Newton’s Mathematical Method

6 thoughts on “Newton’s Mathematical Method”

1. I’m a bit of a heretic with respect to epistemology, so my views might seem strange.

   As I see it, the most important part of Newton’s science is that he developed an extensible coordinate system that could be used for defining scientific measurements. He structured this coordinate system with a lot of mathematical symmetry, which allowed him to extensively use mathematics on his data.

   Unfortunately, traditional philosophy of science has never understood this. I think they are afraid of anything that could hint at some degree of constructionism. You might want to take a look at some of the posts at my own blog.

2. Great questions! I don’t have any real answers, but here are some thoughts about (3). In answering this question, it is important, obviously, to figure out what Bacon’s method of natural history is really about. So my take is that, in many ways, Bacon’s method of induction is a rediscovery of ancient induction, especially Aristotle’s Analytics and Topics, this despite the fact that Bacon was rhetorically at least opposed to Aristotle and the ancients. (I take this line from John McCaskey, who has written an excellent dissertation on this topic). As evidence of Bacon’s ancient roots, or at least similarity thereof, one can look at Harvey’s approval of Bacon, and his use of some of Bacon’s terminology in Ex.25 of the De generatione animalium.

   In this context, histories have a particular use, namely, they provide the data, the set of empirical findings upon which one can make inferences, particularly, causal inferences–thus, in the aforementioned Harvey exercise, Harvey moves from description of the development of creatures, to causal explanation of such creatures by writing, “Wherefore I think it advisable here to state what fruits may follow our industry, and in the words of the learned Lord Verulam, to ‘enter upon our second vintage'”. (Of course, Bacon never talked about a second vintage, but set aside that particular interpretive problem…) The goal for Aristotle’s method (and Bacon’s) was to arrive at definitions, which he understands as statements of the essence of that object (or to use some other phrases in early modern Latin used to designate this concept, its ‘substantia,’ or ‘natura.’) For Aristotle, essences are most often about functions, and thus these sorts of histories and inferences about definitions were of great interest amongst the physicians, who were, of course, interested in the functions of the parts of the body. Amongst the physicians, these historia became experimental in a sense, insofar as the historia reported the results of dissections and observations thereof. Bacon’s histories, then, seem to take this experimental aspect of the physicians quite seriously, in combination with Bacon’s decidedly non-Scholastic, somewhat heterodox interpretation of the ancient strictures on definition and induction.

   There are other uses of historia (for example, the histories of Pliny are their descendants are quite different) in this period, of course, making the job tougher to figure out, but that is my take on Bacon. So, I am no expert on Newton, but does he ever use histories in the Baconian sense as repositories for observational and experimental data?

3. Hi Benny,

   Newton’s early views on method, hypotheses, queries, and experiment show a significant Baconian legacy, but he does not seem to have been committed to the use of natural histories. In fact, Newton was certainly familiar with the Baconian method of natural history – we can see this in his Trinity Notebook. But although he presented natural history specimens to the Royal Society, he never seems to have produced a natural history.

   Your comments on the connection between Aristotle and Bacon are very interesting. Do you know where I can read more about this?

   Cheers,
   Kirsten

4. Hi Neil,

   Thank you for your comments. I’m interested in your claim that the most important part of Newton’s science is the development of his coordinate system. I’m really only just getting started on my project, so there are a lot of gaps in my knowledge. I understood that Newton used the Cartesian coordinate system and that this was crucial in enabling him to develop the calculus, but you’re saying that Newton developed his own coordinate system. Can you tell me more about this?

   Cheers,
   Kirsten

5. Very interesting–did not know about the connection in the Trinity notebook. As for more on the connection between Aristotle and Bacon, see John McCaskey’s website, particularly his dissertation: “Regula Socratis: The Rediscovery of Ancient Induction in Early Modern England” http://www.johnmccaskey.com/

6. More on my comments on coordinate system.

   I was probably a bit cryptic there.

   What I had in mind was this. With Newton’s definitions, when we observed unexpected acceleration, we could assert that there was a force causing that accelerations. This allowed numeric values (for forces) to be ascribed in many situations. For example, we could now consider friction to be a force. We could now ascribe a force to air resistance. We could ascribe a force to viscous motion. This opened up new ways of expressing facts that accounted to familiar phenomena.