## Existential Assumption

Existential assumptions arise from the traditional view of A and E propositions.

In traditional logic it is assumed that no circle is actually empty; that every normal concept actually applies to something in reality. Thus if part of a circle is shaded, one can assume that there is an individual in the nonshaded parts. If a diagram does not include such an X a special existential assumption can be made. It is diagrammed as (x).

WARNING: An existential assumption can be made for a concept that may not apply to anything in reality--such as A BROTHER WHO IS OVER 9 FEET TALL--but not for a concept that cannot apply to anything at all--such as A BROTHER WHO IS AN ONLY CHILD. If a concept cannot apply to anything in reality--if it is logically inconsistent, self-contradictory--then an existential assumption cannot be made for it.

In all exercises only one existential assumption can be made. Typically, the assumption is that the subject class in the premise is not empty. For the proper assumption when there are two premises, see the table of valid syllogisms

For the A proposition: If you assume that the subject term applies to something, then by inference so does the predicate term. On the Venn Diagram, the existential assumption goes in the overlap between the S-circle and the P-circle since the area of the S-circle outside of the P-circle is shaded (i.e., empty). The one placement puts an (x) in both circles!

For the E proposition: If you assume that the subject term applies to something, then the inference that the predicate term applies to something is not valid. On the Venn Diagram, the overlap between the S-circle and the P-circle is shaded (i.e., empty). The existential assumption may only be placed in one of the two circles thus leaving the other empty. It can go in the area of the S-circle outside of the P-circle or in the area of the P-circle outside of the S-circle.