Christine Ladd Franklin

Introduction

Christine Ladd-Franklin (December 1, 1847 - March 5, 1930) completed every requirement for a doctorate in mathematics and logic at Johns Hopkins University in 1882 and was refused the degree because she was a woman. The university handed it to her forty-four years later, at its fiftieth-anniversary celebration in February 1926, by which time she was in her late seventies.

She is remembered for two things that rarely travel together. The first is the antilogism, an economical way of testing whether a syllogism is valid, which logicians still discuss. The second is an evolutionary theory of color vision that tried to reconcile the rival accounts of Hermann von Helmholtz and Ewald Hering by treating the human eye as a record of its own evolutionary history.

She is also a case study in how a scientific field handles a contributor it will not employ. Ladd-Franklin was one of the first two women elected to the American Psychological Association, the first woman admitted to the Optical Society of America, and a steady contributor to the leading journals of the day. She never held a salaried academic post, and for twenty years the experimental psychologists who ran her field refused to let her into the room where their work was argued over.

Early Life and Education

Ladd-Franklin was born in Windsor, Connecticut, the eldest of three children of Eliphalet Ladd, a merchant, and Augusta Niles Ladd. Her mother and her aunt Juliet Niles were committed supporters of women's rights, and as a girl she was taken to suffrage lectures and meetings. Her mother died of pneumonia when Christine was twelve, and she went to live with her paternal grandmother.

She was educated first in a two-year college-preparatory programme at Wesleyan Academy in Wilbraham, Massachusetts, graduating as valedictorian in 1865. Getting to college required an argument. Her grandmother objected that after four years of study she would be too old to marry; Ladd replied that the women of New England so greatly outnumbered the men after the Civil War, and that she was herself so far from conventionally striking, that she had better be able to support herself. She entered Vassar College in the autumn of 1866 and took her A.B. in 1869, finishing in three years.

At Vassar she worked mainly in astronomy under Maria Mitchell, the first woman elected to the American Academy of Arts and Sciences, taking observations for her in the college observatory. She wanted to study physics and settled for mathematics as the next best thing, because women were not admitted to physics laboratories.

The nine years after graduation were spent teaching science and mathematics in girls' schools in Pennsylvania, Massachusetts and New York, work she loathed. In 1872 she wrote in her journal that teaching was something she hated "with a perfect hatred." She kept working on mathematics in the margins of that career, publishing problems and solutions in the British Educational Times and papers in the American journal The Analyst, where she became the first woman to appear in print.

Academic and Professional Career

In 1878 she applied to Johns Hopkins University for a fellowship, signing her application "C. Ladd." The university awarded the fellowship before the trustees realised she was a woman, then tried to withdraw it. James J. Sylvester, who knew her published work, insisted that she be admitted and that she be his student. She held the fellowship for three years, but was denied the title of fellow and was kept off the printed roster of students, the trustees fearing that naming her would set a precedent. She studied mathematics with Sylvester and logic with Charles Sanders Peirce, becoming the first American woman to do formal graduate work in both.

On August 24, 1882, she married Fabian Franklin, a mathematician at Hopkins, and adopted the double surname. That same year she completed all the requirements for the doctorate; the degree was withheld. Her dissertation, On the Algebra of Logic, appeared in 1883 in Peirce's edited volume Studies in Logic by Members of the Johns Hopkins University. In 1884 she attended Lord Kelvin's master class at Hopkins. In 1887 Vassar gave her an honorary LL.D., and the first volume of the American Journal of Psychology, founded that year by G. Stanley Hall, carried her paper on the experimental determination of the horopter.

The turn toward vision came in 1891 and 1892, when she travelled to Germany with her husband and daughter during his sabbatical. She spent the first half in Göttingen working with Georg Elias Müller and the second in Berlin, where she attended Helmholtz's lectures on the theory of color vision as well as Arthur König's. Out of that year came the theory she presented in 1892 to the Second International Congress of Experimental Psychology in London. She returned to Germany alone in 1894 for four further months with König; by her own account the collaboration went badly, and she felt he gave her no useful direction.

Then came the long stretch of work without a post. In December 1893 she was elected to the American Psychological Association alongside Mary Whiton Calkins, among the first women to join. That same year she applied for a teaching position at Johns Hopkins and was refused. From 1901 to 1905 she served as associate editor for logic and philosophy on James Mark Baldwin's Dictionary of Philosophy and Psychology. In 1904, eleven years after the refusal, Hopkins at last allowed her to teach one course a year, an arrangement that had to be renewed annually and ran until 1909. When Fabian Franklin left mathematics for journalism and became associate editor of the New York Evening Post in 1910, the family moved to New York. She taught occasional courses thereafter, at Columbia in 1912-1913, at Clark and Harvard in 1913, and at the University of Chicago in 1914, and was rarely paid for any of it.

In 1919 she became the first woman member of the Optical Society of America, holding member number 118, and presented six papers and two exhibits at its meetings. Between 1894 and 1925 she gave ten papers at APA meetings. She appeared in Who's Who in America for 1901-1902 and 1914-1915. Colour and Colour Theories, the book in which she gathered a lifetime of work on vision, was published in 1929. She died in New York City on March 5, 1930.

Bertrand Russell later recalled receiving a letter from her announcing that she was a solipsist, and that she was surprised there were no others. "Coming from a logician and a solipsist," Russell wrote, "her surprise surprised me."

Major Contributions to Psychology

The antilogism and symbolic logic

Ladd-Franklin's dissertation proposed that the validity of any syllogism could be tested by recasting it as an inconsistent triad, which she called an antilogism: three propositions that cannot all be true at once. To test an inference, deny its conclusion; if the premise pair and the denied conclusion form an inconsistent triad, the inference is valid. Her own illustration ran: "It is impossible that any of these measures should be idiotic, for none of them is unnecessary, and nothing that is necessary is idiotic."

The device replaced the memorisation of moods and figures with a single consistency test. Josiah Royce treated it as a milestone in the algebra of logic, Charles Sanders Peirce's own work responded to it, and Arthur Prior later praised it generously. She returned to the topic in "The antilogism," published in Mind in 1928, forty-five years after the original paper.

The development theory of color vision

By the 1890s the field was split between the Young-Helmholtz trichromatic theory, which posited three receptor processes, and Ewald Hering's opponent theory, which posited six fundamental sensations organised in opposing pairs. Ladd-Franklin's move was to stop treating these as competitors and treat them instead as descriptions of different stages of one evolutionary sequence:

Achromatic vision. The earliest stage, a bare light-dark response mediated by a single undifferentiated visual substance, still visible in the rod-based peripheral retina.
Blue-yellow vision. That substance differentiates, giving a second axis with blue at one pole and yellow at the other.
Red-green vision. The yellow pole differentiates further into red and green.

The sequence carried a set of testable implications. Because red-green sensitivity arrived last, red-green color deficiency should be the commonest form; because achromatic vision is the oldest and most thoroughly consolidated, total color blindness should be the rarest; and because the fovea is the newest part of the retina and the periphery the oldest, the periphery should be comparatively colour-poor. These implications were among the first attempts to bring evolutionary reasoning to bear on a sensory mechanism rather than merely on anatomy.

Binocular vision and the horopter

Before the colour work she had established herself in physiological optics with "The experimental determination of the horopter" (1887), published in the opening volume of the American Journal of Psychology, and she continued to publish on binocular vision, double images and the geometry of corresponding retinal points alongside the colour research.

Major Publications

Ladd, C. (1883). On the algebra of logic. In C. S. Peirce (Ed.), Studies in logic by members of the Johns Hopkins University (pp. 17-71). Boston: Little, Brown.
Ladd-Franklin, C. (1887). The experimental determination of the horopter. American Journal of Psychology, 1, 99-111.
Ladd-Franklin, C. (1889). On some characteristics of symbolic logic. American Journal of Psychology, 2, 543-567.
Ladd-Franklin, C. (1892). A new theory of light sensation. In Proceedings of the International Congress of Experimental Psychology, London (pp. 103-108).
Ladd-Franklin, C. (1896). The higher education of women. The Century, 53(2), 315-316.
Ladd-Franklin, C. (1904). Endowed professorships for women. Publications of the Association of Collegiate Alumnae, 3(9), 53-61.
Ladd-Franklin, C. (1911). The foundation of philosophy: Explicit primitives. Journal of Philosophy, Psychology, and Scientific Method, 8, 708-713.
Ladd-Franklin, C. (1916). Review of an introduction to the study of color vision. Psychological Bulletin, 13(7), 272-275.
Ladd-Franklin, C. (1922). Tetrachromatic vision and the development theory of vision. Science, 55, 555-560.
Ladd-Franklin, C. (1923). Practical logic and color theories. Psychological Review, 29(3), 180-200.
Ladd-Franklin, C. (1925). The theory of blackness. American Journal of Physiological Optics, 6, 453-454.
Ladd-Franklin, C. (1928). The antilogism. Mind, 37, 532-534.
Ladd-Franklin, C. (1929). Colour and colour theories. New York, NY: Harcourt, Brace & Co.

Impact and Legacy

The antilogism is the part of her work that survived intact. It remains the standard illustration of how a consistency test can replace the enumeration of valid syllogistic forms, and it earned her a place in the small group of nineteenth-century logicians whose results are still cited rather than merely historicised.

The colour theory is a different story. It was widely discussed for decades and forced the trichromatic and opponent camps to state their assumptions more precisely, and its evolutionary framing anticipated the comparative approach that is now routine in vision science. But the specific mechanism did not hold up. Hurvich and Jameson's quantitative opponent-process theory, published in 1957, accounted for how signals from three cone types are recombined into opponent channels, and that two-stage picture is what is still taught. Ladd-Franklin's developmental sequence, in which the red-green axis arises by differentiation of a prior yellow process, is not how the field frames the question today. Some of the comparative detail she built on was also simply wrong: she held that most mammals enjoy trichromatic vision, when in fact most are dichromatic.

The harder legacy is institutional. In 1912 she wrote to the organisers of the informal gathering of experimental psychologists known as the Experimentalists, asking to present. "I am particularly anxious to bring my views up, once in a while, for hand-to-hand discussion before experts," she wrote. She was refused, and she wrote again to protest: "a scientific meeting is a public affair, and it is not open to you to leave out a class of fellow workers without extreme discourtesy." The group was convened by Edward Titchener, and contemporary accounts of why women were excluded centre on the men's wish to smoke and speak without restraint. She was never admitted.

The consequence was that a theory about the retina had to be defended in print instead of in the laboratory, and increasingly in footnotes. Colour and Colour Theories is punctuated by long notes reclaiming priority, charging Hermann Ebbinghaus with having absorbed the Purkinje phenomenon without acknowledgement and König with having taken her observation that the fovea is night-blind. Laurel Furumoto, who has done more than anyone to recover Ladd-Franklin's career, read the 1929 book less as a synthesis of research than as a strategy for claiming scientific authority from a position with no institutional base at all. That reading is generous, but it does not change the fact that the book is harder to use as a source than it should be, and that the priority disputes repel readers who might otherwise have engaged with the theory.

Scholars have also pointed at a self-reinforcing pattern: because she was not cited at the time, later historians did not find her in the literature and so did not cite her either, and the omission reproduced itself across generations. Recovering her has required archival work rather than reading the standard histories forward.

Optica, the successor to the Optical Society of America, lists her among the five women in its first class of Fellows, elected in 1959. She had been dead for twenty-nine years. The entry reads less like an election than like a correction the institution did not know how else to make.

Learn More

Hermann von Helmholtz — the Berlin physiologist whose lectures on colour vision prompted Ladd-Franklin to develop her own theory.
Mary Whiton Calkins — elected to the American Psychological Association in the same year as Ladd-Franklin, and likewise refused a degree she had earned.
Edward Titchener — founder of the Experimentalists, the group that excluded women from its meetings.
Gustav Fechner — founder of psychophysics, the tradition of measuring sensation that shaped nineteenth-century vision research.
The history of psychology — how the field's institutions, methods and blind spots took shape.
Feminist psychology — the critique of who has been able to do psychological research and whose work has been credited.

References

Ladd-Franklin, C. (1929). Colour and Colour Theories. Harcourt, Brace.