Are all family resemblance concepts such that no single feature is shared by all the things to which the concept applies?
Some of Wittgenstein's formulations, and explanations based upon them, would suggest an affirmative answer. But I think that a more general, useful notion of a family resemblance concept should not require this.
It should disqualify a concept for family resemblance status that some feature happens to be common to all the things that fall under the concept. It may be that this feature does not sufficiently characterise the things as falling under the concept. That is, just because you can give necessary conditions for the application of a concept, does not mean its application is not based on the kind of criss-crossing network of similarities that Wittgenstein has us imagine. This passage gets it right:
we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres. (PI §67)This makes it clear that there may still be a single fibre running through the thread. It's just that that alone isn't responsible for the strength of the thread.
Are all concepts which do not admit of non-trivial analysis in terms of necessary and sufficient conditions family resemblance concepts?
It seems to be a necessary condition on family resemblance concepts that they do not admit of non-trivial analysis in terms of necessary and sufficient conditions. But it doesn't seem to be a sufficient condition. That is, it seems that there are concepts which do not admit of this sort of analysis and yet are not what we would think of as family resemblance concepts. For example:
- Certain primitive, i.e. undefined, concepts in theoretical use are not family resemblance concepts. For example, the concept of a lever (insofar as it isn't defined).
- A concept that is undefined but very closely tied to experience, e.g. the concept of red.
- Concepts which by design only apply to one thing, such as the concept of God - or, for that matter, just your concept of some particular person you know. (The whole idea of 'individual concepts' is a bit neglected though, and may not strike the reader as being in good standing.)
These do not seem to count as family resemblance concepts, because while they do not admit of non-trivial airtight definitions, there does not seem to be the sort of heterogeneity among the things that they apply to that characterises family resemblance concepts as discussed by Wittgenstein.
This last category, however, invites another question...
Diachronic family resemblance concepts?
It would seem that the concept of a particular person can't be a family resemblance concept in the sense of many different things falling under it not because of a common feature but because of overlapping similarities, because at most one thing does fall under it. But if we consider the individual through time, we start to see the possibility for something like the family resemblance idea applying to the concept of a particular person.
Is 'family resemblance concept' a family resemblance concept?
I think there's potential for a negative answer. At least, it seems to me we can give a precisified version of the idea that is not itself a family resemblance concept. On the other hand, perhaps such a thing would fail to capture the idea in full.