 Though the existence of extensions falls right out of the theory of identity (§2.3) once terms of the form \(\epsilon F\) are added to second-order logic, the existence of extensions that are correlated one-to-one with concepts is a consequence of Basic Law V. The question for Frege’s project, then, is why should we accept as a law of logic a statement that implies the existence of individuals and a correlation of this kind? Frege recognized that Basic Law V’s status as a logical law could be doubted: 