 
Summary: 1
Gödel on computability*
Wilfried Sieg
Carnegie Mellon University
Around 1950, both Gödel and Turing wrote papers for broader audiences.1
Gödel drew in his 1951 dramatic philosophical conclusions from the general
formulation of his second incompleteness theorem. These conclusions concerned
the nature of mathematics and the human mind. The general formulation of the
second theorem was explicitly based on Turing's 1936 reduction of finite
procedures to machine computations. Turing gave in his 1954 an understated
analysis of finite procedures in terms of Post production systems. This analysis,
prima facie quite different from that given in 1936, served as the basis for an
exposition of various unsolvable problems. Turing had addressed issues of
mentality and intelligence in contemporaneous essays, the best known of which
is of course Computing machinery and intelligence. Gödel's and Turing's
considerations from this period intersect through their attempt, on the one hand,
to analyze finite, mechanical procedures and, on the other hand, to approach
mental phenomena in a scientific way.
Neuroscience or brain science was an important component of the latter
for both: Gödel's remarks in the Gibbs Lecture as well as in his later
