Christine Ladd-Franklin—mathematician, logician, and psychologist—was born in Windsor Connecticut, on December 1, 1847. Her father, Eliphalet Ladd, a prominent merchant, and her mother Augusta Niles Ladd, an early feminist, both came from distinguished families. One great uncle, William Ladd, had founded, in 1828, the American Peace Society, a merger of the Christian pacifist societies of Maine, Massachusetts, New Hampshire and New York, and another, John Milton Niles, was a senator from Connecticut and United States Postmaster General under Martin Van Buren.
Six of her maternal ancestors were members of the Constitutional Convention of the Colony of Connecticut. “The first specific influence that led me toward serious intellectual pursuits was my mother’s character and family circle,” Mrs. Ladd-Franklin told an interviewer from The Buffalo Express in April,1918. “My mother was one of four sisters, all of whom were brilliant women. In spite of the fact that they were widely separated by marriage, they would return in the summers to our family home in Windsor, Connecticut, and there led a delightful intellectual life together. Influenced by this atmosphere, accordingly, it is not surprising that when Vassar College was founded, I wanted to go there.”
Her mother died of pneumonia when she was twelve, and her father remarried two years later. Christine moved to Portsmouth, New Hampshire, to live with her paternal grandmother. She spent two years at the Wesleyan Academy in Wilbraham, Massachusetts, completing the same courses as the young men preparing for Harvard and graduating in 1865 as class valedictorian.
Ladd began keeping a diary in 1860, around the time of her mother’s death. Although she would later berate the practice ( “There is nothing more foolish than to write a journal, except the very act and fact of being such a foolish, stupid person”) she continued it at least until 1873. The diary is a rich record of her intellectual and moral discussions with herself and of her life and studies—at Vassar and later.
In an entry, for March 27, 1863, the 16 year old exulted in a “glorious emancipation proclamation for woman….I have been reading an account of the Vassar female college that is to be. Oh! I must go. I must prevail upon my father to send me….Let me study diligently now as preparation.” An entry for July 23, 1866, is a record both of the realization of her dream and of the clarity of argument her later admirers and opponents her would come to recognize:
I have gained an important point with my grandmother. She says she thinks Auntie ought to send me to Vassar. She objected that at the end of four years I should be too old to get married. I assured her that it would afford me great pleasure to entangle a husband but there was no one [in] the place who would have me or whom I would have and out of this place I was destined never to go, gave her statistics of the great excess of females in New England and proved that as I was decidedly not handsome my chances were very small. Therefore since I could not find a husband to support me I must support myself and to do so I needed an education. Grandma succumbed.
With financial support from her aunt, Juliet Niles, Christine Ladd enrolled in Vassar’s second entering class, in 1866.
At first, Vassar seemed not the school she expected it to be. On Sept. 20, 1866, Christine Ladd wrote in her diary, “With great sorrow I at once confess that I am grievously disappointed in Vassar. Instead of the independent University my imagination pictured, I find a fashionable Boarding-school; and instead of the tall intelligent and enthusiastic young women in blue merino that I fancied, I find a troupe of young girls who wear black chamois and are wholly given up to the tyranny of fashion.” She criticized the college for the elementary level of some courses, “the multiplicity of petty rules”, and the lack of an atmosphere of political discussion. She found no student who had declared herself for the rights of women and commented acerbically on discovering Confederate sympathies: “The political status of our pastor has just declared itself, and I am suffering a real ostracism for my negro-worship.”
Christine Ladd’s diary also reveals her frustration with the rigid scheduling of activities. “I so despise the idea that women are not as competent to take care of themselves as men, that they cannot decide for themselves when to go to bed and when to get up, how much exercise to take, how much to pray and go to church.” She once rebelled by loudly refusing to go to the bath time she was assigned by the corridor teacher, Miss Clarke. Later she felt guilty about her outburst of anger; just the day before, they had sat together, listening to the chapel sermon and receiving communion.
As her first year went along, Ladd began to appreciate the challenge of the courses. She studied Latin, Trigonometry, French, Geology, and Music. Despite her expectations, she enjoyed geology, wrote essays, and wrestled with a theological question posed by Professor Farrar on the efficacy of prayer to which she “derived a paradoxical answer.” Despite her academic preparation, she often felt stupid in comparison to her classmates. Describing herself to her diary as the class dunce, she resolved to study harder and was rewarded for her efforts when she passed an examination in Mental Philosophy and was praised by Miss Clarke. The teacher at whom she had recently shouted rebellion, complementing her, kissed her. (1) Even after this success, she thought herself “the personification of stupidity in each and every class I enter.”
Although she wrote home a week later, asking to attend Vassar for two more years, she was forced to leave at the end of the academic year. The following September, she began teaching in Utica, New York. She read German, taught music lessons, and conducted a reading course. She felt that she was good at teaching and enjoyed it, but she did not get along with the other schoolteacher, a Miss Backus, and she ended what she referred to as “the Utica project” after Christmas. In April 1868 she was translating Schiller’s “Des Mädchens Klage”, which she subsequently published in The Hartford Courant. She also devoted herself to botany and collected 150 specimens. In 1868, with assistance from her Aunt Juliet, she returned to Vassar and began writing in German and French in her diary.
In Christine Ladd’s second year at Vassar, she discovered the skills in science that set her on her career as a mathematician, logician, and psychologist. On September 21, just after the beginning of term, she wrote, “I have already distinguished myself in astronomy today,” and on October 15, “I completed an original demonstration in Physics…Then in Astronomy I also had the pleasure of working out an original demonstration of the sextant which was ‘very gratifying’ to Miss [Maria] Mitchell.” She also took Greek and read and recited Sophocles’s Antigone. At this time, she began to write for the student newspaper, The Transcript.
Ladd was particularly at home in astronomy. On October 24, she reported a failed attempt to make observations of Venus with Lizzie Coffin, confiding to her diary, “owing to a mistake of Miss Mitchell’s the star passed too soon for us.” A month later, she was promoted in astronomy: “I do not understand to this day how it happened, but the fact is that I find myself at present alone with Miss Davis and Miss Parsons, the past graduates.” And on December 30: “Miss Mitchell has been exceedingly complimentary to me of late. She does not hesitate to bring my name forward as the Valedictorian of my class.” On April 10, 1869, Ladd gave the inaugural address as the president of the Beta Chapter of the Vassar College Philalethean Society.
On August 18, 1869, graduated from Vassar, Ladd took up teaching again, this time in Hollidaysburg, Pennsylvania. She recorded her daily schedule: “I teach five hours and devote the rest of my time to my private studies. I have just been put in possession of $150 worth of chemicals and apparatus, and I am content to sacrifice even the beauty of my hands to the desire of finding out something new. I take music lessons to very little advantage, and devote myself for the rest to Analytics.” In 1871, Christine Ladd moved to Washington, Pennsylvania, for a higher paying teaching position. On November 14, she noted in her diary an important discovery:
The fates are very good to me. This little town of Washington contains a man who ranks among the first ten or twelve mathematicians in the country, and this man…devotes two evenings in the week to Me. Not only is he a fine mathematician; he is also an enthusiast. He is such a man as one reads of in books but such a man as I have never known before…. Is it a Socrates? Then will I be his most devoted disciple. He shall teach me to make the worse appear the better reason and… my place of residence for the next ten years is Washington.
Ladd’s “Socrates” was George B. Vose, Professor of Mathematics and Engineering at Washington and Jefferson College, who had long been active in mathematical analysis and who had been a frequent contributor to MIT Professor John Runkle’s The Mathematical Monthly. Despite declaring to her diary on January 28, 1872:
Sunday evening is the most miserable time of all the week. The burdens of the morrow look impossible to be borne. Teaching I hate with a perfect hatred….I shall not be able to endure it another year,
Ladd continued to teach science and mathematics, and began submitting problems and solutions to the Educational Times of London and to The Analyst: A Journal of Pure and Applied Mathematics—emulating Vose while still idolizing him: [March 15, 1872] “…Prof. Vose was more than usually angelic. What it is to be a man of genius! I look upon this man with ever increasing wonder.” She probably studied mathematics informally at Harvard in the latter part of 1872, attending the lectures of William E. Byerly and James Mills Peirce—both classmates a few years earlier of Ladd’s Vassar predecessor, Mary Whitney, in the Harvard classes of Peirce’s father, Benjamin Peirce.
Like that of Vassar, the opening, in February 1876, of another innovative institution, Johns Hopkins University, offered Christine Ladd another challenging possibility. The first American university to open as primarily a research institution, Hopkins was formally closed to women. But from the beginning—and despite the trustees’ acceptance of the views of Harvard’s president Eliot, who thought coeducation “a thoroughly wrong idea which is rapidly disappearing” and who advised that “the coeducation of the sexes is not possible in highly civilized communities”—the question of accommodation of qualified women as students was continually debated. In less than a year, Martha Carey Thomas, the daughter of a trustee, applied to be a degree candidate in classics, and in November, 1877, it was decided that women could attend public and special lectures and that they might be assessed and certified as to their accomplishment.
Christine Ladd no doubt knew at least partially of these events, and even as M. Carey Thomas—a few years later, one of the founders and the second president of Bryn Mawr—was deciding to leave Johns Hopkins after her first year to pursue graduate study in Europe, Ladd was applying for admission directly to the eminent British mathematician, James Joseph Sylvester, a luminary in the new research university’s faculty. Sylvester knew of Ladd through her publications in London’s Educational Times, and he urged her acceptance, declaring to Hopkins’s president Gilman that Ladd would be “a source of additional strength to the University.” The university’s excellent online chronicle, “Women at Johns Hopkins University: A History,” summarizes the result:
On April 25, 1878, the executive committee of the Board of Trustees agreed to permit Christine Ladd to attend only the lectures of Sylvester, without her being enrolled as a student. After demonstrating her exceptional abilities, she was soon admitted to the lectures of preeminent logician and philosopher, Charles Sanders Peirce. She proved her worthiness, inventing a technique for reducing all syllogisms to one formula, called the antilogism, which still holds a significant place in logic. “Brilliant” was the term Peirce used to characterize her dissertation, “The Algebra of Logic.” While the Trustees had been willing to permit Ladd’s attendance and even voted her the stipend (but not the title) of a fellow, they stopped short of awarding her the doctorate she had earned.
Ladd completed her degree requirements in 1882, and Peirce gave “The Algebra of Logic” a prominent place in Studies in Logic by Members of the Johns Hopkins University, which he edited and published in 1883. (2)
The very word “antilogism,” let alone Ladd’s elegant conception of it had awaited discovery since the time of Aristotle. In 1928, protesting the appropriation of “both the word and the thing” by the Cambridge logician, William Ernest Johnson, in his Logic (1921-24), Ladd-Franklin offered a clear description of her invention along with an engaging example of it:
The view of logic which I have based upon the antilogism is that to make use of the syllogism is a great mistake when a so much better form of reasoning is at hand. If for the usual three statements consisting of two premises and a conclusion one substitutes the equivalent three statements that are together incompatible (namely, the same two premises and the immediate denial of the conclusion), one has a formula which has this great advantage: the order of the statements is immaterial—the relation is a perfectly symmetrical one. Moreover, any two (or one) of the three statements may be uttered by one party to a discussion and the remaining one (or two) by the other—the incompatibility (or inconsistency) still remains. This is, in fact, the natural form of reasoning in the case of rebuttal or discussion—and it may well be maintained that it was invented before the more abstract and remote syllogism. A little girl of four years of age was making, at her dinner, the interesting experiment of eating her soup with a fork. Her nurse said to her, “nobody eats soup with a fork, Emily,” and Emily immediately replied, “But I do, and I am somebody”. (The connecting logic-word in the case of the antilogism is but, or something equivalent to it, instead of therefore, so, or consequently.)
In an appreciation of Ladd-Franklin’s accomplishment, published in Mind in 1927—the year after Johns Hopkins, in conjunction with the celebration of its fiftieth year, awarded her the doctorate she’d earned 44 years earlier—the Columbia logician Eugene Shen further explicated “Emily’s” utterance— “Not only is this argument an Antilogism, but it also contains an existence term—a thing quite unknown to the ordinary logician”—and provided the appreciation of Ladd-Franklin’s discovery by the eminent Harvard philosopher, Josiah Royce:
The Antilogism was at first called by Dr. Ladd-Franklin the “inconsistent triad”; apropos of it the late Professor Josiah Royce of Harvard was in the habit of saying to his classes: “There is no reason why this should not be accepted as the definitive solution of the problem of the reduction of syllogisms. It is rather remarkable that the crowning activity in a field worked over since the days of Aristotle should be the achievement of an American woman.
A young Hungarian-born mathematics professor, Fabian Franklin, had been one of Ladd’s examiners for graduate work at Johns Hopkins. They married in 1882, and Professor Franklin recalled in 1918 their initial attraction: “As to how my wife and I first became interested in each other, strangely enough, it was through a long discussion we had together on the steps of one of the Johns Hopkins buildings, standing for hours on the steps, debating a point in logic.” Although now occupied with family life, Ladd-Franklin (as she now was) began to move toward the integration of her previous studies with a new field, psychology—particularly, questions of perception and, most particularly, questions of the physiology of vision. (3) A review in Science in1887, described her first publication in the field, an account in The American Journal of Psychology of a new method of experimentally defining the horopter—the three-dimensional area of binocular vision recorded on two retinas—as evidence of the nascent journal’s “more technical character….a very laudable feature, for it serves not only to frighten off the many dilettanti of psychic research, but to justify the strictly scientific methods of psychology.” Ladd-Franklin also received Vassar’s only honorary degree—the LL.D—in 1887.
Fabian Franklin’s sabbatical year, 1891-92 was spent in Germany, where Christine furthered her research in vision, first in the Göttingen laboratory of George Elias Müller, one of the founders of experimental psychology, and then—leaving Fabian in Göttingen with their young daughter, Margaret—in Berlin, where she worked in the laboratory of the physicist, philosopher, and pioneer physiological psychologist Hermann von Helmholtz. Also—although women were no more welcome in German universities than in the United States—she managed to gain entrance to the lectures at the university of the foremost proponent of Helmholtz’s theory of color vision, Arthur König. By the end of the sabbatical year, Ladd-Franklin had developed her own ideas on the subject, which she presented in London at the International Congress of Psychology.
Ladd-Franklin engaged two theories that had dominated color vision thinking since Thomas Young had posited, in 1803, three “primary colors” in retinal perception—red, green, and blue (or violet). As empirically established by Helmholtz and Müller—with the possible detection of two additional “primaries”—this theory had been challenged by the subjective, or “nativist,” “opponent-color” theory of Ewald Hering. Based on cognitive as distinct from retinal behavior and attempting to account for afterimages, color blindness, and the evolution of color vision, Hering proposed that there were three couples of primary colors: red-green, yellow-blue and white-black and that a photosensitive reaction in neural tissue, when turned off by one of these colors, presented its coupled (or opposing) color. Ladd-Franklin proposed a process of three evolving stages in the development of color vision. Black-white vision was the most primitive stage, since it occurs under the greatest variety of conditions, including under very low illumination and at the extreme edges of the visual field. The color white, she theorized, later became differentiated into blue and yellow, with yellow ultimately differentiated into red-green vision. While boldly attempting to wed the two earlier theories into an evolutionary, photochemical hypothesis, she advanced her proposal with modesty: “I make no claim to having hit upon the process which goes on in the photo-chemical substance, but merely to having described a process which might with perfect plausibility result from the action of ether-waves upon the retina, and from which would result all the facts of light-sensation. More than this no hypothesis, in the present state of our knowledge, can hope to do.” Ladd-Franklin’s theory was well-received and remained influential for some years, and its emphasis on evolution is still valid today.
Fabian Franklin left Johns Hopkins in 1895 to become editor of the Baltimore News, but Ladd-Franklin persisted in attempting to secure a teaching and research position at the university. She served as one of two associate editors of the monumental Dictionary of Philosophy and Psychology (1901-5) edited by J. Mark Baldwin of Princeton, and she was one of the four contributors—along with C. S. Peirce, now retired from Johns Hopkins—to the dictionary’s entries on logic. She also wrote most of the section on vision and was first author or a contributor to several dozen other entries. All the while, Ladd-Franklin continued her research in color vision; despite her research and her growing reputation, she never gained a formal academic post from which to conduct and publish her research.
In 1903, Baldwin accepted a professorship in philosophy and psychology at Johns Hopkins. The following year, Christine Ladd-Franklin became the first woman to teach in the Arts and Sciences faculty at Johns Hopkins, although she was allowed to teach only one course each term—a course in mathematics or login in the fall and one on some aspect of vision in the spring—and her appointment as lecturer in philosophy was on a year-to-year basis. She taught at the university for five years, until 1910, when her husband became associate editor of the New York Evening Post, and Ladd-Franklin began teaching at Columbia, again only one course at a time and with no faculty status and no salary.
Christine Ladd-Franklin continued her research and writing on vision, lecturing at Vassar, Clark, Harvard, and Chicago, delivering papers at American and international psychological conferences, and publishing, in 1929, Colour and Colour Theories, a collection of 25 of her scientific writings on the subject. Also, during the 1920’s, Ladd-Franklin produced nine papers on the neurophysiological visual phenomenon known as the “blue arcs of Purkinje,” after their first discovery, in 1825, by the Czech physiologist, Jan Evangelista Purkyně.
Ladd-Franklin remained a vigorous advocate for the advancement of women in many spheres of American life. A frequent correspondent to The New York Times, on December 13, 1921, she scolded the American Academy of Arts and Letters for remaining an all male organization. Noting that Mary Whiton Calkins of Wellesley had been president of both the American Psychological Association and the American Philosophical Association and that “this very month” the annual meeting of the psychological society, at Princeton, would be presided over by Margaret Floy Washburn of Vassar, she asked “Does not the Academy of Arts and Letters (which ought if anything to be further advanced in the humanities than the plain scientists) feel that it is rather old-fashioned?” Again, on May 28, 1924, she advocated discussion groups on economics for women, noting that women, “now that they have been given the vote” had a responsibility to “make themselves intelligent voters.” Ladd-Franklin claimed that the study of economics, because “its doctrines are still under debate,” led to what psychologists called “real thinking” as distinct from “reproductive thinking.” (4)
Her contributions to the Times were not always so serious. On July 30, 1926, for example, she echoed the wry logic of some of her diary entries with a reasoned approach to a crime wave in New York City: Hold-ups are increasing by leaps and bounds. What are we going to do? It happens there is a precedent that we might follow here. There is a well-known community where, other means of support having failed, the inhabitants still managed to get on by taking in each other’s washing. I would like to suggest that in the present crisis we follow this clever plan and support ourselves by means of holding each other up.
Christine Ladd Franklin, self-defining mathematician, logician, psychologist, innovator, and feminist, died of pneumonia on March 5, 1930, at her home on Riverside Drive in New York. She was 82 years old. At her memorial service her colleague, the Columbia philosopher and mathematician Cassius Jackson Keyser, praised the originality and diversity of her contributions, saying they would bear her name “far down the corridors of time to come….Hers was an activity made possible by the union of a virile understanding with the finest intuitions and sympathies of woman.” Fabian Franklin died, at 86, in January, 1939.
- Lepha N. Clarke taught mental philosophy and moral philosophy at Vassar in 1866-7 and English from 1866 until 1872.
- Maria Mitchell cited Ladd’s achievement in a diary entry on February 10, 1887. Reflecting on educational opportunities for women and on the importance of self-direction, she wrote, “Endow the already established institution with money. Endow the woman who shows genius with time….A case at John Hopkins University is an excellent one. A young woman who is already a scholar goes into the institution; she shows what she can do and she takes a scholarship; she is not placed in a happy valley of do nothing—she is put into a workshop where she can work.”
- A recurring theme toward the end of Ladd’s diaries is the weakening of her eyesight; in the final entry, for April 27, 1883, she comments on the completion of her studies at Harvard: “ A pleasant month of pleasure-seeking afterwards, and then home, to use up what was left of my eyes on the columns of the N.Y. Herald.”
- Margaret Ladd Franklin (1883?-1960) followed her family’s feminist tradition. A 1908 Bryn Mawr graduate, she published a critical bibliography, The Case for Woman Suffrage, in 1913. A comment in the volume’s “Introduction” by M. Carey Thomas, president of both Bryn Mawr and The National College Equal Suffrage League (and Christine Ladd’s immediate predecessor in the struggle for coeducation at Johns Hopkins), suggested that Thomas recognized the mother’s verbal zest in the daughter: “The stars of praise, the trenchant criticisms, and the illuminating comments are wholly her own. Were it otherwise the bibliography would lose its value and its special appeal to college women. Only in two or three instances when saints of our suffrage calendar had…received at her hands too black a mark was it suggested that she should soften a somewhat drastic comment.”
Thomas C. Cadwallader and Joyce V. Cadwallader, “Christine Ladd-Franklin (1847–1930)”, in Agnes N O’Connell and Nacy Felipe Russo, eds. Women in Psychology: A Bio-biblographic Sourcebook, New York, 1990
Margaret Ladd Franklin, The Case for Woman Suffrage: A Bibliography, New York, 1913
Stanley Finger, Origins of Neuroscience, New York, 1994
Phebe Mitchell Kendall, Maria Mitchell: Life, Letters, and Journals, Boston, 1896
C. S. Peirce, ed.,Studies in Logic by members of the Johns Hopkins University Boston, Little, Brown and Company, 1883
Scarborough, E. & Furumoto, L., Untold Lives: The first generation of American women psychologists. New York, 1987
“Mrs. Fabian Franklin, Pioneer, Hopkins Alumna, Dies in N.Y.’ New York Bureau of The Baltimore Sun, March 5, 1930
I. Susan Russinoff, “The Syllogism’s Final Solution,” The Bulletin of Symbolic Logic, Vol. 5, No. 4 (Dec., 1999)
“Christine Ladd-Franklin,” Publisher’s Weekly, March 22, 1930
(unsigned review of first volume of The American Journal of Psychology) Science, Vol. X, no. 250
Eugene Shen, “The Ladd-Franklin Formula in Logic: The Antilogism,” Mind, New Series, Vol. 36, No. 141 (Jan., 1927)
C. F. Ladd-Franklin “The Antilogism,” Mind, New Series, Vol. 37, No. 148 (Oct., 1928)
Vassar Miscellany News, June 15, 1932
Henry W. Burr, “Mrs. Ladd-Franklin, A superwoman in the Fields of Logic and Color Perception” The New York Times, June 24, 1922
Christine Ladd-Franklin, “Women and Letters,” The New York Times, December 13, 1921
Christine Ladd-Franklin, “Women and Economics,” The New York Times, May 28, 1924.
Christine Ladd-Franklin, “Holding Each Other Up,” The New York Times, July 30, 1926
“Dr. Ladd-Franklin Eulogized at Funeral,” The New York Times, March 8, 1930
Bruce Bridgeman, (review of R. Stephen Turner, “In the Mind’s Eye: Vision and the Helmholtz-Hering Controversy), The Quarterly Review of Biology, Vol. 71, No. 1 (Mar., 1996)
AAVC Alumnae House Biographical Files
“The History of Colour Vision Science” https://www.psych.ucalgary.ca/pace/va-lab/Brian/history.htm
“Biographies of Women Mathematicians: Christine Ladd-Franklin” https://www.agnesscott.edu/lriddle/women/ladd.htm
“Christine Ladd-Franklin” https://www.webster.edu/~woolflm/christineladd.html
“Women at Johns Hopkins University: A History” https://library.jhu.edu/collections/specialcollections/archives/womenshistory/chapter1.html
- Johns Hopkins’s online account places Christine Ladd-Franklin in the context of women’s history at the university.
CJ, MH, 2008