No and this seems to the thing that Bri and yourself are struggling to understand when you use these "5% probability" statements.
Try it from this approach:
Can I ever say that for a standard die that there is a "1 in million chance that I can roll a zero"?
The answer has to be "no" and the reason why you have to say no is that a die does not contain a "zero side" since it does not exist.
As soon as you state that something has a probability of "existing" you are assuming it can exist therefore when you shove that into an argument about whether something exists or not you have already assumed it can exist.
You mean by standard die a six sided die? I usually use 10 sided ones being an Ars Magica author, and yes there is a 1 in 10 chance one will roll a '0' on that.
OK, yes I fully understand your argument. A zero can not be a possibility on a six sided die (assuming a standard one numbered 1 to 6 - I have plenty of six sided dice with zeros on in my dice collection).
So you are saying that the premise that X is a 1 in whatever chance fails, because X does not exist. So one has to postulate known entities for X to have any meaning? That is true if you use a Frequency interpretation of probability sure - but not if you use Classical, Logical, or Subjective bases for probability.
This is not a frequency probability.
I actually mentioned this about six pages back when I linked to the article on Interpreting Probability in the Stanford Encyclopedia of Philosophy. I think most people never followed the link, because they assumed my comment that our understanding of probability was problematic to mean "we are not very good at understanding probability" - true enough, but not at all what I meant --
http://plato.stanford.edu/entries/probability-interpret/
Bayesian theorems use
Evidential Probability - not
Frequentism. Philosophers of mathematics disagree on whether
Evidential Probability is based on the
Logical, Epistemic, Classical or
Subjective interpretation of Probability, but one thing they all agree on is that it is not a Frequency Probability. So the die analogy, which is a classic example of postulating probability in frequentist terms, fails if applied to a Bayesian theorem.
Somehow I rather suspect Ivor and Linda know far more about maths and probability than I ever will - and they should be able to confirm if I am making these terms up, or if I am in fact completely correct.
I'll get back to discussing Joes objections late tonight - still working flat out on book, just dropped in to say hi.
cj x
