Friday, November 07, 2008

Ockham's Beard

It is a maxim itself of such parsimonious economy:
Entia non sunt multiplicanda praeter necessitatem
Entities should not be multiplied unnecessarily

Also told as:

The simplest explanation is often the best

Or, simpler still: Ockham's razor.

Ockham's razor is wielded with enthusiasm and gusto across countless disciplines, and not without some success. However, there is a weakness in Ockham's razor that calls to be addressed. Or rather, it's less a weakness than a necessary counterpoint that places Ockham's razor in context and defines its limits and bounds.

And that is the principle of Ockham's beard, which goes a little something like this:

The least abstract explanation is often the most accurate
This says that the simplest explanation will likely be imperfect when applied to the concrete world.

This is already trivially acknowledged when, for example, we talk about the application of mathematics or geometry to the real world. It's folly to seek a perfect triangle or circle in the real world, although employing the concept of 'circle' or 'triangle' can often be terribly useful in describing natural phenomena.

Yet Ockham's beard goes beyond this example to universalise the notion that any abstraction will likely imperfectly represent its concrete counterpart. Or in other words, the bristles of Ockham's beard will continue to break through the layers of abstraction, inevitably introducing either inconsistencies within the abstraction or incompatibilities with other abstractions. So we can never have a complete and consistent abstraction of the entirety of reality.

Just roll up Gödel's theorem, vagueness and leaky abstraction, and you're led to Ockham's beard.

This is really just a consequence of employing abstractions in the first place. Any abstraction, by definition, is a subtractive process. It starts with some concrete thing and pares it back to some generalisation; to those things that all these concrete things appear to have in common. No two token stars are exactly alike, yet there is plenty that all token stars have in common; enough to call them all by the abstract denominator, or type, 'star'. Yet, inevitably, that type is vague. Should we strive for perfect accuracy, the singular abstraction, 'star', will not get us far.

The search for the most encompassing abstractions is the direction in which Ockham's razor aims. Yet if it's accuracy we seek, then Ockham's razor leads us up and away from concrete reality.

This is not to say that Ockham's razor is somehow flawed or that we should shy away from its use. In fact, Ockham's razor is a vital tool for us, specifically because we are finite beings with drastic limitations to our cognitive capacity. Were we to seek accuracy above all else, we would have as many abstractions and names for things as there are things - and there are a great many things.

And for those who feel Ockham's beard is too inductive, I claim it is no more or less inductive than Ockham's razor. It, too, is a rule of thumb, a heuristic. Less practical than Ockham's razor, but a valuable cautionary notion; to remember that before we employ the razor, we need to acknowledge the existence of the beard. And at the end of the day, we might find a happy medium in Ockham's five o-clock shadow.


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