The Syllogism's Final Solution

1999 ◽  
Vol 5 (4) ◽  
pp. 451-469 ◽  
Author(s):  
I. Susan Russinoff
Keyword(s):  
Nineteenth Century ◽  
Significant Advance ◽  
Symbolic Logic ◽  
Symbolic Language ◽  
Rigorous Proof ◽  
Final Solution ◽  
Important Work ◽  
Modern Logic ◽  
Johns Hopkins University ◽  
History Of

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.

From Admission Ticket to Contribution: Remarks on the History of an Apologetic Argument

2007 ◽  
pp. 151-164
Author(s):  
Yaacov Shavit
Keyword(s):  
Nineteenth Century ◽  
Academic Discipline ◽  
Jewish Studies ◽  
Final Solution ◽  
Jewish Culture ◽  
Delicate Balance ◽  
History Of ◽  
German Jewish ◽  
Post War ◽  
Jewish Intellectuals

This chapter probes the delicate balance forged by nineteenth-century German-Jewish intellectuals between an array of desiderata. It analyses Jewish acculturation, Jewish participation and partnership in the culture of the enlightened Christian majority, as well as the retention of an essential Judaic character that is deemed superior and unique. The chapter identifies the heroes of Shavit's story that envisioned neither Nazism nor the Final Solution, in which Shavit wonders if their endeavour proved a vain waste of the Jews' cultural vitality and productivity and a disastrous self-delusion. It talks about the renewal of German-Jewish culture and the birth of German-Jewish Studies as an academic discipline in post-war Germany.

19th Century Logic Between Philosophy and Mathematics

1999 ◽  
Vol 5 (4) ◽  
pp. 433-450 ◽  
Author(s):  
Volker Peckhaus
Keyword(s):  
Mathematical Logic ◽  
19Th Century ◽  
Early 20Th Century ◽  
Symbolic Logic ◽  
Modern Logic ◽  
History Of ◽  
And Mathematics ◽  
Correct Reasoning ◽  
The 19Th Century ◽  
The Relationship

AbstractThe history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart).In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided:1. What were the reasons for the philosophers' lack of interest in formal logic?2. What were the reasons for the mathematicians' interest in logic?3. What did “logic reform” mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic?4. Was mathematical logic regarded as art, as science or as both?

A history of some fruit models in wax and other materials: scientific teaching aids and courtly table decorations

2003 ◽  
Vol 30 (2) ◽  
pp. 299-316 ◽  
Author(s):  
Hans-JüRgen Lechtreck
Keyword(s):  
Nineteenth Century ◽  
Fruit Trees ◽  
Visual Aids ◽  
Early Nineteenth Century ◽  
Teaching Aids ◽  
Scientific Teaching ◽  
Glass Marble ◽  
History Of ◽  
By Products ◽  
Wax Models

Two early nineteenth century texts treating the production and use of wax models of fruit reveal the history of these objects in the context of courtly decoration. Both sources emphasise the models' decorative qualities and their suitability for display, properties which were not simply by-products of the realism that the use of wax allowed. Thus, such models were not regarded merely as visual aids for educational purposes. The artists who created them sought to entice collectors of art and natural history objects, as well as teachers and scientists. Wax models of fruits are known to have been collected and displayed as early as the seventeenth century, although only one such collection is extant. Before the early nineteenth century models of fruits made from wax or other materials (glass, marble, faience) were considered worthy of display because contemporaries attached great importance to mastery of the cultivation and grafting of fruit trees. This skill could only be demonstrated by actually showing the fruits themselves. Therefore, wax models made before the early nineteenth century may also be regarded as attempts to preserve natural products beyond the point of decay.

Sign in / Sign up

Export Citation Format

Share Document