Say we flip a quarter and cover it up so we can't see the result. It could either be heads or tails. The probability of it being heads is 50%. But the coin has already been flipped. So, based on your argument above, the probability for it being heads is either 100% or 0% based on whether or not it actually is heads.
Does probability not apply to things that have already happened, even if we don't know the outcome? It seems that you are arguing that probability can only apply to future possibilities and can't really be applied to something that already is, regardless of whether we know the outcome.
Is there a difference in the mathematical sense between probability and possibility?
You bring up a very astute point that probability is being used as an asssesment of someone's certainty and not the actual outcome.
My only caveat is that this doesn't preclude a probability being assigned to god's existence. Though, how it could honestly be anything other than 50/50, I don't know. (How would you weight an argument or a piece of evidence? It seems like it would be necessarily arbitrary.)
Very good point. Doesn't matter how certain someone thinks they are. Their certainty has not bearing on whether it's actually true.
"Say we flip a quarter and cover it up so we can't see the result. It could either be heads or tails. The probability of it being heads is 50%. But the coin has already been flipped. So, based on your argument above, the probability for it being heads is either 100% or 0% based on whether or not it actually is heads.
Does probability not apply to things that have already happened, even if we don't know the outcome? It seems that you are arguing that probability can only apply to future possibilities and can't really be applied to something that already
is, regardless of whether we know the outcome."
That is correct. The coin flip example was exactly how one of my stats instructors explained the difference.
If you flip a coin it has a chance to land on heads or tails. This chance exist every time you flip the coin, you can get either heads or tails. There are two possible outcomes. However, after the coin has landed it is either heads or tails and that will not change no matter how many times you go away and come back to look at it. There are no possible outcomes as the outcome has already resolved.
Probability needs a chance mechanism, as it is a measurement of possible outcomes.
"cover it up so we can't see the result. It could either be heads or tails."
That just means you are taking a guess on what the outcome was (past tense). The probability of you being right is associated with your guess, not the potential outcome of the coin flip (as the coin landed, there is no more potential out come). You can use empirical data and probability to help you make a more reliable guess.
"Is there a difference in the mathematical sense between probability and possibility?"
Here is what every stats teacher keeps drilling into every stats student (paraphrased of course). Statistics does not prove anything, it is not the truth. It is not meant to be considered alone, it is meant to be considered with the rest of the evidence.
A probability distribution is an approximation, it is not the true distribution. Sometimes we can know all possible out comes, like with the coin flip there are only two possible outcomes. We say each side has a 50% chance but that is not exactly the truth, the real chance is based on a number of factors such as which side was face up when was it flipped, the strength of the flip etc, etc, etc.
Now there are also times when the range of possible outcomes is just something we cannot possibly know or is far to large to actually calculate. So we have to use a random selection method, and use either a parametric distribution (and there is a bunch of stuff that goes with that) or we can simulate an distribution based on our data we collected.
"My only caveat is that this doesn't preclude a probability being assigned to god's existence. Though, how it could honestly be anything other than 50/50, I don't know. (How would you weight an argument or a piece of evidence? It seems like it would be necessarily arbitrary.)"
It does not exclude it in a subjective non-scientific sense, but it does exclude it from statistics, as stats is a science that adheres to the scientific method. If God is unfalsifiable for all the other sciences, then the same is true for stats. It really would be nothing other than just the arbitrary assignment of a number.
"How would you weight an argument or a piece of evidence? It seems like it would be necessarily arbitrary."
That would take a lot of explaining, because that is what stats does examines the evidence, but it comes down to the fact that you actually need evidence that fits the scientific criteria to examine.