When two people who are having a conversation do not understand each other, the usual complaint is that they ."are not speaking the same language." This reference to "a common language" generally means that if people are to understand each other, the same vocabulary is essential. However, this reference to a "common language" has another connotation, which is often overlooked: mutual comprehension also requires using the same system of logic, since, despite a widespread misconception, there is more than one.
In any language, the meaning of the words is determined by semantics; its logic, however, is embedded in its syntax. Therefore, "the same language" involves using identical semantics and identical syntax.
Many languages are spoken throughout the Western world. However, understanding among people is possible because all of these languages are based on the same semantic and syntactic categories; one language may differ from another in terms of : linguistic structure; however, all of them are isomorphic. This semantic and syntactic isomorphism makes possible translation, i.e., to reproduce in a given language the image of what has been said in a different one. Thus, the goal of "a common language" is achieved.
These remarks also apply to the relationship between computers and human beings. Let 's consider, for example, a computer program involving the following instructions: read the client's file; identify those who have not paid; send a type-A notice if payment is less than a month overdue; in other cases, send a type-B notice; however, if the client belongs to category 1, do not send any collection notice." These instructions can be written in different computer languages, provided their syntax can handle the logical schema involved in the instructions.
For the computer to execute this program, the circuits in the computer's central memory must be designed to handle the logical functions involved in the syntax of that particular programming language. Without these electronic circuits, the computer would not be able to handle such a program, and so its intelligence module would have to be expanded, or simply replaced.
However, if the logical capacity of the computer is underutilized because the syntax used by the programmer is inadequate, it would be advisable to replace that engineer with another who knows a more advanced language, which can give lnstructions adequate to the intelligence level of the equipment.
There is a centuries-old misunderstanding between the different social groups who live in the territories where the Qoya cultute flourished, especially in regions of present-day Peru and Bolivia. This misunderstanding predates the Spanish conquest, and still exists today because people do not speak the same language nor use the same system of logic.
If this really is the cause of the misunderstanding, one may well ask whose "logical circuits" must be reprogrammed so that all members of our society can fully understand each other.
My research on Aymara logic would appear to suggest some guidelines which could contribute to solving this centuries-old misunderstanding within our society, in which two essentially different systems of logic function at loggerheads.
Applying methods of mathematical logic, I have attempt to determine whether Spanish and Aymara-speaking people make inferences in different ways, and, if so, to identify the differences, the areas of misunderstanding, and the maximum logical understanding that can be achieved.
The idea that there is something special about Aymara which sets it apart from other languages is not new. Both the early scholars and modern linguists who have studied the Qoya language have been fascinated by its highly logical structure. Although they have not, of course, used the powerful methods of mathematics to test their ideas, they have provided very interesting and revealing analyses of key aspects essential to understand the syntax of this language.
These linguistic works are invaluable material which can serve as a starting point for multidisciplinary research, Computer science may contribute not only to an understanding of the language, but also to revitalizing this millenary culture and adapting it to today's modern world.
To achieve this ambitious goal, Aymara-speaking people must have access to world literature. This requires findin. a solution to all the technical problems involved in translating into Aymara. This brings us to the key issues: the problems of misunderstanding, and the psychological effects subsequent to the communication.