Pulsars have been identified with the theoretical objects called neutron stars. The identification is convincing—but not proved. The short rotational periods of millisecond pulsars inform us that the average density (and, therefore, the central density) must be very high—higher than the density of nuclei (5.8). The most obvious inference is that pulsars are the objects conceived of by Baade and Zwicky. However, there is another possibility that has such a fundamental implication that it should not be overlooked. We will find that the conventional interpretation of pulsars as neutron stars—or any any other type of star that is gravitationally bound—can be ruled out if any pulsar is found to rotate at a frequency above a certain limit.