Dan Fabulich says:
> 'What is your name?' 'Clint O'Dell.' 'IT DOESN'T MATTER WHAT YOUR NAME
I would like to take this opportunity to report that I find the above SHOUTED sentences jarring and mildly annoying in their repetition every time I encounter them, about as much as noisy radio ads. This disinclines me to read the posts they head. Are they meant to serve some purpose other than annoying the reader?
> > I know the laws of probability are real not because I BELIEVE in it but
> > because I CAN PROVE IT.
> <devil's advocacy>
> Ahem. I assert that you cannot prove it. Robert attacked probability on
> its strongest side... What would you say to this experiment?
> I assert that it is completely impossible for you to flip a coin 1 million
> times and have it turn up heads every time. When I say completely
> impossible, I mean that it will never EVER happen, no matter how many
> times you try.
> </devil's advocacy>
It gets worse. If he did go ahead and flip the coin and get the result you predict he cannot, you'd probably question the "fairness" of the coin. There is a circularity in the definition of probability which is maddening to contemplate.
Just try defining probability in non-circular terms (synonomous terms marked with "*"): "When we say it is *probable* we mean that it is *likely* ... err, that is, we mean that if we repeat the experiment the proportions of the results will *tend to be*, um, no, the results will have a certain proportion, *within a certain confidence*. Ooops, um, give me a minute ..." So far, the only non-circular definition I have found is a mathematical definition claiming certainty in results iff we take limits as the number of experiments goes to infinity. (Any intermediate gains in certainty at high finite numbers of trials are usually themselves expressed as probabilities, which means it would take an infinite number of them to confirm them with certainty!) Another gambit is to shift the burden off to a "rational wagerer", which merely moves the circularity into the wagerer's head, ensuring it will be out of view.
Oddly, probability appears to be a concept which people intuitively understand but which can only be non-circularly defined in terms of infinite series. I have to wonder if that, too, begs the question, as it is an appeal to a non-testable hypothesis. (If only we could have infinite trials, you'd see!) There's something very fishy about probability.