[FOM] Wittgenstein's '770' in pi

Harold Teichman hteichman at comcast.net
Sun Jul 15 12:03:55 EDT 2007

Hilary Putnam, in several recent essays, has discussed Wittgenstein's
perhaps naïve puzzlement over the sense of assertions like "the sequence of
digits '770' must appear somewhere in the decimal expansion of pi" [see e.g.
Remarks on the Foundations of Mathematics, 2nd Ed., p. 266].

In his paper "Was Wittgenstein Really an Anti-realist about Mathematics?"
[see McCarthy and Stidd, Wittgenstein in America, Oxford (2001), p. 179]
Putnam says:

"What Wittgenstein should have said is that the mathematicians do understand
the question whether 770 ever occurs in the decimal expansion of pi, and
that they have learned to understand such questions by learning to do number

No such statements (about decimal expansions) figure prominently in the
texts on number theory that I have seen.  Could someone refer me to some
actual literature in number theory (or any other part of mathematics) that
has a bearing on this question?

Much obliged.

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