The analogy between chess and mathematics had already been employed and in each case the same problem arose,
国际象棋和数学的关系已经明确了，每一步都是相同的问题，
that of how to choose the right move to reach a given goal—in the case of chess, to achieve checkmate.
就是如何选择正确的移动路径，来到达特定的目标，也就是把对方将死。
Godel had shown that in mathematics there was no way at all to reach some goals, and Alan had shown that there was no mechanical way to decide whether, for a given goal, there was a route or not.
哥德尔曾经说过，在数学中有一些目标是无法达到的，而艾伦则证明了没有一个机械的方法，能够判断是否存在一条路径来达到给定的目标。
But the question could still be asked as to how mathematicians, chess-players or code-breakers did in practice make those 'intelligent' steps, and to what extent they could be simulated by machines.
但是，仍有问题值得思考，那就是数学家、象棋玩家和密码分析人员们，在实际工作中，是如何采取那些理智的做法的，以及机器可以在什么程度上模仿他们。
Although his solution of the Entscheidungs problem and his work on ordinal logics had focussed attention upon the limitations of mechanical processes,
虽然他解决希尔伯特问题、研究序数逻辑时，都是集中研究机械过程的极限，
it was now that the underlying materialist stream of thought began to make itself more clear,
但是现在唯物主义的暗流变得更加明显了。
less interested in what could not be done by machines, than in discovering what could.
相比于机器不能做什么，艾伦更有兴趣研究一下机器能做什么。
He had demolished the Hilbert programme, but he still exuded the Hilbert spirit of attack upon unsolved problems,
他摧毁了希尔伯特的梦想，但仍然怀着希尔伯特的精神，
and enjoyed a confidence that nothing was beyond rational investigation—including rational thought itself.
而且他满怀信心地认为，理性可以解释一切，包括理性本身。