@pagan,
pagan;138266 wrote:
hi videcorspoon
yes thats a good analysis of the word unknowable. But we could be more specific and mean 'unknowable' in the sense of say 'the future' or 'hidden variables' or just plain 'a secret' with respect to a particular time or place, yet which will yield knowable phenomena in a different time or place. This potentially distinquishes the past from the future re the meaning of probability theory ..... but not necessarily so maybe.
"Unknown" and "unknowable" necessarily entail their own particular consequences and differ from one another. It's like saying "measurable" and "immeasurable." If something is unknown, there is a chance that it can be known later. To be unknowable is completely remove the possibility of it ever being known (it becomes a stable generalized set variable). If you attribute "unknowable" to the future, then you may possibly get away for it unless you dismiss induction. However, "hidden variables" are not unknowable, but unknown hidden variables yet to be known. We know they exist if we explicitly say they are hidden.
One other thing I would say though is that probability theory is not a crystal ball by any means. Probability theory is a closed system, like propositional calculus, predicate calculus, indicative calculus, modal calculus, etc. What is specified within the terms of a given proof is law. With this in mind, probability calculus itself is a subset of induction, and induction is never accurate because there exists the possibility that something else could occur which had not previously happened. You could have a 99.9% nearly identical set of events over a given amount of time and have within that frame some outlier which throws off the statistical probability by a potentially wide margin.
pagan;138266 wrote:
eg is it different to know the probability that the dice will be thrown such that a red face is up, compared to it has been thrown but you haven't recieved the information yet? You could argue in the latter case that the probability is 1 for whatever colour because it has happened! And again what is going on for the thought experiment versions of these two scenarios? If this is a different use of probability, then what validity does it have in the real world? If it isn't different in the mind, then what is the same between reality and the mind re probability?
There is something very odd about probability theory. Its sort of brain whirling. The bleeding obvious can turn out to be completely wrong. Why is that?
As an example of probability calculus and to answer your question, consider this extremely simple proof (not
proof proof but calculus proof). A single die is tossed once, however, we need to the probability of an even number landing.
First, there are a few things to consider, such as what modus of probability we will use and what specific rules we choose to attribute to the proof. Modus wise, we use the classical interpretation. What specific rules we use are those of a conditional probability, which is essentially equated to P (A|B), or the probability of A, given B. P (A|B) is the volume of possible outcomes in which A occurs among the possible outcomes of B. The formula is simple;
In a worded explanation, the proof is such that it takes the number of possible outcomes in which A and B occur divided by total number of possible outcomes, which is divided by the number of possible outcomes of B and the number of possible outcomes. This in turn yields the number of correct outcomes in which A and B occur over the number of possible outcomes in which B occurs.
The proof works out to this;
E means the result of the die landing even and L means the possible number of E is less (L) than 5 (assuming the die is 6 sided). In the case of the number of possibilities in which E and L occur, the probability exists such that E and L is true in two of six outcomes, and landing on an even (less than 5) is four in six.
So take this example into context with your questions. You ask, "
is it different to know the probability that the dice will be thrown such that a red face is up, compared to it has been thrown but you haven't received the information yet?You could argue in the latter case that the probability is 1 for whatever color because it has happened," you are right. Based on Kolmogorov's axioms (specifically axiom II), the maximum probability is 1. Axiom 2 states that the minimum probability is zero. Thus, everything in between determines the probability of x, which is pretty much infinite.
As to "
And again what is going on for the thought experiment versions of these two scenarios? If this is a different use of probability, then what validity does it have in the real world", probability is part of a closed system dependant on the truth functional molecular components. We could determine the probability of unicorns menacing the earth feeding on the blood of bunny rabbits and come up with a number. I think a mistake comes when probability theory is taken to be universally applicable and cross systematized. Suffice to say, my proof of unicorns not existing would not mesh well with the proof of unicorns menacing bunny rabbits, or even the ironic proof I have where the bunny rabbits explode once eaten by unicorns and only unicorns.
As to your question,
"If it isn't different in the mind, then what is the same between reality and the mind re probability?" You best ask Rene Descartes about that... but even he could not come to ultimate conclusions, only those which he knew most clearly and distinctly.
As to your question, "
There is something very odd about probability theory. Its sort of brain whirling. The bleeding obvious can turn out to be completely wrong. Why is that?"