Comment by kens

No, logic operations aren't "recognized as necessary". For instance, the IBM 1401—the most popular computer of the early 1960s—did not have logic operations. (This was very annoying when I implemented Bitcoin mining on it.)

The reason that the 4004 is considered a CPU and the 74181 is not a CPU is that the 4004 contains the control logic, while the 74181 is only the ALU.

Of course, "microprocessor" and "CPU" are social constructs, not objective definitions. (For instance, bit-slice processors like the Am2901 were considered microprocessors in Russia.) So you can craft your own definition if you want to declare a particular processor first. cough MP944 cough