Counting Languages in Dialect Continua Using the Criterion of Mutual Intelligibility*

Abstract

This paper shows how it is possible to count languages vs. dialects if, for every pair of varieties, we are given whether they are mutually intelligible or not. The method is to divide the varieties into a minimum number of internally mutually intelligible groups where each group counts as one language. Expressed in terms of graphs (as in discrete mathematics), the method is even easier understood as: applying graph-colouring to a graph over varieties with the intelligibility interrelationships as edges. Graph colouring is already mathematically well-understood and we can easily prove properties intuitively associated with the concepts language and dialect, and remove any fears that these concepts should lead to inconsistencies. The presentation requires only a minimal acquaintance with sets, combinatorics and graphs.

Notes

¹Of course I can think of examples where A and B are closely related and speakers of A tend to understand B but not the other way round. For the sake of an example take Jamaican Creole and Oxford English. But in most (all?) such cases this is because the A speakers have been exposed to B a lot more, and not purely because of their knowledge of A. I see no reason to differentiate this situation from that where A are B aren't closely related, and speakers of A know B as well, but not vice versa.

²See, however, Hockett (1958, pp. 321 – 330) for an embryo to the approach taken in this paper (whose views recollected by, for example, Heine & Köhler (1981, pp. 1 – 3). Note also that the matter is not discussed in the most recent encyclopaedia entry on dialect chains (Heap, 2006).

³Comrie affirms in a personal email (9 September 2005) that the quoted paragraph concerns only this particular definition, and the statements therein that may look as if they quantify also over other intuitive definitions based on the MI, should not be so interpreted.

⁴For readers not familiar with graphs, a graph can be thought of as a set of points (“vertices”) in a two-dimensional space and an arbitrary set of lines (“edges”) between pairs of points. More information can be found in any introductory book on discrete mathematics.

⁵In fact, it is S(n, 1) + S(n, 2) + … + S(n, n), where S denotes the Stirling numbers of the second kind. See, for example, Stanley (1997, p. 33) for more information.