Newton on Experiment and Mathematics

Posted on April 15, 2013 by Kirsten Walsh

Kirsten Walsh writes…

In my last post, I discussed our 20 revised theses and why I altered thesis 5.  In this post, I’ll discuss why I replaced thesis 8.

In 2011, I claimed that:

8.  The development of Newton’s method from 1672 to 1687 appears to display a shift in emphasis from experiment to mathematics.

But at the start of this year, I replaced this thesis with a new thesis 8:

8.  In his early work, Newton’s use of the terms ‘hypothesis’ and ‘query’ are Baconian.  However, as Newton’s distinctive methodology develops, these terms take on different meanings.

Since my new thesis is a replacement of the original thesis, rather than a modification, two explanations are required.  So in today’s post, I’ll tell you why I decided to remove my original thesis 8, and in my next post, I’ll tell you about my new thesis 8.

I originally included thesis 8 because there are some obvious differences in the styles of Newton’s early work on optics and his Principia.  In Newton’s first paper on optics (1672), there is a strong emphasis on experiment.  Experiment drives his research and guides his rejection of various possible explanations of the phenomena under consideration.  Ultimately, he presents an Experimentum Crucis as proof for the certainty of his proposition that white light is heterogeneous.  In contrast, the Principia (1687) displays a strong emphasis on mathematics.  The full title of the work, the Author’s Preface to the Reader, and the fact that Book I opens with 11 lemmas outlining the mathematical framework of the work are just a few features that make it clear that Principia is primarily a mathematical treatise.

I now think that my original thesis 8 is misleading.

Firstly, as I have emphasised on this blog, Newton’s early work had a mathematical style that made it unique among his contemporaries.  While they recognised him as an experimental philosopher, his claims of obtaining certainty via geometrical proofs set him apart from the Baconian-experimental philosophers.  Moreover, his methodological statements show evidence of a tension between experiment and mathematical certainty.  For example, he says that the science of colours,

“depend[s] as well on Physicall Principles as on Mathematicall Demonstrations: And the absolute certainty of a Science cannot exceed the certainty of its Principles.  Now the evidence by wch I asserted the Propositions of colours is in the next words expressed to be from Experiments & so but Physicall: Whence the Propositions themselves can be esteemed no more then Physicall Principles of a Science.”

Secondly, Newton continued to identify as an experimental philosopher until the end of his life.  For example, in the General Scholium at the end of Principia, he says:

“and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.”

This resembles Newton’s earlier emphasis on grounding propositions on empirical evidence, rather than on speculative conjectures.

Thirdly, in Principia, Newton appears to be negotiating a similar tension between experiment and mathematical certainty that we saw in his early work.  For example, in the Scholium to the Laws of Motion he asserts the certainty of his Laws, while at the same time, acknowledging their experimental basis:

“The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds.”

And:

“By these examples [i.e. the experiments mentioned above] I wished only to show the wide range and the certainty of the third law of motion.”

From these three points, we can see that the methodological differences between Newton’s early papers and Principia aren’t as great as they first appear.  But I did not remove my original thesis 8 because I think that the methodology of the 1672 paper is precisely the same as the methodology displayed in Principia.  Rather, I don’t think my original thesis 8 captures what is important about these differences.

As I have explained here, my project is to distinguish between those features of Newton’s methodology that changed, and those that stayed the same.  Some aspects of Newton’s methodology developed over time.  For example, he came to value geometrical synthesis over algebraic analysis.  Other aspects of his methodology varied according to context.  For example, in Opticks, he employs ‘experiments’ and ‘observations’, but in Principia, he employs ‘phenomena’.  But this triumvirate of methodological ideas – experiment, mathematics and certainty – should be considered an enduring feature of Newton’s methodology.

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