Logic For Dummies, 2nd Edition

Chapter 21

Sporting Propositions: Non-classical Logic

IN THIS CHAPTER

Introducing possibility with multi-valued logic and fuzzy logic

Understanding modal, second-order, and paraconsistent logic

Appreciating the mystery of quantum logic

To most people, the question “What if 2 + 2 = 5?” is absurd. I mean, c’mon, asking yourself “What if … ?” in many cases is pointless because you know what you’re pondering can never be true. For example, consider this wacky question: “What if little green Martians landed their flying saucer on my front lawn and drove off in my car?”

But, to logicians, these “What if?” questions are a sporting proposition — a challenge that’s inviting just because it’s so preposterous. By the early 20th century, logic had been reduced to a relatively short list of basic assumptions called axioms. (See Chapter 22 for more information about the axioms of logic.) These axioms were considered self-evident, and if you accepted them, everything else from logic followed.

But, what if you didn’t accept them? What if, for the sake of argument, you changed an axiom the way a baker changes an ingredient in a cake recipe?

Of course, a baker should choose carefully when changing ...