Saturday, March 15, 2008

What counts as a prediction?

I was describing my theory of explanation to a friend, and he suggested that my definition of a predictive theory was too vague.

He gave the example of a religion which explains airplane accidents based on the sinning nature of people around the world. People sin, therefore God punishes us with airplane accidents that are not necessarily directed at sinners. This theory predicts future airplane accidents if people continue to sin. Does the nonspecific prediction of future airplane accidents count as a proper prediction?

Well, the model being proposed looks something like this:

airplane accidents = God(sin)

If these variables represented the probability of an airplane crash and the aggregate of sin or something along those lines, then my standard argument against the theory would be that the function "God" is not defined. The connection between the two variables would be so mysterious that it would be like an infinite order polynomial, and no foreseeable amount of fine tuning will generate a particular prediction. So the original "explanation" would degenerate into a claim that "if we had a predictive theory, it would be explanatory. If we knew the mind of God, then accidents would be predicted and explained." In other words, this is a reference to an explanation we don't have, and it has no explanatory power.

But my friend was not asking so simple a question. He wants to know how we draw the fine line between a predictive theory and a non-predictive one. In particular, is it possible to weaken the prediction and salvage the theory's explanatory power? Can we rig up this formula to represent the mere existence of airplane accidents and sinning? Can we theorize that the mere existence of sinning implies the existence of airplane accidents?

Well, there are a few things that any such theory would have to avoid if it's going to be more than the false pretense of a prediction. The theory can't claim that the elimination of sin is impossible, or that the other factors in airplane crashes make it impossible to test the claim. If a theory did these things, it would merely be pretending to make predictions.

But let's suppose that the advocates of this hypothetical religious theory accept that sin could be eliminated and that their claim is actually testable in principle, even if difficult in practice. Are there any other problems?

Yes. The problem is that God has nothing to do with the prediction.

Suppose I explain the electrostatic force of attraction between two spheres in terms of the electrical charges on each sphere and the square of the distance between the spheres. This is known in physics as Coulomb's law. That is, I provide my prediction as a formula. I can use this formula to explain the force of attraction between charged objects. I can say that sphere A is attracted to sphere B because of Coulomb's law.

Now suppose that I also attribute the attraction between charged objects to the work of undetectable faeries. Something is obviously wrong with this. Faeries are not known for imposing inverse-square laws of attraction. The existence of faeries does not predict the formula. It has nothing to do with the predictive theory, and has simply been gratuitously slapped onto a naturalistic explanation. In short, the faeries aren't doing any predicting.

I could try to wriggle out of this by saying that faeries are ultimately responsible for the attraction, and that by discovering Coulomb's law of electrostatic attraction, we are learning something new about undetectable faeries. However, I could replace the word "faeries" with undiscoverable Theory of Everything (ToE) and claim the same excuse. Yet, everyone would reject this. If a ToE existed and we knew what it was, the theory of everything would predict the electrostatic attraction formula. However, the ToE isn't doing any explaining here. The predictive power of this theory has no more to do with the ToE than it does with faeries. If we had a theory of faeries which cause electrostatic attraction, such a theory would predict Coulomb's law, but we don't have such a theory of faeries, so the faeries predict nothing.

So, we can extend our original list of specious explanations. An theory loses its explanatory power when the theory
  • Fails to make any predictions, and merely restates our observations.
  • Fails to make a prediction because it refers to a theory that we do not have (even though the theory would be predictive if we actually knew any of its details).
  • Makes a prediction, but fallaciously attributes the explanatory power of the predictive relationship to parts of the theory that are non-predictive.
Most of the time when theories fall prey to this last error, they are positing some entity that is alleged to be responsible for the prediction in question. The key to uncovering the error is to ask how this entity is defined.

If the entity refers to the prediction rule itself, there's no problem. This is the case in a scientific law, like Coulomb's law. It is the law itself that is responsible for the prediction (or rather it is simply the nature of the stuff one is observing that it follows the law). Similarly, a physical theory (which leads to many laws) is no problem because posits entities that are components of the prediction-making mechanism. For example, while quarks have never been seen directly, they are the focus for generating many rules about the behaviors of elementary particles. Yet, quarks do not refer to anything more than this. Quarks do not have any existence beyond the predictive theory. For example, quarks do not have any moral status because they are not part of any predictive moral theory.

On the other hand, if the responsible entity is defined outside of our rule-making system, it may be illicit. This is the case for God and the Theory of Everything. In such cases, the entity is presumed to exist independent of any particular set of predictions.

Of course, there is a way for the entity to be defined outside of the rule-making system and yet not be illicit. If the entity is already defined as an element of a known rule-making system, then the entity may have a chance to be explanatory. Here's an example.

The Pacific Ocean is part of a predictive model. If you go to the Western coast of the United States, you'll see a very large body of cool, salty water. This body usually has waves breaking on the shore. This body of water is called the Pacific Ocean, and it is predictive in space, time and numerous physical properties. Hence, if I am in Los Angeles and I walk far enough to the west, I predict I will get my feet wet. Why? Because I have this predictive thing called the Pacific Ocean that is defined by its geographic and physical properties.

Now suppose I am trying to explain the formation of Monterey Bay. I can theorize that the Bay was caused by the action of the Pacific. In this case, the Pacific is not being invented for the purposes of explaining the bay. Rather, it was invented to explain other things, but may also explain the erosion of Monterey Bay. The Pacific becomes explanatory of Monterey Bay when a mechanism is cited by which the Pacific can erode bays.

Every explanatory entity can be defined as "that which predicts X." God and invisible faeries are not defined by what they predict, and so they fail to be explanatory.

Critics of this conclusion will say that not everything that exists is predictive. In other words, they may argue that God exists and is a meaningful concept even if God predicts nothing. I disagree, but this point is irrelevant. The question at hand is whether an entity is explanatory, not whether it exists.

I apologize for the verbosity and lack of clarity in this post. It took me a while to think it through. I'm sure I'll come up with abbreviated ways of saying the same thing.

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