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# Newton’s Method in ‘De gravitatione’

Kirsten Walsh writes…

Newton’s manuscript De Gravitatione (‘De Grav.’ for short) was published for the first time in 1962, but no one knows when it was written.  Some scholars have argued that Newton wrote De Grav. as early as 1664, others, as late as 1685, and there have been arguments for almost every period in between.

Ostensibly, the topic of De Grav. is “the science of the weight and of the equilibrium of fluids and solids in fluids”.  Newton discusses this topic in the form of definitions, axioms, propositions, corollaries, and finally a scholium.  However, the scholium ends abruptly and the manuscript is unfinished.  One of the most notable features of this manuscript is what Hall & Hall describe as a “structural failure”: what begins as a brief discussion of a definition turns into a lengthy and detailed attack on the Cartesian conception of space and time.  This digression is significant.  Firstly, it is useful for understanding the development of Newton’s thoughts on many topics.  Secondly, it supports the view that, in Principia, Newton’s intended opponent was Cartesian, rather than Leibnizian.

In this post, I am not going to talk about Newton’s 23-page digression (which may well form the basis of another post).  Rather, I am interested in the opening paragraph of this manuscript, in which Newton describes his method.  He begins:

“It is fitting to treat the science of the weight and of the equilibrium of fluids and solids in fluids by a twofold method.”

The first, he tells us, is a geometrical method.  He says he plans to demonstrate his propositions “strictly and geometrically” by:

1. Abstracting the phenomena from physical considerations;
2. Establishing a strong foundation of definitions, axioms and postulates; and
3. Formulating lemmas, propositions and corollaries.

The second is a natural philosophical method.  He says he plans to explicate and confirm the certainty of his propositions by the use of experiments.  He says that these discussions will be restricted to scholia, to ensure that the two methods are kept separate.

This twofold method bears striking resemblance to two other aspects of Newton’s work:

1. It accurately describes the method and structure of Principia; and
2. It resembles the quasi-mathematical method he uses to ‘prove’ his theory of colours.

The first point is uncontroversial – almost boring, given how many times it has been mentioned in the literature.  But it shows that this method is in use by Newton at least by the mid-1680s.  My second point, however, requires some explanation.

In an earlier post I argued that, at least in the early 1670s, Newton’s goal is absolute certainty.  He hopes to achieve certainty in the science of colours by making it ‘mathematical’.  The clearest demonstration of his quasi-mathematical method is found in Newton’s reply to Huygens, where he sets out his theory of colours in a series of definitions and propositions, in the style of a geometrical proof.

Despite the resemblance, this is not precisely the same method that Newton is advocating in De Grav. Experiment appears to play a different role.

In his early optical work, propositions are founded on experiment.  So experiment should be the first step in any inquiry.  For example, in a letter written in 1673, Newton says:

“I drew up a series of such Expts on designe to reduce the Theory of colours to Propositions & prove each Proposition from one or more of those Expts by the assistance of common notions set down in the form of Definitions & Axioms in imitation of the Method by which Mathematicians are wont to prove their doctrines.”

But in De Grav., Newton says that experiment is employed to ‘illustrate and confirm’ the propositions.  That is, experiment is supposed to occur as a later step.

This raises several questions about Newton’s methodology.  Is there any practical difference between the two methods?  Does this represent a significant shift in the role Newton assigned to experiment?  Can methodology shed any light on the dating of De Grav.?  What do you think?

Next week, we’ll hear from Peter Anstey.