Sunday, December 31, 2006

Constructing Logical Fallacies for Fun And Profit

The Anthropic Principle is about as Odds-Are-One-y as anything outside this blog gets. We observe that there is life in the universe, ergo the universe must have evolved such that it can support life. In the possible universes where this didn't happen, nobody is hanging around the coffee shop on the corner discussing such things (because of course in universes whose physical laws don't support life, they don't drink coffee. They drink Post-Galactic, Black Hole-Warmed Plasma Beverage. Duh). You might conclude that this is the logical end of the line: there is no point in futher discussing the meaning of us being here versus being not here, because in only one of those cases can there be any discussion of any kind (this is certainly the viewpoint held and frequently advocated by those of us here at OaO). But there are still interesting questions one could ask about what We being Here Now might signify.

If Earth were the only planet one were aware of, one might reasonably wonder what the odds were that this one planet happened to exist at a particular distance from a middle-aged Type-G star such that water could exist in liquid form (yes, I know the odds of this are one, as it has already happened. Be with me in this other, non-OaO place for a second...). This being the popular scientific view for most of the history of man, a reasonable scholar operating under these a prioris might have looked at them and made this seemingly entirely logical inference: "I can think of two explanations for the existence of this planet which can support life. Either it was blind luck or it's the action of an unseen demiurge. The former is incredibly unlikely, therefore by strict laws of probability, it has to be the latter."

Actually, there was a third explanation: the universe is filled with an astronomically large number of stars, an astronomically large number of planets, and has been around for 13.7 billion years or so, so the appearance of at least one planet that has liquid water is not that surprising. The more perceptive among you will notice that the above argument looks an awful lot like an application of Occam's Razor. You might therefore conclude that the flaw in its reasoning is that there was at least one possible explanation our scholar didn't think of. But this is not why the argument is flawed.

We can summarize the logic behind the inference above like this:
  • I observe phenomenon X.
  • Phenomenon X has two possible explanations: E1, which has probability P1 of occurring, and E2 which has probability P2 of occurring.
  • P1 is much lower than P2, therefore E2 is the more likely explanation for X.
First, note that this is not Occam's Razor, which (very roughly) states that a simpler explanation for an observed phenomenon is more likely than a complex one. More to the point, there is no law of logic or mathematics that states this. It's a completely fallacious construction. Here at OaO, we say it this way: once the phenomenon has been observed, any odds go out the window.

As I've learned from The Trouble With Physics, this is of interest to current scientific thinking because they're now asking the same question about the universe. Given that we only observe one universe, it seems rather unlikely that it would be one with physical laws that allowed the formation of stars, galaxies, and planets. Having been fooled the first time around, the popular conclusion is that therefore there must be a multitude of 'verses, all with different physical laws, that can't be detected by current means. It's a good metaphor for the Earth being just one of many planets. But that's the only argument in its favor: again, the argument for it falls into the the same logical hole--the seeming incredible unlikelihood of the only universe we observe supporting intelligent life does not create any likelihood of many unseen others. There's no logical inference that would say that it does.

Next: The Fun and Profit part!

4 comments:

island said...

We observe that there is life in the universe, ergo the universe must have evolved such that it can support life.

No, that's not the anthropic principle, rather, this is a variant, "weak" interpretation of the physics, and it requires an unfounded leap of faith beyond the features of the observed universe to assume that other universal configurations are even possible.

Transient Gadfly said...

My summary at the start is indeed the weak hypothesis, which, as you might have guessed from a cursory glance around the blog, is the only version of the principle that I acknowledge as reasonable.

I'm not sure what the second part of your comment means, though. More precisely, the statement that other observable universes with different physical laws aren't possible seems to require some supporting argument.

Transient Gadfly said...

...sorry, that should read, "other unobservable universes...

Periapse said...

I've always had a problem with even the assertion that the values of various universal constants represent some unlikely miracle, either of odds, deities, or multiple universes. It's not even an OaO problem. For me it just seems extraordinary to assume in the first place that universal constants are part of some stochastic "input state" to the universe. Just by saying that our universe's constants have unlikely values pretty much assumes that variation is somehow possible. This never been observed. Sure, we can do math and plug in different values for the fine structure constant or whatever.

One can remark on the fact that ginger cats are almost always male. How extraordinary! But if we were in a universe where ginger cats were evenly distributed with regard to sex, we'd never wonder about it -- say the weak anthropic folks. Others instead postulate that there are other worlds, and on some of them ginger cats are almost always female. But neither explanation has any merit once you dig deep enough into genetics and sex-linked characteristics, the sex of a ginger cat is not a stochastic process.