There are theoretical limits on one program's ability to fully analyze another that make this so. People can nonetheless recognize and use computers, so therefore people cannot be in the same ontological category as computers.

This argument seems flawed to me. Even if there are theoretical limits to how fully a computer program can analyze another, it does not immediately follow that this means a computer program is incapable of determining if another computer program is in fact a program running on a computer.

I don't need to fully understand all the ins and outs of the Linux source code to determine it's code, and that the code runs on a computer. I don't see why that would be different for a program.

Am I missing something?