Ready? Put on your best straight face, recall that global temperatures have not increased for a decade, and that it’s actually been getting cooler, then repeat with Brenda Ekwurzel, of the Union of Concerned Scientists—what they’re concerned about, heaven knows; perhaps replace “concerned” with “perpetually nervous”—repeat, I say, the following words: “global warming made it less cool.”
Did you snicker? Smile? Titter? Roll your eyes, scoff, execrate, deprecate, or otherwise excoriate? Then to the back of the class with you! Because what Ekwurzel said was not wrong, because it is true that the theory of global warming is consistent with cooler temperatures. The magic happens in the word consistent.
While there might be plenty of practical shades of use and definition, there is no logical difference between a theory and a model. The only distinctions that can be drawn certainly are between mathematical and empirical theorems. In math, axioms—which are propositions assumed without evidence to be true—enable strings of deductions to follow. Mathematical theories are these deductions, they are tautologies and, thus, are true.
Empirical theories, while they might use math, are not math, and instead say something about contingent events, which are events that depend on the universe being in a certain way, outcomes which are not necessary, like temperature in global warming theory. Other examples: quantum mechanics, genetics, proteomics, sociology, and all statistical models: all models that are of practical interest to humans.
Just like with math, empirical models start with a list of beliefs or premises, again, some of which might be mathematical, but most are not. Many premises are matters of observation, even humble ones like “The temperature in 1880 was cooler than in 1998.” The premises in empirical models might be true or uncertain but taken to be certain; except in pedantic examples, they are never known to be false.
It is obvious that the predictions of statistical models are probabilistic: these say events happen with a probability different than 0 or 1, between certainly false and certainly true. Suppose the event X happens, where X is a stand-in for some proposition like “The temperature in 2009 will be less than in 2008.” Also suppose a statistical theory of which we have an interest has previously made the prediction, “The probability of X is very, very small.” An event which was extraordinarily improbable with respect to our theory has occurred. Do we have a conflict?
No, we do not. The existence of X is consistent—logically compatible—with our theory because our theory did not say that X was impossible, merely improbable. So, again, any theory that makes probabilistic predictions will be consistent with any eventual observations.
Global warming is a statistical theory. Of course, nowhere is written down a strict definition of global warming; two people will envision two different theories, typically at the edges of the models. And this is not unusual: many empirical theories are amorphous and malleable in exactly the same way. This looseness is partly what makes global warming a statistical theory. For example, for nobody I know, does the statement “Global warming says it is impossible that the temperature in any year will fall” hold true. The theory may, depending on its version, say that the probability of falling temperatures is low, and as low as you like without being exactly 0; but then any temperature that is eventually observed—even dramatically cold ones—are not inconsistent with the theory. That is, the theory cannot been falsified1 by observing falling temperatures.
It is worth mentioning that global warming, and many other theories, incorporate statistical models that give positive probability to events that are known to be impossible given other evidence. For example, given the standard model in physics, temperature can fall no lower than absolute zero. The statistical global warming model gives positive probability to events lower than absolute zero (because it uses normal distributions as bases; more on this at a later date). But even so, the probabilistic predictions made by the model are obviously never inconsistent with whatever temperatures are observed.
Incidentally, even strong theories, like, say, those used to track collisions at the Large Hadron Collider, which are far less malleable than many empirical models, are probabilistic because a certain amount of measurement error is expected; this ensures its statistical nature (space is too short to prove this).
Now, since, for nearly all models, any observations realized are never inconsistent with the models’ predictions, how can we separate good models from bad ones? Only one way: the models’ usefulness in making decisions. “Usefulness” can mean, and probably will mean, different things to different people—it might be measured in terms of money, or of emotion, or by combination of the two, or by how the model fits in with another model, or by anything. If somebody makes a decision based on the prediction of a model, then they have some “usefulness” or “utility” in mind. To determine goodness, all we can do is to see how our decisions would have been effected if the model had made better predictions (better in the sense that its predictions gave higher probability to the events that actually occurred).
Unfortunately for Ekwurzel, while she’s not wrong in her odd claim, global warming theory has not been especially useful for most decision makers (those that make their utility on the basis of temperature and not on the model’s political implications). It is trivial to say that the theory might be eventually useful, and then again it might not. So far, the safe bet has been on not.
1Please, God, no more discussions of Popper and his “irrational” (to quote Searle) philosophy. This means you, PG!