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Hypotheses and Newton’s Epistemic Triad

Kirsten Walsh writes…

Over the weekend, I participated in a conference on ‘Newton and his Reception’, at Ghent University.  I presented a paper based on my idea that Newton is working with an ‘epistemic triad’.  I had an excellent audience in Ghent, and received some very helpful feedback, but I’d like to hear what you think…

To begin, what is Newton’s ‘epistemic triad’?

In his published work, Newton often makes statements about his purported method in order to justify his scientific claims.  In these methodological statements, he contrasts things that have strong epistemic credentials with things that lack those credentials.  Consider, for example, these passages from his early papers on optics:

    For what I shall tell concerning them is not an Hypothesis but most rigid consequence, not conjectured by barely inferring ’tis thus because not otherwise or because it satisfies all Phænomena … but evinced by ye mediation of experiments concluding directly & wthout any suspicion of doubt. (6 February 1672)
    I shall not mingle conjectures with certainties… (6 February 1672)
    To determine by experiments these & such like Queries wch involve the propounded Theory seems the most proper & direct way to a conclusion. (3 April 1673)

What these passages tell us is that Newton is making a distinction between theories, which are certain and experimentally confirmed, hypotheses, which are uncertain and speculative, and queries, which are not certain, but provide the proper means to establish the certainty of theories.  I call this three-way division Newton’s ‘epistemic triad’, and argue that this triad provides the framework for Newton’s methodology.

To support this argument, I defended the following three theses:

Endurance thesis.  There are some general features of Newton’s methodology that don’t change.  These are characterised by the framework of the epistemic triad.

Developmental thesis. There are some particular features of Newton’s methodology that change over time.  These can be characterised as a development of the epistemic triad.

Contextual thesis. There are some particular features of Newton’s methodology that vary with respect to context (namely, mechanics versus optics).  These can be characterised as an adaptation of the epistemic triad to particular contexts.

The developmental and contextual theses are not news to most Newton scholars.  It is commonly accepted that Newton’s methodology changed in important ways over the course of his life, and that there are methodological differences between Principia and Opticks.  The endurance thesis is more problematic, so I made a special effort to show that Newton’s use of hypotheses is more consistent than we think.  I argued that:

  1. In Principia, Newton appears to be working with the same implicit definition of ‘hypothesis’ that he works with in his early optical papers; and
  2. Hypotheses perform similar methodological roles in all of Newton’s natural philosophical work.

I need to do some more work to properly explicate this methodological role.  But, to state it very broadly, Newton temporarily assumes hypotheses, which act as ‘helping premises’ in his inferences from phenomena.  The fact that a statement may appear in Newton’s writing as a hypothesis, and then reappear later in a query, rule of reasoning, or phenomenon, has convinced many Newton scholars that Newton is inconsistent in his use of hypotheses. Against this conviction, I argue that Newton applies the label ‘hypothesis’ to things that perform a particular function, rather than to a particular claim.

Newton’s Method in Three Minutes

Kirsten Walsh writes…

Last week I competed in the Otago University Three-Minute Thesis Competition.  I had to explain my PhD thesis in no longer than three minutes.  It was challenging indeed, in such a short length of time, to describe my research, communicate its significance and impart my enthusiasm for it – while pitching it at the level of an intelligent non-expert. Fortunately, I had great material to work with. There are so many interesting stories about Newton! Unfortunately, it’s often difficult to figure out which stories are true.

I opted to begin with the ‘approximately true’ story of Newton’s anni mirabilis, or miraculous years.  The general thrust of the story is true, even if some of the particulars are false: the plague years mark a significant turning point in Newton’s scientific work.  As Whiteside pointed out over forty years ago, we may

    “salute this first creative outburst – whether or not contained in one single marvelous year – of a man who twenty years afterwards was to construct a scientific Weltanschauung which is, in its essentials, still ours.”

So, with apologies to those of you with ‘historically sensitive’ ears, here is my script for the three-minute thesis competition:


It’s 1665.  Cambridge has been struck by Plague, and Newton has been sent home from University.  Summer is stretching out before him.  Nice!  What will he do on his extended summer holiday?  Well, he did what I imagine most Scarifies* do on their summer holidays: he invented calculus, discovered the composition of light, and (after watching an apple fall from a tree) conceived the laws of universal gravitation…  Okay, so perhaps Newton wasn’t quite your typical undergraduate student.  The story about the apple is controversial, but everyone agrees about the discoveries.  Scholars have called those years the ‘years of miracles’.

Why were they ‘miraculous’?  Well, these were revolutionary discoveries – and there were so many of them.  They provided the basic material for Newton’s Principia, and his Opticks. Enough material for a lifetime of publications!  And real publications.  Not just those ‘puff pieces’ that fill our journals nowadays.  All in just 2 years!

Furthermore, these discoveries seemed to come out of nowhere.  Newton was able to invent, discover and conceive things no one else could, because seemingly he had invented an entirely new scientific method.  He had come up with a whole new way of mathematising physics, and claimed to have achieved mathematical certainty!  Philosophers and scientists tried to emulate his method.  But no one was as successful as Newton.  Whatever Newton was doing, he was doing it right.  But what was he doing?

This is the central question of my PhD, and it’s a question that dominates discussions of scientific method even now, 300 years later.  But scholars still barely understand what Newton’s method was.  Did Newton really think his scientific theories were as certain as mathematical proofs?  Why did he think his theory of gravity was true, when he couldn’t even say for certain what gravity is?  And, at the centre of it all, the question that’s been keeping me up at nights (as it has kept up generations of Newton-scholars before me): what did Newton mean when he wrote that enigmatic sentence at the end of Principia: ‘Hypotheses non fingo’; ‘I do not feign hypotheses’?

I do not feign hypotheses.  What an odd thing to say.  What does it even mean?  ‘I haven’t invented these hypotheses’?  ‘I didn’t prove them’?  This sentence lies at the heart of my thesis.  Unlike other Newton scholars, I think it describes a crucial aspect of Newton’s method.  What it tells us is that Newton made a distinction.  On the one hand, theories: mathematical, certain, experimentally confirmed.  On the other hand, hypotheses: non-mathematical, uncertain, non-experimental, and speculative.  This distinction is a crucial feature of Newton’s spectacularly successful scientific method.  And I think it’s this distinction that explains Newton’s years of miracles.


The idea of anni mirabiles seems closely-related to the notion of a scientific revolution, which has been much discussed since Kuhn published The Structure of Scientific Revolutions in 1962.  Philosophers of science disagree philosophically over the importance of revolutions to science, and historically over the occurrence of any genuine scientific revolutions.  However, it is interesting to note that historians have recognised several anni mirabiles in the history of science.  For example, 1543, the year that Vesalius published De Humani Corporis Fabrica and Copernicus published De Revolutionibus Orbium Coelestium.  And 1905, the year that Einstein published his three ground-breaking papers in the Annalen der Physik.  What role have these anni mirabiles played in the history of science?  What do they tell us about scientific progress?  Norwood R Hanson once said:

    “It is possible both to be driven by intuition and at the same time to reason carefully.  Most scientific discoveries, indeed, result from just such an intertwining of headwork and guesswork.”

What do you think?


*Otago Undergraduate Students

Does Newton feign an hypothesis?

Kirsten Walsh writes…

Newton’s famous pronouncement, Hypotheses non fingo, first appeared in 1713, but Newton’s anti-hypothetical stance is present as early as 1672, in his first papers on optics.  In his first publication, he introduces his notion of certainty, and insists that his doctine of colours is a theory; not an hypothesis:

    For what I shall tell concerning [colours] is not an Hypothesis but most rigid consequence… evinced by ye mediation of experiments concluding directly & without any suspicion of doubt.

Despite these clear anti-hypothetical themes, a corpuscular hypothesis lies beneath Newton’s theory of light and colours.  What are we to make of this?  Is Newton guilty of feigning an hypothesis? Is Wolff correct when he says that Newton “indulges in hypotheses in those very areas in which they think he abstained from employing them“?

To begin, what does Newton mean by Hypotheses non fingo?  ‘Fingo’ has been variously translated as ‘frame’, ‘make’, ‘imagine’ and ‘devise’. Experts argue that ‘feign’ is the most appropriate translation.  While it has a variety of meanings, such as to form, to invent, to forge, or to suppose erroneously, the word ‘feign’ also carries the nuance of pretence, counterfeit, or sham.  Thus, they argue that while Newton indeed conceived or framed hypotheses, he did not attach any special epistemic status to them.  He maintained a clear demarcation between theories that were supported by experimental results and hypotheses that were merely unsupported speculations.

Now let’s take a closer look at Newton’s early optical papers.  Newton claims that his doctrine of colours is a theory, not an hypothesis, for three reasons:

  1. It is certainly true, because it is supported by (or deduced from) experiment;
  2. It concerns the physical properties of light, rather than the nature of light; and
  3. It has testable consequences.

These are the three key aspects of Newton’s early methodology.  He refers to them again and again throughout the debate that followed the publication of his first optical paper.

Newton explicates his corpuscularian view in his first optical paper and describes light rays as substantial bodies.  But when his opponents accuse him of hypothesising, Newton argues that he is not guilty.  Firstly he argues that this hypothesis is not necessary for his explanation of colours.  Secondly he argues that he attaches no special epistemic merit to his hypothesis because:

  1. It is not supported by experiment;
  2. It concerns the nature of light; and
  3. It has no testable consequences.

While Newton never gives up his corpuscularian view, he attempts to explicate and promote his theory without referring to it.  He argues that he doesn’t need to provide any hypothesis on the nature of light – his theory on the properties of light is sufficient on its own.

I claim that Newton isn’t guilty of violating his anti-hypothetical stance.  He demonstrates that he can distinguish between theory and hypothesis, giving the former higher epistemic status than the latter.  He does not pretend to have empirical support for his corpuscular hypothesis, nor does he try to ‘prop it up’ on other grounds.  Perhaps he regrets having ever opened the proverbial can of worms, for the next time he explicates his theory of light and colours, he does so without any reference to the corpuscular hypothesis or the nature of light.

That Newton can tell the difference between good scientific explanations and speculations is further supported by his use of queries in these early optical papers, but more on this next time.  To conclude,  I think Newton is not guilty of feigning an hypothesis.  What do you think?