Whether digital computers can eventually be as intelligent as humans has been a topic of controversy for decades. Neither side of the debate has provided solid arguments proving this way or the other. After reviewing the contentions, we show in this article that machine intelligence is not unlimited. There exists an insurmountable barrier for digital computers to achieve the full range of human intelligence. Particularly, if a robot had a human’s sentience of life and death, then it would cause a logical contradiction. Therefore, a digital computer will never have the full range of human consciousness. This thesis substantiates a limit of computer intelligence and draws a line between biological humans and digital robots. It makes us rethink the issues as whether robots will remain forever one of the tools for us to use, or they will someday become a species competing with us; and whether robots can eventually dominate humans intellectually.