Kuhn on Wittgenstein

“What need we know, Wittgenstein asked, in order that we apply terms like ‘chair’, or ’leaf’, or ‘game’ unequivocally and without provoking argument?

That question is very old and has generally been answered by saying that we must know, consciously or intuitively, what a chair, or a leaf, or game is. We must, that is, grasp some set of attributes that all games and only games have in common. Wittgenstein, however, concluded that, given the way we use language and the sort of world to which we apply it, there need be no such set of characteristics. Though a discussion of some of the attributes shared by a number of games or chairs or leaves often helps us learn how to employ the corresponding term, there is no set of characteristics that is simultaneously applicable to all members of the class and to them alone. Instead, confronted with a previously unobserved activity, we apply the term ‘game’ because what we are seeing bears a close “family resemblance” to a number of the activities that we have previously learned to call by that name. For Wittgenstein, in short, games, and chairs, and leaves are natural families, each constituted by a network of overlapping and crisscross resemblances. The existence of such a network sufficiently accounts for our success in identifying the corresponding object or activity.”

Notice how Wittgenstein’s definition of meaning is fundamentally a set.

Note also that by his definition there is no single sufficient set, only many, mutually contradictory sets.

If you’re interested in exploring such “set theoretic” ideas about meaning I strongly recommend the whole of Kuhn’s book. Of course I knew Kuhn was famous for proposing scientific progress/knowledge was discontinuous (and partially subjective), but I never realized how much he had to say about the nature of knowledge itself. In fact he defines knowledge fundamentally as sets of examples. This equivalence between sets of examples, the original sense of “paradigm”, and knowledge, is where his famous use of the word “paradigm” in the sense of “word view” or “scientific theory” comes from.

Note also that (I would argue) attempts to base mathematics in set theory 100 or so years ago were not unrelated to an interpretation of “meaning” in terms of sets.

From a discussion entitled “About enwik and AI” on comp.compression, Jan. 2007 (http://newsgroups.derkeiler.com/Archive/Comp/comp.compression/2007-01/msg00018.html.)