In "A mathematician's Miscellany", By J. E. Littlewood, I found this piece of conversation between Littlewood and Wittgenstein:

"Schoolmaster: Suppose x is the number of sheep in this problem

Pupil: But, Sir, suppose x is not the number of sheep

(I asked professor Wittgenstein if this is not a profound philosophical joke, and he said it was.)"

I'm not familiar with the works of Littlewood nor Wittgenstein, so I'm not sure how to interpret this joke. Maybe it's something much more simple than it looks but I'm honestly confused about the profound implication of the joke that Littlewood mentioned. I would really appreciate it if someone can shed some light on me.

  • No idea, but perhaps an unstable reference, like Magritte's painting "This is not a pipe." Or just "solving" by changing the supposition. Wittgenstein was somehow both utterly literal and gnomic, and half the time nobody knew what he meant. Always good for your reputation. Nov 5 '20 at 22:55
  • Goldstein offers some insight:"philosophical problems arise when language is abused, and the way to dissolve any such problem is to locate the point at which, through false analogy or by some other means, the particular pertinent corruption of language occurs.That an abuse engendering conceptual confusion has occurred can be illustrated by bringing the absurdity into the open through a conceptual (or, as Wittgenstein would say, grammatical) joke." In this case the joke brings out the pupil's confusion about the use of "suppose x is" in mathematics, and perhaps philosophers' confusion too.
    – Conifold
    Nov 6 '20 at 0:20

The expression " the number of sheep in this problem" is a definite description , " the so and so".

And definite descriptions seem to be referring expressions, while they may not be, either due to the fact that (1) there is more than one object that satisfies the property, or (2) there is no such object.

More deeply, definite descriptions can be analysed as not referring at all, since they can be paraphrased as existential sentences : there is an x such that x is so and so, and for all y , if y is so and so, then y= x. ( Russsell, On denoting).

What may be judged profound here is that the pupil points ( maybe unconsciously) to the semantic complex status of definite descriptions : when we use a symbol "x" to stand for the supposed referent of a definite description, we always hypothesize the existence of such a referent, so the contrary supposition may appear as equally likely.

What also makes it a joke is that the student does not understand the use of the symbol " x", namely that x is " the number of sheeps" by definition ; in such a way that it makes no sense to dispute as to whether x is reallly , or not, this numnber.

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