The question then arises whether we should include existential commitment in our treatment of universal propositions or not. Once more, we must make a decision. (Remember that we had to make decisions concerning the truth-table definitions of both disjunction and conditionals in Chapter 6.) Classical logic was developed on the assumption that universal (A and E) propositions carry existential commitment. Modern logic makes the opposite decision, treating the claim “All men are mortal” as equivalent to “If someone is a man, then that person is mortal,” and the claim “No men are islands” as equivalent to “If someone is a man, then that person is not an island.” This way of speaking carries no commitment to the existence of any men.
Which approach should we adopt? The modern approach is simpler and has proved more powerful in the long run. For these reasons, we will adopt the modern approach and not assign existential commitment to universal (A and E) propositions, so these propositions do not imply particular (I and O) propositions. All the same, there is something beautiful about the classi- cal approach, and it does seem appropriate in some contexts to some people, so it is worth exploring in its own right. The Appendix to this chapter will show how to develop the classical theory by adding existential commitment to the modern theory.
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