The big cheese isn't getting it right. If we accept the one
electron model, we can
explain any number of sightings of that electron. Note that this electron obeys some very
weird dynamics: for instance, successive
measurements obey the
Pauli exclusion principle, there are several
localisations for the electron, etc. And, of course, there is only the one
positron...
I'm not sure how mass is explained (when building a model of the entire universe, as opposed to locally-measured mass), since presumably we could observe (assuming really good experiments) gravity generated by electron mass.
But the point is that the dynamics will work. So if you still believe in operative definitions in physics, you've got real problems (metaphysically speaking): you cannot give any operative definition that will force the existence of more than one measurable electron, and (Occam's razor!) one electron is the simplest hypothesis explaining all the observed electrons.