In Memoriam
Charles Seiyo Chihara
Professor of Philosophy, Emeritus
UC Berkeley
1932-2020
Professor Charles S. Chihara (July 19, 1932 – February 16, 2020) was an internationally-renowned philosopher of mathematics who was a faculty member of the Department of Philosophy at the University of California, Berkeley, for 37 years. He had a reputation as an excellent and dedicated teacher and his service was characterized in a review as “self-sacrificing and highly meritorious.”
The son of Japanese immigrants, young Charles was sent to an internment camp with his mother and siblings soon after the beginning of World War II. His father also joined them after having spent a year and a half in prison for being a community leader.
Chihara graduated from O’Dea High School in Seattle, which he attended from 1946 to 1950. His further education took place at the University of Seattle (B.S. in mathematics in 1954), Purdue University (M.S. in mathematics in 1956) and the University of Washington (Ph.D. in philosophy, 1960). His dissertation adviser was Abraham Irving Melden. After serving as instructor at the University of Washington in 1959, he spent a postdoctoral year at Oxford University as “Recognized Scholar” in 1960-61. In 1961-62 he returned to the University of Washington and, in the same year, joined the University of Illinois as assistant professor.
In September 1963, Chihara joined the UC Berkeley philosophy department, declining a competing offer from UC Los Angeles, as assistant professor. One of his recommenders described him as “very intense about philosophy, but extremely calm in his intensity”. Chihara remained a professor at UC Berkeley for the rest of his career. He was promoted to associate professor with tenure in 1969, to full professor in 1975, and he retired in 2020. During his career he also served as chair of the philosophy department and of the Group in Logic and the Methodology of Science. He was Mellon Postdoctoral Fellow in 1964-65, a year he spent at the University of Pittsburgh. Other sabbatical leaves included the academic years 1967-68 (spent in Geneva and Oxford), 1972-73 (spent in Cambridge, England), and 1985-86 (spent in Paris). He was twice a recipient of a Fellowship from the National Endowment for the Humanities.
Chihara’s early scholarly contributions focused on the work of Ludwig Wittgenstein, including his philosophy of psychology. Chihara wrote important articles on Wittgenstein that were anthologized several times. Later, he contributed to the philosophy of probability and confirmation theory and to philosophy of logic, especially in connection to the study of modal logic and the paradoxes. These latter works intersected with his main scholarly engagement, the philosophy of mathematics, a field he described in 1967 as “covered more by darkness than light.” It was his goal to bring as much light as possible to the field generally, but especially to the debate concerning the existence of mathematical objects, which was the central inquiry of his five books (four published and one posthumous, unpublished) and of several of his numerous articles. The books are: Ontology and the Vicious-Circle Principle (Cornell University Press, 1973), Constructibility and Mathematical Existence (Oxford University Press-OUP, 1990), The Worlds of Possibility (OUP, 1998), A Structural Account of Mathematics (OUP, 2004), and The Fregean Assumption or Does Philosophy of Mathematics Rest on a Mistake? (unpublished).
Mathematics has long presented a challenge for philosophers, such as Chihara, who have found the existence of abstract objects (i.e. objects that are not spatio-temporally located or causally active) problematic and thus to be eschewed. Mathematical discourse seems to compel us to accept a realm of abstract entities (numbers, functions etc.) that serve as the intended objects of our discourse. That is, since symbols for numbers, functions, etc. behave syntactically the way names for other ordinary objects behave, it would seem that they behave semantically the way names for other ordinary objects behave: that they name abstract, mathematical objects. Thus, in making mathematical statements, we seem to commit ourselves to the existence of those abstract, mathematical objects. But if there are such objects, how can we come to know about them, given that they do not impinge on our sensory organs? Platonists in philosophy of mathematics (also known as “realists”) claim that we have a special intuition, akin to sensory perception, that allows us to intuit these objects and facts directly. Philosophers, who find appeal to such a faculty of intuition mysterious, prefer a more sober ontology where mathematical entities are explained away. In particular, nominalists deny that abstract entities exist and argue that only concrete (i.e. spatio-temporally located and causally active) entities exist.
It was within these clear battle lines that Chihara made his first contribution to philosophy of mathematics. In Ontology and the Vicious-Circle Principle, Chihara gave a masterful exposition of two Platonist philosophers of mathematics (an enthusiastic one, Kurt Gödel, and a reluctant one, Willard Van Orman Quine) and two anti-Platonist ones (Bertrand Russell and Henri Poincaré) and proposed a broadly nominalist solution to the debate by using a theory developed by Hao Wang that could be interpreted as ranging over concrete objects. This solution involved a sacrifice, however. It could not account for all of classical mathematics, only a “predicativist” fragment.
Chihara was unhappy with this and in his second book, Constructibility and Mathematical Existence, he tried to account for all of classical mathematics without commitment to the existence of abstract objects. His inspiration came from the way in which Euclid in his Elements seems to eschew a Platonist commitment to the existence of geometrical entities, such as points and lines, by generating them through constructions. For Euclid, at least according to the reading, to say that “for every two points a, b there exists a line c connecting them” does not presuppose that there is a preexisting universe of points and lines over which “for every” and “there exists” range. Rather, the statement ought to be parsed as “given any two points a, b one can construct a line c joining them”. Analogously to the constructivist reading of Euclid’s existential theorems, Chihara proposed that existential assertions, such as “There exists a prime number between 2 and 5,” in a suitable formalized version of classical mathematics were to be read not as asserting that there already exists such a number, but instead as asserting that it was possible to perform certain mathematical constructions. In this way the problem of existence of mathematical objects was bypassed. The book was also noteworthy for his extended discussion of alternative proposals in the literature (Philip Kitcher, Penelope Maddy, John Burgess, Hartry Field, etc.). Chihara’s proposal became one of the most important proposals for nominalist interpretation of mathematics.
Critics expressed worries that Chihara’s proposal might lead to a kind of Platonism after all. We have seen how the notion of “possible construction” entered in the previous book. But “possibility” is yet another problematic notion that seems to commit us to the existence of Platonic entities, with which we have no sensory contact. Various semantics for modal logic, the logic of expressions such as “possible” and “necessary,” are given in terms of possible worlds. For example, to say that it is possible that a line is constructed between points a and b is to say that there is a possible world in which a line is constructed between points a and b. So possible worlds talk seems to commit us to the existence of Platonic entities: namely, possible worlds. In his third book, The Worlds of Possibility, Chihara applied strategies similar to those he had deployed in the two previous books to show that one can talk about possible worlds without committing oneself Platonistically to their existence. He argued against David Lewis, Alvin Plantinga, and Graham Forbes, and proposed a constructivist semantics for a version of the classical system of modal logic called S5. Thus, just as he had eschewed commitment to the existence of abstract objects in the case of classical mathematics, here Chihara proposed a strategy for avoiding commitment to the existence of possible worlds. In a nutshell, Chihara argued that one could talk the talk of mathematical realists and modal realists without incurring in any of their ontological commitments. Needless to say, since this is philosophy after all, much discussion was sparked but no ultimate consensus emerged.
Chihara’s fourth book, A Structural Account of Mathematics, explored one of the most influential accounts concerning the nature of mathematics: structuralism. Structuralism is a philosophy of mathematics that claims that mathematics is not about specific objects but rather about structures such as the natural number structure, the real number structure, etc. According to this point of view, it makes no sense to ask what the symbol “1” stands for. “1” can be interpreted only as denoting something characterized within a structure. This kind of philosophy is potentially friendly to the nominalist and Chihara uses a version of structuralism to pursue his nominalist program. Whereas in the previous books in philosophy of mathematics, Chihara developed special theories that admitted of a nominalist interpretation, in this case he “analyzes mathematical systems currently used by scientists to show how such systems are compatible with a nominalist outlook.”
Chihara’s last book, The Fregean Assumption, continues in the wake of the above themes by investigating what Chihara calls the “Fregean assumption”, i.e. the assumption that mathematics is about the actual world. He claims that this presupposition — which “has strongly influenced the ontological and epistemological writings of the majority of the Anglo-American philosophers of mathematics” — leads to a Platonist point of view. The book is devoted to dismantling the grounds that make the Fregean assumption seem obvious and inevitable.
Charles Chihara is survived by his wife, Carol; his daughter Michelle, who has also followed an academic path; and his granddaughters, Iris and Harper.
According to Michelle, he “took joy in small things while touching lightly on big accomplishments.” He “spent long hours writing in his wood-paneled office in the Berkeley hills” and enjoyed detective stories — many of which he read in French, Westerns, musicals, and American football. She adds: “His work is very complex. His love was simple.”
Paolo Mancosu
2020
The son of Japanese immigrants, young Charles was sent to an internment camp with his mother and siblings soon after the beginning of World War II. His father also joined them after having spent a year and a half in prison for being a community leader.
Chihara graduated from O’Dea High School in Seattle, which he attended from 1946 to 1950. His further education took place at the University of Seattle (B.S. in mathematics in 1954), Purdue University (M.S. in mathematics in 1956) and the University of Washington (Ph.D. in philosophy, 1960). His dissertation adviser was Abraham Irving Melden. After serving as instructor at the University of Washington in 1959, he spent a postdoctoral year at Oxford University as “Recognized Scholar” in 1960-61. In 1961-62 he returned to the University of Washington and, in the same year, joined the University of Illinois as assistant professor.
In September 1963, Chihara joined the UC Berkeley philosophy department, declining a competing offer from UC Los Angeles, as assistant professor. One of his recommenders described him as “very intense about philosophy, but extremely calm in his intensity”. Chihara remained a professor at UC Berkeley for the rest of his career. He was promoted to associate professor with tenure in 1969, to full professor in 1975, and he retired in 2020. During his career he also served as chair of the philosophy department and of the Group in Logic and the Methodology of Science. He was Mellon Postdoctoral Fellow in 1964-65, a year he spent at the University of Pittsburgh. Other sabbatical leaves included the academic years 1967-68 (spent in Geneva and Oxford), 1972-73 (spent in Cambridge, England), and 1985-86 (spent in Paris). He was twice a recipient of a Fellowship from the National Endowment for the Humanities.
Chihara’s early scholarly contributions focused on the work of Ludwig Wittgenstein, including his philosophy of psychology. Chihara wrote important articles on Wittgenstein that were anthologized several times. Later, he contributed to the philosophy of probability and confirmation theory and to philosophy of logic, especially in connection to the study of modal logic and the paradoxes. These latter works intersected with his main scholarly engagement, the philosophy of mathematics, a field he described in 1967 as “covered more by darkness than light.” It was his goal to bring as much light as possible to the field generally, but especially to the debate concerning the existence of mathematical objects, which was the central inquiry of his five books (four published and one posthumous, unpublished) and of several of his numerous articles. The books are: Ontology and the Vicious-Circle Principle (Cornell University Press, 1973), Constructibility and Mathematical Existence (Oxford University Press-OUP, 1990), The Worlds of Possibility (OUP, 1998), A Structural Account of Mathematics (OUP, 2004), and The Fregean Assumption or Does Philosophy of Mathematics Rest on a Mistake? (unpublished).
Mathematics has long presented a challenge for philosophers, such as Chihara, who have found the existence of abstract objects (i.e. objects that are not spatio-temporally located or causally active) problematic and thus to be eschewed. Mathematical discourse seems to compel us to accept a realm of abstract entities (numbers, functions etc.) that serve as the intended objects of our discourse. That is, since symbols for numbers, functions, etc. behave syntactically the way names for other ordinary objects behave, it would seem that they behave semantically the way names for other ordinary objects behave: that they name abstract, mathematical objects. Thus, in making mathematical statements, we seem to commit ourselves to the existence of those abstract, mathematical objects. But if there are such objects, how can we come to know about them, given that they do not impinge on our sensory organs? Platonists in philosophy of mathematics (also known as “realists”) claim that we have a special intuition, akin to sensory perception, that allows us to intuit these objects and facts directly. Philosophers, who find appeal to such a faculty of intuition mysterious, prefer a more sober ontology where mathematical entities are explained away. In particular, nominalists deny that abstract entities exist and argue that only concrete (i.e. spatio-temporally located and causally active) entities exist.
It was within these clear battle lines that Chihara made his first contribution to philosophy of mathematics. In Ontology and the Vicious-Circle Principle, Chihara gave a masterful exposition of two Platonist philosophers of mathematics (an enthusiastic one, Kurt Gödel, and a reluctant one, Willard Van Orman Quine) and two anti-Platonist ones (Bertrand Russell and Henri Poincaré) and proposed a broadly nominalist solution to the debate by using a theory developed by Hao Wang that could be interpreted as ranging over concrete objects. This solution involved a sacrifice, however. It could not account for all of classical mathematics, only a “predicativist” fragment.
Chihara was unhappy with this and in his second book, Constructibility and Mathematical Existence, he tried to account for all of classical mathematics without commitment to the existence of abstract objects. His inspiration came from the way in which Euclid in his Elements seems to eschew a Platonist commitment to the existence of geometrical entities, such as points and lines, by generating them through constructions. For Euclid, at least according to the reading, to say that “for every two points a, b there exists a line c connecting them” does not presuppose that there is a preexisting universe of points and lines over which “for every” and “there exists” range. Rather, the statement ought to be parsed as “given any two points a, b one can construct a line c joining them”. Analogously to the constructivist reading of Euclid’s existential theorems, Chihara proposed that existential assertions, such as “There exists a prime number between 2 and 5,” in a suitable formalized version of classical mathematics were to be read not as asserting that there already exists such a number, but instead as asserting that it was possible to perform certain mathematical constructions. In this way the problem of existence of mathematical objects was bypassed. The book was also noteworthy for his extended discussion of alternative proposals in the literature (Philip Kitcher, Penelope Maddy, John Burgess, Hartry Field, etc.). Chihara’s proposal became one of the most important proposals for nominalist interpretation of mathematics.
Critics expressed worries that Chihara’s proposal might lead to a kind of Platonism after all. We have seen how the notion of “possible construction” entered in the previous book. But “possibility” is yet another problematic notion that seems to commit us to the existence of Platonic entities, with which we have no sensory contact. Various semantics for modal logic, the logic of expressions such as “possible” and “necessary,” are given in terms of possible worlds. For example, to say that it is possible that a line is constructed between points a and b is to say that there is a possible world in which a line is constructed between points a and b. So possible worlds talk seems to commit us to the existence of Platonic entities: namely, possible worlds. In his third book, The Worlds of Possibility, Chihara applied strategies similar to those he had deployed in the two previous books to show that one can talk about possible worlds without committing oneself Platonistically to their existence. He argued against David Lewis, Alvin Plantinga, and Graham Forbes, and proposed a constructivist semantics for a version of the classical system of modal logic called S5. Thus, just as he had eschewed commitment to the existence of abstract objects in the case of classical mathematics, here Chihara proposed a strategy for avoiding commitment to the existence of possible worlds. In a nutshell, Chihara argued that one could talk the talk of mathematical realists and modal realists without incurring in any of their ontological commitments. Needless to say, since this is philosophy after all, much discussion was sparked but no ultimate consensus emerged.
Chihara’s fourth book, A Structural Account of Mathematics, explored one of the most influential accounts concerning the nature of mathematics: structuralism. Structuralism is a philosophy of mathematics that claims that mathematics is not about specific objects but rather about structures such as the natural number structure, the real number structure, etc. According to this point of view, it makes no sense to ask what the symbol “1” stands for. “1” can be interpreted only as denoting something characterized within a structure. This kind of philosophy is potentially friendly to the nominalist and Chihara uses a version of structuralism to pursue his nominalist program. Whereas in the previous books in philosophy of mathematics, Chihara developed special theories that admitted of a nominalist interpretation, in this case he “analyzes mathematical systems currently used by scientists to show how such systems are compatible with a nominalist outlook.”
Chihara’s last book, The Fregean Assumption, continues in the wake of the above themes by investigating what Chihara calls the “Fregean assumption”, i.e. the assumption that mathematics is about the actual world. He claims that this presupposition — which “has strongly influenced the ontological and epistemological writings of the majority of the Anglo-American philosophers of mathematics” — leads to a Platonist point of view. The book is devoted to dismantling the grounds that make the Fregean assumption seem obvious and inevitable.
Charles Chihara is survived by his wife, Carol; his daughter Michelle, who has also followed an academic path; and his granddaughters, Iris and Harper.
According to Michelle, he “took joy in small things while touching lightly on big accomplishments.” He “spent long hours writing in his wood-paneled office in the Berkeley hills” and enjoyed detective stories — many of which he read in French, Westerns, musicals, and American football. She adds: “His work is very complex. His love was simple.”
Paolo Mancosu
2020
