Today George Boole is regarded as one of the founders of the computer age that now dominates our culture.

His algebra lies at the base of computer circuit design and of most computer programming languages and Booleans power the algorithms of the ubiquitous search engines. As a result two years ago the bicentenary of his birth was celebrated extensively and very publically. All of this would have been very hard to predict when his work on the algebra of logic first saw the light of day in the nineteenth century. His first publication *Mathematical Analysis of Logic* (1847) was largely ignored by the wider world of mathematics and his definitive presentation of his logic *An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities* fared little better, initially attracting very little attention. It was only some time after his death that Boole’s logical works began to attract deeper interest, most notably in Germany by Ernst Schröder and in America by Charles Sanders Peirce.

In 1883 Peirce published *Studies in Logic*: *by Members of the Johns Hopkins University*, edited by himself it contained seven papers written largely by his students. Of central interest is the fact that it contains a doctoral thesis, *On the Algebra of Logic*, written by a women, Christine Ladd.

Christine Ladd’s life story is a casebook study of the prejudices that women, who wished to enter academia suffered in the nineteenth and early twentieth centuries. Born 1 December 1847 (the year Boole published his first logic book) in Windsor, Connecticut the daughter of Eliphalet and Augusta Ladd, she grew up in New York and Windsor. Her mother and her aunt Julie Niles brought her up to believe in education for women and women’s rights. Her mother died in 1860 but her father initially supported her wish for advanced education and enrolled her at Welshing academy in a two year course for preparing students for college; she graduated as valedictorian in 1865 but now her father opposed her wish to go on to college. Only by arguing that she was too ugly to get a husband was she able to persuade her father and grandmother to allow her to study at the women’s college Vassar. She entered Vassar in 1866 but was forced by financial difficulties to leave before completing her first year. She now became a schoolteacher until her aunt helped her to finance her studies and she returned to Vassar.

At Vassar the pioneering female astronomer Maria Mitchell took her under her wing and fostered her developing interest in physics and mathematics.

Due to the fact that women could not do experiment work in laboratories she was forced to choose mathematics[1] over physics, a decision that she regretted all of her life. She graduated from Vassar in 1869 and became a secondary school teacher of mathematics and science in Washington, Pennsylvania. Over the next nine years she published six items in *The Analyst*: *A Journal of Pure and Applied Mathematics* and three in the *American Journal of Mathematics*. More importantly she took a very active part in the mathematical questions column of the *Educational Times*, the journal of the College of Preceptors in London, a profession body for schoolteachers. This mathematical questions column was a very popular forum for nineteenth century mathematicians and logicians with many leading practitioners contribution both question and solutions. For example the nineteenth-century Scottish logician Hugh McColl published his first logical essays here and Bertrand Russell’s first mathematical publication can also be found here[2]. Ladd contributed a total of seventy-seven problem and solution to the *Education Times*, which would prove highly significant for her future career.

In 1878 she applied for and won a fellowship to study mathematics at the Johns Hopkins University. Her fellowship application was simply signed C. Ladd and the university had assumed that she was male. When they realised that she was in fact a woman, they withdrew their offer of a fellowship. However the English professor of mathematics at Johns Hopkins, James J. Sylvester, who knew of Ladd’s abilities from those *Educational Times* contribution insisted on the university honouring the fellowship offer.

At the time Johns Hopkins did not have a very good reputation but Sylvester did, in fact he was a mathematical star, not wishing to lose him the university conceded and allowed Ladd to take up her three-year scholarship. However her name was not allowed to be printed in circulars and basically the university denied her existence. At the beginning she was only allowed to attend Sylvester’s classes but as it became clear that she was an exceptional student she was allowed to attend classes by other professors.

In the year 1879 to 1880 she studied mathematics, logic and psychology under Charles Sanders Peirce becoming the first American women to be involved in psychology. Under Peirce’s supervision she wrote her doctoral thesis *On the Algebra of Logic*, which was then, as mentioned above, published in 1883. Although she had completed all the requirements of a doctoral degree Johns Hopkins University refused to award her a doctorate because she was a woman. They only finally did so forty-four years later in 1927, when she was already seventy-eight years old.

In 1882 she married fellow Johns Hopkins mathematician Fabian Franklin and became Christine Ladd-Franklin, the name by which she is universally known today. As a married woman she was barred from holding a paid position at an American university but she would lecture unpaid for five years on logic and psychology at Johns Hopkins and later at Columbia University for thirty years.

In the 1880s she developed an interest in vision and theories of colour perception publishing her first paper on the subject in 1887. She accompanied her husband on a research trip to Germany 1891-92 and used the opportunity to study with the psychologist Georg Elias Müller (1850–1934) in Göttingen

and with the physiologist and physicist Hermann von Helmholtz (1821-1894) in Berlin.

In 1894 she returned alone to Germany to work with physicist Arthur König (1856–1901), with whom she did not get on and whom she accused of having stolen her ideas, and again in 1901 to work with Müller.

As a result of her researches she developed and published her own theories of colour vision and the causes of colour blindness that were highly influential.

Ladd-Franklin was a tireless campaigner for women’s rights and even persuaded the inventor of the record player, Emile Berliner, to establish a fellowship for female professors, the Sarah Berliner postdoctoral endowment, in 1909, which she administered for the first ten years and which is still awarded annually.

She herself continued to suffer rejection and humiliation as a female academic. In 1904 the British psychologist Edward Titchener (1867–1927) founded a society for experimental psychologists, “The Experimentalists”, and although he knew Ladd-Franklin well her barred her, as a woman, from membership. A decision, which she fought against in vain for many years. Women were only permitted to attend following Titchener’s death.

Despite the discrimination that she suffered Christine Ladd-Franklin published many papers in the leading journals and her work was held in high regard. She died of pneumonia, aged 82, in 1930. Today the American Association for women in Psychology have an annual Christine-Ladd Franklin Award, awarded for significant and substantial contributions to the Association.

Although she struggled against prejudice and discrimination all of her life and never received the formal recognition that should have been her due, Christine Ladd-Franklin made significant contributions to the fields of Boolean algebra and colour vision for which she is highly regarded today. Through her fighting spirit and unbending will she helped open the doors of scientific research and academia for later generations of women.

* *

[1] It is interesting to note that barred from access to academia and its institutions a small but significant number of women managed to some extent to break through the glass ceiling in logic and the mathematics in the nineteenth century, because these are subjects in which one can make an impression with nothing more than a pencil and a piece of paper.

[2] In my days as a logic historian I spent a not very pleasant two weeks in the British Newspaper Library in Colindale (the tenth circle of hell), amongst other things, going through the *Educational Times* looking for contributions on the algebra of logic. During this search I came across the Bertrand Russell contribution, which I showed, some time later, to a leading Russell scholar of my acquaintance, who shall remain here nameless. Imagine my surprise when shortly afterwards an article was published by said Russell expert explaining how *he had discovered* Russell’s first ever mathematical publication in the *Mathematical Questions* column of *The Educational Times*. He made no mention of the fact that it was actually I who had made the discovery.

Reblogged this on Project ENGAGE.

(sp) Sanders

Bugger!

(sp) Colindale. The British Newspaper Library (printed papers) is now housed at Boston Spa.

I suspect that failure to credit the original discoverer happens more often than academics would like to admit to.

Putnam (in ‘Peirce the Logician’) traces Russell and Whitehead’s use of the quantifier through Whitehead back to Ladd-Franklin and Owen Mitchell

Boole’s logic didn’t originally have quantification. The first system of logic with quantification was Frege’s Begriffsschrift from 1879. Both Schröder and the Johns Hopkins logicians added quantification to Boolean algebra. Whitehead’s original work in logic was done in algebra of logic so it’s more than plausible that he had it from Mitchell/Ladd.

Peirce had a way of handling quantification as early as his 1870 “Logic Of Relatives”. Incipient as it is I believe it to be far advanced in principle, and I did not run into anything like it until I started studying category-theoretic approaches to logic in the 1980s. See my (someday continuing) notes here —

☞ Peirce’s 1870 Logic Of Relatives

When I share this to Facebook, FB in its brilliance uses the Arthur Konig photo.

Remember when Facebook let you choose the photo from a page you were sharing? Good times!

My WordPress account automatically posts my posts to Twitter and Facebook. For Twitter it automatically takes the first picture, in this case Boole, and for Facebook one near the end, as you say in this case König. On Twitter I deleted the automatic post and replaced it by hand with a picture of Christine Ladd-Franklin. On Facebook I left the automatic post up but also posted by hand with a Christine Ladd-Franklin portrait.

And yes Facebook sucks!

If you create a “community page” for a topic then it still allows you a bit of flexibility in the choice and uploading of pictures for a post. See, for example —

☞ Peirce Matters

Great article, thanks!

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The picture caption mis-spells Edward Titchener’s last name.

Thanks! Autocorrect strikes again!

I am having trouble parsing the first footnote. I think there was a word dropped, and a comma would help:

It is interesting to note that

althoughbarred from access to academia and its institutions,a small but significant number of women managed to some extent to break through the glass ceiling in logic and the mathematics in the nineteenth century, […]Pingback: Peirce’s 1903 Lowell Lectures • Comment 4 | Inquiry Into Inquiry