A partial index of discussion notes is in http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html
I have always thought that this merely showed Wittgenstein's inability to think at an appropriate level of abstraction, although he was outstandingly good at producing examples to challenge over-simple philosophical theories. When he proposed his own alternatives he was not so good. I think he recognized this and that is why he tried to claim that the job of philosophy is not to solve problems by producing new theories, but to dissolve them by removing the temptation to treat them as hard or interesting problems -- which he compared with "showing the fly the way out of the fly-bottle" (a kind of insect trap), in PI 309. (Or something like that.)
Gilbert Ryle also recognized the difficulty in saying what is common to instances of a complex concept, e.g. "thinking", "being angry", "attending" and suggested that they should be described as being "polymorphous" a rather vague notion possibly suggested by the fact that some physical substances can take different visible forms despite having a common underlying structure (e.g. carbon as graphite and as diamond). But as far as I know he never made that notion very precise. However, I suspect he partly understood something very important that was later re-discovered and made far more precise in the second half of the twentieth century by mathematical logicians, programmers and computer scientists, building, wittingly or unwittingly, on Frege's work in the previous century on generalising the concept of a mathematical function to include higher order functions, and work by Church, Kleene and others, developing higher order logics and the Lambda Calculus, and Typed versions of Lambda Calculus.
Leaving aside what Ryle may or may not have intended I think the key idea that is missed by the family resemblance theory is that things that do not have any shared properties (such as height, colour, number of components, habitat, visible behaviour) may nevertheless have something more abstract in common which can be described in terms of a common schematic description, which contains gaps (in the sense in which function symbols contain gaps according to Frege), that when the common description is suitably instantiated (by plugging the gaps in various ways) produces different instances.
For example, consider what might be meant by a biologist describing an animal as an "efficient forager". This label could be applied to animals of very different types (living in water, on land, in mud, in air, in the bark of some plant, etc.) with very different physical forms and very different physical movements. What they have in common that justifies calling the succesful foragers might be that they form instantiations of O in something like the following abstract description:
O is a living organism and O consumes physical matter of type F (Food), which O obtains by performing actions A which bring O to instances of F using fairly direct routes and O needs to consume at least quantity Q of F per time period T, and the actions A have the effect that O regularly consumes at least Q of F in each period T.In some real cases this would have to be made more complex to allow for O requiring different types of food.
The different organisms that satisfy this description (when instanting O) may require very different types of F, and perform very different actions A, and need very different quantities Q per period T. So the appearances, sizes, habitats, and visible behaviours of an earth-worm, an insect, a fish that feeds on algae and a grazing mammal may all be very different, and yet they all satisfy the above schematic description with all the variables except O existentially quantified.
This sort of schematic specification is common-place in object-oriented programming languages that allow definitions of "multi-methods" that are applicable to objects of very different types. The label "parametric polymorphism" is often applied to method specifications where newly defined concepts have parameters, and what exactly the method does depends, in a systematic way, on the combination of parameters supplied.
I suspect there are far more concepts used in ordinary human languages that have this kind of polymorphism than has generally been acknowledged and that in many cases the parameters that specify the interpretation are not supplied explicitly in a linguistic form, but have to be inferred from context. This can lead to mistaken theories about the vaguess or indeterminacy of the concepts, and also to false theories of meaning such as Wittgenstein's family resemblance theory.
This point is discussed in relation to spatial prepositions in
http://www.cs.bham.ac.uk/research/projects/cosy/papers/#dp0605and to sorites paradoxes in
Spatial prepositions as higher order functions: And implications of Grice's theory for evolution of language.
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/sorites.html
Sorites -- A New Analysis Based on Context
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham