# THE CLASSICAL THEORY

The difference between classical and modern logic is simply that the classi- cal approach adds one more assumption—namely, that every categorical proposition is about something. More technically, the assumption is that A, E, I, and O propositions all carry commitment to the existence of something in the subject class and something in the predicate class. To draw Venn dia- grams for categorical propositions on the classical interpretation, then, all we need to do is add existential commitment to the diagrams for their mod- ern interpretations, which were discussed above.

But how should we add existential commitment to Venn diagrams? The answer might seem easy: Just put an asterisk wherever there is existential commitment. The story cannot be quite so simple, however, for the follow- ing reason. The Venn diagram for the E propositional form on the modern interpretation is this:

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The plus sign indicates that an E proposition carries commitment to the ex- istence of something in each class, even though it does not explicitly assert that something exists in either class.

From this new diagram, we can get the contradictory of a proposition by substituting shading for asterisks and asterisks for shading, as long as we also add plus signs to ensure that no class is empty, and drop plus signs that are no longer needed to indicate this existential commitment. When this pro- cedure is applied to the previous diagram, the shading becomes an asterisk in the central area, and we can then drop the plus signs in the side areas be- cause the central asterisk already assures us that something exists in both circles. Thus, we get the (modern and classical) diagram for the I proposi- tional form. Moreover, when this procedure is applied to the diagram for the I propositional form, it yields the above diagram for the E propositional form on the classical interpretation.

It might not be so clear, however, that E and I propositions are contra- dictories on their classical interpretations; let us see why this is so.