Among the native languages of America, one has lasted and flourished despite the passage of centuries. This language is Aymara, the language spoken by the Colla (1) in the Tiahuanaco empire. These people settled the shores of Lake Titicaca three thousand years ago and still inhabit Bolivia and Peru. Neither the Incas nor the Spaniards were able to wipe out the vigorous ancestral language of the native peoples of the Altiplano (High Plateau). Both Quechuan and Spanish were forcibly impossed upon the Aymara rather than accepted willingly. However, they were unable to wipe out the Aymara language. Despite 500 years of attempts to eliminate it, the language of the lupihakes ("shining beings") still thrives in the millenary Andes. Almost two million people speak it.

Is there something special about this language that sets it apart from the many languages spoken in the Americas? The answer is yes. The first person to realize this was the Roman Jesuit Ludovico Bertonio who published a grammar and a vocabulary of the Aymara language in the early 17th century. He found that this language is remarkably fertile and articulate; that its pronunciation is unusually regular, and that it is better able than Spanish or Latin to handle abstract concepts. The learned linguist was so surprised by all this that he concluded Aymara could not be a natural language, but have been created artificially. In the early 19th century similar views were raised even more strongly by a Bolivian scientist, Emeterio Villamil de Rada, in his book, "The Language of Adam". Unfortunately, the reast of his research manuscripts could not be found after his death.

A century later, the Aymara language fascinated numerous Peruvian, European, and Bolivian scholars (some of the latter speaking Aymara as their native language). Among the latest, bolivian researchers is Iva Guzmán who is neither a linguist nor a fluent speaker of Aymara. He is an engineer and mathematician specializing in computer science who became interested in Aymara by chance: as he was writing some articles on the teaching of mathematics to Bolivian children, he wondered if the thought patterns involved were identical for both Aymara- and Spanish- speaking people. He found that, in principle, they are not. This surprise finding made him a full time student of Aymara.

What was this difference identified by Guzmán? Basically, it comes down to this: the logic of Aymara is trivalent, and thus differs from the bivalent logic of Spanish. That is to say, the syntax of this indigenous language is based on a non-Aristotelian logic: it has not only the two values of tradicional Western logic, true or false, but three: true, false, uncertain. The logic of Spanish complies with the "principle of the excluded third"; so, inferences can only be drawn from premises which are necessarily true or false. In Aymara, logic is non-dichotomous; statements are constructed with suffixes instead of connecting words, and it is possible to arrive at conclusions from doubtful or barely plausible premisses. In other words, something can be "both perhaps true and perhaps not true"-- whether we, non-Aymara people, believe it or not --. Ambiguity has value, uncertainty matters. So, we are confronted with more than usual conflict between two different, but comparable vocabularies. We are dealing with two diametrically opposed ways of thinking which reflect cultures which are very distant from one another. Thus, the risk of failure to communicate is not just a problem of semantic differences; for example, for anyone who thinks in Aymara, "the past is in front and the future behind."

Guzmán is eager to communicate his result to all readers --not only to other specialists like himself. In this report on the research sponsored by the IDRC, the author explains in several ways the difference mentioned above: there are chapters densely packed with logical arguments and mathematical demonstration for linguists and speakers of Aymara; for the layman, there are simple enlightening examples, and even an a musing -- but effective -- instructional text: an imaginary dialogue between Aristotle and an Aymara "Indian".

What, we may ask, are the implications of distinction found by the bolivian researcher?

It was favourable implications for the aymara-speaking community from the point of view of social communication. Aymara-speaking people communicate among themselves using a very precise linguistic tool which is remarkably effective for conveying feelings, thougths, and actions. However, from the point of view of social contract between Aymara- and non-Aymara speaking populations within the same country, it is not advantageous for either group. The sharp contrast between the two types of reasonic sets up serious barriers to communication between the Colla culture and the one brought by the Spanish colonizers. Sometimes the gap is so wide that translation into Spanish is almost impossible, especially when dealing with modal statements, which require an acceptance of the value of incertitude, or "principle of symmetric doubt" typical of Aymara, This greatly augments the problems of communication, not only between these two language groups, but also between organizations promoting development -in fields such as education, agriculture, and health-- and the Aymara peasants who constitute 25% of the Bolivian population. In the other hand, the syntax of Aymara is algorithmic, which greatly facilitates translations from any other language into Aymara. (The reverse, however is not true). On this basis, a great many books printed in Spanish could be translated into Aymara using electronic equipament, which would expand the cultural horizons of the Aymara people. This would require a review of the approach to the literacy and a change in the techniques used in the Altiplano to teach the peasants to read and write. Nowever, this would not improve social communication (2) between Aymara- and non-Aymara speaking people -- a no less desirable goal.

Finally, as the reader will see, there is much food for the thought in Guzmán's study.

It is the pleasure of the international Development Research Centre (IDRC) to sponsor, and to publish in book form research such as this. At the same time, the IDRC is sponsoring a systematic description of radio programs in aboriginal languages, mainly Aymara. The work is being carried out by the Universidad Católica de Bolivia. These broadcasts started 20 years ago, and deserve special attention due to their spontaneity and liveliness. In both cases, our goal is to help science to better serve those groups, like the aboriginal peasants, who are hardest hit by the vicissitudes of underdevelopment.

The reader may or may not agree with the views presented by Guzmán in this book. They are, however, not easy to disregard, since no one can dany their potential impact upon social communication, rural education, linguistics, logic, mathematics, and even computer science and cultural anthropology. For that reason, the usefulness of this work trascends the borders of Bolivia and Peru.

Former IDRC
Regional Assistant Director
for Latin America and the Caribbean

(1)Translator's Note: The standard spelling in both Spanish and English is "Colla". Some authors have used "Kolla" (see bibliography); IGR uses "Qoya"; this latter spelling is used in the body of this work.

(2) The forerunner study in this field is Xavier Albo's "Languages, Schools and Radio stations in Bolivia". Oruro: Instituto de Investigación Cultural para Educación Popular. Publicaciones Especializadas en Educación Popular, Doc. No. 7-8, serie D, 1973. 29 p.


Social communication basically demands a multidisciplinary approach; specialized studies have no pratical meaning if they are not directly related to concomitant disciplines. Thus, this monograph draws upon the fields of linguistics, mathematics, and logic to analyze the problem involved in communicating with Aymara-speaking people. The author hopes readers will be patient enough to follow him in this persuit, attempting to integrate in their own minds the apparently unrelated material presented in this monograph.

Strictly speaking, the results of my research into Aymara logic are presented in Chapter 4. The central aspect of these findings is analyzed in section 4.7, where the "Aymara siwi" is discussed. Those readers well versed in logic and the Aymara language may proceed directly to this chapter. For the others, those aspects of Aymara and formal logic needed to follow my discussion on this subject have been presented in summary form.

My sicere thanks go to the International Development Research Center of Canada, and especially to Dr John E. Woolsten, without those encouraging support it would not have been possible to prepare this monograph.

I also wish to thank Ulla Wesner and her collaborators for their untiring and patient work in typing a text as difficult as this with a word processor while enduring the many corrections involved in elaborating the trivalent truth-tables and the ortography of the Aymara language.

Iván Guzmán de Rojas

Chapter index