So my thoughts on this lead me to believe that this may be a philosophical question as much as a mathematical question. That said, I find it hard to believe that no mathematician has ever contemplated the issue. My hypothetical will sound silly at first but please read through the question because it does raise a serious question.
If one claims that if I can snap my fingers once I will transform into an elephant, and if I clap my hands I will turn into an elephant for a minute then a lion, how would statistics deal with calculating the relative odds of these two occurrences?
One thought is that the odds of the elephant transformation occurring alone is greater than both the elephant and lion transformations. I think at first this seems logical because the odds of two events happening, more so in sequence, are generally considered less likely than one of the events. However, after further reflection, I think this answer is wrong.
My reasoning is that statistics is a science and therefore its assertions must be based on scientific data. There must be some standard of evidence before anything is accepted as possible. I think we will all agree that there is zero evidence in all of human history to support the proposition that either event is possible. Further, all applicable fields of human knowledge would support that it is impossible for either event to happen. Thus, IMO, absent any evidence to contradict all applicable human experience, statistics, as a science, must conclude that both the elephant event alone and the elephant + lion event must be considered to have an equal 0% chance of occurring.
While the above hypothetical is silly, this question has real applications in philosophical debates, which I would rather not specifically detail to eliminate the odds of creating bias.
Thank you for your consideration.
Thank you all very much for commenting! Obviously, some very intelligent people have afforded me some of their valuable time.
I read all of the comments more than once and I must admit, it’s clear that all of the commenter’s proficiency with mathematics so far outpaces my own that at times I find myself struggling to understand some of what is written. My proficiency is with debate and reason, which is why I came here for guidance.
Nonetheless, I feel fairly certain I am not getting the answer that must exist, but rather advanced mathematical analysis. My fault I’m sure so let me rephrase my question.
My judgment and thinking on this subject persuades me that there must be a mathematical axiom that directly deals with my issue. I see now that I should have made that point clear. My thinking is as follows:
Everyone can remember the classic example of the odds of any outcome in rolling a true six sided die, one in six. To my thinking for that to be true certain outcomes must be disregarded because they are impossible by all human experience, such as the die turning into a butterfly and flying away, or the rules of gravity failing to force the die to the floor.
If such silly outcomes, and countless others, were not eliminated from consideration, the odds of any particular outcome of rolling a six sided die would not be one in six but something less. So based on this thinking, my question is what is the mathematical axiom that dismisses from a statistical equation these silly outcomes that defy all human experience.
Apologies if I defer from speaking in mathematical ease on this issue but (obviously) I do not have mathematical expertise so I can’t really think well in that language. Nonetheless, my reasoning tells me there must be a math/scientific axiom that addresses this issue.
So Lord Shark the Unknown, user296602, Siong Thye Goh, r.e.s., and BruceET have put a "hold" on my inquiry because it is "off topic."
Please explain why so I can respect your opinion and change my inquiry appropriately.
Ok so it seems that the answer is that statistics works with the assumptions one brings to the equation and does not extend to evaluating the quality or veracity of those assumptions or the methodologies by which those assumptions are drawn.
Thus, it appears my question is more about scientific method.
Thank you all for your time and consideration.