As in the case of immediate inferences, the premises of syllogisms will con- tain more information—specifically, existential commitment—on the classi- cal interpretation than they do on the modern interpretation. This will make some syllogisms valid on the classical approach that were not valid on the modern approach.
We begin our study of this matter with an example that has had a curious history:
All rectangles are four-sided. All squares are rectangles.
Some squares are four-sided.
The argument is peculiar because its conclusion is weaker than it needs to be. We could, after all, conclude that all squares are four-sided. The argu- ment thus violates the conversational rule of Quantity. Perhaps for this rea- son, this syllogism was often not included in traditional lists of valid syllogisms. Yet the argument is valid on the classical interpretation of exis- tential commitment, and our diagram should show this.
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