Since 1950, artificial intelligence has taken the limelight of modern day computing.

Alan Turing’s lecture at the London Mathematical Society, February 20, 1947

In his lecture, Turing presents the argument against a machine being “intelligent”:

It might be argued that there is a fundamental contradiction in the idea of a machine with intelligence. … It has for instance been shown that with certain logical systems there can be no machine which will distinguish provable formulae of the system from unprovable … Thus if a machine is made for this purpose it must in some cases fail to give an answer.

On the other hand if a mathematician is confronted with such a problem he would search around and find new methods of proof, so that he ought eventually to be able to reach a decision about any given formula. This would be the argument.

Turing then responds to this argument as follows:

Against it I would say that fair play must be given to the machine. Instead of it sometimes giving no answer we could arrange that it gives occasional wrong answers.

But the human mathematician would likewise make blunders when trying out new techniques. It is easy for us to regard these blunders as not counting and give him another chance, but the machine would probably be allowed no mercy. In other words then, if a machine is expected to be infallible, it cannot also be intelligent. There are several mathematical theorems which say almost exactly that. But these theorems say nothing about how much intelligence may be displayed if a machine makes no pretence at infallibility.