In the same way, owning a physical object is ridiculous. Quantum mechanically, you can't tell the difference between an electron in your object and an electron somewhere else. So you end up owning an particular arrangement of electrons and protons, not the electrons and protons themselves. We can then apply the same reductio ad absurdum by examining somebody who claims to own a very small object, say a single electron.

The sensible way to define property is defining it by those cases where the state protects your rights to it. One defines intellectual property in exactly the same way.