Family Resemblance - Formal Models

Formal Models

There are some simple models which can be derived from the text of §66-9. The most simple one, which fits Wittgenstein's exposition, seems to be the sorites type. It consists in a collection of items Item_1, Item_2, Item_3... described by features A, B, C, D, ...:

Item_1: A B C D
Item_2: B C D E
Item_3: C D E F
Item_4: D E F G
Item_5: E F G H
......... . . . .

In this example, which presents an indefinitely extended ordered family, resemblance is seen in shared features: each item shares three features with his neighbors e.g. Item_2 is like Item_1 in respects B, C, D, and like Item_3 in respects C, D, E. Obviously what we call 'resemblance' involves different aspects in each particular case. It is also seen to be of a different 'degree' and here it fades with 'distance': Item_1 and Item_5 have nothing in common.

Another simple model is described as:

Item_1: A B C
Item_2: B C D
Item_3: A C D
Item_4: A B D
It exhibits the presence of a constant degree of resemblance and the absence of a common feature without extending to infinity.

Wittgenstein rejects the disjunction of features or 'properties', i.e. the set {A,B,C,D,..}, as something shared by all items. He admits that a 'sharing' is common to all but deems that it is only verbal:

if someone wished to say: "There is something common to all these constructions – namely the disjunction of all their common properties" – I should reply: Now you are only playing with words. One might as well say: "Something runs through the whole thread – namely the continuous overlapping of those fibres".