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# SUBALTERNS

On the classical approach, there must be something in this circle somewhere. If there is something in the overlapping region SP, then the I proposition is true. If there is something in the nonoverlapping region of S, then there must be something else in the circle for P, because P cannot be empty on the classical approach; therefore, the O proposition is true. Thus, either the I proposition or the corresponding O proposition must be true, so they cannot both be false. We already saw that they can both be true. Consequently, corresponding I and O propositions are subcontraries.

Subalternation is the relationship that holds down the sides of the classical square of opposition. Quite simply, an A proposition implies the corresponding I proposition, and an E proposition implies the corresponding O proposition. This relationship depends on the existential commitment found on the classical approach and does not hold on the modern approach.

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The validity of subalternation is illustrated by the following diagrams:

An A proposition includes a plus sign where the corresponding I proposi- tion includes an asterisk, but both symbols indicate that something lies in the middle area. Thus, the information for the I proposition is already included in the diagram for the A proposition, which means that the A proposition implies the I proposition.

The same point applies to the implication on the right-hand side, because the diagram for an E proposition includes a plus sign in the same area as the asterisk in the diagram for the corresponding O proposition. The diagram for the E proposition also has a plus sign in the rightmost area. If something exists in that area, then something exists in either that area or the middle area, which is what is meant by the plus sign on the line in the diagram for the O proposition. Thus, an E proposition implies its corresponding O proposition.

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