§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 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 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".