Essentially Silly

Saturday, October 15, 2005
Via Tyler Cowan at shortstop to Russell Roberts at first, we find this article by Michael Mandel.

In it, he criticizes, not so much the recent Nobel Memorial Prize to Aumann and Schilling (no, it's not really a Nobel Prize, it's a Bank of Sweden Prize) but the notion that game theory is useful in economics. He says:

Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes -- from full cooperation to near-disastrous conflict -- are consistent with the game-theory version of rationality.


And I'm afraid that, in a development that also results in the immediate collapse of my metaphor in the first paragraph, both Cowan and Roberts have missed the catch. Mandel is making a category error in the whole argument: game theory is not a "scientific theory", it's a "mathematical theory", and the two are completely different orders of knowledge. It's a silly error, and an error of essence, not accident.

My point, however, isn't just to point out an error by two eminent bloggers, or make fun of a person writing for Business Week — although the temptation to do so when reading a column by a guy who happens to point out that he's a "journalist with a Ph.D." is pretty intense — but to use this as an example to talk about the same category error that happens over and over again, notable in talk about Intelligent Design, or about the status of atheism.

The error is actually simple in this case: "game theory" is a mathematical construct, not a theory in the sense of prediction and confirmation or falsification. His argument that game theory is not predictive is like making the argument that arithmetic is not predictive, or noting that euclidian geometry breaks down in the real world. von Neumann and Morganstern started with some basic observations and developed a mathematical theory based on combinatorics and probability which has turned out to be useful in thinking about other situations.

The category error lies in confusing the mathematical formalism with the use economists happen to make of it --- just like it would be a category error to claim that geometry is a dead end because it doesn't predict what a surveyor sees accurately.

To me, the thing that really struck me about this category error, though, is how common this becomes. In intelligent design, the ID theorists claim that "Darwin's theory of evolution" is false because it can't predict everything or can't explain everything — a standard that fits mathematical constructs, not natural science.

On the other hand, the devout atheists assert that notions of Diety must be false because they can't be confirmed with science; a category error for a number of reasons, but most specifically because it has logical issues in that a Deity could create a universe in which all experiments to confirm or deny the Diety's existence are true, false, or equivocal. (For a fuller discussion of this, see Steven Brams book Superior Beings: If They Exist, How Would We Know? : Game Theoretic Implications on Omniscience, Omnipotence, Immortality and Incomprehensibility.)

There are different kinds of knowing, different kinds of "truth": mathmatical, scientific, metaphysical.

How often do category errors among the kinds of truth lead to human suffering?

Update: revised "accident" for "argument" above: an error.

4 comments:

chuck said...

Hmmm... looks like anonymous knows how to get by the spam filters.

StY, would you say that attributing any physical reality or consequence to a Deity is a category error? It seems to me that one needs to define precisely what kind of Deity one is talking about in order to make that judgement. The existence of Jinns, for instance, is an hypothesis that can be tested, as they operate in the physical world.

MeaninglessHotAir said...

chuck, Looks like word verification got turned off somehow by accident and they were all over us.

Seneca the Younger said...

StY, would you say that attributing any physical reality or consequence to a Deity is a category error?

Hmmm. What do you mean by "physical reality or consequence"? It would appear that there is a physical universe, so a Creator thus must have some physical consquence. Ergo sum. Credo.

What I would consider a category error would be an attempt to use the scientific mode of knowing to prove or disprove the existence of Deity, because a superior Creator could create existance in such as way as to thwart any such experiment. If it can't be determined by experiment, it's unknowable to the scientific mode.

Notice, however, that for the devout atheist, this often leads to another category error, the assertion that if it isn't knowable by science, it's therefore, and by that very fact, not knowable. This can be proven by counter-example: no physical experiment can be proposed to determine the standing of the Axiom of Choice, but the axiom is none the less knowable in some sense, and has consquences that can be applied.

chuck said...

because a superior Creator could create existance in such as way as to thwart any such experiment.

Such a creator could, I suppose, create a universe that didn't require the postulate of a creator to explain it's features. Though one would still be left with the question as to why there was a universe in the first place. And, of course, the problem of the source of the building materials.

but the axiom is none the less knowable in some sense, and has consequences that can be applied.

I always thought the axiom of choice seemed plausible and it brings a satisfying consistency to mathematics. But it is not clear to me that it is "knowable" as opposed to merely imaginable. Nor is the number of choices unrestricted: one can only choose as many times as there are elements in some set.

Hmmm... this sort of thinking makes my head hurt.