The linguistic and epistemological constraints on finding and expressing an answer to the title question are reviewed. First, it is recalled that "fields" are defined in terms of their effect on "test charges" and not in terms of any, even idealistically considered, primary, native innate qualities of their own. Thus, before fields can be discussed, the theorist has to have already available a defined "test particle" and field source. Clearly, neither the test nor the engendering particles can be defined as elements of the considered field without redefining the term "field." Further, the development of a theory as a logical structure (i.e., an internally self consistent conceptual complex) entails that the subject(s) of the theory (the primitive elements) and the rules governing their interrelationships (axioms) cannot be deduced by any logical procedure. They are always hypothesized on the basis of intuition supported by empirical experience. Given hypothesized primitive elements and axioms it is possible, in principle, to test for the 'completion' of the axiom set (i.e., any addition introduces redundancy) and for self consistency. Thus, theory building is limited to establishing the self consistency of a theory's mathematical expression and comparing that with the external, ontic world. Finally, a classical model with an event-by-event simulation of an EPR-B experiment to test a Bell Inequality is described. This model leads to a violation of Bell's limit without any quantum input (no nonlocal interaction nor entanglement), thus substantiating previous critical analysis of the derivation of Bell inequalities. On the basis of this result, it can be concluded that the electromagnetic interaction possesses no preternatural aspects, and that the usual models in terms of waves, fields and photons are all just imaginary constructs with questionable relation to a presumed reality.