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/ms....)