Philosophy 167: Class 9 - Part 1 - Descartes on Galileo: the Lack of Foundations for the Theory in Two New Sciences.

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

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Synopsis: Discusses Descartes' belief that Galileo did not properly establish the foundations for his theory of projectile motion.

Philosophy and science.
Descartes, Rene, 1596-1650.
Galilei, Galileo, 1564-1642.
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All right, let me dig in. I'm gonna start with the Descartes letter to Mersenne on Galileo. I put the whole of the Latin up. Drake translated part of it. There is a decent edition of Descartes' letters in English. Decent meaning maybe 10% of the letters are in this.
But the choices are not great from a science point of view. And worse than that, they too simply translated the part of the letter that they wanted to translate, not the whole letter. The letters to Mersenne are just filled with physics. Physics that never made it into a book.
So, if you're actually serious about studying Descartes in the 1630s and 1640s, the principle place you have to look is in the letters. Now, this particular letter what happened is one of Descartes' principal supporters and somebody supporting him in publication, after he died, collected as many letters as he could and put them out in three substantial volumes.
They're now run many more volumes than that now that they've all been collected. They were by no means complete, like some of the letters Mersenne were not in the volumes. But the nice thing is, somebody in England decided to translate the into Latin. And that got published in 1668, and we know that Newton read a letter in it because he cites letter number 96 in volume two of the Latin edition of Descartes' letters, cites it and it's a very specific citation.
He names it his letter 96 part two. And the letter itself is not the most interesting but he's citing for a particular point. Well this letter is 91 it's about five pages earlier in the text. So there's a certain presumption that he didn't just open book letter 96 and read only it, that he had read quite a substantial portion of the letters.
And therefore, will have read this one. And when we get to Newton, you can start asking yourself, to what extent did this letter shape the way in which the Procipia is written? Because there's a lot. It's guesswork, but there's a lot of reason to believe this letter had significant affects on it.
But we'll get there later in this semester and then the beginning of next semester. So there's a series of comments the first one after remarking, I'm not going to quote the whole thing, remarking that, Galileo is not so bad after all, he's rejected the scholastics and he's at least ready to do mathematics, but then he jumps on them.
But he seems to me, very faulty and continually making digressions and never stopping to explain, come back to that completely, any matter which shows that he has not examined things in order and without having considered the first causes of nature. He has only sought the reasons of some particular effects and thus he is built without foundation.
The Latin there is. I'll talk about this later. It's almost always translated now as explain. It's not one of the standard listing of meanings of in Latin dictionaries. And of course the word we derive from it is explicate, lay out in detail, work out in detail. And that's the word he uses.
Everywhere you see the word explain, in any of the two translations we're looking at tonight, it is always. Is never perfectly good Latin word. But now the key point here, without foundation is built without foundation, that's the principal complain Descartes has against Galileo, and the phrase he connects with it is you're looking only at particular effects.
Considered the first causes of nature without having considered the first causes of nature. He has only sought the reasons of some particular effects. Now, I'm gonna start using the word, and I'm not unique in this, calling it Galileo's engaged in piecemeal science. He's not doing as it were a scientific theory of everything.
The next ones are criticisms of days one and two. I obviously just selected a few of the criticisms here to make my points. You can read them all. So the first one is about the speed at which light is transmitted. We know Galileo tried to measure the speed of light and he remarks on that.
Not successfully, but tried to measure actually with mirrors in a fairly clever move from fair distance near Florence. But it's Descartes' view that light travels instantaneously and he's here suggesting you can tell that from eclipses of the moon. When I say suggesting it, he's not saying here that light travels instantaneously.
And he actually never says it in the Principia. Margaret Wilson told me, and I've never seen the passage. Margaret Wilson was a professor at Princeton who was a Descartes expert. She's the one who told me that he definitely thought the speed of light is instantaneous. The second of these comments he says rightly the bodies descend more unequally fast in water than in air.
But he says nothing at all about the cause and he is wrong in saying that water does not at all resist being divided. Resistance to being divided we think of as viscosity. They thought of it as the time, as internal friction was the most common phrase for it.
I just call your attention to that. Then third. Everything he says about the speed of bodies descending in the void is built without foundation, nulo fundamento. For first he should have determined what weight is, and if he had known the truth, he would've known that it is nothing in the void.
So, the principle comment I wanna make there, other than once again he's saying without foundation, and that's the theme here that I wanna drive home, from Descartes' point of view, Galileo proceeded without foundation. I don't like now the word weight as the translation of gravitas. We have three words where they had two.
Weight, heaviness, and gravity. And they had gravitas and pondus. And pondus is the word you naturally translate weight and gravitas is naturally translated heaviness. So you start talking about the mechanism, then you translate it, gravity, but Drake knew what he was doing, so I left it there. We'll have to worry about that the last week, because Newton starts playing with words.
He doesn't have the word mass yet. That comes very late and he's trying to find a word for it. And he starts messing around with gravitas and pondus and similar such words. Pondus is heavily used in Lucretius. Then Descartes on day three, the part we read. He supposes that the speeds in falling weights are always increase equally which I formally believed like him, but I now believe I can prove it's not true.
So he thinks he can prove that gravity does not vertical fall, in the absence. He didn't say, in the absence of air resistance. For Descartes it's impossible to be in a vacuum, so saying it's in the absence of a resisting medium actually makes no sense for him. But the comment is, when he worked with Beakmann, he did indeed derive to Galileo law of free fall, the 1357 progression, etc., independently of Galileo with Beakmann.
And, by this time, 1638, which is, of course, four years before the Principia, Descartes's Principia appeared. He's saying no no that's just wrong. Then the bottom one he supposes that the degrees of speed of the same body over different planes are equal when the elevations are equal which he does not prove, and is not exactly true.
And since everything that ensues depends on those two assumptions one can say it is entirely built in the air. Now that's the path-wise Independence, and of course the version of the book to new sciences that Descartes saw, which is the first edition did not have anything substantial in the way of approve for an argument for path-wise independence.
It got added in the second but I don't think that would have convinced Descartes any more that it's a well founded principle. Again, it's among Descartes principles, one can argue it's the one that's most survived. It's a very fundamental principle, but Galileo's principle, and Descartes is jumping on it.
All right, day four, he adds another assumption to the preceding two, which is no more true. Namely, that bodies thrown in the air go uniformly fast along horizontal, but in falling, their speeds increase in the squared ratio. That's of course a mistake. That may be, I don't know if that's mine or Drake's, I don't remember of the distance.
So he's saying that the parabola doesn't really hold because they don't go uniformly fast along the horizontal. You can make of that what you wish. He never addressed projectile motion in any. I'd have to look more thoroughly in the letters. One of the frustrating things about the letters is you really have to get the Adam, Tannery volumes.
How many, six or seven volumes of letters? It's something like that. It's quite a number of volumes of letters and go through them one by one. There's no substitute for that, you just have to go through the letters one by one. But the bottom one that I've singled out is the one I really wanna jump on.
Yet he makes use only of this converse, the converse up. This is the complaint that he has no way of proving, that oblique projectile, it gives you the same complete parabola that horizontal projectile from its peak gives you, given the same so-called sublimity and that's the complaint, and then he adds yet he makes only of this converse, the oblique projectile problem and all the rest of his fourth discourse.
Which he seems to have written only to explain the force of cannon shots fired at different elevations. Moreover, it's to be noted that in sending forth his assumptions, he excludes artillery in order to make them more easily excepted. Yet toward the end it is mainly to artillery that he applies his conclusion.
That is to say, in a word, that all is built in the air. Okay, so what Galileo's done from Descartes is provide some very nice clean mathematics, but that it has no real foundation whatsoever. It's all built in the air. What's the relationship to the empirical world? Descartes is denying that it has any, but he's also complaining Galileo did nothing to show it has.
Then the final one, I threw in there just to give you the irony of it. Descartes had two people in France that he was particularly competitive with Fermat and Gesendi. Competitive may not be the right word, really didn't get along with. Okay, now Gesendi of course was a real pain to him because Gasendi was presenting the Lucretian picture of atoms, etc., to which he was so opposed.
But the striking feature to me here is if he's got Fermat and Galileo in his sights, he decides to defend Galileo against Fermat rather than Fermat against Galileo. So, the two complaints. One of them is Fermat complains about what we would now call infinitesimals, smaller and smaller magnitudes between any two points.
And Descartes, in effect, says that's silly to complain about it. And then he says Fermat complains about Galileo on projectile because he doesn't take into account the curvature of the Earth. And it's not gonna describe a parabola to the center of the Earth. Which of course Galileo said.
And what he said is, Fermat's not paying attention. Because Galileo assumed that gravity acts on parallel lines. Which is quite correct. At any rate, these are the complaints. And Drake, which I did include for you, Drake's comments amounted to saying, see what a philosopher does when he looks at real science.
He doesn't understand real science, right? Now Drake's background was a philosophy undergraduate at Berkeley, which he did not go on to graduate school. He became a banker. He was always bitter about his philosophy education. Thought it was a waste. When he finally got interested in Galileo and then became the world's leading English speaking exert on Galileo he continued to berate philosophy a great deal even though he ended up in Toronto at the Institute for the History and Philosophy of Science and Technology, IHPST where my lots of good friends are and lots of contacts I have.
But he was never sympathetic with philosophers. But look, I'm gonna come back to this at the end more extensively. I think that remark is just dead wrong. This has nothing to do with philosophy. Descartes and everybody else is faced with the same circumstance. It's a circumstance a lot like what happened in the beginning of the 20th century after the realization that Newton was false all along and we had to go to general relativity.
You get people like Percy Bridgman inventing operational definitions, and in the book in which he presents them, he says we never wanna have this kind of mistake again. As if some how or other, you can prevent having prior science be overturned. And it was an enormous shock that the most highly tested theory in the world gets overturned very abruptly by general relativity.
They were in the same position. They had a 1400 year theory, Ptolemy. And it got overturned, overturned rather abruptly with the phases of Venus. So looking at it it's natural to say, what went wrong there? And if you think about it here's a reading of Ptolemy. He worked empirically with very, very weak foundations.
The foundations that are presented in the first 15 pages which are put in there presumptively. Maybe the Earth is turning but there's no indication it is so let's the stars turn. The demand for circular motion is inferred from the fact that the stars seem to describe circles so let's do everything in circles.
It's not exactly a careful foundation. And then the standard complaint against them was that it was not physically realizable. The equant, etc., were not realizable with the spheres. So you can look at that and say, okay, we don't want anything like Ptolemy ever again. The way we're gonna have to prevent it, is to proceed from secure foundations making sure that what we're saying is physically proper, okay?
So I see all of this predecessors of Galileo's as Galileo not doing that. He's doing something much more like Ptolemy of having a mathematical device that works for certain things, he can work out a rich theory. The actual relation in Descartes' case relation, you're writing a paper on this.
In Descartes' case, excuse me, Galileo's case, the actual relation to the empirical world is throughout somewhat ambiguous. Okay, it's not clear what the relation is. Ptolemy had much clearer relation to the empirical world, other than of course he totally ignored, and the people who followed him totally ignored all the observable discrepancies between calculation and observation and bought into what?
Sufficient explication of a small thing. Namely, the sailing and phenomenon. But that's the very complaint Descartes' lodging all over again. So, I'll come back to this in greater length, but I do not think one should dismiss these complaints, purely that this is the reaction of a philosopher to fist rate science.
I just think that's totally wrong. Now what we're gonna do instead of it, will come to, later. Any questions on that, that letter? Keep it in mind, I'll keep bringing it up when we get to Newton. Because there are places in Newton where it looks like he's very worried about supplying proper foundations right at the beginning.
And that wasn't true in the papers with which he discovered the stuff he's famous for. It was true when he wrote the.