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Moral Certainty

Toni Vogel Carey connects the dots.

The quaint-sounding term ‘moral certainty’ dates back to c.1400. The Oxford English Dictionary defines it as “a degree of probability so great as to admit of no reasonable doubt.” In the seventeenth century it became an important term in the law; according to a commentator in 1677 it meant “such a certainty as may warrant the judge to proceed to the sentence of death against the indicted party.” By the eighteenth century ‘moral certainty’ had become interchangeable with ‘beyond a reasonable doubt,’ not only in the law, but also in philosophy and polite conversation – even in religion, where it was argued into the nineteenth century that the truth of Christianity could be proven “beyond a reasonable doubt” (see p.31 of Barbara Shapiro’s paper referenced at the end).

Of course, if you’re not sure whether guilt has been established beyond a reasonable doubt, it might not help much to ask whether it has been established to a moral certainty. Then again, it might, for the two phrases have somewhat different connotations. One goes to the idea of external, objective proof, the other to the subjective question whether one feels able in good conscience to convict and sentence a fellow human being. DNA evidence today is capable of satisfying both criteria; but of course this is a relatively recent development, and I’m getting way ahead of myself.

We speak of a scientific revolution in the seventeenth century largely because of a paradigm shift from qualitative to quantitative thinking. Aristotle had understood science as the study of qualitative causes, and this idea became set in stone for some 2,000 years until Galileo declared in 1623 – in a remark so familiar it’s in Bartlett’s – that the universe is written in the ‘language’ of mathematics, without which we cannot understand a single ‘word’ of it.

Another difference was that Aristotle and the scholastics had seen the world in terms of either-or dichotomies: true or false, hot or cold, motion or rest. By contrast, Galileo saw rest not as the opposite of motion, but as the lowest degree of slowness (a speed of zero). His idea of a scientific law was a mathematically ordered continuum leading to an ideal limit-case, something we never expect to be reached. Aristotle defined science in terms of what occurs “always” or “for the most part” (Metaphysics 1027a20); Galileo’s view was that it deals with what occurs at the ideal limit, and so never (Carey 2012). In his last work Two New Sciences (1638), he gave this account of his law of falling bodies (1974, p.76):

“If we find in fact that moveables of different weight differ less and less in speed as they are situated in more and more yielding mediums: and that finally, despite extreme differences in weight, their diversity of speed in the most tenuous medium of all (though not void) is found to be very small and almost unobservable, then it seems to me that we may believe, by a highly probable guess, that in the void all speeds would be entirely equal.”

Galileo’s methodological continuum has been called the first principle of relativity. In a thought experiment in 1632, Galileo realized that a sailor working below deck on a windowless ship traveling on a perfectly smooth sea would not be able to tell whether the ship was moving or stationary. And by similar reasoning, he suggested, it would make no difference to our experience whether the Sun revolves around the Earth or the Earth revolves around it. This in itself didn’t prove that the Earth ‘moves’, but it made the idea less counterintuitive, just as watching ships disappear over the horizon had made it less counterintuitive that the Earth might be round rather than flat.

Beneath decks on a calm sea, could you tell whether you are in motion or at rest?

Galileo wasn’t saved from the Inquisition by the fact that he did not introduce the idea of a heliocentric universe, but merely supported Copernicus, who did. Needless to say, however, Copernicus and Galileo prevailed; and so did the method of approximation to an ideal limit. Robert Boyle (1627-91), who studied in Italy during Galileo’s lifetime, built his ideal gas law on the concept of a methodological continuum. And another who abandoned either/or opposites for “a world of continua,” Lorraine Daston writes in Classical Probability in the Enlightenment, was Jakob Bernoulli (1655-1705). He introduced the idea of degrees of probability from zero to one, “a graduated spectrum of belief… from total ignorance or uncertainty to firm conviction or ‘moral’ certainty.” Among other things, this helped to “bridge the chasm between the absolute doubt of the skeptics and the dogmatic certainty of the scholastics.”

Probabilities could be combined to increase the degree of certainty. Testimony by two or more witnesses was more convincing and provided greater certainty than the same testimony by a single witness. Boyle spoke of a “concurrence of probabilities” that “mount to a moral certainty” (Shapiro p.30). In eighteenth-century America, James Wilson, a signer of the Declaration of Independence and the Constitution, and an early Justice of the Supreme Court, spoke of a continuum of evidence rising by “insensible gradation, from possible to probable and from probable to the highest degree of moral certainty.” (Shapiro p.47)

If probability was important in the law, it was essential to the insurance industry. In 1777 Buffon set moral certainty equal to a probability of 0.9999; and reckoning from existing mortality tables, he pronounced it a moral certainty that a healthy 56-year-old man would survive the next 24 hours. Adam Smith remarked in Wealth of Nations (1776) (I.x.b.27), “Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets the nearer you approach to this certainty.” In London, however, you could buy insurance against almost anything, even “losing at the lottery.” (Daston pages 77, 164, 207, 348) Quantification had its virtues; but one effect of rendering moral certainty mathematical was to de-moralize it (Hankins p.630).

Simplicity and Moral Certainty

Philosophers and theoretical scientists alike have historically placed a high value on simplicity, or explanatory parsimony. Thales reduced everything to water, Heraclitus to fire – and flux. Duns Scotus and William of Occam codified this in the scholastic principle known as Occam’s Razor: “Plurality is not to be posited without necessity”; or, “What can be done with fewer would in vain be done with more.”

Occam’s Razor resurfaced in modern science as Newton’s first Rule of Reasoning in his Principiaof 1687:

“We are to admit no more causes of natural things than such as are both true and sufficient to explain the appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”

Newton was not known for generosity in crediting others (I dished the dirt on Newton in Philosophy Now Issue 88). But he cites Galileo numerous times in the Principia, understandably, since he relied heavily on the Galilean continuum in working out his laws of motion, and in uniting such diverse phenomena as the revolution of the planets, the tides, and the fall of an apple under the single principle of gravitation.

You may not have heard of Dugald Stewart, the last of the constellation of Scottish Enlightenment thinkers who included David Hume and Adam Smith; but few philosophers were more highly regarded in the first half of the nineteenth century. In 1820 former President John Adams wrote to former President Thomas Jefferson: “I think Dugald… has searched deeper and reasoned more correctly than Aristotle, Descartes, Locke, Berkeley, Hume…” (Adams-Jefferson Letters, pp.560-1). I mention Stewart here because he connected the dots from explanatory parsimony to probability to moral certainty:

“The probability of a hypothesis increases in proportion to the number of phenomena for which it accounts, and to the simplicity of the theory by which it explains them; and… in some instances, this probability may amount to a moral certainty.” (Works 1829, 2: 299-300; italics original.)


Squared paper had been used since the seventeenth century for designing ships. But not until well into the eighteenth was it used for plotting data, and the term ‘graph’ was coined only in 1878 (Hankins pages 605 and 608). It was mainly the astronomer and polymath scientist John Herschel (son of William Herschel, who discovered the planet Uranus in 1781) who put this method on the map. And as late as 1833 squared paper was still so new that Herschel took pains to write out minute instructions how to construct it. He used it for calculating the orbits of double stars, which (unlike objects in your rear-view mirror) tend to be farther away from each other than they appear. In effect he had to find “the best approximation of the orbit from very poor data” (p.609). He solved this problem by recording the points he observed, and drawing a simplifying curve through as many points as possible. He called his method ‘graphical’ (p.608).

Herschel’s friend and fellow scientist William Whewell called it the ‘method of curves,’ and used it himself to study the tides. By correcting for errors of observation and “random fluctuations caused by wind, barometric pressure, and the like,” Whewell found that the method of curves provided a result “more true than the individual facts themselves.” Herschel pronounced it “a conviction approaching a moral certainty” that the resultant ellipse is “close to the correct orbit” – good enough to consider the risk of error “more or less infinitesimal,” something “we make up our minds to disregard” (pages 618 and 630-1).

Graphing may at first seem like a simple mechanical procedure. But two observers may plot the same dots and yet not connect them by the same curve; so graphing falls somewhere “between observation and theory.” Beyond a mere “sum of the particulars” (the dots), it involves “a subjective leap dependent on judgment.” Either you “see the law or you do not.” (Hankins pages 621-2, 625, and 633)

Herschel’s Preliminary Discourse on the Study of Natural Philosophy (1830) is said to be the first original book on scientific method to appear since Francis Bacon’s Novum Organum of 1620 had helped launch the Scientific Revolution. Among other things, Herschel refers here to “that general law which seems to pervade all nature – the law… of continuity.” Even something “generally regarded the most opaque in nature,” he says, is “possessed of some slight degree of transparency.” Thus “opacity is not a contrary or antagonist… of transparency, but only its extreme lowest degree.” (section 200; italics original.)

Herschel associated this form of continuity with the idea that “nature does not act by leaps.” And Charles Darwin, who was greatly influenced by Herschel’s book, adhered to this same gradualist principle. Thirty years later, however, Herschel saw fit to argue against Darwin that homo sapiens couldn’t have evolved gradually from the lower animals, but must have been expressly created by God. (I wrote about John Herschel, and the tortured back-and-forth between him and Darwin on this point, in Philosophy Now Issue 48.)

Not-So-Moral Certainty

As two recent U.S. Supreme Court rulings (in 1984 and 1994) attest, the term ‘moral certainty’ is no longer in use, and few judges or jurors even know what it used to mean (Shapiro 51). The term went into decline after 1850, when Herschel introduced the term ‘practical certainty’ in place of ‘moral certainty’ in order “to avoid the ambiguities in the word ‘moral’.” (Hankins pp.618 and 630-1)

So it is interesting that in 1996 Philosophy Now ran an article (in Issue 15) by Peter Lloyd called ‘The Dangers of Moral Certainty’. What Lloyd meant by moral certainty, though, had little to do with probability, or graphing, or a continuum ending in an ideal limit. What he meant was certainty about morals. He drew a contrast, in fact, between this ‘dangerous’ kind of moral certainty and the ‘public certainty’ available in the sciences, which are ‘open to all comers’ with the time and resources to repeat the relevant experiments and see for themselves.

The motto of the Royal Society of London, which played a crucial role in the Scientific Revolution, was Nullius in verba, meaning, “Take no one’s word for it.” So Lloyd’s point has long been a truism. But is it true? How many will ever hear the sound of two black holes colliding, the little ‘chirp’ that recently confirmed Einstein’s general theory of relativity? For that matter, how many can even understand Newton’s Principia or Einstein’s general relativity theory, much less work out the laws of gravity and relativity on their own?

Nor is this the only problem with the idea that scientific certainty is available to all, or even most. As we saw with the method of graphing, different people look at the same thing and see it differently. This goes to Thomas Kuhn’s famous notion of paradigm shifts. The Aristotelians looked at a swinging body, Kuhn says in The Structure of Scientific Revolutions (1970, p.119), and saw something “falling with difficulty;” Galileo looked at it and saw a pendulum, which led him to the laws of falling bodies and motion along an inclined plane.

Another problem with Lloyd’s thesis is that even when knowledge has been available for centuries, philosophers don’t necessarily get the message. Take the difference between Aristotle’s qualitative and Galileo’s quantitative methods. During the 1960s, in addition to Kuhn’s idea of revolutionary paradigm shifts, philosophers of science were trying to find workable analyses of such notions as law-likeness, disposition and tendency, and dealing with the intractable ceteris paribus (‘other things being equal’) clause. Nobody seemed to realize that Galileo had long ago provided a concept of lawlikeness that allows us to bypass and ignore these ‘other things’. One who did see this clearly was Kurt Lewin, the ‘father’ of social psychology. He wrote in 1931 that Galileo had replaced “dichotomous classifications [like] the distinction between lawful and chance events [with] continuous gradations,” so that “whether the event described by the law occurs rarely or often has nothing to do with the law. Indeed, in a certain sense, the law refers only to cases that are never realized, or only approximately realized, in the actual course of events.” Lewin thought the field of psychology in 1931 was facing many of the “theoretical difficulties [that had] culminated in the conquest over Aristotelian ways of thinking in physics” in the seventeenth century (1931, pp.144-6 & 152-3)

Even though the laws of ideal gases in physics, of perfect speakers and hearers in linguistics, and of perfect competition in economics, are well known to most college-educated people today, in psychology and philosophy the method of successive approximation is still seen through a glass darkly, if at all. In these two fields, not much seems to have changed since 1931, or even since the seventeenth century. Moral certainty came into use, caught on, and then went out of vogue. The method of approximation that supported it scientifically in the work of Galileo, Boyle, Bernoulli and others came and stayed, but has yet to fully catch on. I wouldn’t call that progress.

© Dr Toni Vogel Carey 2017

Toni Vogel Carey has been a regular contributor to Philosophy Now since 2002, and serves on its US advisory board. She is an independent scholar who also publishes in scholarly journals, gives papers at scholarly conferences (Oxford, Sorbonne, Princeton, Aberdeen, Toronto, Rotterdam…), and is concurrently at work on three books.


• ‘Always or Never: Two Approaches to Ceteris Paribus’, Erkenntnis 77, Toni Vogel Carey, 2012

Two New Sciences, Galileo Galilei, 1638 translation. S. Drake, 1974

• ‘A “Large and Graceful Sinuosity”: John Herschel’s Graphical Method’, Isis 97, Thomas L.Hankins, 2006

• ‘The Conflict between Aristotelian and Galilean Modes of Thought in Contemporary Psychology’, Journal of General Psychology 5, Kurt Lewin, 1931

Principia Mathematica, Sir Isaac Newton, 1687, 1726 translation, A. Motte, 1995

• ‘“Beyond Reasonable Doubt”: The Neglected Eighteenth-Century Context’, Law and Humanities 8, Barbara Shapiro, 2014


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