Perhaps I could have better phrased the complaint; I wasn't attempting to dive into the philosophical. The point was that the meteorologist is not "wrong" if it rains on a 30% chance or if the high temperature is off by a couple of degrees. Meteorologists deal with a lot of uncertainty (that they don't always communicate to us effectively). People need to understand that a 30% chance of rain only means that it likely won't rain (roughly 2:1 against). Still wouldn't hurt to take an umbrella.
As for the philosophical, I'd have to claim that a Probability is a quantitative expression of predictive uncertainty that exists within an informational system such as the human brain or, yes, weather prediction models. Come to think of it, that might actually be helpful for people to understand the weather report. I just don't trust my coworkers to be able to parse most of those words.
The point was that the meteorologist is not "wrong" if it rains on a 30% chance
Well, is the forecast falsifiable, then? Can it be wrong? How would you know?
Probability is a quantitative expression of predictive uncertainty that exists within an informational system such as the human brain or, yes, weather prediction models.
So the probability exists purely in the map, but not in the territory? I am not sure quantum mechanics would agree.
Alternatively, what single concept from statistics would most improve people's interpretations of popular news and daily life events?