[Lingtyp] A universal related to the traditional square of opposition

[Omri Mayraz]

Dear Colleagues,

I am working on a project related to the traditional square of opposition
(see entry <https://plato.stanford.edu/entries/square/#ModRevSqu> in the
Stanford Encyclopedia of Philosophy), in which I propose a cross-linguistic
generalization which I believe to be an absolute language universal. I was
wondering whether anyone is aware of potential counterexamples.

The traditional square of opposition represents the logical relations
between four logical forms:

A: All men are mortal.
I: Some men are mortal.
E: No men are mortal.
O: Not all men are mortal.

Larry Horn (1972) proposes a generalization regarding the lexicalization of
logical words, which appears to be an absolute universal (1). For example,
English has a root for 'all' (A), 'some' (I), and 'no' (E), but it
expresses the O form with a complex expression: 'not'+'all'.

(1) No language has a root with the meaning of 'not all' (the O form).

In my study, I propose a related universal:

(2) No language expresses the O form with zero-marking of quantificational
force.

In other words, the O form may only be expressed with an overt quantifier,
as in (3), and never as (4), where there is no overt quantifier.
Consequently, (4) is uniformly interpreted as E.

(3) Not all men are mortal.
(4) Men are not mortal.

A related question is whether in all languages the A and E forms can be
expressed with zero-marking of quantificational force, as in (5-6). Notice
that (5-6) are more likely to tolerate exceptions relative to the
overtly-marked forms, but their meanings are nonetheless similar.

(5) Men are mortal. (≈All men are mortal)
(6) Men are not mortal. (≈No men are mortal)



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