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AnlamK comments on Is Rationality Maximization of Expected Value? - Less Wrong
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No, probability theory also has non-frequency applications.
Yes. This is the core of a Bayesian approach to decision making. The usual interpretation is that the probabilities reflect your state of knowledge about events rather than frequencies of actual event outcomes. Try starting with the LW wiki article on Baesian probability and the blog posts linked therefrom.
Obviously, this needs more discussion but the kind of thought I was trying to motivate was the following:
How is that saying a non-repeating singular event has a very small probability of occurring different from saying it will not happen?
This was motivated by the lottery paradox. Questions like, when you buy a lottery ticket, you don't believe you will win, so why are you buying it?
Examples like these sort of pull my intuitions towards thinking no, it doesn't make sense to speak of probabilities for certain events.