Skip to Navigation Skip to Content Skip to Search Skip to Site Map

Newton on Certainty

Kirsten Walsh writes…

A few weeks ago, I said that in Newton’s early optical papers:

    Newton claims that his doctrine of colours is a theory, not a 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.

From this set of criteria, we can see that early-Newton’s strong anti-hypothetical stance is closely related to his goal of generating theories that are certainly true.  Students from Florida have pointed out that Newton’s criterion of certainty seems to set the bar quite high.  Indeed it does.  So today I will explain early-Newton’s goal of absolute certainty and why he thought it was achievable.

For Newton, absolute certainty is closely related to mathematics – he wants to achieve certainty in the science of colours by making it mathematical.  In his first letter to the Royal Society, he says:

    A naturalist would scearce expect to see ye science of those become mathematicall, & yet I dare affirm that there is as much certainty in it as in any other part of Opticks.  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 (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly & without any suspicion of doubt.

In a letter to Hooke, Newton says, ideally the science of colours will be “Mathematicall & as certain as any part of Optiques”.  However, absolute certainty is difficult to achieve because 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.

Thus, Newton thinks that absolute certainty is also closely related to experiment.  It is no accident that, in his first paper, Newton attempts to establish the physical principles of colour experimentally by focussing on refrangibility rather than colour of light.  It would have been difficult to measure precisely changes in colour, but Newton was able precisely to measure degrees of refraction and lengths of refracted images.  He hardly even mentions colour until he believes he has established that white light is a mixture of differently refrangible rays.  When he is ready to reveal his theory of colour, he does so by first asserting that there is a one-to-one correspondence between refrangibility and colour of light rays.  Newton claims that he has established the physical principles of colour with absolute certainty.

When he reveals his theory of colour, he does so in a quasi-mathematical style.  In a letter to Oldenburg, Newton says:

    I drew up a series of such Expts on designe to reduce ye 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.

This quasi-mathematical ‘proof’ of his theory of colours is set out in his reply to Huygens.

To summarise, Newton’s mathematical method and his experimental method are linked by his notion of absolute certainty.  Newton claims his theory of colours is certainly true, because (1) his physical principles are established experimentally and are certainty true, and (2) he can use these physical principles as the basis of his mathematical proof.  That a lengthy and sometimes heated debate followed Newton’s original paper, shows that his opponents weren’t as convinced by his careful demonstration as he was.

Comments are closed.