Archive for January, 2012

Aymara, trivalence, competing satisfaction and modality

January 6, 2012

In his monograph on the trivalent logic of Aymara, Ivan Guzman de Rojas sets out to show that a trivalent logic can reach conclusions unavailable to bivalent logic. I want to tease out the import and accuracy of this extraordinary claim, and try to understand its significance for modal logic.

Consider two circumstances: p) there’s smoke; q) there’s fire.



language and logic, English and Aymara

January 5, 2012

Following up on the last post —

If English were incapable of expressing ternary logic, then Aymara could not be described in English. It does not seem too contentious, then, to conclude that any natural language, like English, Spanish (Rojas’ original) or Aymara, can express any known logic. The means will no doubt differ: analytic languages would express notions of uncertainty with word-morphemes (like “might”); agglutinative and inflectional languages should express them with affixal morphemes.

The notions seem to drive the languages, not the other way around. (more…)


January 4, 2012

I see that Wikipedia’s article on ternary logic references Aymara “a Bolivian language famous for using ternary rather than binary logic.” Aside from the vaunted adjective “famous,” I am skeptical of the claim that Aymara uses a ternary logic rather than binary, skeptical also of the presupposition that natural languages use a particular logic rather than another logic, and skeptical as well of the implicature that other languages use only binary logic, infamously or otherwise.

Much of the excitement over Aymara derives from a monograph written  in the 1980’s by an engineer and machine translation pioneer, Ivan Guzman de Rojas, who observed that Aymara indicated in its inflections the degree of certitude of its respective assertions. He takes these as logical operators, just as “not” can be taken in English as a negation operator: in English, “not” takes a true statement into a false one, and a false one into a true one. E.g.,

snow is white =>True;  snow is not white =>False

snow is green =>False; snow is not green =>True

Aymara, however, also uses an inflection that takes a true statement into a neither-true-nor-false statement. This shows, he claims, that Aymara uses a third truth value, neither-true-nor-false, which is used for uncertainty.

He says, further, that the ternary logic allows the Aymara people to derive logical conclusions that are not available in binary logic, and that the Aymara people think differently from people who are limited to binary logic.

It may already have occurred to the reader that English does have exactly such an operator, “might”:

snow will fall;  snow will not fall; snow might fall

that is, “might” takes an assertion or its negation into an uncertainty.

Does this mean that English has a third truth value? Well, yes and no. (more…)