Jim,

I don't think I have misunderstood you.  Maybe we should go over the basics, to make sure there is no confusion.

W. takes the notion of family resemblance to indicate sets which are not bound together by a common element, but which are grouped according to various overlapping similarities.  Our notions of such sets are family resemblance concepts, which are employed in the absence of definitions which fully account for their use.  Yet, this does not discount the possibility of drawing definitions to suit our needs.  As far as interpreting W. goes, we seem to agree on this much, I think.

It is important to dwell for a moment on what constitutes the grouping of a family resemblance set.  The grouping is something we do.  It does not precede our use of the family resemblance concept.  Rather, it is constituted by our use of that concept.  Family resemblance sets are grouped by application of the concepts which indicate them.  The concepts determine the sets.  Thus, Wittgenstein regards games as a family resemblance set because the concept of games is a family resemblance concept. 

If you were to turn it around and claim that "game" is a family resemblance concept because the set of all games lacks a common, defining ingredient, it would mean the set of all games existed independently of our categorization, as if there were a definable set of all games and we just didn't know its boundaries.  Yet, as Wittgenstein says, our inability to give a definition for "game" is not a result of our ignorance.  It is a result of the fact that no definition has been given.  (See the quotes I offered in my last post.)  We cannot isolate the set of all games because no well-defined set exists as such.  But, as W. says, we can define such a set for a special purpose.  The application of the concept "game" is not realized in the world ahead of time.  We can thus disagree about how to apply the concept of "games" without being able to appeal to a rule to decide who is right--again, not out of ignorance, but because the concept is not completely circumscribed by rules.

You seem to take it as trivial that W. claims we can employ concepts in the absence of all-encompassing definitions.  Yet, if you will grant this trivial point, Wittgenstein's conclusion seems to follow.   That is, unless you suppose that our employment of concepts mysteriously matches with independent rules for their application, even if we do not know of them; in which case, if we do disagree on the application of a concept, there is a sense in which one of us is right, and the other is wrong, even though we have no means of knowing it.  Wittgenstein clearly does not embrace such a view, and neither do I.  There is no basis for regarding the set of all games apart from the rules we use to regard that set.  If our rules are not all-encompassing, then the set of games is a family resemblance set.

Your objection is that there really is a common feature for all games, and that we have such a feature in mind (somehow, perhaps unconsciously) when we talk about games.  However, this is highly unlikely, considering the way we learn how to use the term "games."  Even if there is a common feature, such a feature is not obviously what defines games as such.  It seems more likely that such a feature would be wholly coincidental, since we do not appeal to it and are so far unaware of it, despite our complex use of the term "game."  (Consider why it is that W. constantly reminds us to look at how our language is used and learned.)  Thus, W. predicts that no such feature is to be found.  But to overcome W., it is not enough to suggest a common feature shared by all games.  You would rather have to find a feature which defined games as such.  That is, you would have to show that the feature in question was operant in our conceptualization of games.  To undermine the notion of family resemblance (as it applies to games), you would have to show that our grouping together of games relies on some recognition of that shared feature.

Of course, even if you were to succeed in demonstrating that "game" is not a family resemblance concept (and I wish you luck on that quest, though I do not expect you will succeed), you will not have undermined the notion of family resemblance.  For the notion has many other applications, both in and apart from Wittgenstein's Investigations.

Regards,

Jason
Dec. 1, 2009