Venn Diagrams

And the Modern Square of Opposition

Section 4.3

Aristotle and Boole:

All Tom Cruise’s movies are hits

All unicorns are one-horned animals

First statement suggests that Tom Cruise has made some movies. But what about the second? Does this suggest that there are unicorns? Should universal statements be interpreted as implying that the things talked about actually exist? Or not?

Aristotle said yes, that as long as the universal proposition is about existing things, then the statements have existential import. Thus:

All pheasants are birds No pine trees are maples All satyrs are vile creatures

Implies the existence of pheasants Implies the existence of pine trees Does not imply the existence of satyrs

The first two have existential import because their subject terms denote existing things, while the third does not.

Boole said no, that universal propositions carry no existential import. That is, they never imply the existence of the things talked about. Thus:

All trucks are vehicles No roses are daisies All werewolves are monsters

Does not imply the existence of trucks Does not imply the existence of roses Does not imply the existence of werewolves

That is, the Boolean standpoint is neutral about existence. Note, though, that the Aristotelian and the Boolean interpretations agree regarding particular statements. Those do have existential import. Thus, "some tigers are mean" implies that there is at least one tiger, and that tiger is also mean.

Either standpoint may be taken. We'll primarily be using the Boolean standpoint in this chapter, but in chapter five we'll reconsider the Aristotelian standpoint.