No I'm not. My first comment in response to Bernard's post about/with which you started arguing was:
EFLImpudence said:
Surely that which is vanishingly small cannot be a probability.
Ahhhh! At long last, I think I now understand the 'problem' which has led to all this discussion and disagreement, and I suppose it is largely my fault for not looking carefully enough at what you had written - which related to a different use of the word "probability" from that which Bernard had used in the post to which you were responding:
bernardgreen said:
I am never happy when probabilities are dismissed simply because they are vanishly small.
The word "possibility" can be used in two different senses, both of which are documented in dictionaries ....
Firstly, as I now realise was probably what you were thinking about (and have been talking about all the time), it can be used to mean "probable" - as in "such an event is a probability". In that sense, it is analogous to such statements as "such an even is a certainty", "such an event is an impossibility" etc.
The second sense it which the word can be used [as in bernard's post to which you were responding, Eaton's document and everything I and JohnD have been saying (and, indeed, IMO by far the most common way one sees the word used)] - refers to an indication of the '
extent to which something is likely to happen'. It is therefore used as "the probabilty is X" (or, per bernard's post, "the probabilities are X"), where X can be a number, percentage, or some descriptive words such as high/large, low/small or, even, 'vanishingly small'. Although you call that use of the word "probability-theorist-speak", it is also, as I have indicated, the first definition in the Oxford Dictionary.
If you accept that, do you agree that "being a probability" (which is what you have seemingly been talking about throughout) is totally different from "having a probability of X" (which is what bernard, Eaton, JohnD and I have been talking about)? If so, do you also accept that although a rare event "is not a probability", it does "have a probability ('of X')" (second sense) - where X can be a number, or even such things "vanishingly small"?
If your answers to both those questions are 'yes', then I think that this discussion has (eventually!) reached a fairly conclusion, and I apologise for not having realised earlier that you were talking about a different use/meaning of the word from that which the rest of us were talking about.
Kind Regards, John