ABSTRACT Although in recent years Christine Ladd-Franklin has received recognition for her contributions to logic and psychology, her role in late nineteenth- and early twentieth-century philosophy, as well as her relationship with American pragmatism, has yet to be fully appreciated. My goal here is to attempt to better understand Ladd-Franklin’s place in the pragmatist tradition by drawing attention to her work on the nature and unity of the proposition. The question concerning the unity of the proposition – (...) namely, the problem of how to determine what differentiates a mere collection of terms from a unified and meaningful proposition – received substantial attention in Ladd-Franklin’s time, and would continue to interest analytic philosophers well into the twentieth century. I argue that Ladd-Franklin had a distinct theory of the proposition and solution to the problem of the unity of the proposition that she developed over the course of her writings on logic and philosophy. In spelling out her views, I will also show her work interacted with and influenced that of the pragmatist who was her greatest influence, C.S. Peirce. (shrink)

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Before the early 1990s, accounts of classical American philosophy paid relatively little attention to the work and intellectual contributions of women philosophers. However, as early as 1991, a number of contemporary feminist philosophers and historians began to devote more focused attention to women philosophers whose intellectual achievements had been marginalized or forgotten. One woman philosopher whose contributions have still gone unnoticed is that of American logician, mathematician, and color theorist Christine Ladd-Franklin. This paper argues that Ladd-Franklin's feminist (...) efforts to increase the opportunities for women in professional academia were influenced not only by her work as a woman scientist and her reading of feminist literature but also by her understanding of pragmatism and her interaction with Charles Peirce. Specifically, Ladd-Franklin's arguments to increase academic research positions for women and her criticisms of male-only scientific societies point out how discrimination on the basis of gender violates Peirce's first rule of reason that one ought not block the road to inquiry and expose the unscientific nature of gender discrimination by contrasting the pragmatic meaning of acquiring a doctorate with the institutional practice of barring women from making intellectual contributions by denying them professorial positions. (shrink)

Journal Name: Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique Volume: 2013 Issue: 196 Pages: 139-161.

In this paper the relations between the almost unknown Spanish mathematician Ventura Reyes Prósper (1863-1922) with Charles S. Peirce and Christine Ladd-Franklin are described. Two brief papers from Reyes Prósper published in El Progreso Matemático 12 (20 December 1891), pp. 297-300, and 18 (15 June 1892) pp. 170-173 on Ladd-Franklin, and on Peirce and Mitchell, respectively, are translated for first time into English and included at the end of the paper.

Christine Ladd-Franklin is often hailed as a guiding star in the history of women in logic—not only did she study under C. S. Peirce and was one of the first women to receive a PhD from Johns Hopkins, she also, according to many modern commentators, solved a logical problem which had plagued the field of syllogisms since Aristotle. In this paper, we revisit this claim, posing and answering two distinct questions: Which logical problem did Ladd-Franklin solve in (...) her thesis, and which problem did she think she solved? We show that in neither case is the answer “a long-standing problem due to Aristotle.” Instead, what Ladd-Franklin solved was a problem due to Jevons that was first articulated in the nineteenth century. (shrink)

This paper sketches the antilogism of Christine Ladd-Franklin and historical advancement about antilogism, mainly constructs an axiomatic system Atl based on first-order logic with equality and the wholly-exclusion and not-wholly-exclusion relations abstracted from the algebra of Ladd-Franklin, with soundness and completeness of Atl proved, providing a simple and convenient tool on syllogistic reasoning. Atl depicts the empty class and the whole class differently from normal set theories, e.g. ZFC, revealing another perspective on sets and set theories. Two (...) series of Dotterer and the theorem proved by Russinoff are re-characterized in antilogistic formulas corresponding to the square of opposition and twenty-four moods of syllogism. Then the restricted equivalence between two forms of antilogism and minimal inconsistency is built up, implying the internal connection between antilogisms and minimal inconsistency and leaving two related conjectures not proved. Besides, this paper provides a new explanation for the reason why contrariety, subcontrariety, and subalternation and the nine special moods require the non-empty assumption. (shrink)

On 21 August 1912 Christine Ladd-Franklin, by then an established logician, wrote a letter to Bertrand Russell. He replied on 27 September 1912, followed by another letter on 16 November of that year. After a hiatus on his side in 1913–14, they exchanged letters again in 1915. The main topic of their conversations is solipsism: a theme that was important for Russell throughout his writings. In fact, in some of his works he famously mentions his encounters with (...) class='Hi'>Ladd-Franklin, hinting at a difference of opinions and her inability to see the inconsistency in what she claimed. After analysing the correspondence, with some letters resurfacing only recently, one sees a completely different picture: Russell not only does not object to what she claims, he even agrees with her! This article aims to show what really transpired as evidenced by the letters, of which seven of the extant eleven are reproduced in full with annotations. (shrink)

In 1883, while a student of C. S. Peirce at Johns Hopkins University, Christine Ladd-Franklin published a paper titled On the Algebra of Logic, in which she develops an elegant and powerful test for the validity of syllogisms that constitutes the most significant advance in syllogistic logic in two thousand years. Sadly, her work has been all but forgotten by logicians and historians of logic. Ladd-Franklin's achievement has been overlooked, partly because it has been overshadowed by the (...) work of other logicians of the nineteenth century renaissance in logic, but probably also because she was a woman. Though neglected, the significance of her contribution to the field of symbolic logic has not been diminished by subsequent achievements of others.In this paper, I bring to light the important work of Ladd-Franklin so that she is justly credited with having solved a problem over two millennia old. First, I give a brief survey of the history of syllogistic logic. In the second section, I discuss the logical systems called “algebras of logic”. I then outline Ladd-Franklin's algebra of logic, discussing how it differs from others, and explain her test for the validity of the syllogism, both in her symbolic language and the more familiar language of modern logic. Finally I present a rigorous proof of her theorem. Ladd-Franklin developed her algebra of logic before the methods necessary for a rigorous proof were available to her. Thus, I do now what she could not have done then. (shrink)