Isotopic Spin of Antiparticles

The eigenvalues of ${\tau }_3$, the isotopic spin operator describing protons and neutrons, are usually taken as +1, -1 respectively. At first sight there appears to be some arbitrariness in the corresponding assignments for antiprotons and antineutrons, since either +1, -1 or -1, +1 seem to be logical possibilities; however, it is shown that in order to construct a theory involving nucleons, mesons, and the electromagnetic field which is invariant under electric charge conjugation only the first possibility is allowed.