If this was a philosophy forum rather than a programming one, I might pursue this thread further.
Obviously I meant "really exists" in a very prosaic sense. When you start talking about what conceptual ideas really exist, life gets very complex, very fast. I know from the history of math just how complex a question this is. For instance standard mathematics insists that virtually all numbers which exist can never be specified in any way, shape, or form. Yet in what sense do they exist..? (And how do you model this state of affairs in a computer?)