Thanks! Everything you say seems to land squarely in my opponent's camp, with the focus on the concept of an action or event, requiring some sort of partially ordered index (like time). But you included the clause "but doesn't have to be". I'd like to hear more about what you conceive probability theory to be without events, actions, time, etc.
For the sake of this argument, anyway, my concept is affine to Grant's: "the study of probability spaces". Probability, to me, is just the study of the sizes of sets where all the sizes are normalized to the [0,1] interval. We talk of "selecting" or "choosing" subsets or elements from larger sets. But such "selection" isn't an action in time. Such "selection" is an already extant property of that organization of sets. Likewise, the "events" of probability are merely analogous to the events we experience in subjective time. Those "events" are (various) properties or predicates that hold over whatever set of sets is under consideration. Those "events" don't _happen_. They simply _are_. Since your language seems to depend on the idea that those predicates must _happen_ (i.e. at one point, they are potential or imaginary, and the next they are actual or factual), yet you say they don't have to, I'd like to hear you explain how "they don't have to". What are these "events" absent time (or another such partially ordered index)? p.s. FWIW, I have the same problem with the concept of "function" and asymmetric transformations. I accept the idea of a non-invertible function. But by accepting that, am I forced to admit something like time? Or, asked another way: As all the no-go theorem provers keep telling us (Tarski, Gödel, Wolpert, Arrow, ...), are we doomed to a "turtles all the way down" perspective? On 12/13/2016 05:03 PM, Robert Wall wrote: > At the risk of exposing my own ignorance, I'll also say your question has to > do with the ontological status of any random "event" when treated in any > estimation experiments or likelihood computation; that is, are proposed > probability events or measured statistical events real? > > For example--examples are always good to help clarify the question--is the > likelihood of a lung cancer event given a history of smoking pointing to some > reality that will actually occur with a certain amount of uncertainty? In a > population of smokers, yes. For an individual smoker, no. In the language of > probability and statistics, we say that in a population of smokers we /expect > /this reality to be observed with a certain amount of certainty > (probability). To be sure, these tests would likely involve several levels of > contingencies to tame troublesome confounding variables (e.g., age, length of > time, smoking rate). Don't want to get into multi-variate statistics, though. > > Obviously, time is involved here but doesn't have to be (e.g., the > probability of drawing four aces from a trial of five random draws). An event > is an observation in, say, a nonparametric Fisher exact test of significance > against the null hypothesis of, say, a person that smokes will contract lung > cancer, which we can make contingent on, say, the number of years of smoking. > Epidemiological studies can be very complex, so maybe not the best of > examples ... > > So, since probability and statistics both deal with the idea of an event--as > your "opponent" insists--events are just observations that the event of > interest [e.g., four of a kind] occurred; so I would say epistemologically > they are real experiences with a potential (probability) based on either > controlled randomized experiments of observational experience. But is a > potential ontologically real? 🤔 > > Asking if those events come with ontologically real probabilistic properties > is another, perhaps, different question? This gets into worldview notions of > determinism and randomness. We tend to say that if a human cannot predict the > event in advance, it is random ... enough. If it can be predicted based, say, > on known initial conditions, then using probability theory here is misplaced. > Still, there are chaotic non-random events that are not practically > predictable ... they seem random ... enough. Santa Fe science writer and > book author George Johnson gets into this in his book /Fire in the Mind/. -- ☣ 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
