In the preceding discussion of existential import, it was shown why, in the Boolean interpretation of propositions adopted in this book, most of the inferences that traditionally were thought to be valid are not valid. These inferences mistakenly assume that certain classes have members, thereby committing the existential fallacy. This fallacy is committed in each of the arguments presented below. Explain the point or points at which, in each argument, the mistaken existential assumption is made.

(1) No mathematician is one who has squared the circle; therefore,

(2) No one who has squared the circle is a mathematician; therefore, 

(3) All who have squared the circle are nonmathematicians; therefore, 

(4) Some nonmathematician is one who has squared the circle.