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Hypotheses (Non) Fingo

Toni Vogel Carey considers Sir Isaac Newton’s most (in)famous remark.

For two centuries and more, Isaac Newton (1642-1727) was the very god of science, and commentators still hang on his every word, especially his most famous dictum, hypotheses non fingo. Besides, this saying makes for some intriguing, if not very flattering, stories about Newton himself.

The relevant passage occurs in the final General Scholium of Newton’s Principia (1687). (The book’s full title is Philosophiae Naturalis Principia Mathematica, or The Mathematical Principles of Natural Philosophy). Here is the original English translation of 1729 by Francis Motte, which is still in use:

“Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power … I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses [hypotheses non fingo]; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy … To us it is enough that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”

Quite aside from its being in Latin, the Principia was such a difficult work that Newton, who apparently wanted it to be inscrutable to all but a few savants, advised the general reader to skip nearly all of Books I and II. (Unfortunately for the reader, this advice is proffered at the beginning of Book III.) So the average person, and most who were considerably above average, needed some sort of study notes to navigate the Principia. This made vulgarizations, or popularized glosses, indispensable, and in some cases very influential. Voltaire’s in 1738, although ‘lite’ on math, did much to convert the French from Cartesian to Newtonian science during the 1740s, which was very late, since the Principia had been taught at Scottish universities since the 1690s. The best vulgarization was by a Scottish protégé of Newton, Colin Maclaurin, who was appointed to the University of Edinburgh in 1725 on Newton’s recommendation, and who did more to introduce the Principia to England than Newton himself – who held the Lucasian chair at Cambridge from 1669 to 1702, and was President of the Royal Society of London from 1703 until his death in 1727!

Much, and I do mean much, has been made of the term fingo, and whether it should be taken to mean ‘frame’ or ‘make’ or ‘fashion’ or ‘feign’. Motte opted for ‘frame’, but ‘feign’ has become the favorite, because of its connotation of falseness, and Hume used the term this way more than once in his Treatise of Human Nature. But the constant reinterpretation of the phrase looks like little more than an attempt to construe hypotheses non fingo in a consistent way in the light of Newton’s lack of consistency even just in the General Scholium itself.

Let me explain. In contrast to the austerely mathematical treatise as a whole, this section contains a good deal of conversational and highly controversial commentary. Preceding the passage in question, Newton asserts not only that God is “infinite, omnipotent and omniscient,” but what’s more, that “to discourse of [God] from the appearances of things does certainly belong to Natural Philosophy.” As if that were not enough, following the passage in question is another “extravagant hypothesis,” to quote the Newton scholar I.B. Cohen (in Isis #53). This one concerns “a most subtle Spirit which pervades and lies hid in all gross bodies; by the force and action of which Spirit the particles of bodies mutually attract one another at near distances” – to wit, an all-pervading gravitational ‘aether’. You can already see why hypotheses non fingo is not exactly a slam-dunk.

Hypotheses, Phenomena, Rules

Three editions of the Principia appeared during Newton’s lifetime. However, serious study of the development of his thinking from the first to the third editions did not begin in earnest until the mid-twentieth century, when history of science became a recognized discipline. The evolution of the Principia from 1687 to 1726 is important, for one thing because the General Scholium did not appear until the second edition of 1713, nor therefore did hypotheses non fingo. And for another, only in the third edition of 1726 do we find all four of Newton’s ‘Rules of Reasoning’ (Regulae philosophandi). Briefly:

1. “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” This is Newton’s principle of parsimony (which I wrote about in PN issue 81). His short version of Ockham’s Razor is, “More is in vain when less will serve.”

2. “To the same natural effects we must, as far as possible, assign the same causes.” He gives the examples of respiration in man and beasts, and the fall of stones in Europe and America. This principle is often stated the other way around, with a more predictive intent, i.e., from like causes we can infer like effects.

3. “Qualities … found to belong to all bodies within the reach of our experiments are to be esteemed the universal qualities of all bodies whatsoever.” This is Newton’s principle of induction.

4. “We are to look upon propositions collected by general induction from phaenomena as accurately or very nearly true … till such time as other phaenomena occur by which they may either be made more accurate, or liable to exceptions.” This rule renders scientific conclusions at root conditional, always subject to correction. The science scholar Alexandre Koyr é called it Newton’s “rule of prudence and of good sense.”

Book III is particularly revealing from our standpoint, because in 1726 it opens with the four ‘Rules’, whereas in 1687 it opened with a section labeled ‘Hypotheses’. Nine ‘hypotheses’ were scattered through the work in the first edition, of which only one survived as such in the second and third. But one hypothesis did survive as such, which means that hypotheses non fingo was evidently contradicted in the Principia itself. As for the other eight, six Hypotheses were renamed Phaenomena in later editions, and two were renamed Regulae philosophandi.

Up to a point, then, we can take Newton to be saying, I do frame hypotheses, I just call them rules. But Newton was surely right to call them rules, since they did for scientific method what Euclid’s axioms did for geometry and Aristotle’s laws (non-contradiction, etc) did for logic.

Newton vs. Hooke (It’s Not Even Close)

The story of Newton is first and foremost that of his science. But much of the rest is about his endless vituperative verbal battles, most notably with Robert Hooke (1635-1703) and Gottfried Leibniz (1646-1716). The war with Hooke in particular is relevant here, since it is intertwined with hypotheses non fingo. It began in 1672, when Newton’s first paper, on light and color, was presented to the Royal Society of London, and he was elected a Fellow. Hooke, who was already powerful in the Society, and possessed extraordinary knowledge and creativity in all matters scientific, had his own ideas about light (basically a wave theory), which led him to call Newton’s particle theory “only a hypothesis.”

Hooke’s problem was that while he initiated promising new ideas about almost everything, it was others who brought them to completion, and, to Hooke’s consternation, got credit for them. According to the Dictionary of National Biography he had a “jealous” and “peevish temper,” and was later to complain about the Principia that he “gave Newton the first hint” of the theory of gravitation. There was much truth in this; but Newton was the one who took it over the finish line.

Even before the Principia, however, things had already gone from bad to worse between the two men. For consider Newton’s second-most-famous saying: “If I have seen further it is by standing on the shoulders of giants.” This idea, which goes back to the first century, was hardly original with Newton. But most scholars have considered it a gracious expression of modesty on his part, which has done much to counter his reputation as haughty, dictatorial and even cruel. More than once, Dudley Shapere writes in his entry on Newton in the Encyclopedia of Philosophy, “he used the power of his reputation or office to crush others.”

Looks here, though, are deceiving. The shoulders-of-giants remark appeared in a letter in 1675/76, written to none other than Robert Hooke. And Hooke had been beset from his teenage years by a malady that made him look increasingly hunchbacked. Far from being a gracious compliment, then, or even just “an attempt to pacify Hooke,” as Shapere suggests, Newton was, if anything, upping his vindictiveness to new levels.

My Newton gossip comes mostly from a paper by Mordechai Feingold (‘Mathematicians and Naturalists: Sir Isaac Newton and the Royal Society’ in J.Z. Buchwald and I.B. Cohen, eds., Isaac Newton’s Natural Philosophy), and from Frank Manuel, who wrote in his 1968 psychological biography A Portrait of Newton: “When the enemy was very powerful, as in the case of Robert Hooke, he tended to withdraw, to avoid, to hide away, to bide his time. But entrenched in office, he used virtually every means at his disposal to defeat an antagonist, and he required total submission, public humiliation, annihilation.”

The Royal Society

The phrase hypotheses non fingo may have originated with Henry Oldenburg, the first Secretary (executive director) of the Royal Society, who praised members in 1667 for “neither feigning nor formulating hypotheses of nature’s actions,” but rather seeking out “the thing itself.” In any case, Oldenburg’s importance to the Society from its inception in 1660 cannot be exaggerated. Almost instantly and singlehandedly, through his deft diplomacy in handling scientific correspondence and his editing of the Philosophical Transactions, the first important scientific journal, he made the Society the hub of scientific communication worldwide. T.H. Huxley would later declare that “if all the books in the world except the Philosophical Transactions were destroyed, it is safe to say that the vast intellectual progress of the last two centuries would be largely preserved.” Unfortunately, when Oldenburg died in 1677, Robert Hooke, who lacked Oldenburg’s people skills, not least in handling Newton, succeeded him as Secretary.

The war between Newton and Hooke, while intensely personal, played out within a larger split within the Royal Society’s mathematical and experimental factions. To be sure, this too had a lot to do with Newton, for the Society’s troubles began with its contested decision to publish the Principia: it was only through great persistence that the astronomer Edmund Halley (of comet fame) managed to shepherd the work to publication.

Before 1687 the experimental and mathematical wings of the Society had coexisted peacefully enough. And according to Feingold, until Newton’s Presidency commenced in 1703 the empiricists remained tolerant of the mathematicians, but not conversely: the mathematicians were already dismantling “the very cornerstone upon which the English empiricist scientific tradition stood: experiments and observations” (from ‘Mathematicians and Naturalists’). And for the quarter-century that Newton presided over the Society, his mathematical faction kept the empiricists completely subjugated.

The roots of the Royal Society were strongly empiricist, and it took a powerful force to counter this bent. Newton provided that force. But as soon as he died, the empiricists regained the upper hand in a bitter election which left the mathematicians less-than-gracious losers. The one person whose reputation miraculously emerged unscathed was Newton himself, who continued to be seen as “the greatest man that ever liv’d.” (quoted in Feingold op cit p.77) Alexander Pope penned the famous epitaph:

“Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light.”

The praise here was for Newton’s physics and optics, the science of light. But at the Royal Society the skies, which had been bright until Newton showed up, soon turned dark and menacing.

Hypotheses Fingo

The factionalism within the Royal Society was noteworthy for its hostility; but it reflected a mathematical-empiricist split which characterized modern science from its inception. On one side, Galileo proclaimed that the book of nature is written in the language of geometry, without which we cannot understand a single word of it. On the other, Francis Bacon decreed that the way to do science is by generalization from observed instances, with “Mathematic and Logic… but the handmaids of Physic.” Nearly four centuries later, science is still divided along these methodological lines.

The elephant in the room in this story was Newton’s other great work, the Opticks, which appeared in 1704, just after he became President of the Society. Written and published in English, this book was far more accessible than the Principia, and it was read and studied by professionals and lay people alike. Moreover, as Cohen notes, the Opticks was where “eighteenth-century experimentalists [could] find Newton’s methods.” Yet judging by his stance at the Royal Society, you would think Newton had never written anything but the Principia. Even before becoming President he remarked haughtily that he “first proved his inventions by geometry and only made use of experiments to make them intelligible and to convince the vulgar.”

I don’t mean to suggest that Newton’s position on hypothesizing was any clearer in the Opticks than in the Principia. In its final Query 31 (which dates from the second edition of 1718), Newton talks about “making Experiments and Observations, and … drawing general Conclusions from them by Induction … For hypotheses are not to be regarded in experimental Philosophy.” That sounds very Baconian. But as Cohen notes, far from following hypotheses non fingo in the Opticks, Newton “let himself go, allowing his imagination full reign and by far exceeding the bounds of experimental evidence.”

From the outset, as I said, the Royal Society had a strong Baconian (empiricist) bias, as did the English-speaking world generally. But as time went on and facts kept piling up, it became increasingly obvious that they were failing to arrange themselves so as to yield satisfactory conclusions. Disillusionment inevitably set in, and by 1875 even the entry on Bacon in the Encyclopaedia Britannica was denouncing the “inductive formation of axioms by a gradually ascending scale” as one that “no science has ever followed, and by which no science could ever make progress. The true scientific procedure is instead that of hypothesis followed up and tested by verification.” Against that backdrop, it makes little sense to make hypotheses non fingo the formula to which “the whole Newtonian epistemology is reduced,” as Alexandre Koyré put it.

Much Ado

What emerges from Newton scholarship since 1950 is a position on hypothesizing that most today would find quite reasonable and middle-of-the-road, I think:

• According to Larry Laudan (in The Methodological Heritage of Newton, ed. R.E. Butts and J.W. Davis), in the early seventeenth century ‘hypothesis’ stood for “unproven postulates, axioms or first principles of any science” – an interpretation common since Aristotle and Euclid – and this was what Newton meant by it in the first edition of the Principia, where it carried no pejorative connotation. Cohen too says that Newton sometimes used ‘hypothesis’ and ‘axiom’ interchangeably, which helps to explain the transition from ‘hypotheses’ in the first edition to ‘rules’ in the third.

• Laudan also quotes a letter from Newton to Oldenburg:

“The best and safest method of philosophizing seems to be, first diligently to investigate the properties of things and establish them by experiment, and then seek hypotheses to explain them. For hypotheses ought to be fitted merely to explain the properties of things and not attempt to determine them.”

Newton was not opposed to hypotheses, then, so long as they were kept within the proper, explanatory, bounds.

• Cohen says that ‘hypothesis’ could also serve as a synonym for ‘suspicion’, a term used in the first paragraph of the Preface to the Principia; or for ‘assumption’, as in Newton’s proviso, “on the assumption that the centre is (isn’t) stationery.” Newton himself used the term ‘conjecture’ in another comment that speaks directly to the hypotheses non fingo passage:

“It is not the Business of Experimental Philosophy to teach the Causes of things any further than they can be proved by Experiments. We are not to fill this Philosophy with Opinions which cannot be proved by Phenomena. In this Philosophy Hypotheses have no place, unless as Conjectures or Questions proposed to be examined by Experiments.”

• What seems to be the new consensus, expressed by Cohen and others, is that when Newton asserted hypotheses non fingo, he did not mean it as a sweeping methodological statement. Given his hypothesizing, that would make little sense. Rather, Newton was saying only that he would not frame/feign hypotheses about the cause of gravitation.

• My own hypothesis about hypotheses non fingo goes to Newton’s real passion, which was not physics but alchemy. He wrote something like a million words on the subject, far more than on any other. In 2007 the History of Science Society announced a new transcription of Newton’s manuscript Of Nature’s Obvious Laws & Processes in Vegetation, his youthful ‘theory of everything’, which shows that he “linked alchemy to his early theory of gravitation.” Newton must have been constantly on guard lest his patently hypothetical alchemical ideas might come to light; for that would have made him liable to censure, if not dismissal, from Cambridge University, to say nothing of his vulnerability to valid criticism from scientific peers. And we know how Newton reacted to criticism.

The question that emerges from all this, I think, is: What has all the fuss been about? Hypotheses non fingo looks like a cause célèbre created mostly by commentators trying, just as they did in his own day, to make Newton perfectly right. The “greatest man who ever liv’d” was buried nearly three centuries ago; yet apparently he still has the power to intimidate.

Toni Vogel Carey, a philosophy professor in a former life, is on the US board of advisors for Philosophy Now, and writes about the history of ideas.