Grace Notes

What does it mean to say what the probability of something is. For example when the weatherman says that there is a 30% chance of rain, what does that really mean?

Start with the simplest thing, a coin toss. A fair coin toss. The odds of a head coming up are 50%. But when we toss the coin it’s either heads or tails. One possible meaning is that if we toss the coin often enough, we’ll get approximately 50% heads. Mathematicians make this precise, but in terms of probability. So we’ve replaced the probability of the outcome of simple coin toss with a complicated mathematical gadget, again defined in terms of probability.  It is a mathematical advance, but not a philosophical one.

Another way to think about this is to consider wagering on the outcome. Here the rational view would look with equal favor on taking either heads or tails, with each player wagering a like amount. But this does not entirely get us out of the difficulty. There are risk averse people who consider the loss of a dollar worse than the gain of a dollar good, and they would have to be offered compensation before they would be willing to accept the wager. Say heads wind $1.25 while tails loses $1.oo. That certainly doesn’t match the 50-50 probability we associate with a fair coin toss. Or someone who, perhaps for superstitious reason, only wants to bet one way.

The fact that the toss is to occur doesn’t get us out of the difficulty either. Toss the coin into a box where the outcome is unknown. Wagering is still reasonable on whether the outcome will be revealed as a head or a tail. Yet it is already determined.

This leads me to ask: is probability of an event occuring intrinsically bound up with the subject, and not just the object?

This entry was posted on Saturday, April 18th, 2009 at 8:40 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.