The very question is whether the critics made good arguments. You are assuming the conclusion.
It’s assuming the conclusion to think critics agreed with Aristarchus’s criticism of a naive heliocentric theory?
Yes, Archimedes says that Aristarchus’s position is a minority. Not dubious. I do not see that in the quotes at all.
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 through your head when you read those bits from Sand Reckoner, how do you parse it?
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?
Gee, if only I had quoted the opening and ending bits of the Sand Reckoner where Archimedes explained his goal...
Many people object to Copernicus on the grounds that Joshua made the Sun stand still, or on grounds of wind, without seeming to realize that they object to the daily rotation of the Earth, not to his special suggestion of the yearly revolution of the Earth about the Sun. If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes. Archimedes was a smart guy who understood what Aristarchus was saying. He seems to accept Aristarchus’s argument that heliocentrism implies a large universe. If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
Ptolemy does give a reason: he says wind. He has the drawback of being hundreds of years late, so maybe he is not representative, but at least he gives a reason. If you extract any reason, that is the one to pick.
The principal purpose of the Sandreckoner is to investigate infinity, to eliminate the realm of un-nameable numbers, thus to eliminate the confusion between un-nameably large and infinite. But there are many other choices that go into the contents, and they may be motivated by secondary purposes. Physical examples are good. Probably sand is a cliche. But why talk about astronomy at all? Why not stop at all the sand in the world? Or fill the sphere of the sun with sand, stopping at Aristarchus’s non-controversial calculation of that distance? Such choices are rarely explained. I offered two possibilities and the text does not distinguish them.
If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you. I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.
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 through your head when you read those bits from Sand Reckoner, how do you parse it?
Gee, if only I had quoted the opening and ending bits of the Sand Reckoner where Archimedes explained his goal...
Many people object to Copernicus on the grounds that Joshua made the Sun stand still, or on grounds of wind, without seeming to realize that they object to the daily rotation of the Earth, not to his special suggestion of the yearly revolution of the Earth about the Sun.
If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes.
Archimedes was a smart guy who understood what Aristarchus was saying. He seems to accept Aristarchus’s argument that heliocentrism implies a large universe. If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
Ptolemy does give a reason: he says wind. He has the drawback of being hundreds of years late, so maybe he is not representative, but at least he gives a reason. If you extract any reason, that is the one to pick.
The principal purpose of the Sandreckoner is to investigate infinity, to eliminate the realm of un-nameable numbers, thus to eliminate the confusion between un-nameably large and infinite. But there are many other choices that go into the contents, and they may be motivated by secondary purposes. Physical examples are good. Probably sand is a cliche. But why talk about astronomy at all? Why not stop at all the sand in the world? Or fill the sphere of the sun with sand, stopping at Aristarchus’s non-controversial calculation of that distance? Such choices are rarely explained. I offered two possibilities and the text does not distinguish them.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you.
I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.