§29. Perhaps you say: two can only be ostensively defined in this way: "This number is called 'two'". For the word "number" here shows what place in language, in grammar, we assign to the word. But this means that the word "number" must be explained before the ostensive definition can be understood.—The word "number" in the definition does indeed show this place; does show the post at which we station the word. And we can prevent [actual, practically arising] misunderstandings by saying: "This colour is called so-and-so", "This length is called so-and-so", and so on. That is to say: misunderstandings [actually] are sometimes averted in this way. But is there only one way of taking the word "colour" or "length"?—Well, they just need defining.—Defining, then, by means of other words! And what about the last definition in this chain? (Do not say: "There isn't a 'last' definition". That is just as if you chose to say: "There isn't a last house in this road; one can always build an additional one".)

Whether the word "number" is necessary in the ostensive definition depends on whether without it the other person takes the definition otherwise than I wish. And that will depend on the circumstances under which it is given, and on the person I give it to.

And how he 'takes' the definition is seen in the use that he makes of the word defined.

—————————

Could one define the word "red" by pointing to something that was not red? That would be as if one were supposed to explain the word "modest" to someone whose English was weak, and one pointed to an arrogant man and said "That man is not modest". That it is ambiguous is no argument against such a method of definition. Any definition can be misunderstood.

But it might well be asked: are we still to call this "definition"?—For, of course, even if it has the same practical consequences, the same effect on the learner, it plays a different part in the calculus from what we ordinarily call "ostensive definition" of the word "red".

ELUCIDATION

  1. In the end we will be reduced to defining primitives ostensively. Analysis in terms of other words comes to an end.
  2. The primary purpose of the references to "misunderstandings" is not to raise a kind of sceptical doubt concerning whether A has the same concept as B, despite a finite number of checks by application. This sceptical doubt can be pursued into the forthcoming sections on rules, and is associated with Kripke. W.'s primary purpose, however, is to emphasise how complicated language acquisition is, and how ultimately inconclusive - because this is evidence against his presupposition, in the Tractatus, that language works by setting up simple associations (ostensive definitions) between things in the world (and aspects of things), words, and meanings (in the mind) - presumably definitively taught by pointing and saying. The word 'Two', without the previously-existing place-setting 'Number' (which we may have presumed, but which we have no right to presume), is like a lever which is not attached to any mechanism (§6). If the learner's later use indicates that it is understood, in the way that other users in the community understand it, it will be because the learner has understood (implicitly or explicitly) what we refer to as 'number'.
  3. W. hints that each ordinary language user, because of the underdetermined nature of this process (no last verbal definition is possible, and ostensive definition appears underdetermined), could be 'taking' the ordinary words in subtly individual ways. (The kind of scepticism which interests Kripke) This possibility also undermines his nice, tidy, unified, Tractatus-self. It implies that there is no realx, once-and-for-all, definition of 'red' - the proper, true, definition. All there is, is the multiplicity of actual users of the word, and the word doing the job that it manages to do for them.