The fallacy used to declare the League of Nations inadmissible under the pretense that it is incompatible with the concept of the state can be analysed as the joint work of three nominal definitions. If instead of states we would take individuals, this method would produce the strange result that an institution to protect individuals is proscribed by law. It is shown that the fallacy is present in the writing of several eminent legal scholars. A similar fallacy sometimes also appears in a theoretical field such as arithmetic, where it has been used by some philosophers such as Leibniz and mathematicians such as Grassmann, Peano and Poincaré to prove that arithmetic theorems are analytically true.