What is the real probability that a person will be murdered tomorrow somewhere in the world? It seems like there should be a right answer to this.
I would accept that there is a true, correct, mathematical probability for that, which is very close to (but less than) 1. This is an hypothesis that I cannot prove, but I believe it anyway.
Why would one think it’s guaranteed to happen?
One might think so because one has a flawed understanding of probability.
Or one might deploy the word "guaranteed" in a probabilistic sense, meaning that they believe the probability to be so close to 1 that the alternative is not pragmatically worth considering.
It would likely be because someone was murdered every day for many years. But this is nothing more than an inductive inference.
I think that's a straw man. Yes, if indeed one has that statistic to draw on (do we?) then by inference one could predict that there will also be at least one murder tomorrow. But that's no basis for assigning probability 1 to such an event, nor any other specific probability. Anyone coming to such a conclusion on that basis would fall into the "flawed understanding of probability" group.
Where does probability come here or even needed as a concept to talk about whether there will be a murder somewhere in the world?
Quantitative probability is not particularly useful in this area, because for most practical purposes, the exact mathematical probability of real-world events is not computable. On the other hand, qualitative probability is foundational. We can often estimate fairly well how likely or unlikely one event is either on its own or relative to an alternative. We make such estimates all the time, and rely on them in making decisions.
What is the probability that
there will be a murder tomorrow in your city? As you can imagine, it
would depend on how you interpret probability
and what class of past
events you use.
You seem to be assuming an inferrential approach. This is certainly the statistician's method for estimating the probability of an event, but it gives you only an estimate, often with an associated confidence estimate, not a true, exact probability.
Do you look at the murder rates of your city or the
country? What about the time period? What should that be? What makes
one interpretation more valid than the other? If there is no clear
answer to this, does this mean that the concept of probability is
No, it means that statistical inference is qualified by a set of subjective assumptions. The methodologies of statistical inference are related to probability, but they do not compute true probabilites in the sense you seem to mean.
I can imagine a retort being that it is subjective but one can make
models based on certain classes of past data and see which models
predict the future better.
Yes. That's more or less a description of science.
But that doesn’t tell you what the
“correct” probability is.
True. So what?
Where is the concept of probability actually needed here?
There in particular, mathematical probability is the framework by which we understand statistical inference. However, exact numeric probabilities of real-world events indeed are not needed for most purposes.
No doubt one can go a very long way in philosophy without involving the concept of probability. Eventually, however, one has to come to grips with the fact that in the real world, we often* need to make decisions without sure, advance knowledge of all the outcomes of each choice. A rational decision under these circumstances must be based on some evaluation of the likelihood of some of the outcomes of each alternative.
It does not matter whether the exact mathematical probability of various outcomes under various conditions is known or even hypothetically computable. I use probability if I judge, for example, that because I am plastered, the risk of being in an automobile accident or being arrested for DUI is is too great, and the consequences too severe, for me to accept driving myself home as a rational decision. (And I hope that I retain so much reason in that diminished state.)