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Now that we know we have an endless array of potential theories, we must return to the selection of universally acceptable principles to choose from among those theories. William of Ockham famously endorsed one key principle of interpretation, now named “Ockham’s razor” in his honor. He claimed, “entities should not be multiplied beyond necessity.” In other words, the simplest explanation—one that cuts away all the unnecessary bits—is the best. This rule is still a central principle for hermeneutics, because it can quickly eliminate all but a handful of potential theories from the pool of consideration.

Occam’s razor has its problems, however. As the counting example shows, it’s not guaranteed to always give us the correct answer. Guessing that my formula was ‘y = 2x’ is much simpler than guessing my formula was ‘y = 2x + 1 - (x - 4) ÷ (x - 4)’. Applying Occam’s razor in this case will inevitably lead us away from what turns out to be the intended formula. In spite of that, ‘y = 2x’ is still a good guess to have made even though it didn’t turn out to be the right answer in the end. Since it’s a simple enough formula for us to fit into our heads it has practical advantages as a hypothesis, such as that it makes it easier us for us to come up with the formula, remember it, and work out all its consequences. On top of that, with a simpler proposed formula, we are more likely to encounter test cases to contradict our guess, letting us know that we need to revise it. If I had been allowed to continue giving number pairs and said, “four and undefined,” it would have been immediately clear to you that the formula ‘y = 2x’ is incorrect and that a new formula is needed, whereas if you had guessed that my formula was like that but undefined for thirteen million five hundred and sixty, the evidence against this would not have shown up as readily. On top of all this, a simpler formula is more easily inferred by others, which makes it superior for collaborative purposes. Since our formula is simple, we can reasonably expect that others who are attempting to come up with an interpretation will create one similar to ours if ours is simple, and by working with them, we can point out bits of data that may require revision away from a simpler theory.

We have seen the difficulty of interpretation, because the part must inform the whole and the whole the part; and because any set of data points can be connected in an infinite number of ways, and so we recommended simplicity as a key quality for an interpretation, even though it may not always give the right answer. But what does it mean for something to be simple?

The philosopher Wittgenstein once worried about a related problem. Suppose that you show someone a set of examples to teach her how to count by twos, and at first she does so correctly—“2, 4, 6, 8 …”—but when she gets up to 1,000, she suddenly shifts to “1,004, 1,008, 1,012 …” while claiming she is still going on in the same way. What can be said to such a person? Because of the problem of underdetermination, she seems to have deduced the formula for counting by two incorrectly. However, if she thinks like a normal human being, we can tell her, “No, the formula you are using is too complex, since it treats numbers above and below 1,000 differently. You must use a simpler formula!” While it is a leap to conclude that everyone everywhere will agree with our assessment of what is simple, so long as our learner has a relatively normal human brain, in this case surely she will see what we mean and correct herself.

Can we always assume that everyone will see simplicity in the same way? What could we say to our learner if she stubbornly insisted that her way of counting by two seems simple to her? While it seems fairly clear that changing how one adds at 1,000 is less simple arithmetically because the formula to express it would be longer when written down, it is less clear that we can precisely define simplicity for other interpretations.

While it seems simpler to assume that the Master Sword of