Simple Approximations to a Fractal World

In an insightful comment on the post below, tireless commentor Constant elucidated a helpful way of thinking about moral rules:

The picture that results is of a set of limits, or metaphorically speaking a set of fences that you are not to cross, not to trespass. It is not a set of valuations assigned to every possible thing you might do. . . . morality is a set of fences where, if you cross them, you will be violating morality and will be in the wrong, but if you do not cross them, then you are fine. . . .

This also explains why the rules are easy to understand and to state, and why they have exceptions. They’re easy to understand because they need to be easily knowable by everyone. Simple rules are like straight fences. Rules aren’t actually visible, they’re in the mind and not in the physical world as actual fences. And similarly, if you were constructing invisible fences, the best sort of fence you could construct would be a straight fence, because it’s a lot easier to guess where all the different parts of an invisible straight fence are than it is to guess where all the different parts of a crazy curvy fence. All you have to do is bump against the straight fence at two points and then you’ve pretty much got the layout in your head, because two points define a line. But two points do not define a crazy curve. Analogously, the rules need to be simple. Rules, like invisible fences, need to be as simple as possible most of the time.

The way I would phrase this is that the terrain of ethics is fractal, and deciding whether something is right or wrong is analogous to deciding whether a point lies on the inside or the outside the fractal's boundary. When you're far from its boundary that's an easy call to make: you can approximate the boundary with a simple curve such as an ellipse and use that rough heuristic to make the judgement. But because the boundary exhibits ever-finer levels of "roughness" as you look more closely at it, you need ever-more nuanced approximations the closer the point is to the actual boundary. A hypothetical example that seems to show that a proposed ethical rule gets the wrong answer in some cases is merely a way of showing that a proposed approximation passes through the boundary.

There is no easy way to decide every case a priori, simply because in order to do so we'd need to know the complete perimiter, which, having finite minds, we can never do in practice. This is why anyone who claims to be able to decide all possible ethical questions based on a few simple and self-evident axioms is selling snake oil: There's no such complete set of axioms, and the best we can hope for is an approximation that serves us well in all the sorts of cases we've tested it against up to now. Rules are, in a sense, made to be broken -- and then reshaped anew. But equally important for beings with finite minds, our decisions come more quickly and easily the simpler our approximation is, which is why we should seek for rules that are (in the words of some German wiseguy) as simple as possible -- but not simpler.

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