Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.
Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.
You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.
Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting.
The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century.
This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.
The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity.
The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz.
What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.
The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.
Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:
Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.
[…]
I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.
Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.
Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.
Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.
In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.
In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote:
1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration.
Relative, apparent, and common time […] is commonly used instead of true time.
2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…
Newton is saying that space and time have a separate existence and all objects exists within them.
In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects.
In his third letter to Clarke he wrote:
As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.
Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton.
Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.
The Renaissance Mathematicus 
Thanx very much for another great post.
I think a ‘not’ may be missing from this sentence –
‘Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could NOT accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory.’
Thx!
This most enjoyable post stimulates a few thoughts.
Quite so. Some have even argued that Newton’s 2nd law is vacuous for this reason, really just defining force in terms of acceleration. A milder version of this criticism, associated with the philosopher Quine: Newton’s laws acquire meaning only as enmeshed in the whole web of Newtonian physics.
In 2004-2005, the Nobel prize winner Frank Wilczek wrote a series of essays, offering a personal perspective:
You also write, “as we now know it was actually Leibniz who was closer to how we view time and space than Newton,” a reference to the theory of general relativity, I believe. True enough, but I think it’s worth mentioning that GR enshrines curved spacetime, a mathematical structure of considerable heft: in mathspeak, a 4d Riemannian manifold with pseudo-metric of signature (-1,1,1,1). Why should that be the structure of the universe (above the quantum scale)? The physicist’s best response is still Newton’s operative or instrumentalist philosophy.
Leibniz subscribed to the Cartesian vortices, one of the more fun discarded theories. E. J. Aiton wrote an excellent book on the topic, The Vortex Theory of Planetary Motions, where he traces its roots to Kepler’s celestial physics.
Ole Rømer made the first measurement of the speed of light in 1676 by timing the eclipses of Jupiter’s moon Io. In Newtonian physics, the speed of light is no more significant than the speed of sound; it is only with Einstein’s Special Theory of Relativity that the speed of light becomes the speed limit of the universe.
Cartesian vortices [1] always struck me as what a good Catholic would come up with once the idea of angels pushing the planets around became untenable. 😉
Leibniz, although from Lutheran stock, was also quite close to Roman Catholicism.and advocated the reunification of the Lutheran and Roman Catholic churches.
Click to access fidv06n01-1997Sp_046-gottfried_wilhelm_leibniz_the_un.pdf
[1] If you imagine space as being filled with a non-viscous, incompressible fluid, which is driven in rotation by a body at its centre (the Sun), you would expect vortices to form (as they do if you simulate them in, say, a bucket of water). Unfortunately, you end up with the wrong dynamics when you try to go from a qualitative to a quantitative theory, which I think is covered in Aiton’s book and is mentioned at the end of the SEP article on Descartes’ Physics.
Well, first off, Newton defined lots of quantities in terms of ratios and proportions, not equality. That might be a little confusing for modern readers. and cause them to incorrectly conclude that Newton’s definitions were circular. As a rule of thumb, people on the caliber of Newton don’t usually define things in a straightforwardly circular manner. Something more complicated is probably going on with Newton’s mathematics. (Sidenote: i’ve never really been convinced that the terms of a ‘theory’ get their ‘meaning’ only when enmeshed in the whole theory. I could write about this a lot, but i’ll just skip over that for now.) Here’s my other two thoughts:
1. The extent to which Newton was an ‘instrumentalist’ is very overplayed, i think. People seem to mistake the fact that he put high priority on measuring things wit some sort of fictionalism.
2. I don’t accept that the best ‘defense’ physicists have for curved spacetime is some sort of ‘operationalist’ philosophy. To be honest, my mathematical knowledge isn’t solid enough to speak too much about this, but I think the best reason physicists have for accepting curved spacetime theories is because they seem, experimentally, to be true!
That is an operationalist philosophy! GR “saves the phenomena”, in the old-fashioned lingo.
The people arguing that Newton’s 2nd law, taken by itself, is vacuous, have no problems understanding ratio and proportion. It’s actually quite simple: if you don’t have an independent definition of force, then the 2nd law doesn’t say anything all by its lonesome.
However, already in the Principia, we do have additional assumptions about force apart from the 2nd law, explicit or explicit to various degrees. We have the law of universal gravitation, we have the 3rd law, we have the vector sum law for combining forces, and we have the assumption that mass is conserved. Certainly in a standard modern physics course, the students learn how to compute a wide variety of forces. Put that together with the 2nd law, and you have something. That’s what Quine meant, It’s also what Wilczek meant by the “culture of force”:
Yeah, you’re probably right about ratios and proportions; I definitely want to look into it more. I have a copy of Newton’s Principia: The Central Argument, and one of the things the authors wrote was that inattention to the details of ratio and proportion can lead people to falsely conclude that some of Newton’s definitions are circular, but I don’t really know enough math (yet, i’m going to school for math, i also like history) to be sure if that;s true. However, i’m still unconvinced about operationalism. From what I understand, operationalism(or instrumentalism?) is a type of philosophy where you stay neutral on claims of truth or falsity about theories and just focus on how much they “save the phenomenon.” On a side note: I read somewhere in James Evan’s History and Practice of Ancient Astronomy that “saving the phemoneon” was a more complicated concept than a lot of modern authors think, and that it didn’t necessarily commit one to an instrumentalist philosophy. Thanks for the reply.
Just to be clear, I looked back at Newton’s Principia: The Central Argument. What the authors said was – i’m paraphrasing a bit – that Newton’s definition of Force is not quite the same thing as F = ma (although the quantity ma was definitely related to force for Newton), and that the F = ma definition came from Euler a bit later. They wrote that Euler’s ‘algebraic’ definition of F = ma *did* require an independent definition of the basic units of force, but that with Newton it was more complicated. I’m not sure if that makes sense.
I agree that Newton’s definition of force isn’t the same as F = ma, because then it would be impossible to consider statics.
IIRC, the F = ma formulation came from Euler. (Newton’s formulation of the second law is closer to “force = change in momentum”.)
Which is still not a definition of force but a description of what happens when force is applied
In my freshman physics class, as I recall Professor Goodstein argued that we had independent definitions for neither force nor mass, and therefore f = ma had no actual meaning whatever, not even as a definition. I don’t recall how (or if) he ever resolved this issue.
I mean, f = ma is an actual law that’s applied to understand the behavior of mechanical systems. Presumably he wasn’t saying f = ma is literally a meaningless scratch of symbols? That would seem to conflict with the observation that people do indeed calculate with f = ma. (This entire conversation as gotten me curious about classical mechanics btw. 🙂 )
It would be interesting to see how ‘Newtonians’ like Laplace dealt with the seeming circularity of Newton’s second law, if they did.
I suspect that the lack of engagement with Newton’s ideas in England was largely due to the lack of mathematical capability. (Westfall’s biography of Newton makes it clear that most academic positions at the time were basically sinecures.) By all accounts, few people attended Newton’s lectures and fewer still would have understood what they heard there.
The structure of the Principia itself also posed challenges. As Clifford Truesdell put it in his essay “The Role of Mathematics in Science as Exemplified by the Work of the Bernoullis and Euler”:
Truesdell goes on to attribute much of the progress in what we now call “Newtonian” mechanics to Euler, from 1738 onwards.
What you say is largely correct but this situation was not due to positions being sinecures but to a genuine rejection of a mathematics based science by the Baconians who largely controlled English science throughout most of the eighteenth and well into the nineteenth centuries.
Babbage et al famously led a rebellion agains their dominance during the first half of the nineteenth century following the death of Joseph Banks in 1820, an arch Baconian, who had ruled the Royal Society for 50 years.
And yes, what is now largely taught as Newtonian physics is a synthesis of Newton’s work with that of Descartes, Huygens and Leibniz and some lesser figures such as Émilie du Châtelet, cast in the calculus of Leibniz, created by Euler, several Bernoullis and various French mathematician/physicists such as Varignon.
Poor old Hans Sloane. First in conflict with Newton and now with those who want to remove his name from history due to his wife owning part of a plantation with slaves.