What is the minimum feature structure for a valid family resemblance definition?

Question

As part of a research project, I am trying to better understand Wittgenstein's family resemblance definitions. I have come across various interpretations of this idea and I want to check my understanding.

Let us suppose that a word TERM could be defined in terms of five different features j, k, l, m and n, but in a family resemblance way. So, as distinct from a necessary and sufficient definition where all of j, k, l, m and n are required features of any specimen of TERM, these features define TERM according to a family resemblance relationship. I have seen a few different interpretations of this idea:

A. A specimen of TERM may have any one of j, k, l, or m, or any combination thereof, but it must have at least one of these four features.

B. A specimen of TERM must have any two of j, k, l, or m, or any combination thereof, but it must have at least two of these four features.

C. A specimen of TERM must have any one of (j and k) or (j and l) or (j and m), or any combination thereof, but it must have at least one of these pairs.

D. A specimen of TERM must have feature j. It might also have any of features k, l, or m, or any combination thereof, but not necessarily; only j is required.

Here is my understanding: I think that B definitely qualifies as a valid family resemblance definition in the sense that Wittgenstein originally meant it. However, I am not sure about A, because if some specimen of TERM have only one feature from the list, then it is possible that they might bear little resemblance to other specimens. For example, there might be four specimens J, K, L and M, each of which has only one feature, j, k, l and m, respectively. In that case, in what sense is there any "resemblance" among them? But I am rather confused on this point.

Concerning C and D, I realize that they are functionally equivalent in describing the same relationships, but I list them distinctly because I have seen them expressed in these distinct formats. Regardless, neither of them matches my understanding of what Wittgenstein meant by a family resemblance definition.

Based on these different versions that I have seen, I have two related questions:

1. Which of the variations listed above is a valid family resemblance definition in the sense that Wittgenstein originally meant it?

2. Related to options A and B, is there a minimum number of features required for a family resemblance definition?

Answer 1

That's not quite how the concept of family resemblance works. Family resemblance points to the idea that categories and classes are often formed by a process of pairwise comparison that doesn't necessarily follow consistent rules. Vygotsky gave a clear example with young children, who will often group things oddly: say, picking up a big blue marble and putting it next to a big red marble, then picking up a small blue marble to put next to the big blue marble, then picking up a small green marble to put next to the small blue marble... So with an actual family we might find that:

• John looks like his brother Jake (because of general face shape)
• Jake looks like his cousin Jane (because of something in the eyes)
• Jane looks like her aunt June (because of the way the walk and wear their hair)
• June looks like her cousin Juan (because they have similar mouths)
• But Juan and John don't really look much like each other at all

Logicians and philosophers like to think in terms of analytical categories — categories that have clear and defined rules of inclusion/exclusion — but real-world categories rarely comply so nicely. I mean, if we think about the category 'car' it's fairly clear what we mean on a weak median, but the edges are fuzzy. Is a three-wheeled vehicle a car or a motorcycle? Where do we draw the line between a car and a truck or van?

Categorization is a non-linear feedback (hermeneutic) problem where we build and establish relationships progressively by cross-checking chains of family resemblances. For instance, we develop the concept of 'playground ball' by loosely comparing things that get used as playground balls, excluding things that seem to fall too far from the center without analytically defining what that center is. Breaking the process down into simple, concrete, operationalizable variables is an appealing idea, but not one that works as well as we might hope.