[Wang's Paradox] A proposition of mathematician Wang Hao on mathematical logic has been internationally defined as "Wang's Paradox".
Wang Hao (May 21, 1921 – May 13, 1995) was a Chinese-American mathematical logician, computer scientist, and scientist born in Jinan, Shandong Province. In 1939, he entered the Department of Mathematics of Southwest United University and studied under Mr. Jin Yuelin. After receiving his bachelor's degree in 1943, he entered the Philosophy Department of the Graduate School of Tsinghua University, and in 1945, he received a master's degree with a thesis entitled "On the Basis of Empirical Knowledge".
Wang Hao was interested in philosophy in middle school, and when he was in junior high school, he read Engels's anti-Dühring and Ludwig Feuerbach and the End of German Classical Philosophy at the suggestion of his father. When he was in high school, he happened to get Jin Yuelin's "Logic" (1935), which contained about 80 pages of the contents of the first volume of B. Russel's famous book "Principles of Mathematics", which he felt was both attractive and easy to understand, so he thought: "We should first try to learn the easier mathematical logic, and make better preparations for learning dialectics later." ”
In his first year of college, he audited Wang Xianluo's symbolic logic class and systematically studied the first volume of "Principles of Mathematics". He learned German by reading Hilbert-Ackermann's Fundamentals of Mathematical Logic (1938 edition). Later, I read the first volume of Hilbert-Berners's Foundations of Mathematics (two-volume collection, 1934 edition). In 1942 he listened to Shen Youding's lecture on Tractatus (1921) by L. Wittgenstein (1889-1951), read R. Carnap's Logical Syntax of Speech (1934 edition), and began writing a treatise on Hume's inductive problems.
Recalling this intense and meaningful study life, Wang Hao said: "From 1939 to 1946, I was in Kunming and enjoyed the joy of living poorly and eating abundant spiritual food. Especially because he and Mr. Jin (Yue Lin) and several other gentlemen and classmates have common interests and implicitly agree with the value standards of course, they feel happy, and thus be able to turn work into a basic need, and become the main pillar of their own life in the future. My wish is that more and more Chinese youth can have the opportunity to enjoy such a light happiness! During his studies (1943-46), Wang Hao also served as a mathematics teacher.
In 1946, Wang Hao went to Harvard University in the United States, where he met the famous contemporary American philosopher and logician W.V. Quine (1908-), and immediately began to study the formal axiom system he founded, and soon improved the system, and some of its results were written as a doctoral dissertation. At Quinn's suggestion, the title of the paper was An Economic Onto1ogyfor C1assical Analysis. In 1947 he began teaching assistant for Quinn's Advanced Logic and Philosophy of Language; he received his Ph.D. in 1948 and remained at Harvard University; he was a junior fellow from 1948 to 1951 and an assistant professor of philosophy from 1951 to 1956. In 1949, when Quinn temporarily left Harvard, Wang Hao succeeded him in teaching advanced logic classes, introducing Gödel's incompleteness theorem in a fairly complete way.
From 1950 to 1951, Wang Hao went to the Institute of Mathematics of the Swiss Federal Institute of Technology in Zurich to engage in postdoctoral research. He went to England in 1954 as a Rockefeller Foundation Fellow. From 1954 to 1955, he presided over the second John Locke Lecture on Philosophy at oxford university in the United Kingdom. He received a master's degree from Ballyole College, Oxford, in 1956. From 1956 to 1961 he was a Senior Lecturer in The Philosophy of Mathematics at the University of Oxford. During this period, he chaired a seminar on maintaining Genstein's "Views on mathematical foundations". Most of the leading philosophers at Oxford University attended the seminar. From 1961 to 1967, he returned to Harvard as professor of mathematical logic and applied mathematics. After 1967, he was a professor of mathematics at Rockefeller University and presided over the logic research department of the university. From 1975 to 1976, he visited and worked at the Institute for Advanced Study in Princeton.
Since 1953, Wang Hao began to study computer theory and machine proof. Because on the one hand he keenly felt that mathematical logic, which was considered to be too precise in form, very cumbersome and of no practical use, could play an excellent role in the field of computing; on the other hand, because of the founding of New China, he wanted to learn more useful things in order to return to serve the motherland in the future. To this end, he also held a number of positions as a research engineer at Burroughs (1953-954), a technical specialist at Bell Telephone Laboratories (1959-1960), and a visiting scientist at ibm research centers (1973-974).
After 1972, Wang Hao returned to China several times. In 1973 he wrote Meditations on a Visit to China, which was widely published in newspapers and magazines. He was also a professor at Peking University in 1985 and a professor at Tsinghua University in 1986.
Books published by Mr. Wang Hao
Wang Hao has published more than 100 papers. His major publications include:
A Survey of Mathematical Logic (l962);
From Mathematics to Philosophy (From Mathematicematicsto Phlcosophy, 1974); Popular Lectures on Mathematical Logic, available in both Chinese and English;
"Beyond Analytic Philosophy - Doing Justiceto Whatwe Know" (l986), the author gives a detailed introduction to the ideas of russell, Wittgenstein, Karnap and Quinn, the representatives of analytic philosophy, and gives a dense analysis and powerful criticism, the main argument is that their philosophy can not be used for human existing knowledge, especially mathematical knowledge, Provide the basics. Since the author is very familiar with the work of these four people, and even has direct contact with some of them, his criticism is very profound. Sir P. Strawson of the University of Oxford commented: "The main and profound interest of philosophers in Wang Hao's book is that it records the views of a brilliant, brilliant and perceptive philosopher on the development of the so-called 'analytical' or 'Anglo-American' philosophy in this century. "Wang's book is a rich, fascinating contribution to the history of modern philosophy and meta-philosophy."
Hao Wang is a Fellow of the American College of Arts and Sciences, a Foreign Fellow of the British Academy of Sciences, and a Member of the Society of Semiotic Logic. In 1983, wang Hao was awarded the first Milestone Prize at the automated Theorem Proving special annual meeting in Denver, USA, co-sponsored by the Lnternational Joint Confernceon Artificial Intone and the American Mathematical Society. In recognition of his pioneering contributions in the field of mechanical proof of mathematical theorems.