Example: You want to calculate a probability = you attribute practical use to it and value and thus make it visible and open for interpretation.
I don't understand how you justify the "thus" in the above. I don't really know what it means to interpret something visible. I can measure approximately something visible and somebody else could measure it using different techniques. Are these different interpretations? Just different measurements.
But I know in saying that, I've misunderstood you. I think I know what you mean but also I don't know how to reinterpret it so that I can see the force of what you say.
To be able to do that, the probability first must exist as its own likelihood to occur within and from within the problem or structure you study. If there is no probability it can't occur. If it can't occur you are looking at perfection.
salaam.
Is probability an objective feature of something? Is it purely subjective? Is it something beyond either of those?
We could say that we really are looking at perfection but have only an imperfect way of understanding it. We could say that what we are looking at is imperfect but how we look at it is perfect.
Its not clear what perfection is here.
Suppose I toss a coin and ask what the probability of getting heads is.
The first theory I would come up with is the symmetry theory of probability. I would say that the coin is for all intents and purposes symmetrical - heads is as likely as tails. I would say that there is a 50/50 chance of getting heads or tails. I would like to put this thus:
"I know that heads is no more likely than tails, but I know nothing about which one it will be. So probability is a statement about what I don't know relative to what I know."
Perhaps I am not satisfied with this so I test the frequentist theory of probability, and I toss the coin many times and see with what frequency I get heads or tails. If statistically I can confirm my hypothesis that heads is as likely as tails, does this confirm the symmetry of the coin or my statement about probability? No. I might have a new theory:
"It is empirically true that heads are just as likely as tails. So probability is a property of an experimental apparatus."
I could go on and give other theories a run, and I could look at more imperfect cases. But I think people will start complaining.
Where does this figure of 1/2 come from? If we can find it in different cases using different methods, surely it says something about the reality of tossing the coin and not the methods?
I almost convince myself sometimes. But no, there are just different - but logically related - methods. We can refer to them as probabilities not because there is a true probability in-itself that these are interpretations of, but because "probability" can be used as an umbrella term.