## Squiggly Logic

So, I’ve spent some of my free time over the holidays trying to catch up on fascinating, dissertation-relevant books that I happen to own. The rest of my free time was spent eating ham and reading The Other Boleyn Girl. I think the previous review covered “historical novels with sex in” pretty handily, so instead I’ll turn to The Complementary Nature, by Scott Kelso and David Engstrom.

The conceit of the book, which is much more philosophical than I took it for on the shelf, is that things in scientific thinking come in pairs, and even ways of relating pairs come in pairs, and that there are several ways of resolving these pairs (or pairs of pairs, or.. you get the idea). The authors come up with a method for expressing these pairs - e.g. matter~energy or part~whole - that may or may not be silly (especially since the ~ has an entirely different meaning in formal logic). As a way to indicate that dualisms are irreducible, it’s interesting. Visually, I don’t think it incorporates enough of the overlap and intertwinedness and ‘duckrabbit’-y sense that they are trying to convey, but then, I can’t fault scientists for choosing the least silly-looking option. I’m glad there is a solid philosophical foundation under the field of movement dynamics, and the concept that “contraries are complementary,” arguably the central theme of TCN, is helpful in bouncing around ideas about alignment between speakers. If contraries are complementary, then if Left is the contrary of Right (Left~Right), it should be expected that the motion or shape of Left is complementary to that of Right. If Physical~Mental is a contrary pair (one cannot be the other), then perhaps motion in the Physical state will be complementary to motion in the Mental state.

The nicest evidence that this is, in fact, the best thing I’ve read all week is not a summary of the authors’ thoughts, however, but a demonstration that reading this book has put me somewhat back in the philosophical saddle. All their talk of Aristotle, Kant, Spinoza, and Zeno has caused me to re-approach Zeno’s paradox knowing something about how language works. Or at least, how Frege thought language worked.

In order for a racing turtle to reach the finish line, it first needs to cover half the ground between itself and the finish line, right? Okay. Now that it’s halfway there, it has to cover half the ground between the midpoint and the finish line. At that point, it must cover half the ground between the 75% mark and the finish line. When it has made 6 or so of these halfway points, it will have covered about 96% of the way to the finish line. Surely, only one or two more steps to go! However, the keen minds among you will have deduced that the poor turtle will, in fact, NEVER reach the finish line no matter how many times he reaches the midpoint between where he is and where he wants to be. It is always receding inverse-exponentially away from him. He can only approximate crossing the finish line by being directly next to it in an “I’m-not-touching-you!” sort of way.

One solution to Zeno’s paradox is to make it a problem about spatial semantics. When we say to our racing turtle, “the finish line is here,” we are actually locating a line infinitesimally further away - the asymptote of the turtle’s approach, which as we all know, he will never reach. The only reasonable denotation of the phrase “the finish line” (or any other terminus) is the last point through which it is actually possible to pass before reaching the asymptote - the point exactly halfway between the asymptote and the point which is located the smallest calculable distance from the asymptote. The asymptote casts a shadow in the direction of the approacher, and it is this shadow to which we refer when we say “the finish line.” Talking about a terminus is a case in which the shadow of the thing may have more substance than the thing itself.