The Language of Argument

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V a l i d i t y f o r C a t e g o r i c a l A r g u m e n t s

Two cases are obvious: Both I and E propositions validly convert. From

an I proposition with the form “Some S is P,” we may validly infer its con-

verse, which has the form “Some P is S.”

S P

I: Some S is P. Converse of I: Some P is S.

P S

S P

E: No S is P. Converse of E: No P is S.

P S

S * P

O: Some S is not P.Converse of O: Some P is not S.

P S

Notice that in this case the information is not in the center but is instead

off to one side. As a result, the information changes when the diagram is

flipped. The asterisk is in a different circle—it is in the circle for S in the

diagram for an O proposition, but it is in the circle for P in the diagram for

the converse of the O proposition. That shows that an argument from an O

proposition to its converse is not always valid.^1

From an E proposition with the form “No S is P,” we may validly infer its

converse, which has the form “No P is S.”

Notice that in both these cases, the information (the asterisk or shading) is

in the center of the original diagram, and the diagram for the converse flips

the original diagram. Thus, the two diagrams contain the same informa-

tion, since the diagram for the converse has exactly the same markings in

the same areas as does the diagram for the original propositional form. This

shows that E and I propositions not only logically imply their converses but

are also logically implied by them. Because the implication runs both ways,

these propositions are said to be logically equivalent to their converses, and

they always have the same truth values as their converses.

The use of a Venn diagram also shows that an O proposition cannot always

be converted validly. From a proposition with the form “Some S is not P,” we

may not always infer its converse, which has the form “Some P is not S.”

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