instruere...inlustrare...delectare Disputations

Tuesday, February 14, 2006

A gap-truthed simile

Zippy offers the sort of argument I thought he was alluding to in earlier comments here.

It seems to me that this depends on a specific and highly technical definition of "gap" -- one that uses the expression "complete and consistent" in the mathematical sense -- and it's far from clear to me that it is the only reasonable definition.

Consider a certain curling rock, traveling across the ice. Is there a "gap" in our knowledge of what caused it to move?

My contention is that whether there is a "gap" depends on what class of "knowledge" we're speaking of. If the class is kinematics, then no, there really isn't a gap: we know that when one rock smacks into another at a given point with a given velocity, it causes the smacked rock to travel in a predictable direction at a predictable speed.

If you keep asking "Why," as in, "Why does a moving rock cause a stationary rock to move?," you soon move out of the sphere of kinematic knowledge. Much the way a parent soon moves out of the sphere of parental knowledge when faced with an inquisitive child and says, "Because it just does, okay?"

But that is a gap in the knowledge of the individual, not in the set of knowledge of the given science. (Analogically, there is a gap of an infinite number of numbers between 0 and 1, but there is no gap between them in the ordered sequence of whole numbers).

Without thinking too much about it, I'm guessing this would make a particular body of scientific knowledge incomplete. But being incomplete needn't mean there are "gaps." A gap, to me, suggests a missing piece between two pieces that I have, and the sort of questions kinematics can't answer don't have kinematic answers beyond them. Scientific knowledge need not have gaps, even if it must (per Goedel) leave some questions unanswered.

Now, whether this notion of "gap" has any relevance to anything is a separate question.

And let me again insist that God is God of everything: of what we know, of what we don't know, of what we can't know. Knowledge and mystery are not contradictory. We know the laws of motion, but that doesn't mean there is no mystery to motion, or to objects capable of motion. Trying to separate knowledge and mystery -- not within a science, but within a person -- is what gives rise to the "God of the gaps" fallacies.