Choice & Inference

Gärdenfors’s work on conceptual spaces hinges on a principle for natural concepts, which he has dubbed Criterion P in (2004, Minds and Matter), among other places.

Criterion P: A natural concept is a convex region of conceptual space.

He mentions a conjecture from Berlin and Kay (1969) that, although different languages divide the color circle in different ways, all divisions seem to divide basic color terms into convex regions. So, if point x in the color wheel is counted as red and point y is counted as red, then all points of the color wheel on the line segment between x and y are counted as red, too. On the other hand, the term ‘grue’, Gärdenfors argues, is artificial because it does not correspond to a convex region in the conceptual space of color. (Indeed, it fails to be so by design.) Thus, ‘grue’ does not denote a natural concept by Criterion P. Thus, the projectability of ‘blue’ and ‘green’ but non-projectability of ‘grue’ and ‘bleen’, on Gärdenfors proposal, can be explained by the non-logical Criterion P for natural concepts.

Questions: (1) What is the status of Berlin and Kay’s conjecture? Is convexity an accepted feature of basic color concepts? (2) Assuming that theirs is a reasonable account of color concepts, do you think Gärdenfors’s strategy to extend this account to natural concepts in general is persuasive?