### Wittgenstein, Turing, and the ‘Finitude’ of Language

#### Abstract

I argue that Wittgenstein’s rule-following considerations and Turing’s 1936

demonstration of the insolubility of Hilbert’s decision problem have a common

root in thinking about the ability of finite signs to capture infinite

procedures or meanings. In the 1939 Lectures on the Foundations of Mathematics,

in direct response to Turing, Wittgenstein clearly rejects finitism and suggests

that the problem of the meaning of the infinite is to be addressed by

considering the finite symbolic “grammar” of infinite procedures and

capabilities. This bears similarities to Turing’s own application of the

“diagonal procedure,” which also captures, I argue, the problem of how infinite

procedures are represented by finite signs.

#### Keywords

philosophy; 20th century philosophy; Wittgenstein Ludwig; incompleteness; formalism; finitism; infinity

### Refbacks

- There are currently no refbacks.