Re natural numbers, people in our society (a technicist one) seem to forget that "natural numbers" are actually a social construct, there's nothing "natural" about them, they're not "innate"/"pre-existing" in a Platon-like universe of ideas, they only helped us from some-point on to do some technicist stuff (from collecting taxes in Roman times to sending rockets to the Moon in the 1960s) but I'm not sure that the Universe as a whole "cares" so much about them.
We as a species did have the opportunity at some point in our past of not "choosing" the natural numbers way (and of not choosing the principle of non-contradiction more generally speaking), I'm talking about Heraclitus and presumably some other of his disciples, but we chose not to.
As such, we could "meet" an alien society which has chosen the Heraclitus way, or any other way that doesn't involve "separating" stuff into "units" (like natural numbers are), or of thinking about the Universe as "stuff", or any other idea/concept that is not currently in use by our society. In which case all this trouble would have been for nothing, only helps with our existential solipsism as a species.
Those aliens could have then asked, similar to Parmenides: where does a star "end" for you to be able to "count" it as a separate entity? From the wiki page [1]:
> and thus despite appearances everything exists as one, giant, unchanging thing
The pre-socratics were a very interesting bunch, again, it's a social-constructed presumption to think that those possible aliens have all chosen the way of Aristotle and Platon like we did.
It's not clear where the Solar system ends, and it's not clear where a star ends. There are several criteria and they give different numbers. But they have all the same order of magnitude that is much smaller than the distance between the stars. For most orbital calculations you can take the star as a single point, and assume that the space is empty. Aliens probably had done a similar approximation and can count star easily.
We as a species did have the opportunity at some point in our past of not "choosing" the natural numbers way (and of not choosing the principle of non-contradiction more generally speaking), I'm talking about Heraclitus and presumably some other of his disciples, but we chose not to.
As such, we could "meet" an alien society which has chosen the Heraclitus way, or any other way that doesn't involve "separating" stuff into "units" (like natural numbers are), or of thinking about the Universe as "stuff", or any other idea/concept that is not currently in use by our society. In which case all this trouble would have been for nothing, only helps with our existential solipsism as a species.