Wednesday, October 24, 2007

The Two Sides of a Coin

Lately, I have been working on a heuristic for systematic thinking that I believe is very powerful. I'd like to share it with you. Maybe you can help me refine it. For a long time I have found myself alternately embracing opposing viewpoints. At first this bothered me. It seemed to be non-committal, indecisive and not useful for decision-making. However, I have come to see it as quite useful, indeed.

Tetradrachm of Athens, 5th BCE. The obverse features Athena, goddess of the city. The reverse, shows Athena's owl companion, a symbol of the city itself.  This silver coin helped make Athens a financial power due to its unusual purity and high quality minting

There's no such thing as a one-sided coin. It's a package deal.

Today I was listening to the Philosophy Bites podcast featuring Anthony Grayling, a prominent advocate of atheism. When asked about agnosticism he rejected it as a "wishy washy, fence sitting kind of view". He went on to attempt to draw a parallel between the belief in "faeries" with a belief in any supernatural phenomenon, and therefore to reject agnosticism on the basis that if faeries aren't real then it is silly to hold out for any view that isn't strictly naturalist. I mention this because it is what provoked into writing about this topic today.

When I have found some set of rules that nicely explains a given aspect of reality I also find myself invariably dissatisfied with them. There always seem to be things that I believe are correct, but that those rules cannot reach. This, I think, is related to the idea of incompleteness in mathematical logic. Kurt Gödel provided a rigorous proof that any system of formal logic, which is sufficiently complex to be interesting, is incomplete. That is, there are true and false "statements" within its rules that the rules themselves cannot derive. (A note to mathematical logicians: I am not claiming this is a rigorous definition or application of Gödel, consider it loosely-coupled)

Similarly, the rules-based systems you and I use to make decisions about morality, politics, aesthetics and the like are also incomplete. There are things that we can feel are correct but cannot show as correct. This is what lead to my alternate embracing of first one idea, then the opposing one. Was that wrong?

Many of the greatest thinkers in history, particularly those with a "spiritual" bent are described as confusing the people around them by first embracing one idea, then its apparent opposite. This seems inconsistent and mysterious. Maybe it isn't. Let's take a very simplified example from politics. Our hypothetical left- and right-wingers are faced with a problem. The poor need to be fed. Excluding actual extremists, who might either suggest that everyone should be fed by the government (putative left) or that people who cannot feed themselves should be allowed to die (putative right) we are left with two sides that agree some people should be helped by the government and the some people should be completely on their own.

The difference between them is that on the left, expansion of the government program is the tendency or even goal, which on the right it is contraction of the program. Is one of these positions "correct" to the exclusion of the other? I don't think so. I also don't think that an artificial "middle" is correct, either. That is, the ideological "average" of the left and right is not an effective position. What then, can we make of this?

This is where the coin comes in. If we imagine the problem to be solved, which both sides agree upon, as the coin, we can see that the two sides of the coin can be analogous to the two positions. The coin itself is a good coin, We all like it. If we are on one face, though, we cannot see the other at all. It appears that the other face is mutually exclusive with our face. If we look at the coin, though, we see that both faces are required. So, it is my contention that when we find ourselves with what we consider a "good set of rules" we should immediately seek out the opposing view. That view is actually complementary to our own. It literally completes it. When we come to a conclusion with our own rules we then need to analyze with "their" rules and refine our conclusion.

Sometimes, it seems wise to actually adopt a opposition opinion where our own system seems deficient. Sometimes it is just a matter of polishing our own ideas. Eventually, we might stop thinking of our "side" as the "correct" one and instead embrace the entire coin. Then it becomes a matter of where to draw the line in tension between the two. In that idea I believe is the essence of how the world operates.

I will write more on that, later.

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