Logical Relativism: Logic, Grammar, and Arithmetic in Cultural Comparison

In this essay, we question the plausibility of logical relativism, which we take to be the claim that people in other cultures may follow, believe in, or subscribe to a different form of logic from “our” Western logic.¹ In other words, logical relativism argues that classical logic (including the law of noncontradiction [LNC] and the law of the excluded middle [LEM]), rather than being universal, may only be locally true—that is, applicable only within a culture’s limits. The question whether every culture accepts the LEM is part of long-running arguments about the rationality of different cultures. Since it is typically assumed that “we” (Westerners) accept the LEM, the existence of a culture that did not subscribe to the LEM would, it has been argued, demonstrate either: 1) that that culture falls short of the universal standard of rationality (since it does not reason according to classical logic); or 2) that the culture is nonetheless rational, but that the laws of classical logic are not a universal standard of rationality.

Logical relativism is often seen as being supported or indeed inspired by comparative studies that demonstrate that other cultures do not conform to classical logic. For example, the Azande² are sometimes viewed as eschewing the LEM, as a result of the following beliefs: The Azande believe that witchcraft is hereditary. Since clan members are related, and this is a small community, this would seem to entail that as soon as one clan member is identified as a witch, all clan members are thereby witches. However, the Azande also believe that a clan may have members that are, and members that are not, witches. Taken together, these beliefs seem to implicate the Azande in a contradiction. The question of logical relativism thus seems to be an empirical one, to be demonstrated (or possibly refuted) by anthropological studies of how other cultures “think”:

Relativistic views about logic have surfaced in the works of social anthropologists, cognitive scientists, and philosophers. Reports by anthropologists about the thinking habits of remote peoples have led to the suggestion that rules of logic may have only a local rather than universal authority.³

Can one without further ado simply assume that all the people the anthropologists have canvassed subscribe to the LEM? If one could, that would greatly strengthen the case for the universality of logical principles. The problem is that the Azande, for example, have been taken to be a people who rejected it. . . . it becomes an empirical question which available set of logical principles best accords with a practice of a particular people. A particular set of logical rules then becomes a model for that specific style of reasoning.⁴

In this essay, we question the sense in which it is “an empirical question which available set of logical principles best accords with a practice of a particular people.” We neither argue that logical principles are universal, nor that they are relative; rather, we investigate the role that logical principles are given in accounts of cultural practices (both “at home” and “away”), and we question whether there is much sense in trying to characterize the way a whole culture “thinks” in terms of formal logical systems.

Logical relativism is often justified as a reaction against an earlier Western cultural imperialism according to which other cultures were viewed as less rational than Western cultures.⁵ Against this suppose imperialism of Western rationality, two slightly different forms of logical relativism emerged, one arguing for an “alternative logic” in other cultures, the other for a “symmetric treatment” of the examples.

With respect to the Azande, some people have argued that although there may be a contradiction in Zande beliefs, this contradiction only appears if we investigate their beliefs according to classical logic. If we evaluate these beliefs according to an alternative logic, then the contradiction disappears: “Primitive magico-religious thought incorporates an alternative logic to our ‘standard’ one within the terms of which the apparent inconsistencies are not inconsistencies at all.”⁶ According to this argument, the Azande are as logical as...