1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….
At what point did the apple cease to be an apple?
This new way of thinking already is used in air conditioners, enabling them to constantly adjust the room temperatures with varying amounts of cooling air instead of operating as either “off” or “on.” Its major contention is that only mathematics is really bivalent—either/or, right/ wrong, 1/0—and that everything else is multivalent—a matter of degree. Most of reality is neither black nor white but gray, as René Descartes discovered when he melted the ball of wax. At some point it changed from wax ball to non–wax ball, but where exactly was that point? You can try the experiment yourself, suggests Bart Kosko in his antiscience science book, Fuzzy Thinking (see “For Further Exploration”). Place an apple in your hand and ask yourself, “Is this an apple?” Your answer will clearly be yes. Now eat the apple and ask yourself the same question. Just as clearly, your answer will now be no. The issue is, At what point did the apple cease to be an apple? Kosko explains, “When you hold half an apple in your hand, the apple is as much there as not. The half apple foils all-or-none descriptions. The half apple is a fuzzy apple, the gray between black and white.” Fuzzy logic is commonplace in “smart” computers that recognize and translate handwritten characters; camcorders; auto engines, transmissions, brakes, and cruise controls; elevators; microwave ovens; televisions; and many other electronic devices. Fuzzy logic works because it takes into account the reality that nothing is absolute, that everything is a matter of degree. Aristotle taught us bivalence—something is either A or not-A—and this logic prevailed for 2000 years. Eastern systems, like Taoism and Buddhism, have always recognized the contradictions at the heart of what-is and asserted that things are both A and not-A. We can see glimmers of this multivalent view in the ancient paradoxes of Western thought. If a liar from Crete says that all Cretans are liars, does he lie? It seems the only way out of the paradox is that the Cretan both lies and doesn’t lie at the same time (A is not-A). Applied to ethics, fuzzy logic helps us see that a person may not be clearly either alive or not alive, a person or not a person, but somewhere on the line between those two alternatives. Instead of arguing violently about whether life begins at conception, quickening, viability, or birth, fuzzy logic suggests we begin by granting that life begins at all those times—to a certain degree.