2012-06-12

Problem-Solving and Logical Sequence

In order to solve any difficult problem, we have no choice but to resort to deductive logic. In the realm of philosophy – and especially in the realm of Austrian-flavored economics – there exist some passionate opinions about whether our deductive reasoning is a priori, a posteriori, or based solely on perception. Heck, there are plenty of other theories we could include here, but I’d like to side-step the issue a bit to avoid direct commentary on that particular subject matter. For now, it suffices to note that complex problems cannot truly be solved without deductive logic, regardless of at which point the theory is generated.

As the term deductive implies, this kind of problem-solving requires iterative thinking: First, we do A, then we do B, then comes C, and so on. Consider climbing a ladder. We start on the bottom rung and work upwards, rung-by-rung. It’s possible to skip a few rungs, but only up to a point. What I mean is, we can’t start at the top rung, and then move to the middle rung, then the bottom rung, then the second-to-highest rung, and so on. (That is, we cannot do this for the average ladder. There may be ladders out there that are sufficiently short, or having sufficiently few rungs, or sufficiently spaced rungs to make any rung order available, but we’d be getting far too pedantic if we considered abnormal ladders for the sake of mere metaphor.)

So, solving a problem with deductive reasoning involves a starting point (the ground), an endpoint (the top of the ladder, or the destination reached with the aid of the ladder), and a sequence of middle steps that preclude abnormalities.

What if you wanted to climb from Point A to Point B, so you climbed a ladder, and you ended up at Point C? If that happened, you have committed at least one of the following errors:
·         You had the wrong starting point,
·         The endpoint is not what you thought it was,
·         You used an inappropriately shaped/sized ladder.

Let’s consider each one of these possibilities individually.

Wrong Starting Point
The important thing about this situation is that your problem-solving process was basically correct. The ladder was the correct size, the rungs behaved the appropriate way. From a different starting point, you would have ended up at Point B. You simply started from Point D instead.

In the real world, this might describe a situation in which a basic assumption was incorrect. To use the terminology of logic, your system is valid but false. You accurately predicted the outcome of an alternate scenario. Your only mistake was that the current scenario is not what you thought it was.

Economists tend to be good logicians. They can usually be counted on to come up with a valid logical argument for the economic conditions they anticipate. However, if their starting point is all wrong, they won’t reliably explain the economy. If the “natural rate of unemployment,” for example, is 2.0% rather than 2.5% (or whatever), then this discrepancy may fully account for the economist’s error.

More to the point, if there is no “natural rate of unemployment,” or if it is impossible to know, then no logical series of problem-solving steps starting from a known natural rate of unemployment can ever lead us to greater understanding of the economy itself.

Wrong Endpoint
In this situation, it is also important to note that the ladder-climber’s ladder is exactly correct. The logic is valid, and the starting point is correct. What went wrong? How did you end up at the wrong Point?

One possibility is that the endpoint is not what you thought it was. Seen from the ground, you saw a ledge 15 feet up. You climbed a 15-foot ladder and realized that the ledge was not flat at the top, so there is no destination at which to arrive. Point C is merely a point on the face of a cliff, not the ledge (Point B) at which you expected to arrive.

We often see real-world examples of this. Consider the passionate novice politician who wins the election, only to discover that the system does not behave as anticipated, and he cannot accomplish what he expected to accomplish. Consider the central banker who sets an inflation target of X%, only to discover that X% is the wrong target for the economic conditions.

Another possibility is that we were looking at a ledge at Point C, mistakenly believing it to be a ledge at Point B. This is a case of mistaken identity.

In the real world, this might be a climate scientist who believes that X degrees of global temperature increase will create an irreversible chain-reaction, only to discover that it does not. Or, it might be an economist who believes that a free-market money supply is essentially a barter system, when in fact it is not (sorry Prof. Rowe).

Wrong Ladder
In this situation, the starting point or the endpoint could be correct or incorrect – but most importantly, you are using the wrong ladder.

If you start from Point A, your basic assumptions are correct; it’s your theory that’s all wrong. Note here that it doesn’t really matter if you end up at Point B because your doing so was nothing more than an accident, a mistake. On a different day, you probably wouldn’t have. If you don’t end up at Point B, though, you’ll never get there without using a different ladder, i.e. revising your theory.

This one is actually easier to see in the real world than in the abstract. Sometimes financiers correctly predict market movements, but it’s pure dumb luck, no different than gambling. Other times, they get it wrong and suffer losses. Sometimes economists get it right, sometimes they get it wrong. But they have only ever explained something when they use the right theory, built from the correct assumptions, to describe the conditions we wanted to know about from the very beginning.

Conclusion
If you want to tackle difficult problems, you need more than just a good theory. You need more than just a good “algorithm” that will take you through an iterative, deductive process. You need to start from a correctly identified set of assumptions, and you need to ensure that what you are describing is what you had in mind  in the first place. If these conditions aren’t satisfied, then you haven’t explained anything at all.