If probability is objective, what is its nature? What kind of thing does P denote? Is it sensible to be realists regarding probability?
>>8229890
Probability is not objective. Probability is shit.
I've thought of a better model for probability in where if something has a bigger chance of happening, it will always happen.
For example, for any coin in existence if you flip it, it will always fall in the same face because all coins have a deformity that will make it have a 50.000000000001% of being heads or tails instead of the other possibility.
This world would be objectively better for us mathematicians. However, other things like dice rolls would get realy fucked up.
You throw a dice and want it to fall in either 3,4,5 or 6. Because it has a higher chance to fall on these numbers that on the other possibility (1 or 2) it will always fall in 3, 4, 5 or 6.
But you can also frame this probability the other way around. Your chances of getting 1,2,3 or 4 instead of 5 or 6 are very high so it will always happen.
So in configuration will dice land? Always on 3 because in this objective probability universe 3 is the only number that can satisfy both realities.
Also if you frame your probability in terms of getting a 1,2 or 3 instead of a 4, 5 or 6 then that is 50/50 so the probability function will collapse to the systems previously defined and the dice will still roll a 3 every single time.
Basically, this universe is gay as fuck.
>>8229904
>this universe is gay as fuck.
I mean the universe we currently live in is shit. The universe I am describing is simply just better.
>>8229904
>I've thought of a better model for probability
This should be entertaining.
>>8229904
What you are describing sounds like possibility theory
https://en.wikipedia.org/wiki/Possibility_theory
>>8229992
fuzzy logic is fuzzy
Probability is not objective. It relates to your subjective epistemic state.
For example, someone else might have knowledge you don't have, and therefore assign different probabilities to various predictions, even though you are equally rational.
>>8229890
I would suggest that P denotes temporal density of a some qualitative attribute assigned to some object.
Yes, but how can I win a game of black-jack 66.6666666..% of the time?
>>8229890
Probability depends on whether you take the frequentist or bayesian philosophy.
Let's say, in a coin flip, the probability that it lands heads is P = 0.5.
Frequentist: If you flip the coin over and over and over, the probability relates to the frequency of how many times the result happens overall. AKA, I flip 10 billion times, and it lands heads 5 billion times, the frequency is 0.5. Extend this to all probability, and an infinite amount of repeats.
Bayesian: The probability P = 0.5 represents the belief you have that the coin will land heads. In another context, it's what you predict given that there is *uncertainty* and unknowns; that is, you take the fact that you don't have 100% of the information into account. This is often used in the context of past data + original belief, aka bayes law.
Which philosophy you take depends on the problem, ideally. For exampe, frequentist approaches don't really make sense for the phrase, "The probability that Trump wins is 0.55", as this election only happens once. While you can image it happening over and over in parallel universes and using the frequency of wins, this would be wrong: If you held this election 10000 times over, whoever wins will always win and whoever loses will always lose *unless you change something in that parallel universe*. In this situation, the bayesian approach is better, as it represents your belief given the uncertainty (AKA given that you don't have all the information necessary to make the decision).