In an 1839 letter, poet Elizabeth Barrett Browning recounted the following tale about Lady Mary Shepherd:
“Lady Mary (so her daughter told me) used to waltz until she was tired, and then sit down to write about algebra …. She used to keep Miss Shepherd up to three or four in the morning after a conclave of waltzers, to hear … vocal dissertations upon spirit & matter & such high arguments.”
Waltzing on the one hand, and mathematics and metaphysics on the other: this captures Mary Shepherd’s dual life. Born in 1777 in a castle outside Edinburgh, she was the daughter of the 3rd Earl of Rosebery and was educated by private tutors at home. In 1808 she married London barrister Henry John Shepherd, and the couple joined the active intellectual and social scene of the London elite. Her many friends included mathematician Charles Babbage, poet Samuel Taylor Coleridge, economist David Ricardo, and Mary Shelley, author of Frankenstein. Shepherd’s name appears frequently in British newspapers from the 1810s until her death in 1847, as she attended and hosted parties, balls, and concerts in London and Brighton, and spent time in spa towns such as Cheltenham, Bath, and Tunbridge Wells. She was often accompanied by her eldest daughter, who later wrote a memoir that is now our primary source of information about Shepherd’s life.
Despite her busy family and social life, Shepherd found time to write two philosophical treatises. In 1824, she published An Essay upon the Relation of Cause and Effect, which raises various objections to David Hume’s theory of causation and causal inference and presents her own alternative account. Three years later, she published Essays on the Perception of an External Universe, and Other Subjects Connected with the Doctrine of Causation. This ambitious volume engages with the work of George Berkeley, Scottish philosophers Thomas Reid and Dugald Stewart, and French “sensationalists” such as Condillac, and contains ingenious arguments against external-world skepticism. She also later published three essays in popular magazines.
Shepherd’s work was generally well received in her day. In his 1848 History of the Philosophy of the Mind, Robert Blakey wrote that Shepherd’s writings displayed “great acuteness and subtility”; astronomer Thomas Forster considered her 1827 book to be “the best metaphysical book of our times”; and the scientists William Whewell and Sir Charles Lyell reportedly described Shepherd as an “unanswerable logician, in whose argument it was impossible to find loophole or flaw”. Shepherd’s daughter even asserts that Whewell used one of Shepherd’s books in his teaching at Cambridge.
Shepherd did have detractors; John Cam Hobhouse, friend of Byron, wrote in his diary that “She is quite a fool!” and even her friend Ricardo said in a letter to James Mill that “you know that in her company there can be no time for work of any description.” But this attitude was likely a manifestation of a general prejudice against “bluestocking” intellectual women who did not keep quiet. The novelist Amelia Opie reported in an 1813 letter that at one party that included Lady Mary Shepherd, the German physician Johann Spurzheim, and the philosopher Thomas Brown (later taken to task by Shepherd in her 1824 book on causation), “Lady Mary began her dialogue at ten, and it was not over at a little past twelve.” Professor Brown, Opie wrote, “listened occasionally, and with an anatomizing eye, for he does not like literary women; therefore a woman, entering his own arena, must have called forth all his reviewer bitterness.” This telling comment about the misogynistic reception Shepherd sometimes encountered also likely explains why, after her death, Shepherd’s work fell out of view. Her books were rediscovered only in the 1980s by pioneering scholar Eileen O’Neill, and have only recently begun to receive attention from historians of philosophy.
Shepherd’s main goal in her two treatises was to show that we can know, through reason, that various metaphysical principles are necessary truths. Her 1824 book focuses on our knowledge of two causal principles: first, that nothing can come to exist without a cause other than itself (the Causal Principle); second, that like causes necessarily have like effects (the Causal Likeness Principle).
David Hume had argued that there is no rational justification for these causal principles, and that our only basis for claims about causal relationships is habit formed through experience. According to Hume, we cannot really be said to know that the sun will rise tomorrow, just that we expect that the sun will rise tomorrow because we are so used to having seen that happen in the past. While Hume’s arguments had been first presented some eighty years before, his account of causation was still the subject of fierce debate in Shepherd’s day. Indeed, in 1805, a candidate for the Chair of Mathematics at Edinburgh University had nearly been denied the position because certain Church of Scotland clergy objected to his endorsement of Humean causation. Thus this was very much a live issue when Shepherd entered the debate.
In contrast to Hume, Shepherd argued that we can know through reason that the Causal Principle and the Causal Likeness Principle are necessary truths. She maintained that it is inconceivable that something could come into existence without a cause. Causal connections, she argued, are necessary connections. And because causal connections are necessary connections, once we have identified what caused some given effect, we can know with absolute certainty that when another cause of that type occurs in similar circumstances, the same effect will occur. Contra Hume, she insisted that we can know this even if we have only seen the causal relationship once. For example, once we are able to ascertain that a piece of gold melts at a temperature of 1064° C, we can know, with complete certainty that every subsequent piece of gold heated to that temperature (under similar circumstances) will melt.
Of course, we can only find out what causes gold to melt through experience. But one experience is enough to establish this causal fact, according to Shepherd’s argument. One interesting upshot of her view is that truths about physical causes and their effects turn out to be necessary truths that are known a posteriori – that is, on the basis of experience. We can only learn the melting point of gold through experience; but one carefully controlled scientific experiment is all that is needed to know that it is a necessary truth that gold melts at 1064° C. Shepherd thus posited a category of necessary a posteriori knowledge long before Saul Kripke argued for such a category in the 1970s lectures that later formed the basis for his book Naming and Necessity.
Another striking feature of Shepherd’s theory of causation is her insistence that causal relationships occur synchronously, not sequentially. That is, the action of the cause occurs at the same time that the effect is brought about. As she understood causation, two or more causes must come together, or “mix,” and in this mixing, they thereby give rise to an effect. Consider making a cake. Shepherd would say that the ingredients are among the causes of the cake batter: when the ingredients “mix,” the batter is the result. But the ingredients are only some of the batter’s causes; strictly speaking, the ingredients plus the action of a spoon or electric mixer are the causes. While the existence of the ingredients does precede the existence of the batter, the coalescence of the ingredients and the mixing action synchronously produce the batter. When the batter is put in a container in the oven, the heat “mixes with” the batter and, synchronously, produces the cake.
In her 1827 book, Shepherd drew on the theory of causation defended in her first book in order to take on external-world skepticism. Hume had argued that belief in an external world is merely a fiction of the imagination, and Berkeley had defended an idealist philosophy in which all we can know are ideas. Shepherd wanted to combat these views, but without taking the route defended by Scottish “common-sense” philosopher Thomas Reid, who had maintained that such skepticism can be combated by pointing out that we have a “natural instinct” to believe an external world exists. For Shepherd, the only way to dispel skepticism was to provide a knock-down proof to show that we can know through reason (not instinct, not the imagination) that an external world of continually-existing objects must exist independently of us. The objects in this external world are the causes of our sensory perceptions: an object “mixes” with our sense organs and our mind, producing (at that very time) a sensory perception as their effect.
Mathematical analogies pervade Shepherd’s writings. She used an algebraic analogy to illuminate the relationship between our sensory perceptions and the external world; our perceptions of colour, shape, taste, and so on are like “algebraic signs, by which we can compute and know the proportions of their qualities” and thereby understand objects in the external world. She appealed to the mathematical concept of an “exponent”, in the older sense in which “the exponent of a ratio” of two terms is their quotient, to express the relationship between body and mind, whereby the brain is the “exponent” of the soul. And, as Shepherd understood causation, causal relationships can be expressed by equations. Since she argued that effects do not follow their causes, she thought it misleading to express a causal relationship between a cause A and an effect C as “A followed by C”. We should say, rather, that “A x B = C”, where that means that when two items A and B “mix” or conjoin, item C arises. For Shepherd, the causes A and B are, literally, factors, entities that produce something else when multiplied together.
Indeed, Shepherd argued against Hume that when we make some inference on the basis of past experience and conclude that future instances will resemble those past instances, this inference can be as certain as our knowledge that what is true of a circle in one diagram will be true of all other circles. In other words, she assimilated physical induction to mathematical proof. Various philosophers have held that the epitome of certain knowledge is mathematical knowledge; Descartes, for example, maintained that we should aspire to produce metaphysical proofs with conclusions as certain as those as of geometry. However, Shepherd turned this view on its head: causal reasoning is the epitome of certainty, with mathematical knowledge just a special instance of causal reasoning. “The science of mathematics”, she wrote, “is truly but one branch of physics”. Thus, while mathematics provided Shepherd with a rich source of analogies for understanding our knowledge of the physical world, she saw its certainty as derivative: mathematical truths are necessary truths because they, like causal reasoning in the physical world, depend on the principle that “like causes must have like effects”.
Even when Shepherd was on holiday, philosophy and mathematics were part of her life. Among the very limited extant correspondence from Shepherd is a letter (now in the British Library) that she wrote to Charles Babbage in 1826, inviting him and his wife to join her family at a house in Tunbridge Wells. She noted that the house contained a pianoforte, and promised “tea in the garden.” But she also promised to “talk philosophy” with Babbage “a good deal” and reported that her household was “all busy in algebra” and that she had “begun to do it regularly”. The letter ends with her conviction that the algebraic methods she is studying are “fraught with meaning”. Music, maths and metaphysics: all were mixed in the life of Lady Mary Shepherd.