Excellent! My opponent will be very happy when I make that concession. It's interesting that, for this argument, I've adopted the Platonic perspective despite being a constructivist myself. And it's interesting that my current position (that the math world is extant and static) seems to rely a bit on viewing probability theory as a special subset of math overall. But that perspective seems to encourage me to think about the ontological/metaphysical aspects. Perhaps it's only because I'm not a mathematician.
Thanks! On 12/13/2016 05:00 AM, Eric Charles wrote: > I don't have an answer per se, but I have some relevant information: > > Back in the early days of statistics, one could become a pariah in the eyes > of the field if it became suspected one had surreptitiously used Bayes' > Theorem in a proof. This was because the early statisticians believed > future events were probable. They really, deeply believed it. They were > defining a new world view, to be contrasted with the deterministic world > view. If you smoked, there was a probability that in the future you might > get cancer; it was not certain, nothing was predetermined. In such a > context, any talk of backwards-probability is nonsensical. After you have > lung cancer, there is not "a probability" that you smoked. Either you did > or you did not; it already happened! Thus, at least for the early > statisticians, people like Fisher, time was inherent to claims about > probability. > > Now, it is worth noting that one can wager on past events of any kind, > given someone willing to take the bet. And in such a context, Bayes' > Theorem can be mighty useful. The Theorem is thus quite popular these days, > but that is a different matter. Whatever the results of such equations are > --- between 1 and 0, having certain properties, etc. --- so long as the > results refer to past events, Fisher and many others would have insisted > that the result is not "a probability" that said event occurred. > > Also, from what I can tell, as mathematicians became more prevalent in > statistics, as opposed to the grand tradition of scientist-philosophers who > happened to be highly proficient in mathematics, such > ontological/metaphysical points seem to have become much less important. -- ␦glen? ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
