Tag Archives: Henry M. Sheffer

Y. R. Chao and Henry Sheffer added to the Mathematics Genealogy Project

I mentioned in an earlier post that my “grandteacher”, Y. R. Chao 趙元任, did his dissertation on a problem in logic, even though he is best known for his work as a linguist and composer. (Though I think that his Language and Symbolic Systems, 1968, and his methodology in descriptive and historical linguistics all clearly show his predilections.)

I’m happy to say that Mitch Keller, who runs the Mathematics Genealogy Project, has now agreed that both Chao and his teacher, Henry Sheffer, deserve to be listed in the records there, even though their degrees were from departments of Philosophy. Chao’s entry is here and Sheffer’s can be found from it.

It seems that none of Chao’s students has a degree in a strictly mathematical field, though perhaps some will be found in the future.

Y. R. Chao on his dissertation (1974)

Yuen Ren Chao 趙元任, the historical and descriptive linguist of Chinese, wrote his doctoral dissertation on logic in Harvard’s Department of Philosophy (1918). He later recalled:

Professor [Henry M. Sheffer] was really very meticulous; he was in charge of my thesis on “Continuity: A Study in Methodology,” concerned with the question of the difference between a difference of degree and difference of kind, and when it’s a difference of kind, is it also a difference of degree.

I remember at the defense of the thesis, at which Professor William Ernest Hocking was chairman, after they announced that I had passed the examination, Professor Hocking asked me, “Do you feel that writing on such a subject has had any effect on your life?” I said, “Certainly it didn’t help me in my habits of indecision.”

…

[from First "Green Letter", Peking, 1921:] [My dissertation] prov[ed] that it was impossible to prove anything and conclud[ed] that no universal proposition was true.

Quoted from an oral history interview with Rosemary Levenson, 1974. Now posted at http://content.cdlib.org/view?docId=hb8779p27v&chunk.id=div00023&brand=calisphere&doc.view=entire_text . Accessed 20111129.

Doctoral pedigrees

The Mathematics Genealogy Project at North Dakota State University documents lines of academic filiation (primarily through doctoral degrees) in mathematics. It makes for interesting reading. Though my degree is “Asian Linguistics”, I can connect myself to the mainstream mathematical tree through a sub-branch of four progenitor Doktorväter:

  • Josiah Royce, 1878 (Philosophy)

  • Henry M. Sheffer, 1908 (Philosophy)

  • Yuen Ren Chao 趙元任, 1918 (Philosophy)

  • Jerry Norman, 1969 (Oriental Languages)

[Update 20111213: Chao and Sheffer are now in the tree; see this post.] Sheffer and initially Chao studied logic, a field developed at Harvard by Royce. Sheffer is best known for having introduced the NAND operation to Boolean logic. Chao’s main scholarly contributions were in Chinese historical phonology and modern grammar. Jerry Norman has pioneered the rigorous study of Chinese dialect classification, which you might say is a type of applied logic.

Through Royce, I can trace my “pedigree” to various luminaries of the Humanist era: Erasmus, Vesalius, Ficino, Copernicus, Leibniz, and Marin Mersenne, a student of prime numbers after whom is named the Mersenne twister, a pseudo-random number generator now widely used on personal computers. To Kant, as well, and to non-Humanists like Thomas à Kempis and Thomas Cranmer. Most lines peter out in the early 15th century; earlier stragglers include the mathematician and theologian Heinrich von Langenstein, an antecedent of Copernicus who received his Theol. Dr. in 1375, while the neo-Platonist Georgios Plethon Gemistos seems to have received the first of his degrees in 1380.

There is romance in seeing one’s connection to people like Leibniz and Erasmus, but it means little beyond that. Does anyone with a PhD today, in any field, not belong to those lines of filiation? As of today, Erasmus is shown to have 95301 descendants listed in mathematics alone. I have learned an enormous amount from Jerry Norman, and it is justice to call him my Doktorvater. I find myself in strong agreement with Chao’s model of formal Chinese historical phonology, too, and I have a special love for logic. But the model of linguistic fieldwork I use owes considerably more to Robert Austerlitz and Li Fang Kuei 李方桂 than to Chao, whose approach I consider altogether too literary. I also identify myself intellectually with my maternal grandfather, who left school when he was 12 but was a voracious reader and lifelong pursuer of ideas. At best, all that a paper pedigree can do is remind me to try to be true to the effort that generations of scholars, known and unknown, have made in order to seek knowledge and see clearly — to those ideas and those people all human beings are equally heirs.

There is at least one program available to generate graphs from the Project: see http://www.davidalber.net/geneagrapher/.