Cassius Jackson Keyser
Encyclopedia
Cassius Jackson Keyser was an American
mathematician
of pronounced philosophical inclinations.
), then became a school teacher and principal. In 1885, he married a fellow student at the Normal School, Ella Maud Crow of Ridgeway, Ohio. He completed a second undergraduate degree, a BSc, at the University of Missouri
in 1892. After teaching there, at the New York State Normal School (now SUNY New Paltz), and at Washington University, he enrolled as a graduate student at Columbia University
, earning the MA in 1896 and the Ph.D.
in 1901. He spent the rest of his career at Columbia, becoming the Adrain Professor of Mathematics (1904–27) and Head of the department (1910–16). He retired in 1927.
Keyser was one of the first Americans to appreciate the new directions in the foundation of mathematics, heralded by the work of Europeans such as Richard Dedekind
, Georg Cantor
, Giuseppe Peano
, Henri Poincaré
, David Hilbert
, Ernst Zermelo
, Bertrand Russell
, and A. N. Whitehead. He was also one of the first to appreciate the mathematical and philosophical importance of his fellow American Charles Sanders Peirce. Alfred Korzybski
, founder of general semantics
, named Keyser as a major influence. While at Columbia, Keyser supervised only three PhDs, but they all proved quite consequential: Eric Temple Bell
, the logician Emil Post, and Edward Kasner
.
He became a member of the American board of the Hibbert Journal, and made contributions to that and other philosophical journals. Together with the New International Encyclopedia
and his Columbia colleague John Dewey
, Keyser helped found the American Association of University Professors
(AAUP). He was a fellow of the American Academy for the Advancement of Science, and a member of the American Mathematical Society
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
of pronounced philosophical inclinations.
Life
Keyser's initial higher education was at North West Ohio Normal School (now Ohio Northern UniversityOhio Northern University
Ohio Northern University is a private, United Methodist Church-affiliated university located in the United States in Ada, Ohio, founded by Henry Solomon Lehr in 1871. ONU is accredited by The Higher Learning Commission and the North Central Association of Colleges and Schools. ONU is a sister...
), then became a school teacher and principal. In 1885, he married a fellow student at the Normal School, Ella Maud Crow of Ridgeway, Ohio. He completed a second undergraduate degree, a BSc, at the University of Missouri
University of Missouri
The University of Missouri System is a state university system providing centralized administration for four universities, a health care system, an extension program, five research and technology parks, and a publishing press. More than 64,000 students are currently enrolled at its four campuses...
in 1892. After teaching there, at the New York State Normal School (now SUNY New Paltz), and at Washington University, he enrolled as a graduate student at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, earning the MA in 1896 and the Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1901. He spent the rest of his career at Columbia, becoming the Adrain Professor of Mathematics (1904–27) and Head of the department (1910–16). He retired in 1927.
Keyser was one of the first Americans to appreciate the new directions in the foundation of mathematics, heralded by the work of Europeans such as Richard Dedekind
Richard Dedekind
Julius Wilhelm Richard Dedekind was a German mathematician who did important work in abstract algebra , algebraic number theory and the foundations of the real numbers.-Life:...
, Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
, Giuseppe Peano
Giuseppe Peano
Giuseppe Peano was an Italian mathematician, whose work was of philosophical value. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in...
, Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, Ernst Zermelo
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.-Life:He graduated...
, Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
, and A. N. Whitehead. He was also one of the first to appreciate the mathematical and philosophical importance of his fellow American Charles Sanders Peirce. Alfred Korzybski
Alfred Korzybski
Alfred Habdank Skarbek Korzybski was a Polish-American philosopher and scientist. He is remembered for developing the theory of general semantics...
, founder of general semantics
General Semantics
General semantics is a program begun in the 1920's that seeks to regulate the evaluative operations performed in the human brain. After partial program launches under the trial names "human engineering" and "humanology," Polish-American originator Alfred Korzybski fully launched the program as...
, named Keyser as a major influence. While at Columbia, Keyser supervised only three PhDs, but they all proved quite consequential: Eric Temple Bell
Eric Temple Bell
Eric Temple Bell , was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life...
, the logician Emil Post, and Edward Kasner
Edward Kasner
Edward Kasner who studied under Cassius Jackson Keyser, was a prominent American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department...
.
He became a member of the American board of the Hibbert Journal, and made contributions to that and other philosophical journals. Together with the New International Encyclopedia
New International Encyclopedia
The New International Encyclopedia was an American encyclopedia first published in 1902 by Dodd, Mead and Company. It descended from the International Cyclopaedia and was updated in 1906, 1914 and 1926.-History:...
and his Columbia colleague John Dewey
John Dewey
John Dewey was an American philosopher, psychologist and educational reformer whose ideas have been influential in education and social reform. Dewey was an important early developer of the philosophy of pragmatism and one of the founders of functional psychology...
, Keyser helped found the American Association of University Professors
American Association of University Professors
The American Association of University Professors is an organization of professors and other academics in the United States. AAUP membership is about 47,000, with over 500 local campus chapters and 39 state organizations...
(AAUP). He was a fellow of the American Academy for the Advancement of Science, and a member of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.
Books & pamphlets by Keyser
- Mathematics and the Question of the Cosmic Mind, with Other Essays.
- 1914. Science and Religion: The Rational and the Super-Rational
- 1916. The Human Worth of Rigorous Thinking. Columbia Univ. Press.
- 1922. Mathematical Philosophy, a Study of Fate and Freedom.
- 1932. The meaning of mathematics.
- 1935. A glance at some of the ideas of Charles Sanders Peirce.
- 1935. Three great synonyms: RelationRelation (mathematics)In set theory and logic, a relation is a property that assigns truth values to k-tuples of individuals. Typically, the property describes a possible connection between the components of a k-tuple...
, transformation, functionFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
. - 1936. Panthetics.
- 1938. A mathematical prodigy: history and legend.
- 1938. Roger BaconRoger BaconRoger Bacon, O.F.M. , also known as Doctor Mirabilis , was an English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through empirical methods...
. - 1938. Benedict Spinoza.
- 1939. The Role of Mathematics in the tragedy of our modern culture.
- 1941. Charles Sanders Peirce as a pioneer. Internet Archive Eprint. A lecture given on May 18, 1935 at the Galois Institute of Mathematics at Long Island University.
- 1942. Thinking about thinking.
- 1947. Mathematics as a culture clue.
- 1952. The rational and the superrational: studies in thinking.
- 2005. Mathematics. Michigan Historical Reprint Series.
- 2005. Mathematical Philosophy: A Study of Fate and Freedom (Lectures for the Educated Laymen). Michigan Historical Reprint Series.