Originally posted by twhitehead
Yes, I meant unconventional.
[b]I assume the whole of modern conventional science of statistics and probability theory is based on some kind of rigorous definition of probability (which I am not sure if I ever seen yet ) ?
The textbooks all seem quite rigorous and consistent to me.
Doesn't an explicit definition serve a purpose there?
Y ...[text shortened]... used to mean something different? '
And also why assign a numeric value to a binary position?[/b]
Are you saying: 'its got a purpose because everyone else has a purpose for their definitions' ?
No, I am saying 'my definitions has a purpose' (to define what I mean by probability ) .
I mistakenly thought you might be suggesting there is no point of a definition for probability which is why I pointed out the conventional definition for it has a purpose.
And also why assign a numeric value to a binary position?
You mean to a truth value? I think I have already answered that with "...my definition just happens to logically imply that analytic propositions have a probabilities is merely an accidental consequence of what I mean by probability."
And I am not asking 'why have a definition?' I am asking 'why borrow a word that is typically used to mean something different? '
Because what it more typically means is very nearly but not exactly what I mean by it and I simply cannot get my head around that exact convention meaning. I am simply incapable of forcing myself to think of probability in such a way as to reject the idea as truth values being equivalent to probabilities -
If you were to ask me my 'degree of certainty' that 1+1=2 and that I haven't make a mathematical mistake, I would both think and say "total certainty" i.e. I assign that 'degree of certainty', which I believe to be totally rational and therefore a true probability according to what I always naturally mean by probability, a probability of 1 (even though I wouldn't naturally explicitly say the superfluous comment of "It has a probability of 1" after I just said "total certainty" ) I find any other way of thinking about it too unnatural for my mind and, to my mind, even if/though not to other minds, perverse.
So, it has a purpose when applied to synthetic propositions?
It has no purpose applied to synthetic propositions. It is merely a matter of deduction from my definition of probability that is applies to synthetic propositions, whether I like it or not.
Does the conclusion of a logical deduction have to have a purpose to be flawless and correct?
Having said all that, You make me think I better not put into my book the definition of what exactly I always naturally mean by the word probability but rather make both my explicit definition of probability I put in my book and everything else I say in my book contrived to comply to the exact conventional meaning -I really don't like that! But cannot risk the repetition of my book being tarnished by heavy criticism of going against conventional wisdom -not worth the risk no matter how I look at it.
So I think I should explicitly state an extra criterion to my definition of probability I explicitly gave earlier in this thread that goes something like:
4, a probability cannot take on a value of exactly 1 or 0. One consequence of this is that no synthetic propositions can ever have probabilities, only analytic propositions can have probabilities.
One complication of that is that some philosophers consider the distinction between synthetic propositions and analytic propositions blurred and possibly meaningless. I will have to look into that matter later.