  We formulate a premetric version of classical electrodynamics in terms of the
excitation H and the field strength F. A local, linear, and symmetric spacetime
relation between H and F is assumed. It yields, if electric/magnetic
reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding
Euclidean signature (which is, nevertheless, discussed in some detail).
Moreover, we determine the Dufay law (repulsion of like charges and attraction
of opposite ones), the Lenz rule (the relative sign in Faraday's law), and the
sign of the electromagnetic energy. In this way, we get a systematic
understanding of the sign rules and the sign conventions in electrodynamics.
The question in the title of the paper is answered affirmatively.
