Posted: Jan 08, 2015 9:13 pm
Lowpro wrote:Again I agree with all the stuff you've posted (mostly). The issue I have is that when you wanted to make a probability of placing the coin heads up or assuming it landed heads up from a flip are independent to the fact it's found face up. Maybe that's what you meant the entire time (and after reading again, it probably was). I just didn't interpret it that way when I read it.
There's a big difference between the sample space of "heads or tails" aka [0,1] from the coin being flipped and NO SAMPLE SPACE, where the agent makes the coin face up. The latter makes the coin impossible, it's nonsensical. So yes this was purely a semantics issue to me, that's all. Have a nice day chap!
As you say I think we agree on almost all of this (which is good, since it's mathematically grounded, so we should expect quite a lot of agreement between informed individuals!), and a little disagreement over the margins which doesn't really matter.
There is a sample space in the latter example - it only has one outcome with nonzero probability though. Clearly there is nothing impossible about the idea of an agent placing a coin heads face up (although in my original example the agent is a fairy creating the coin from nothing, which I agree is impossible). My point was only that even though we can be certain that if an agent has placed the coin heads face up it will be face up (and this I feel as a tautology is about as certain as it gets) it tells us nothing about the distribution of how often coins actually are placed heads face up as opposed to tossed - although again we can be pretty certain that such a distribution actually exists and we could attempt to chart it by observing humans covertly in some location they may fiddle with change, such as a public cafe.