Glen,
On closer reading of the issue you are interested in, and upon
re-consulting the sources I was thinking of (Bunge and Popper), I can
see that neither of those sources directly address the question of
whether time must be involved in order for probability theory to come
into play. Nevertheless, I think you may be interested in these two
sources anyway.
The works that I've been reading from these two folks are: /Causality
and Modern Science/ by Mario Bunge and /The Logic of Scientific
Discovery/ by Karl Popper. Bunge takes (positive) probability to
essentially be the complement of causation. Thus his book ends up being
very much about probability. Popper has an eighty page section on
probability and is well worth reading from a philosophy of science
perspective. I recommend both of these sources.
While I'm at it, let me add my two cents worth to the question
concerning the difference between probability and statistics. In my
view, Probability Theory /should be /defined as "the study of
probability spaces". Its not often defined that way - usually something
about "random variables" appears in the definition. But the subject of
probability spaces is more inclusive, so I prefer it.
Secondly, its reasonable to say that a probability space defines
"events" (at least in the finite case) as essentially a set of
combinations of the sample space (with a few more specifications).
Nothing is said in this definition that requires that "the event must
occur in the future". But it seems that many people (students) insist
that it has to - or else they can't seem to wrap their minds around it.
I usually just let them believe that "the event has to be in the future"
and let it go at that. But there is nothing in the definition of an
event in a probability space that requires anything about time.
I regard the discipline of statistics (of the Fisher/Neyman type) as the
study of a particular class of problems pertaining to probability
distributions and joint distributions: for example, test of hypotheses,
analysis of variance, and other problems. Statistics makes some very
specific assumptions that probability theory does not always make: such
as that there is an underlying theoretical distribution that exhibits
"parameters" against which are compared "sample distributions" that
exhibit corresponding "statistics". Moreover, the sweet spot of
statistics, as I see it, is the moment and central moment functionals
that, essentially, measure chance variation of random variables.
I admit that some folks would say that probability theory is no more
inclusive than I described statistics as being. But I think that it is.
Admittedly, what I have just said is more along the lines of "what it is
to me" - a statement of preference, rather than an ontic argument that
"this is what it is".
As long as we're all having a good time...
Grant
On 12/13/16 12:03 PM, glen ☣ wrote:
Yes, definitely. I intend to bring up deterministic stochasticity >8^D the
next time I see him. So a discussion of it in the context QM would be helpful.
On 12/13/2016 10:54 AM, Grant Holland wrote:
This topic was well-developed in the last century. The probabilists argued the
issues thoroughly. But I find what the philosophers of science have to say
about the subject a little more pertinent to what you are asking, since your
discussion seems to be somewhat ontological. In particular I'm thinking of
Peirce, Popper and especially Mario Bunge. The latter two had to account for
quantum theory, so are a little more pertinent - and interesting. I can give
you more specific references if you are interested.
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