The resolution of the Entscheidungsproblem would seem to answer this question in the negative: http://en.wikipedia.org/wiki/Entscheidungsproblem http://en.wiki

The resolution of the Entscheidungsproblem would seem to answer this question in the negative: http://en.wikipedia.org/wiki/Entscheidungsproblem http://en.wikipedia.org/wiki/Entscheidungsproblem However, it does not place limits on the quality of approximation. This suggests that the development of AI will proceed gradually rather than suddenly (I've always disliked the term "singularity"; exponentials don't have those) since the infinite case is not going to be solved.