The Legend of Zelda and Philosophy_ I Link Therefore I Am - Luke Cuddy [56]
Underdetermination
Before explaining what those principles might be, let’s illustrate the difficulties associated with having facts without a theory that connects those facts. Suppose we’re playing a mathematical guessing game. I’ll give you a series of pairs of numbers, and you have to guess the formula for the series. If I say, “one and two; two and four; three and six,” you might blurt out, “the formula is ‘y = 2x’, and next in the series is four and eight!”
But you would be wrong, because the formula I was using was actually ‘y = 2x + 1 - (x - 4) ÷ (x - 4).” Normally, the last part of the equation drops out, since it is equivalent to one minus one. However, four minus four is zero, so if x is four, y equals 2 × 4 + 1 - 0 ÷ 0, but zero divided by zero is not defined in arithmetic, so there’s no answer to this problem. It seemed obvious that my formula was just to double the first number in the pair, but in actuality there was another formula that fit the facts at hand just as well as the “double first the number” formula.
The larger problem is this: when we’re given a set of pairs of points, it doesn’t matter how many points we are given; we still can’t say for sure what formula was meant to describe them because there are an infinite number of variations on the normal formula that one would expect to describe it. My formula excluded four, but it could just as easily have excluded any other number, making it just one variation of one method of describing the points out of an infinite pool of alternative functions. (In addition to variations on the same method, there are also many other methods to employ for mapping the points that use advanced mathematical functions like sine and cosine.)
The problem is called “underdetermination,” and its first recognition as a serious problem is commonly ascribed to the philosopher and mathematician Leibniz. If his negative conclusion is that there is no one formula that best describes a set of points, at least on the positive side, Leibniz proved mathematically that every finite set of points, no matter how simple or complex their distribution, can be described by some group of mathematical functions. We don’t have to worry that we will encounter a set of points without a corresponding set of descriptive functions. If these properties hold for the highly restricted process of mathematical interpretation, it should be clear that they will hold for interpreting other, less rigorous, informal logical systems as well.
When we interpret the Zelda series, we have an infinite number of choices for how to interpret anything in any game of the series. (Which is not to say that anything goes as an interpretation, just that there are infinite variations on what does work. Similarly, the formula above couldn’t have been ‘y = 3x’, though it could have been any one of an infinite number of other formulas.) Reflecting briefly, we can see the wide range of possible interpretive theories for the Zelda universe that are available to us: maybe all of the games are a dream by the Zelda in The Adventure of Link ; maybe all of the games are the work of a powerful, but unseen wizard, who causes all of the seeming plot holes and inconsistencies; maybe hyper-intelligent Cuccos are the real power behind Ganon’s evil magic; and on and on.
That there are an infinite number of possible interpretations may seem like very bad news since it makes reaching agreement on a single, correct interpretation even harder. And yet that there are an infinite number of interpretations for everything is also good news since we no longer need worry that, in their sloppiness, the game designers have made the games truly contradictory. Any apparent contradictions in the timeline can be resolved by just proposing a new and more complicated theory to explain away the seeming inconsistency. As the philosopher’s cliché has it, “When faced with a contradiction, make a distinction.”
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