If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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The very question is whether the critics made good arguments. You are assuming the conclusion.
People make stupid arguments all the time. Anaxagoras was prosecuted for heresy and Aristarchus may have been. How many critics of Copernicus knew that he was talking about what happens over the course of a year, not what happens over the course of a day?
Yes, Archimedes says that Aristarchus's position is a minority. Not dubious. I do not see that in the quotes at all. Yes, Archimedes probably uses Aristarchus's position for the purposes of worst-case analysis to get numbers as large as possible; indeed, they are larger than the numbers Ptolemy attributes to Aristarchus. As I said at the beginning, I do not claim that he endorsed heliocentrism, only that he considered it a live hypothesis.
One mystery is what is the purpose of the Sandreckoner. Is it just about large numbers? Or is it also about astronomy? Is Archimedes using exotic astronomy to justify his interest in exotic mathematics? Or is he using his public venue to promote diversity in astronomy?
It's assuming the conclusion to think critics agreed with Aristarchus's criticism of a naive heliocentric theory?
I disagree strongly. I don't see how you could possibly read the parts I quoted, and italicized, and conclude otherwise. Like, how do you do that? How do you read those bits and read it as anything else? What exactly is going throu... (read more)