Jean van Heijenoort

Jean Louis Maxime van Heijenoort (/væn ˈhaɪ.ənɔːrt/; [van ɛjɛnɔʁt]; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist.

Van Heijenoort was born in Creil, France. His family's financial circumstances were difficult as his Dutch immigrant father died when van Heijenoort was two. He nevertheless acquired a powerful traditional French formal education, to which his French writings attest. (He also published in Spanish.) Although he eventually became a naturalized American citizen, he visited France twice a year from 1958 until his death, and remained very attached to his French extended family and friends.

Political views

In 1932, he joined the Trotskyist movement (recruited by Yvan Craipeau) and the Communist League. Very soon thereafter, the recently exiled Trotsky hired van Heijenoort as a secretary and bodyguard, primarily because of his fluency in French, Russian, German, and English. Thus began seven years in Trotsky's household, during which he served as an all-purpose translator, helping Trotsky write several books and keep up an extensive intellectual and political correspondence in several languages.

In 1939, van Heijenoort moved to New York City to be with his second wife, Beatrice "Bunny" Guyer, where he worked for the Socialist Workers Party (US) (SWP) and wrote a number of articles for the American Trotskyist press and other radical outlets. He was elected to the secretariat of the Fourth International in 1940 but resigned when Felix Morrow and Albert Goldman, with whom he had sided, were expelled from the SWP. Goldman subsequently went on to join the US Workers Party but Morrow joined no other party/grouping. In 1947, he too was expelled from the SWP. In 1948, he published an article, called "A Century's Balance Sheet" in which he criticized that part ofMarxism which saw the "proletariat" as the revolutionary class. He continued to hold other parts of Marxism as true.

Van Heijenoort was spared the ordeal of McCarthyism because everything he published in Trotskyist organs appeared under one or other of more than a dozen pen names.[1] Moreover, Feferman (1993) states that van Heijenoort the logician was quite reticent about his Trotskyist youth, and did not discuss politics. Nevertheless, in the last decade of his life he contributed to the history of the Trotskyist movement by writing the monograph With Trotsky in Exile (1978), editing a volume of Trotsky's correspondence (1980), and advising and working with the archivists at the Houghton Library in Harvard University, which holds many of Trotsky's papers from his years in exile.

Academic work

After completing a Ph.D. in mathematics at New York University in 1949 under the supervision of J. J. Stoker, he taught mathematics there but evolved into a logician and philosopher of mathematics, in good part because of the influence of Georg Kreisel. He began teaching philosophy, first part-time at Columbia University, then full-time at Brandeis University, 1965-77. He spent much of his last decade at Stanford University, writing and editing eight books, including parts of the Collected Works of Kurt Gödel.

The Source Book (van Heijenoort 1967), his book on the history of logic and of the foundations of mathematics, is an anthology of translations. It begins with the first complete translation of Frege's 1879 Begriffsschrift, which is followed by 45 historically important short pieces on mathematical logic and axiomatic set theory, originally published between 1889 and 1931. The anthology ends with Gödel's landmark paper on the incompletability of Peano arithmetic. For more information on the period covered by this anthology, see Grattan-Guinness (2000).

Nearly all the content of the Source Book was difficult to access in all but the best North American university libraries (e.g., even the Library of Congress did not acquire a copy of the Begriffsschrift until 1964), and all but four pieces had to be translated from one of six continental European languages. When possible, the author of the original text was asked to review the translation of his work, and suggest corrections and amendments. Each piece included editorial footnotes, all references were combined into one list, and many misprints, inconsistencies, and errors in the originals were corrected. Especially important are the remarkable introductions to each translation, most written by van Heijenoort himself. A few were written by Willard Quine and Burton Dreben.

The Source Book did much to advance the view that modern logic begins with, and builds on, the Begriffsschrift.Grattan-Guinness (2000) argues that this perspective on the history of logic is mistaken, because Frege employed an idiosyncratic notation and was far less read than, say, Peano. Ironically, van Heijenoort (1967a) is often cited by those who prefer the alternative model theoretic stance on logic and mathematics. Much of the history of that stance, whose leading lights include George Boole, Charles Sanders Peirce, Ernst Schröder, Leopold Löwenheim, Thoralf Skolem, Alfred Tarski, and Jaakko Hintikka, is covered in Brady (2000). The Source Book underrated the algebraic logic of De Morgan, Boole, Peirce, and Schröder, but devoted more pages to Skolem than to anyone other than Frege, and included Löwenheim (1915), the founding paper on model theory.

Personal life

Van Heijenoort had children with two of his four wives. While living with Trotsky in Coyoacán, now a neighborhood of Mexico City, van Heijenoort's first wife left him after clashing with Trotsky's spouse. Van Heijenoort was also one of Frida Kahlo's lovers; in the film Frida, he is played by Felipe Fulop. Having parted company with Trotsky in 1939 for personal reasons, van Heijenoort was innocent of all circumstances leading to Trotsky's 1940 murder. Van Heijenoort himself was also murdered, in Mexico City 46 years later, by his estranged fourth spouse whom he was visiting at the time. She then took her own life.

• 1967a. "Logic as Language and Logic as Calculus", Synthese 17: 324–30.
• 1978. With Trotsky in Exile: From Prinkipo to Coyoacán. Harvard University Press.
• 1985. Selected Essays. Naples: Bibliopolis.

Books which Van Heijenoort edited alone or with others:

• 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press; reprinted with corrections, 1977.
• 1986, 1990. Kurt Gödel: Collected Works, Vols. I, II. Oxford University Press.
• 1968. Jacques Herbrand: Ecrits Logiques. Presses Universitaires de France.
• 1980. Leon et Natalia Trotsky: Correspondance 1933-38. Paris: Gallimard.