Counting Languages in Dialect Continua Using the Criterion of Mutual Intelligibility

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. In terms of graphs (as in discrete mathematics), the method is even easier understood as: applying graph-coloring 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, as well as remove any fears that these concepts should lead to inconsistencies. The presentation requires only a minimal acquaintance with sets, combinatorics and graphs.