- #36
fbs7
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Buzz Bloom said:Hi fbs:
This seems like a very strange question to me. If you say x ∈ X, you know something about x and X. Presumably you would know if x is a random variable if someone you believe to be knowledgeable tells you it is a random variable. What is needed by someone with the appropriate knowledge is that the process for obtaining values for x is a random process. So the randomness of a variable is determined by whether the process for obtaining values for the variable is a random process.
I am guessing you have some uncertainty about what it means for a process to be random. A random process is a process for which it is impossible by any means to know in advance what a particular value will be. This is the distinction between a random process and a pseudo-random process. If the process is pseudo-random, and you know the nature of this process and its initial conditions, in principle you can calculate the next value it will generate.
I hope this is helpful.
Regards,
Buzz
Appreciate it. I was stuck with the matter that logic is completely deterministic. If you have propositions A, B, C that are either true or false, then you'll always get other propositions D, E, F that are true or false as consequence from that. No changes, ever. So if f(x) = x2 and x=2, then always f(x) = 4. If so, then how could a "random" value ever be the result of a logical sequence from true/false propositions?
The Cox formulation untied that knot for me, through that abstract concept called "plausibility", which isn't mathematically defined -- it's an axiom. From what I understood, you don't have to define the process of rolling a dice, we just have to assume that plausibility(rolled-a-3) exists and ∈ [0..1]. Similarly, with Cox you don't need to define a process through which a ghostly hand will "choose" a fruit from a bag of fruits -- what's the hand? what's choosing? There's no need for that; you just assume that ∃ picked-an-orange and that plausibility(picked-an-orange) = plausibility(picked-an-apple) = plausibility(picked-a-lemmon) to get all kinds of useful calculations from that. There's no violation of determinism of logic that way.
I'm probably murdering poor Cox here, but that's how I untangled that knot, in my mind