even".

The following languages have these pairs:

• German: gerade — ungerade;
• Italian: pari — dispari;
• Portuguese: par — Ímpar;
• Spanish: par — impar;
• Russian: чётное — нечётное.

Note that for all of them 'even' is expressed by the basic form and 'odd' is derived from that form.

Other languages like English use different words even and odd.

Edit:

I modified the question in reaction to the comments to reduce the number of possible results.

Are there languages where odd is expressed by the basic term and even is derived from that?

Answer 1

I think your question may reflect an instance of a much more general pattern. That is, suppose you find an expression X in a language, and another expression Y in that language, and you believe X and Y to stand in a "privileged" relation (two types elaborated below). It seems that, across languages, one is likely to find that X and Y occur as simplex (i.e., nondecomposable) lexical items asymmetrically: i.e., if Y occurs as a simplex lexical item in the language, so does X. But simplex X occurring in a language does not guarantee expression of simplex Y.

One concrete example to explain one notion of a "privileged" relation between two expressions is privileged antonymy. Consider the adjectives tall and short: we "feel" that these expressions are related in a way that makes the inferences in (1) and (2) valid, but not that in (3) (despite long on occasion meaning something very similar to tall):

1. Mary is taller than John |= John is shorter than Mary
2. Mary is shorter than John |= John is taller than Mary
3. Mary is longer than John !|= John is shorter than Mary (where !|= reads as "does not entail")

Given what was discussed in the first paragraph above, we thus expect a language to exist where there is no word for short, but that conveys such a meaning via negating the positive adjective, e.g. not tall. One never expects to find a language that does the reverse, e.g. where short occurs with not short, and expression of simplex tall fails to occur.

Describing strong versus weak meanings, Larry Horn in his 1972 dissertation gives nice examples using the dual modals must and may, and adjectives like (un)able and (im)possible, to observe that in general, it seems the "positive" or "stronger" of a dual occurs as an expression simpliciter, while the "negative" or "weaker" is likely to occur as a combination of the positive/stronger expression with a negative marker. Note that such a synthetic construction carries exactly the (logical) meaning of what the negative/weaker expression as a simplex lexical item would carry.

Horn has some speculations about why this asymmetric pattern may obtain, but it has not so far been explained in detail, and how far such phenomena extend throughout lexical semantics is (I think) unknown. Understanding that the patterns even/ odd and even/ not even exist cross-linguistically, as opposed to odd/ not odd, feels of the same flavor of the above spread of examples. It is unclear to me how one might cast the pair even/odd in terms of antonymy or strength, however.