How can you prove that the Earth is round philosophically? (Details in the text post)

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Some background: My SO told me an anecdote about her metaphysics class where her professor asked them how can they proved that the earth is round and the prof stumped every answers to his question even they gave facts (don’t worry, it’s just an ice breaker, it was just for fun as a class introduction). I don’t know any specific details on how the professor replied to the students and I’m just curious how it was possible to prove that the earth is round philosophically, or at least, in the perspective of philosophy.

Another reason I’m curious about this is because I remember watching that Vsauce video about the past where Michael talked about the Last Thursdayism. I have a gut feel that deductive reasoning or philosophical razors have something to do with this.

EDIT:Some terminologies

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In philosophy there is the “Raven Paradox” which basically boils down to the statement that “All ravens are black” which is irrefutably true unless one is hatched that is white. The same could be said about the roundness of earth with respect to the shape of every other planet that we can see. If every other planet that we can see is round then it stands to reason that earth is also round.

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