We don’t *know* in the way we *know* that 2+2=4. What we *know* is their position in the sky, the spectrum of the light from them, their parallax, couple of other things. The rest is inference.
We have a model of how stars work that is consistent with all known observations (basically based on the *exact* light we see from them, and their surrounding environment) which gives us a prediction of their age. If we got a new model we would have a different prediction. But it’s really pretty settled, probably settled enough to count as a fact for all intents and purposes if you put the right error bars on the age.
Generally speaking science is in the business of inferring things or disproving inferences, not proving them the way a mathematician would understand it – we can say ‘if this is not true, X and Y things would also not be true, and we are very sure of those things’ but there are a whole swathe of things that are ‘this is how we understand and talk about the world, but they could in theory still be disproved’.
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