Irving H. Anellis

From Philosopedia

Anellis, Irving H. (1946 – )

Anellis was born in Chicago, Illinois, the son of food microbiologist Abe Anellis (1914–2001).

He holds degrees from Northeastern University (B.A., 1969), Duquesne University (M.A., 1971), and Brandeis University (Ph.D., 1977).

Anellis was a doctoral student of historian of logic Jean van Heijenoort. His early research had centered on mathematical logic, in particular in proof theory and metamathematics, and on applications of logic to algebraic structures. He researched the work of Bertrand Russell in set theory and logic; of Charles Sanders Peirce in algebra and algebraic logic; and on the history of proof theory, with special reference to the roles of the Löwenheim-Skolem Theorem and Herbrand's Fundamental Theorem; and the history of logic and mathematics in Russia.

While working on a manuscript of Charles Peirce dating from around 1890, Anellis found that he dealt with what today is known as the Hilbert's Ninth and Tenth Problems, and another manuscript, "An Outline Sketch of Synechistic Philosophy," identified as composed in 1893, in which Peirce unmistakably presents the truth-table matrix for a proposition and its negation that is essentially equivalent in its contemporary formulation as material implication.

He is a Visiting Research Associate at the Indiana University-Purdue University at Indianapolis (IUPUI), where he is in charge of writing and revising annotations for Peirce's texts on logic and mathematics, and is a member of the advisory board of the Hilbert-Bernays Project, which is engaged in preparing a dual-language (German-English) edition of David Hilbert's and Paul Bernays' Grundlagen der Mathematik. In the talk "How Peircean Was the “Fregean” Revolution in Logic?" that he gave in Indianapolis at IUPUI, he explained that:

The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912–1986) and Donald Angus Gillies. The innovations and characteristics that comprise mathematical logic and distinguish it from Aristotelian logic, according to this conception, created ex nihilo by Gottlob Frege (1848–1925) in his Begriffsschrift of 1879, and with Bertrand Russell (1872–1970) as its chief. This position likewise understands the algebraic logic of Augustus De Morgan (1806–1871), George Boole (1815–1864), Charles Sanders Peirce (1838–1914), and Ernst Schröder (1841–1902) as belonging to the Aristotelian tradition. The “Booleans” are understood, from this vantage point, to merely have rewritten Aristotelian syllogistic in algebraic guise.

The most detailed listing and elaboration of Frege’s innovations—and the characteristics that distinguish mathematical logic from Aristotelian logic—were set forth by van Heijenoort. I consider each of the elements of van Heijenoort’s list and note the extent to which Peirce had also developed each of these aspects of logic. Anellis considers the extent to which Peirce and Frege were aware of, and may have influenced, one another’s logical writings."

Anellis has been Visiting Research Associate at the Peirce Edition since 2008. He taught IUPUI’s “Intermediate Symbolic Logic” and Intensive Reading in “Advanced Symbolic Logic” in the Fall 2009 semester. His doctoral director at Brandeis University (1977) was differential geometer and historian of logic Jean van Heijenoort. He has taught in both philosophy and mathematics departments at various colleges and universities, including the University of Florida, Mississippi Valley State University, the University of Minnesota-Duluth, and the University of Iowa, worked as a Research Associate at the Bertrand Russell Editorial Project at McMaster University (Hamilton, Ontario), served as a contributing editor to the Peirce Edition starting with Volume 5, and was founding editor of the journal Modern Logic.

His research specialties are in mathematical logic and set theory, with emphases in metamathematics, proof theory, model theory, Boolean algebra, lattice theory and Boolean groups, and set-theoretic foundations of analysis and number theory; history of logic, with emphases in proof theory, model theory, algebraic logic, Peirce, Russell, geometry, logic and the axiomatic method, and mathematical logic in Russia and the Soviet Union; and history of mathematics, with emphases in universal algebra, 10th to 17th century Russian mathematics, and history of mathematics education in Russia.

He is currently working on a historiographical, philosophical, and sociological investigation into the history of the transition from algebraic logic to logistic (the first-order function-theoretic calculus) as the canonical standard of mathematical logic; and his book

Evaluating Russell: The Logician and His Work, is due to be published by Docent Press in 2012.

Anellis has been on the board of directors of the Bertrand Russell Society.

He wrote Van Heijenoort: Logic and Its History in the Works of Jean Van Heijenoort (1994).