- The Enculturation of Logical Practice
[A] reason against epistemological over-confidence is the knowledge that other people hold, with as much confidence, beliefs incompatible with one’s own. And this motive operates in the sphere of logic, too; the very plurality of logical systems speaks against our possession of any infallible capacity to ascertain the truths of logic.S. Haack 1
Reason (is) domesticated to its unproblematic work within distinctive culturally determinated domains of discourse.K. Nielsen 2
One of the more intractable questions in theoretical anthropology is whether the empirical thesis of relativism—that there is a diversity of world views—can be carried over into the theoretical thesis of relativism—that criteria of rationality, logic, and truth are local. There is strong resistance, especially among philosophers, against an answer in the affirmative. They point to the universality of logic and criteria of validity. 3 In challenging their position, one therefore faces [End Page 381] the huge task of arguing that criteria of logic are not transcendental but emergent, i.e., that they emerge from a particular embodiment of reasoning. This is the task that I have set myself. Fulfilling it forced me to look at disciplines like anthropology, philosophy of science, history of mathematics, and philosophy of logic, and to critically assess their built-in assumptions about the foundations of logic.
Two angles can be distinguished in the general discussion of the universality of logic. The first is directed at the question of the applicability of the standard Western logical canon to non-standard modes of thought. Some aspects of Azande and Nuer thinking have featured heavily in this debate. 4 In a sense, this angle is basically empirical. [End Page 382] The second angle, however, is more theoretical. The starting point is the doctrine of the psychological unity of humankind: people’s psychological make-up is everywhere the same. The laws of logic—taken as codifications of the laws of thought—that are applied to the nature of human thinking are regarded as fixed and archetypal, providing an Archimedean fulcrum in the realm of thought. The laws of logic, in other words, are taken as bridgehead principles constructed out of the materials responsible for the “central core of human thinking.” 5 The two issues are not independent of one another. The Western codification of the laws of logic is automatically taken as the right one and hence as universally valid. Arguments for that case are, however, hard to come by.
The argument of this paper is aimed at undermining the integrity of both of these interrelated defense lines. Central to my argument is the assumption that any kind of thinking is a practice of manipulation and interaction with external resources. Logical thinking is no exception; it is the manipulation of and interaction with external conceptual resources 6 —external because the meaning of concepts is, after all, a public affair. Whereas Bourdieu argues that “[p]ractice has a logic,” 7 my argument hinges on the reverse: logic is a practice. Bourdieu adds that the logic of practice is “not that of a logician,” something that also applies to my practice of logic in the sense that non-standard logic has to be used to account for the practice. [End Page 383]
This paper is organized as follows. I start by developing the notion of style of practice as a device to handle and assess knowledge claims. Next I spell out the arguments against the local embeddedness of logical inferences, followed by my arguments in its favor. In construing logic as the science of inference, the following claims, in particular, are defended: a) the paradox of material implication points to the impropriety of inference; b) this suggests such a cleavage between formal logic and informal argument that the former is of no help in elucidating the latter; c) holding on to the idea that a formal system should aspire to represent deductive inferences means providing a better and more useful theory of implication, i.e., developing a non-standard logic; d) this undermines much of the debate on Western logic versus Azande logic conceived in terms of standard logic versus non-standard logic—standard logic...