An Explication of the Antilogism in Christine Ladd-Franklin's "Algebra of Logic" – Early Life and Education

From an early age, Christine Ladd aspired to attain an education, despite knowing that many challenges and obstacles would lie in her way. Born on December 1, 1847, in Windsor, Connecticut, she was on the cusp of having access to higher education as a woman, as in the latter part of the 19th century women began to have more opportunities for both undergraduate and graduate education [Green and LaDuke 2009, p. 6]. From the age of twelve, Ladd expressed a desire to obtain an education, and at the age of fifteen, she was sent to a preparatory school, the Wesleyan Academy in Wilbraham, Massachusetts [Green and LaDuke 2009, p. 17]. In 1866 (the second year the college was in operation) she was able to attend Vassar College in Poughkeepsie, New York; however, she was unable to continue taking courses the following year due to financial difficulties. All was not lost, though, as in 1868 a generous aunt enabled her to return to Vassar, allowing Ladd to complete her studies and graduate in 1869 [Green 1987, p. 122].

Image of Christine Ladd-Franklin, from MAA’s Women of Mathematics poster

Even after the financial problems had been resolved, Ladd faced challenges. As was typical for women, she found employment options limited by her gender. In the 19th century, women were employed primarily in two categories of occupations: manual labor at industrial factories or home-based labor as servants [Goldin 1980, p. 82]. Although she was capable of working at a scientific career, according to Margaret Rossiter strong resistance within the scientific community kept women from entering the workforce in roles such as university professors or government researchers since these were seen as male occupations [Rossiter 1980, p. 381]. Instead, Ladd put her education to use in a rapidly-growing third category of women's employment: teaching in schools. For nine years she held a variety of different teaching positions. As she taught, Ladd continued to pursue an even higher level of education. While at Vassar, Ladd had studied languages, physics and astronomy. After graduation, she drifted toward mathematics, later explaining that she took up the subject because it was similar to her other interests, namely physics, and because it could be done without any apparatus since, as a woman, she could not obtain access to laboratory facilities [Green 1987, p. 122]. Thus, in the 1870s, in between teaching positions, she also made contributions of problems and solutions to the Educational Times of London, and attended classes in mathematics and science at a number of universities when given the opportunity [Green and LaDuke 2009, p. 37].

1885 photograph of Hopkins Hall,
on the original downtown Baltimore campus of The Johns Hopkins University, Public Domain

Though she had received an undergraduate degree, Ladd remained determined to continue her education. In 1878, Ladd applied to the graduate school at the newly-opened Johns Hopkins University in Baltimore, despite being unsure whether the university would admit her on the basis of her gender. As she had feared, the board of trustees only consented to letting her attend lectures without being charged tuition [Green and LaDuke 2009, p. 223]. As a result, Ladd, though never officially allowed to enroll, spent the next four years at Johns Hopkins. During this time, Ladd continued her contributions to the Educational Times; submitted papers to The Analyst, published by Joel Hendricks in Des Moines, Iowa, and the American Journal of Mathematics, published by Johns Hopkins University; and became interested in symbolic logic, which she studied under the guidance of Charles S. Peirce (1839–1914). Her studies culminated in a dissertation on this subject, "On the Algebra of Logic," which would have completed the requirements for a PhD had she been formally enrolled. That her work was highly regarded by Peirce and the entire mathematics department is evidenced by the fact that the university published her dissertation in the 1883 volume, Studies in Logic by Members of The Johns Hopkins University [Green 1987, p. 122].