Helen Verran reveals that in contrast to the one-to-many model found in Western number systems, Yoruba thinking operates by figuring things as wholes and their parts. Quantity is not absolute but always relational. Certainty derives not from abstract logic, but from cultural practice and association

Helen Verran, Science and an African Logic, University Of Chicago Press, 2001.
read it at Google Books


Does 2 + 2 = 4? Ask almost anyone and the answer will be an unequivocal yes. A basic equation such as this seems the very definition of certainty, but how is this so?
In this captivating book, Helen Verran addresses precisely that question by looking at how science, mathematics, and logic come to life in Yoruba primary schools. Drawing on her experience as a teacher in Nigeria, Verran describes how she went from the radical conclusion that logic and math are culturally relative, to determining what Westerners find so disconcerting about Yoruba logic and to a new understanding of all generalizing logic. She reveals that in contrast to the one-to-many model found in Western number systems, Yoruba thinking operates by figuring things as wholes and their parts. Quantity is not absolute but always relational. Certainty derives not from abstract logic, but from cultural practice and association.
A powerful story of how one woman's investigation into an everyday African situation led to extraordinary conclusions about the nature of numbers, generalization, and certainty, this book will be a signal contribution to philosophy, anthropology of science, and education.


Anthropology as Ontology is Comparison as Ontology by Helen Verran:

A claim that emerges about at about the halfway mark of Holbraad, Pedersen, and Viveiros de Castro’s (2013) paper provides my beginning:
“The anthropology of ontology is anthropology as ontology; not the comparison of ontologies, but comparison as ontology.”
I complement the claim that “anthropology as ontology . . . is comparison as ontology” by insisting that the entities we deal with in doing anthropology are themselves comparisons. The exemplar I have in mind here is numbers, like those multiple numbers I met in Nigerian classrooms. Numbers are formalized comparisons, solidified clots of relations; all the more solid for being formalisms. As things, numbers are familiar comparison participants in many collectives
My claim, that the entities we deal with and through in anthropology are comparisons, can lead us to recognize ontic tensions, which might become an ontological politics. However, that passage from recognizing entities as comparisons participant in ontic tensions, to recognizing the possibility of ontological politics, differs from the insight that anthropology as ontology is comparison as ontology. The latter acknowledgement amounts to recognizing that anthropology is a political ontology, one of several acting in any collective in which ethnography is pursued. It is within the force fields of those political ontologies—including anthropology’s, that the ontic tensions of a collective might (or might not) emerge as ontological politics.
That emergence of an ontological politics in a collective in which an ethnographer is participant can be felt as a disconcertment. I see this experience as a form of epistemic disconcertment, when negotiations around what is known and how it is known become evident as fluid. I felt this in Nigerian classrooms as I describe in my beginning stories in Science and an African Logic (2001). I met new numbers, brought to life by teachers who we might think of as ontic innovators. The new numbers that these teachers brought to life were participants in those classrooms, along with the “official number” of the primary school curriculum. Classroom routines were designed to ensure the dominance of that number but it did not stop Yoruba number entering the classroom. Many of the children dealt with and through Yoruba number in their out-of-school lives as young market vendors, and it still had influence, and the capacity to interrupt the smooth workings of the Western number of modern administration.
In the re-performance of those classrooms in the writing of an ontologically-focused ethnography as an analytic text, yet another number came to life as participant comparison. This number was, like many of those the teachers brought to life in their experimenting, both and neither the number of the official primary school curriculum and Yoruba market number. But the ethnographer’s number differed from those of the experimenting teachers in having its metaphysical commitment made explicit. That making explicit, albeit in re-performance, is an expression of a political ontology. While perhaps a benign political ontology, which by making its metaphysical commitments explicit announces itself as proceeding in good faith, it is nevertheless a political ontology, one that takes its place in the tense political landscapes of those classrooms. It abuts and abrades the political ontology of the numbers promoted by the modernizing school curriculum, and the resisting and sometimes subverting political ontology that is forged and sanctioned in the Ooni’s palace at the center of town, and a perhaps inchoate political ontology enacted by the teachers who must manage their large classes of restless children with few resources.
Recognizing contesting political ontologies, including that which enters with ethnography, makes clear that what was happening with numbers there in those Nigerian classrooms. I experienced disconcertment as immanent ontic tensions clotted in becoming as an ontological politics within the force fields of mutually interrupting political ontologies. And that tension zone is, it seems to me, exactly where an ontologically-sensitive ethnography is located and where it should stay in its re-performance as analytic text.
Staying in that place of tension where ontic tensions clot (or not) as ontological politics within the force fields of political ontologies, the ethnographer has a chance of discriminating divergences and convergences: generative, or exploitative, or unfruitful doings of difference. So here we find the possibility of judgment, of critique. Meta-critique was rightly written out of ethnography, but ethnography located in that imagined zone of ontological tension can and should engage a form of infra-critique, gesturing at possible generative tensions, while explicitly refusing others.

References

Holbraad, Martin, Morten Axel Pedersen, and Eduardo Viveiros de Castro. 2013. “The Politics of Ontology: Anthropological Positions.” Position paper for roundtable discussion. American Anthropological Association annual meeting, Chicago.

Verran, Helen. 2001. Science and an African Logic. Chicago: University of Chicago Press.