Philosophy 167: Class 2 - Part 15 - A Crisis in Mathematical Astronomy: the Calculational Equivalency of Three Different Systems, and the Attraction of Pyrrhonism.

Smith, George E. (George Edwin), 1938-


  • Synopsis: Points out that there is no way to choose between the 3 systems if the only form of empirical data we have are observed longitudes and latitudes; places astronomy in the historical context of the mid-16th century and reviews the rise of Pyrrhonism.

    Opening line: "At any rate, what I want to lead up to now, and I've got four minutes, I'll do my best with this. What we've got here ... read more
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At any rate, what I want to lead up to now, and I've got four minutes, I'll do my best with this. What we've got here in the 1590s is three systems. With no apparent empirical way of choosing among them if the only form of empirical data we have are observed longitudes and latitudes.
Now, this is the discipline that in the universities was the most exalted. I'll run it off modern physics. The people who actually did mathematical astronomy made clear to everybody else in the universities that they weren't as good as them because they couldn't do it. Okay? They were lesser intellects because they couldn't do the really hard stuff.
Now picture what academics are going to do when you get to a situation, and astronomy has three totally disparate systems with no way to choose among them. You're gonna attack that discipline, and that's exactly what happened. The discipline started becoming a subject of ridicule. Now the oddity to this is, all the way back to Ptolemy we've known multiple representations of the same observations.
Astronomers have always known that. What happened here was the multiple representations were so disparate from one another that now everybody could understand that that's not a minor thing, multiple representations. Okay? And what every astronomer knew, they knew two things. Well, every astronomer knew this. The three systems can be mathematically transformed into one another.
That's what you get to write about as your first assignment, is the three systems. Let me pass that out in the last minute. Now each of the systems had its own parameters, so the individual versions of the systems were not directly translatable. But the point is you could take a Ptolemaic system with its constants, turn it into a Tychonic system, turn that into a Copernican system, and back and forth.
All of them were saving exactly the same observations, so all of them would reproduce the same thing. And that came out as a deep challenge to whether one should take seriously what astronomy is doing at all, other than simply having different ways of summarizing a set of observations.
Now, let's put that in context. This is the middle of the Protestant Reformation. 1521 is Luther. 1533 is Henry VIII, if you wanna count him. Two years later is Calvin. The Church is under a total onslaught. But, equally now, what's the other most exalted subject in universities? Theology.
And we've suddenly got theology with no authority for deciding anything. In the middle of that, the most important defense of skepticism ever written, Sextus Empiricus' Outlines of Pyrrhonism. Pyrrho was the person who replaced Plato in the academy, forcing Aristotle to start his Lyceum as a separate school. Pyrrho was a skeptic.
What Pyrrhonism did, do we need more copies?
Okay, I'll just pass out some more. What Pyrrhonism says, among many other things as skepticism, is that theoretical knowledge of the empirical world is impossible. It's a take off, of course, from Plato. Because the empirical world is irregular, imperfect, etc.
So don't try. Simply give up. Pyrrhonism swept some parts of the intellectual world in the second half of the century we're talking about, for a reasonably apparent reason, namely, all sorts of intellectual authority was collapsing. The leading Pyrrhonist by far was Montaigne. And Montaigne, in his most famous essay, the Apology for Raymond Sebond in 1580, has this passage.
The sky and the stars have been moving for 3,000 years, everybody had so believed, until it had occurred to Cleanthes, etc., and to Nicetas to maintain that it was the Earth that moved through the oblique circle of the zodiac, turning about its axis. And in our day Copernicus has grounded this doctrine so well that he uses it very systematically for all astronomical deductions.
What are we to get out of that, unless, that we should not bother which of the two is so? And who knows whether a third opinion 1,000 years from now will not overthrow the preceding two? Tychonism was 8 years, not 1,000 years, okay? Now this was a highly prevailing attitude in some circles challenging mathematical astronomy as an empirical discipline.
But with the Pyrrhonism thrown in there, challenging whether it's possible to establish true empirical knowledge, knowledge of the empirical world at all, okay? This course starts in 1600 because it's with the recognition of this challenge to astronomy that Kepler, among others, your reading for next week will be precisely on this.
Kepler, among others, and everybody else we will read in this course, will be trying to show empirical knowledge is possible, and struggling to do so. And every one of them, but one, Huygens, is going to offer a solution to the Copernican, Ptolemaic, Tychonic problem. Because it was almost that had to be settled in order to convince people that empirical science is really possible.
So I built up, I'm over time by two minutes, I'm gonna stop. The whole point of the first two weeks is to get us to this point in 1600 where it really becomes seriously questionable what sort of knowledge, theoretical knowledge, we can achieve of the empirical world. Can we get past mere appearances and multiple representations of them?
And that's what the rest of this course is going to be about, including Newton's Principia. Because Newton's Principia, of course, is designed to show the Copernican system is true and to end all this worry. Okay, so that's the context. Henceforth we're gonna be going more slowly. Next week, for the first time, you read some primary source material.