p_min

In discussing the "fine-tuned universe" argument at PZ Myers' blog Pharyngula, I tackle the usual fallacy regarding unlikelihood. In many arguments advanced by so-called Intelligent Design theorists, it is argued that the very low likelihood of some physical state forces the observer to concede the point that design has been involved.

Indeed, this argument-by-unlikelihood is the foundation of intelligent design.

It's crap. This is what I say
(original typos included for posterity's sake)

As a final note, this "fine-tuning" argument, like many arguments involving probability advanced by IDers, (not that I'm accusing steve of being one) is based on the implicit notion that events that are highly improbable could not possibly have happened by chance.

Whenever this kind of argument occurs, I have to ask: just what is the minimum p value for which something with probability p can happen by chance? People who make these kinds of arguments misunderstand the relationship of probability and statistics with science. All that probability and statistics can do is assign relative value to competing, well-form scientific hypotheses. Statistics alone cannot be used as a justification for an argument or theory. Even if somebody were to say "the probability of the universal constants being exactly what they are is 10^-425665327" I would say: "so what?" Setting aside for the moment the dubious premise that this probability can be well-defined and meaningful, it still doesn't mean a damned thing to describe the probability of an event when we already know that the event has happened.

Since we know the event has happened, and we know that there is no lower bound p_min which forms the mathematical boundary of chance, telling me that p[X] is really, really low for some event X for an event X that I observe does not imply, by itself, that the event X did not happen by chance.

As a demonstration of this principle: get a bag full of, say, 100 20-sided dice. Roll them in order, noting the number rolled on each. Whatever result you get, the odds of it having happened by chance is 20^-100. And that's a really, really small number! And yet, to all apperances, that result just happened by chance.