Gödel 's failure to discover unsolvability of the decision problems for predicate logic and Peano arithmetic may be an example. Gödel had all necessary tools: arithmetization, diagonalization, and an equation calculus for defining computable functions.

However, as he admitted later, was misled by his incompleteness proof into thinking that there could not be an absolute definition of computable function -- he expected one could always form new computable functions by diagonalization. It was only when Turing came up with the definition via Turing machines that Gödel realized he was mistaken.

Gödel 's failure to discover unsolvability of the decision problems for predicate logic and Peano arithmetic may be an example. Gödel had all necessary tools: arithmetization, diagonalization, and an equation calculus for defining computable functions.

However, as he admitted later, he was misled by his incompleteness proof into thinking that there could not be an absolute definition of computable function -- he expected one could always form new computable functions by diagonalization. It was only when Turing came up with the definition via Turing machines that Gödel realized he was mistaken.