To establish this result, we posited (for reductio) a
universal Turing machine capable of solving the general halting problem, and then considered whether it halts when given its own machine number.
This claim is motivated in part by the belief that a computer must be able to do anything which a mind can do, because a modern computer is, in principle, a
UNIVERSAL Turing Machine and also in part by the claim that 'the raw computational power of a modern digital computer is about 10,000 times greater than that of the brain'.