209
Between Philosophy and Mathematics: General 
Trends in Dissemination, Teaching, and 
Research on Mathematical Logic in 1930s China
Jan VRHOVSKI*
Abstract
This article studies some central developments in the propagation and teaching of math-
ematical logic in 1930s China. Focusing on the emergence of a twofold disciplinary ap-
proach to mathematical logic, namely as a discipline studied and disseminated by Chinese 
philosophers on the one hand and mathematicians on the other, this paper explores one 
of the key turning points in the development of the academic notion of mathematical 
logic in China. Apart from casting some light on the teaching of mathematical logic 
in the framework of both philosophical as well as mathematical spheres of inquiry, this 
article also provides some preliminary insights into the circumstances surrounding the 
first systematic introduction of mathematical logic into the modern standardized system 
of education, which gradually took shape over the late-1920s and early 1930s in China. 
Keywords: mathematical logic, mathematics, philosophy, China, Republican Period
Med filozofijo in matematiko: splošne težnje v širenju, poučevanju in razisko-
vanju matematične logike na Kitajskem v 30  letih 20  stoletja
Izvleček
Članek preučuje osrednje razvojne smernice v širjenju in poučevanju matematične logike na 
Kitajskem v 30. letih 20. stoletja. Osredotočen na pojav dveh različnih znanstvenih pristo-
pov k matematični logiki – namreč kot disciplini, ki so jo preučevali in širili kitajski filozofi 
na eni strani ter kitajski matematiki na drugi – nadalje preučuje eno izmed osrednjih točk 
obrata v razvoju matematične logike kot akademske discipline na Kitajskem. Poleg tega, da 
pojasnjuje, kako se je predmet poučevalo v sklopu tako filozofskih kot tudi matematičnih 
raziskav, članek prav tako podaja nekaj preliminarnih vpogledov v okoliščine, ki so obdajale 
prvi sistematični poskus vključitve matematične logike v moderni standardizirani sistem 
izobrazbe, ki je postopoma nastajal na Kitajskem v 20. in 30. letih 20. stoletja. 
Ključne besede: matematična logika, matematika, filozofija, Kitajska, republikansko 
obdobje 
* Jan VRHOVSKI is currently working as a research fellow at the Faculty 
of Arts, University of Ljubljana.
 Email address: jan.vrhovski@ff.uni-lj.si
DOI: 10.4312/as.2022.10.2.209-241
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210 Jan VRHOVSKI: Between Philosophy and Mathematics...
Introduction 
By the early 1930s, mathematical logic as a notion and field of study became an 
integral element of the efforts of nationalist government to modernize Chinese 
education both at the higher as well as the secondary levels. Catalysed by the 
efforts of a group of Chinese philosophers, educated either at foreign institutions 
or Chinese universities in the centre of intellectual modernization in the 1920s, 
mathematical logic as a subject of teaching and research became established as one 
of the central pillars of modern philosophical studies as early as in the late 1920s. 
By the early 1930s, as a widely renowned paragon of university-level curricular 
reformation, the Department of Philosophy at the reformed National Qinghua 
University (Guoli Qinghua daxue 國立清華大學, official English name Tsinghua 
University) became the first centre of teaching and research in mathematical logic 
nationwide, prompting the start of a new wave of dissemination and advancement 
of mathematical logic in Chinese academia. 
This article represents a follow-up to one of my previous publications entitled 
“‘Qinghua School of Logic’: Mathematical Logic at Qinghua University in Pe-
king, 1926–1945” (Vrhovski 2021a), which surveyed the development of teaching 
and research of mathematical logic at Qinghua University in the late-Republican 
period. The main aim of this article is to supplement the results of this earlier 
article by presenting a more general overview of the development of mathemat-
ical logic as a subject of teaching and research in 1930s China. In the course of 
following discussion, these developments will be presented through the prism of 
two contending currents of approach towards studying and teaching mathemat-
ical logic that formed by the early-1930s: that is, mathematical logic as a part of 
Chinese academic philosophy on the one hand, and mathematics on the other. 
With regard to their conceptual extensions—i.e. as the constituents of broad-
er theoretical discourses of both respective disciplines—the distinction between 
these two currents shall be referred to as the philosophical and mathematical 
“notions” of mathematical logic. The main reason behind introducing such a dis-
tinction resides in the fact that, for the most part, the advancement of the latter 
had been conducted in the context of the wave of popularization of mathematics 
in the 1930s. More importantly, the application of a conceptual disparity of this 
kind can serve as an ample explanation for the relatively rapid “mathematization” 
of mathematical logic which took place in Chinese academia in the early 1950s. 
Thus, in the broadest sense, in line with the above-mentioned article on the so-
called “Qinghua School of Logic”, this study will provide a background for the 
subsequent surveys on the development of mathematical logic in the People’s 
Republic of China (1949–). Aside from a brief overview presented by Rafael Suter 
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(2020) in his contribution to the Dao Companion to Chinese Philosophy of Logic 
and specific sections of Xu Yibao’s doctoral dissertation from 2005, this study will 
be one of the first such contributions to the Western scholarship on the history 
of logic in Republican China. Furthermore, it will be first study highlighting the 
parallel development of mathematical and philosophical notions of mathematical 
logic in this context. 
The Ariadne’s thread of the following discussion will interconnect three main 
parts: In the first chapter I will take a closer look at teaching and research in 
mathematical logic in the context of philosophical departments at Chinese 
universities. Because the main features, directions, and achievements of the 
Qinghua School have already been discussed in detail in the above-mentioned 
article, only a brief summary of the developments at Qinghua will be given, 
while the main focus of the chapter will reside with the developments at other 
universities of similar status, including Peking University and the reformed 
National Wuhan University, and finally also the gradual introduction of essen-
tials of mathematical logic in the modernized and standardized textbooks for 
higher secondary schools, normal schools and universities. Correspondingly, 
the second chapter will closely examine the development of mathematical logic 
in the context of Chinese mathematicians’ research and efforts at popularizing 
mathematical logic in the 1930s. Finally, the third and the last section will be 
reserved for concluding remarks and a brief analysis of the value of the main 
findings of this survey for our understanding of the following period of math-
ematical logic. 
Mathematical Logic as Part of Academic Philosophy:  
From Qinghua to Wuhan University 
As already mentioned in the introduction, mathematical logic as a part of ac-
ademic discipline of philosophy reached its full bloom in the progressive en-
vironment of the Department of Philosophy at Qinghua University. In the 
framework of the flourishing of modern Western philosophy at the department, 
mathematical logic became one of the pillars of both undergraduate and later 
also graduate studies of philosophy. As such, mathematical logic as formulated 
in the works of Bertrand Russell and his and Whitehead’s monumental Prin-
cipia Mathematica was taught as part of the basic and advanced courses on logic 
both at the level of the institute of humanities and specialized studies in phi-
losophy. Apart from its early inclusion into the mandatory and selective courses 
on logic, from the late-1920s on mathematical logic was also one of the main 
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research foci of the leading senior members of the department, such as Jin Yue-
lin 金岳霖 and Zhang Shenfu 張申府. Concurrently with the formation of the 
first generations of graduates specialized in logic, mathematical logic also be-
came one of the leading specializations of those alumni of the department who 
either continued their studies at Western universities or upon graduation joined 
the department as junior lecturers—such as, for instance, Shen Youding 沈有鼎 
and Wang Xianjun 王憲鈞. While at the earliest stage the style and content of 
teaching of mathematical logic at Qinghua University was more or less epito-
mized in Jin Yuelin’s renowned textbook Logic (Luoji 邏輯), the later genera-
tion of Qinghua-trained logicians ushered in a wider selection of contents from 
contemporary advances in European circles of modern logicians. Thus, by the 
mid-1930s the range of content relating to mathematical logic taught at the 
department included: the system of Principia, advances of the “Harvard School” 
of symbolic logic, symbolic logic as advanced by the members of the Vienna 
Circle—from Carnap to Gödel, down to theories of many-valued logic of the 
Polish Circle of modern logicians. In line with the general trends in the field, 
as still extant in Western academia in the 1920s and 30s, mathematical logic at 
Qinghua was taught in strict cohesion with analytic philosophy, in particular, 
and in direct connection with traditional and modern Western philosophy, in 
general. In other words, mathematical logic was more or less considered as an 
advanced form of traditional formal logic, which still shared the same discipli-
nary framework with its predecessor. (See Vrhovski 2021a) 
From the early 1930s on, the influence of the Qinghua School of Logic and its 
slowly growing circle of analytic philosophers extended far beyond the university. 
After the former student and propagator of Russell’s philosophy Fu Tong 傅銅 
rejoined the reopened Peking University as the head of the Department of Phi-
losophy in 1929, interest in modern logic and analytic philosophy was gradually 
rekindled at the department. Consequently, in addition to the advancement of 
a special study group for logic (lunlixue zu 論理學組) in the framework of the 
Philosophical Research Society (Zhexue yanjiuhui 哲學研究會) (see Guoli Bei-
jing daxue 1929, 68), his strong inclination towards modern Western philosophy 
probably also prompted a new wave of integration of courses on analytic philoso-
phy and mathematical logic into the basic curriculum at the department. Subse-
quently, in the early 1930s, the undergraduate and graduate students of philoso-
phy at Peking University were able to attend a series of lessons given by professors 
from the neighbouring Qinghua University, from Zhang Shenfu’s introductory 
course on mathematical logic and Russell, to Jin Yuelin’s specialized lectures on 
Mill, epistemology and so on. In this regard, the developments relating to the 
teaching of mathematical logic at Beijing’s most prestigious universities had their 
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213Asian Studies X (XXVI), 2 (2022), pp. 209–241
epicentre at the early studies of Western modern logic and philosophy at Qinghua 
University.1 
The second important wave of spreading the Qinghua-type of teaching of math-
ematical logic at Chinese universities came with the first generations of graduates 
of the Qinghua philosophical department, or in rarer cases through the work of 
scholars who had in any way been affiliated or in touch with the developments at 
Qinghua. Naturally, in parallel with the spread of the Qinghua Circle’s influence 
by means of personal ties and fostering a new generation of outstanding Chinese 
scholars, the dissemination of the notion of mathematical logic as taught and 
researched at the department was to a much larger degree conducted by means 
of publications, which included research treatises and propaedeutic articles on 
one side, and the dissemination of certain types of textbooks on the other. Apart 
from Peking University, another instance of the introduction of content related 
to mathematical logic by an alumnus of the Qinghua school was the reformed 
National Wuhan University (Guoli Wuhan daxue 國立武漢大學).
National Wuhan University was officially established in 1928. It was founded as 
an attempt to combine a number of smaller institutions of higher education from 
Hubei, including the recently established (1926) National Wuchang University 
(Guoli Wuchang daxue 國立武昌大學), into one major and modernized univer-
sity. Owing to its relatively late establishment, and through the influence of a the 
newly rising tide of modernization of Chinese academic philosophy, the earlier 
National Wuchang University already boasted a relatively theoretically pertinent 
and updated curriculum for logic. In the framework of the Wuhan University’s 
Department of Philosophy, the first major advance towards a modernized course 
in logic came in the year with the appointment of Tu Xiaoshi 屠孝實 (courtesy 
name Zhengshu 正叔, 1898–1932) as a lecturer of logic (Guoli Wuhan daxue 
1931, 73, 82). Tu was a graduate of Waseda University in Tokyo and a former pro-
fessor of philosophy at Peking University, who in 1926 wrote and published the 
highly influential textbook Logic Primer (Mingxue gangyao 名學綱要), which also 
encompassed a short introduction to early algebraic logic (Boole and De Morgan) 
based on Jevons’ Elementary Lessons on Logic. 
In 1932, Tu was replaced by Wan Zhuoheng 萬卓恆 (1902–1948), a graduate of 
philosophy from Qinghua and Harvard Universities. Prior to his tenure at Wu-
han University, Wan taught philosophy at the North-Eastern University. During 
his professorship at Wuhan, between 1931 and 1948, Wan was generally known 
1 On the earlier developments in teaching and propagating modern logic at Peking University, see 
Vrhovski (2021b). On development of the academic discipline of Chinese philosophy at Chinese 
universities in the 1920s and 1930s, see Lin (2012), etc.
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214 Jan VRHOVSKI: Between Philosophy and Mathematics...
as a lecturer of logic who specialized on mathematical logic.2 Wan’s reputation 
as a professor of philosophy who understood mathematical logic and lectured 
about Principia Mathematica extended beyond the circle of professors and stu-
dents at the university. Even though Wan did not produce any writings related to 
mathematical logic or even logic, he is mentioned in some contemporary Chinese 
histories of modern logic in China as one of those philosophers from Republican 
China who were engaged in teaching and spread of mathematical logic.3 Beside 
logic (lunlixue), Wan also taught other courses related to contemporary Western 
philosophy and epistemology. The official overview of courses and programs at 
the National Wuhan University from 1932 reveals that the first course on logic 
organized by Wan had already assumed a modern outlook. The content of Wan’s 
lectures from 1932 covered the following topics: various problems in formal log-
ic, forms of deduction and contemporary logic (Guoli Wuhan daxue 1932, 23). 
In the following years, apart from an elementary course Wan also organized an 
advanced course on logic (called “Logic 2, Lunlixue er 論理學二”), which was 
offered as an elective course for students of philosophy. In 1934, the elementary 
course was devoted exclusively to an overview of Aristotelian logic and aimed 
at presenting a general outline of the principles of human thought and the idea 
of correct thinking. The advanced course, on the other hand, consisted of three 
main parts: Aristotelian logic, symbolic logic (mathematical logic) and theory of 
induction (Guoli Wuhan daxue 1934, 26–27, 33). According to the reminiscences 
of Wan’s former student Xiao Shafu (萧箑父, ?), the part of the lectures related 
to symbolic logic revolved exclusively around the Principia Mathematica, covering 
the parts about the basic principles and logical calculi (Xiangren 2017, 26). The 
content of the elementary course changed again in 1936, when it was reorgan-
ized to include 1) formal logic and 2) the scientific method, while the content 
of the advanced course remained unchanged (Guoli Wuhan daxue 1936, 33, 40). 
In the same year, two elementary textbooks were prescribed: beside the by then 
already standard textbook Essentials of Logic by Wolf, there was also Logic (Lun-
lixue 論理學 (1931)), written by Fan Shoukang 範壽康 (1895–1983), another 
professor of philosophy at Wuhan.4
2 Beside He Lin’s mention of Wan as one of the leading contemporary Chinese philosophers who 
specialized in mathematical logic, there are also accounts and reminiscences of his former students, 
most notably the philosopher Xiao Shafu. See Li Mianyuan (2016); Li Weiwu (2009); Xiangren 
(2017). 
3 See, for example, Shi and Zeng (1998, 29–33).
4 The textbook was published as a part of Kaiming Pedagogical Textbooks (Kaiming shifan jiaoben 
開明師範教本). It was designed in accordance with a psychological approach to logic (logical 
psychologism), which favoured the experimental logic of American pragmatists above other types 
of modern logic. As a matter of fact, even though in his historical introduction Fan did mention 
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Mathematical Logic as a Mathematical Field of Research:  
The Wuhan Circle of Mathematicians 
As indicated in the introduction, before the 1930s mathematical logic was still 
generally understood as a field of studies researched by, so to say, “philoso-
phers-logicians”. This also meant that the predominant notion of mathematical 
logic in the Chinese intellectual world was still understood in the context of 
modern Western philosophy. However, this understanding underwent signif-
icant changes in the early 1930s, when a few young mathematicians who re-
turned from their studies in Europe decided to engage in research of the foun-
dations of mathematics and mathematical logic. One of the most important 
centres for the concentration of such interest in mathematical logic was the 
aforementioned Wuhan University. After Fu Zhongsun’s 傅種孫 and Zhang 
Bangming’s 張邦銘 translation of Russell’s Introduction to Mathematical Phi-
losophy in the early 1920s (see Russell 1922), the following developments rep-
resented the first major shift of identity of mathematical logic in China, which 
in the 1930s started its twofold evolutionary path. One of the young scholars 
who was at the forefront of this transformative process was the mathematician 
Tang Zaozhen 湯璪真 (Tang Tsao-Chen, 1898–1951). Tang, who completed 
his graduate studies in mathematical logic at the Universities of Berlin and 
Göttingen, became the main driving force behind the research on mathematical 
logic at the mathematical department of Wuhan University. The importance 
of Tang Zaozhen and the circle younger mathematicians at Wuhan University 
has already been noticed by Xu Yibao (2005), who briefly mentioned Tang in 
his doctoral dissertation Concepts of Inf inity in Chinese Mathematics. He wrote:
After graduating from Department of Mathematics of Beijing Teachers 
College in 1919, TANG taught mathematics at Beijing Teachers Col-
lege for Girls. In late of 1923, he went to Germany to pursuit his further 
study in mathematics. During the next two and a half years, Tang studied 
mathematical logic or symbolic logic of Boole as one of the mainstream currents in contemporary 
logic, it was only a brief mention, ignoring all its main contributors who succeeded Boole. Moreo-
ver, he treated mathematical logic as a less important branch of the formalist school in philosophi-
cal logic, and instead devoted more attention to idealist conceptions of logic. Fan also regarded the 
pragmatist logic of Dewey as one of the most important logical schools of the time, which con-
tented against logic formalism, as manifested in mathematical or symbolic logic (Fan 1931, 1–26). 
One of the immediate consequences of his view of logic led Fan to exclude the most important 
contemporary contributions to theory of deduction from the textbook. Instead, Fan’s outline of the 
science of reasoning derived its broadness from the inclusion of a great number of metaphysical and 
phenomenological meditations on logic. Thus, for example, beside deductive and inductive reason-
ing, he also discussed the notion of analogical reasoning (leibi tuilun 類比推論) etc. The textbook 
also maintained a notion of Chinese logic as reflected in traditional Chinese philosophy.
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216 Jan VRHOVSKI: Between Philosophy and Mathematics...
primarily differential geometry and mathematical logic at University of 
Berlin and University of Göttingen. When he returned in 1926, he was 
appointed as Professor of mathematics at National Wuchang Univer-
sity (the predecessor of Wuhan University). At the University, he used 
Wilhelm J. E. Blaschke’s textbook for teaching his course on differential 
geometry. Mathematical logic was not on the curriculum of the Univer-
sity, but TANG did not lose his interest in it. Although his focus was 
on Clarence Irving Lewis’s calculus of strict implication, and was not 
directly related to aspects of the infinite, it does show how quickly Chi-
nese mathematicians began to respond to this new area for their own 
research. TANG published three articles on the subject in the Bulletin 
of the American Mathematical Society. In the first of these, “The Theorem 
p − 3q = pq = p and Huntington’s Relation Between Lewis’s Strict Impli-
cation and Boolean Algebra,” he shows that the theorem “p − 3q = pq = p” 
holds true in Lewis’s system, and that it strengthens a previous result of 
Edward Huntington. Based on this result, TANG went on to show that 
where any implication “p − 3q” is asserted, then “p − 3q = i,” from which 
it follows that any two asserted implications are strictly equivalent, and, 
in particular, that any two of Lewis’s first eight postulates can be deduced 
from each other. TANG also studied algebraic postulates for Boolean 
rings. (Xu 2005, 189–90) 
As pointed out by Xu, Tang’s main contribution to mathematical logic consist-
ed in his treatment of Huntington’s discussion of Lewis’s theory of strict im-
plication and the theorem “p ⥽ q .=. pq = p”. Although Xu’s account of Tang’s 
main contributions to mathematical logic is close to complete, some additional 
points related to Tang’s work must still be added. Firstly, we need to point out 
that Blaschke’s differential geometry was one of the central subjects of Tang’s 
studies in Germany. Apart from mathematical logic, in the early 1930s Tang also 
focused on other branches of mathematics, such as for example, Levi-Civita’s ab-
solute differential calculus, which he also translated into Chinese (Cheng Minde 
1994 I, 60–71). Tang’s translations also included Hans Hahn’s “Set-Theoretical 
Geometry”, which was first published in 1930 in the Quarterly Journal of Science of 
the National Wuhan University (Guoli Wuhan daxue like jikan 國立武漢大學理科
季刊). Secondly, according to the biography composed by his son Tang Xiangsen 
湯湘森, Tang researched mathematical logic throughout the entire wartime pe-
riod. If this is true, the same or similar could also apply to the research activities 
of the group of mathematicians working closely with Tang (ibid., 68). Unfortu-
nately, no textual evidence is preserved to confirm these claims. Finally, Tang was 
also one of the founding members of the Chinese Mathematical Society. From 
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217Asian Studies X (XXVI), 2 (2022), pp. 209–241
its official inauguration in 1935, Tang assumed a series of important positions in 
the society—he was one of its 21 council members elected in 1935 and a mem-
ber of the society’s executive council in 1936 (Ren and Zhang 1994, 30, 52). At 
the second annual meeting of the society, which took place at Qinghua Science 
Museum in 1936, Tang also read his two articles on strict implication, published 
in the same year in the Bulletin of American Mathematical Society. Thus, together 
with Zhu Gongjin—about whom we shall say more in the next section—Tang 
was one of two most important members of the society, who maintained an in-
terest in contemporary mathematical logic and contributed to its advancement 
in Chinese mathematical circles. Interestingly, both Zhu and Tang had studied 
mathematics at Göttingen University in Germany, although only the latter con-
tributed scientifically to the field. Furthermore, in the 1930s both participated in 
activities related to science education. Tang was also invited to take part in the 
1933 consultative symposium on astronomy, mathematics and physics organized 
by the Ministry of Education. 
Another Wuhan mathematician, who (probably under the influence of Tang 
Zaozhen) engaged in research on topics related to mathematical logic, was Xiao 
Wencan 蕭文燦 (1898–1963), an assistant professor of mathematics at Wuhan.5 
Xiao started his path in higher education at the Guizhou Province Normal Col-
lege in Guiyang (graduating in 1916). In 1921, he enrolled in Wuchang Higher 
Normal College (predecessor of Wuhan University), majoring in mathematics. 
Upon graduation in 1925 he joined the university as a lecturer in mathematics. 
Concurrently, he also worked as a lecturer of mathematics at the China University. 
Later, in 1937, he went on a scholarly exchange to Germany, where he studied 
consecutively at the Universities of Berlin and Leipzig. Xiao returned to China 
in 1940, after he was awarded a doctoral degree in mathematics from University 
of Leipzig. Working under Tang Zaozhen, back in the early 1930s, Xiao Wencan 
also devoted a part of his work to problems related to mathematical logic, more 
precisely to Cantor’s transfinite set theory.6 Between 1933 and 1934, Xiao pub-
lished a series of articles entitled “Set Theory ( Jihelun 集合論)” in the university’s 
Quarterly Journal of Science, in which he delivered a systematic introduction to 
Cantorian set theory. The collection of Xiao’s four articles on set theory was re-
printed in the form of a monograph (Jihelun chubu 集合論初步 (Elementary Set 
Theory)) in 1939. In the same journal Xiao also published a Chinese translation 
5 For a condensed biographical account on Xiao Wencan, see Li and Xiao (2005). 
6 Xu Yibao and his doctoral supervisor Joseph Dauben claim that Xiao was the first Chinese math-
ematician to have provided a systematic overview of Cantor’s set theory (Xu 2005, 200; Dauben 
2002, 267).
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218 Jan VRHOVSKI: Between Philosophy and Mathematics...
of Hardy’s work “Orders of Infinity (Wuqiongda zhi jie 無窮大之階)”.7 In his 
dissertation, Xu Yibao commented on Xiao Wencan’s and Zhu Gongjin’s contri-
butions to the propagation and spread of mathematical logic in the following way: 
Xiao’s and Zhu’s articles, together with Chinese translations of Russell’s 
work, kindled further interests in mathematical logic in China. As a re-
sult, in the 1930s a number of Chinese students of mathematical logic 
were able to carry out their own research. By the time TANG Zaozhen’s 
third article was published in America, another Chinese student had 
written his dissertation on mathematical philosophy and the theory of 
sets at the University of Paris. This was ZENG Dinghe 曾鼎鉌, also 
known as TSENG Ting-Ho.8 The major parts of ZENG’s thesis dealt 
with set theory and transfinite numbers. In retrospect, one may regard 
ZENG’s thesis as superficial and sketchy.9 It nevertheless represents the 
beginning of serious and important work that Chinese logicians would 
soon make to mathematical logic. (Xu 2005, 200–1) 
Although Xu’s summarization of Xiao’s contributions is somewhat biased, he 
might have made a pertinent remark regarding mathematical logic as a subject 
studied by Chinese mathematicians. Furthermore, the contributions by Xiao and 
Zhu, which must be regarded as introductory works or attempts at the popular-
ization of mathematical logic and set theory as one of its constitutive branches, 
could indeed have been pivotal for kindling the Chinese mathematician’s interest 
for the above-named fields of studies, especially because they both purported to 
convey their mathematical content rather than philosophy-related categories. 
7 Xu (2005, 200) mistakenly believed that Xiao’s two articles were authored by Xiao himself. In truth, 
they were a translation of above-named work of the British mathematician Hardy. In addition to 
that, Xu also noted that the notion of infinity was of great interest to Chinese mathematicians of 
the time (see Hardy 1932; 1933). 
8 His name was also written 曾鼎龢 (Zeng Dinghe). In 1938 Zeng was awarded a PhD degree for 
a doctoral dissertation entitled “La philosophie mathématique et la théorie des ensembles (Math-
ematical Philosophy and Set Theory)”; see Tseng 1938.
9 This were the exact words of Frederic B. Fitch, who reviewed Zeng’s doctorate in 1943 (The Journal of 
Symbolic Logic 8 (2) ( June 1943): 56–57). Fitch said: “This is a philosophical and historical survey of 
various topics in modern mathematics, such as set theory, probability, transfinite numbers, and math-
ematical logic. The treatment is somewhat sketchy and often superficial. In discussing mathematical 
logic no mention is made of Gödel, although literature as later as 1936 is referred to.” (Fitch 1943, 56) 
Zeng’s doctorate was listed in the bibliography of Bernays’s and Fraenkel’s 1958 book Axiomatic Set 
Theory (although the latter wrote only the introductory parts and provided some bibliographical data). 
Consequently, in his letter to Bernays from March 14th, 1958, Gödel inquired about the content of 
Zeng’s work: “Ich habe bemerkt, dass Sie in Ihrem neuen Buch über Mengenlehre einen gewissen 
Tseng[g] Ting-Ho zitieren. Ist diese Arbeit interessant? (I noticed that in your new book on set the-
ory you cite a certain Tsen[g] Ting-Ho. Is that paper interesting?)” (Gödel and Solomon 2014, 152) 
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219Asian Studies X (XXVI), 2 (2022), pp. 209–241
Mathematical Logic and the Popularization of Mathematics: 
Zhu Gongjin and Hilbertian Foundations of Mathematics and 
Mathematical Logic 
Another important Chinese mathematician, who to some extent contributed to 
the introduction and propagation of mathematical logic as a branch of mathe-
matics in China, was the well-known educator and popularizer of mathematics 
Zhu Gongjin 朱公謹 (also known as Zhu Yanjun 朱言鈞, 1902–1961). Zhu 
started his pursuit of mathematical knowledge at Qinghua College, where he 
completed the basic preparatory course. In 1921, he was awarded a scholarship 
for undergraduate studies at the renowned Göttingen University in Germany. 
In the years he subsequently spent in Göttingen, Zhu eventually specialized in 
applied mathematics and was in 1927 awarded a doctoral degree in mathematics 
for his thesis on the theory of differential equations, entitled On Existence Proofs of 
Certain Types of Single-Variable Functional Equations. After he returned to China 
in 1927, he worked as a professor of mathematics at Guanghua University, Cen-
tral University, Shanghai Medical School, Normal Faculty of Zhejiang University, 
Datong University and Shanghai Jiaotong University. With the establishment 
of Chinese Mathematical Society in 1935, Zhu became one of its permanent 
council members and one of the most productive contributors to its periodical 
publications the Shuxue tongbao 數學通報 (Bulletin of Mathematics or Bulletin 
des Sciences Mathematics) and the Shuxue zazhi 數學雜志 (Mathematical Review) 
(Zhang Youyu 1991, 2).
Although Zhu spent almost seven years at the University of Göttingen in Germa-
ny and obtained a PhD in mathematics studying under two of the most famous 
and well-established mathematicians of the time, David Hilbert and Richard 
Courant, upon his return to China he ended up working at relatively marginal 
universities, such as Guanghua University and Jiaotong in Shanghai, although 
also at some more prominent universities, such the Central University in Nanjing. 
Although his direct influence on the theoretical development of mathematics in 
China seems to be (at least in when it comes to documentation) somewhat ob-
scured by the marginality of the institutes of his employment, in the late 1920s 
and 1930s Chinese intellectual world his voice was loud and clear. Zhu was prob-
ably the most prolific popularizer of general and specific aspects of mathematics 
in early 1930s China. His numerous articles introducing different aspects and 
problems of advanced mathematics (especially analysis), philosophy of mathe-
matics and finally also his translations of writings by important mathematicians 
like Dedekind or Hilbert, were not only published in university-affiliated peri-
odicals, such as the Shuxue zazhi 數學雜志, but also in magazines devoted to 
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popularization of Western science.10 It was especially the latter that established 
his role as a popularizer of applied mathematics in China. 
Among Zhu’s articles introducing various topics, theories or branches of mathe-
matics, there were also some that explicitly or implicitly involved the principles of 
contemporary mathematical logic. Two of the most influential such articles were 
“An Introduction to Mathematical Logic (Shuli luoji daolun 數理邏輯導論)” 
from 1936 and “Essentials of Mathematical Logic (Shuli luoji gangyao 數理邏
輯綱要)” published in two parts in 1933 and 1934. Although the articles only 
expounded on a rather elementary notion of mathematical logic, their signifi-
cance lay in another aspect: because Zhu was introduced to mathematical logic as 
a mathematician, he regarded its content to be primarily a part of mathematics. 
Consequently, his articles usually implicitly indicated that the research on math-
ematical logic ought to be reserved exclusively for mathematicians. As such, in-
troductions to mathematical logic or set theory done by mathematicians were of a 
different value to those done by philosophers, for they each derived from different 
theoretical or practical contexts and ultimately also influenced separate academic 
spheres of discourse. 
As an ardent popularizer of mathematics who also maintained a considerable 
interest in mathematical logic and the foundations of mathematics, Zhu often 
also wrote articles commenting upon the relationship between mathematics and 
logic on one side, and modern philosophy on the other.11 More importantly, a 
10 For the general significance of translations—and for highlighting some general problems linked to 
translations of Western vocabulary—see for instance Ciaudo (2021, 36).
11 Zhu’s earliest publications on philosophy of mathematics were a series of articles written in re-
sponse to contemporary misinterpretations of the nature of mathematics, proposed by Chinese 
adherents of pragmatism who propagated Dewey’s experimentalist theory of logic and science. 
In 1928, in an article entitled “A Refutation of Experimentalism (Bo shiyan zhuyi 駁實驗主義)”, 
Zhu emphasized that mathematical knowledge is a priori and as such a formal expression of the 
unchanging principles of the universe. What Zhu argued against was the experimentalist position 
that the universe is subjected to constant change and that the main task of science is to constantly 
realign itself with the current state of the universe. In order to corroborate his position, Zhu used 
the example of ontologically positive concept of logical laws, which are manifested in axiomatic 
systems of mathematics. As examples thereof he listed three axiomatic (jiben yuanli 基本原理) 
systems of geometry as developed by Euclid, Riemann, and Lobachevski. Having expounded on 
the concepts of consistency and non-contradiction as concrete examples of the application of log-
ical laws in mathematics, he explained the difference between different kinds of judgments as de-
fined by Kant, shedding some light on the epistemic value and sufficient conditions of the truth 
of mathematical axioms. In short, Zhu’s principal aim was to portray the objectiveness of logic, as 
the main condition of mathematical truth, through a system of laws reflecting the a priori structure 
of reality. This implies that mathematical judgements and inferences are beyond experimental in-
quiry and that mathematical judgments were a priori synthetic judgments. In a sequel to the article, 
Zhu directed his criticism against the philosophical viewpoints of Hu Shi and Dewey. Similar was 
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221Asian Studies X (XXVI), 2 (2022), pp. 209–241
closer reading of his philosophical writings on mathematics and modern logic 
reveals that one of his principal sources was the teaching of the leading mathe-
matical formalist of the time, David Hilbert. As noted above, Zhu’s connection to 
Hilbert’s mathematical and logical formalism can be traced back to the former’s 
studies in Göttingen. Consequently, one of the main parts of Zhu’s populari-
zation of modern mathematical logic also consisted of introducing the work of 
Hilbert. Thus, for example, in an article published as early as 1929 Zhu discussed 
the differences between Brouwer’s intuitionist “theory of sets” (tuanlun 團論) and 
Hilbert’s formalist idea of contradiction (ziweiyu 自違語) in the same theory. 
Interestingly, Zhu discussed both schools as offshoots of two currents in mathe-
matics, analogous to those in modern cosmologies which derive from advances in 
modern physics (see Zhu Yanjun 1929b). In another article from 1932, Zhu gave 
a lengthier exposition on Hilbert’s life and his theory of axiomatics (yuanlishuo 
原理說), axiomatization of arithmetic, as well as other aspects of Hilbert’s views 
on questions related to the fundaments of mathematics, some of which were also 
intrinsically linked to mathematical logic (see Zhu Yanjun 1932, 2–8). Finally, 
in 1935 Zhu published an updated version of his evaluation of intuitionism and 
formalism. In this sequel to his first such mediation from 1929, Zhu focused 
both on set theory and theories of inference in mathematics, covering three main 
topics: Poincare’s view on mathematical inference and set theoretical questions, 
the rise of intuitionism and Russell’s mathematical logic. The main topic of Zhu’s 
second survey was still Hilbert’s views on axiomatization of mathematics. Zhu’s 
writings on the foundations of mathematics from this period reveal that his views 
on the subject remained within the constraints of Hilbertian theory, which he 
came into contact with during his studies in Germany. He did not discuss, for 
instance, the developments in the Polish School of Logic or, most importantly, 
Gödel’s results related to the above-mentioned problems and topics. Even in his 
“Critiques of Mathematical Axiomatics (Shuxue yuanlixue zhi piping 數學原理
學之批評)” from 1937, the primary aim of which was to outline criticisms raised 
against Hilbert’s project of axiomatization of mathematics, Zhu made no mention 
of these important contemporary contributions. 
In the early 1930s, Zhu edited a series of short discussions on practical or pure-
ly theoretical curiosities of mathematics, which was regularly published in the 
Guanghua daxue banyuekan 光華大學半月刊 (Guanghua University Fortnightly). 
intended also in Zhu’s other writings from the late 1920s, such as, for example, “New Geometry 
and Philosophy (Xin jihexue yu zhexue 新幾何學與哲學)”; “From Theory of Knowledge to Crit-
ical Theory (Cong renshilun dao pipinglun 從認識論到批評論)”; “On the Relationship Between 
Metaphysics and Natural Science (Xuanxue yu ziran kexue de guanxi 玄學與自然科學的關係)”, 
and “Socrates and Leonard Nelson (Sugeladi yu Na’ersong 蘇格臘底與納爾松)”, which were all 
published in 1929. 
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These discussions were subsumed under a common title “Shuli congtan 數理叢
談 (Mathematical Discussions)”, and by the year 1934 the number of individual 
discussions already reached twenty.12 Furthermore, in 1936 Zhu published yet an-
other series of writings introducing the advances in foundations of mathematics 
and mathematical logic in the above-mentioned periodical. The series bore the 
title “Casual Conversations on Set Theory ( Jilun xiaotan 集論小談)”, and was 
written in form of a dialogue between Zhu and a colleague of his, who was also 
a professor of mathematics (see Zhu 1936c; 1937b (first and last part)). Through 
dialogues Zhu touched upon various questions related to the recent advances in 
foundations of mathematics. Perhaps the most important feature of these conver-
sations was that they were written from the mathematical perspective—treating 
set-theoretical problems and mathematical logic as an integral part of mathemat-
ics, which, as also pointed out by Zhu himself, had been often entirely neglected 
(see Zhu 1936c, 28). Even though the title of the conversations implies a sense of 
casualness and elementariness, the dialogues also touched upon more advanced 
topics in set theory, mathematical logic and even number theory, all of which 
were bound together in meta-mathematics of Hilbert. The conversations were 
published in ten parts between 1936 and 1937. 
In 1935 and 1936, Zhu also published a series of other propaedeutic articles on 
topics related to the foundations of mathematics and mathematical logic. Such 
were, for example, the series of articles entitled “Methods of Inference in Math-
ematics (Shuxue zhong zhi tuili fangfa 數學中之推理方法)”. Other relevant 
articles from the same period were “The Origins of Mathematical Knowledge 
(Shuxue renshi zhi benyuan 數學認識之本源)”, “Topological Geometry and Our 
Views on Space (Dingxing jihexue yu wuren zhi kongjian guan 定性幾何學與
吾人之空間觀)” and so on. The common thread interconnecting the majority of 
his writings from 1930s was again Hilbert’s theory of foundations of mathemat-
ics (axiomatics, geometry, arithmetic, set theory). Whenever Zhu required the 
assistance of more philosophical views on mathematical principles he resorted 
to philosophy of Leonard Nelson, one of his former professors at university in 
Göttingen and a close friend of Hilbert’s. In 1928, one year after he had returned 
to China, Zhu even published a short booklet commemorating Nelson’s life and 
work.13 
12 Eight of these chapters were also published in form of a book in 1947.
13 Nelson passed away in 1927. The mentioned booklet bore the title Nelson—A Philosopher of Critical 
Rationalism (His Life and Teaching) (1928c).
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223Asian Studies X (XXVI), 2 (2022), pp. 209–241
Introduction of Mathematical Logic of Hilbert and Ackermann, 
1933–1936
Zhu’s pivotal contribution to the introduction of Hilbertian symbolic logic in 
China took form in two lengthier articles outlining the essential concepts of 
mathematical logic. The first article, entitled “Essentials of Mathematical  Logic 
(Shuli luoji gangyao 數理邏輯綱要)”, was published in 1933 in the Zhexue 
 pinglun journal. Here, Zhu’s approach to mathematical logic was similar to his 
other publications: he essentially described mathematical logic as a version of 
formal logic which assimilated the most advanced knowledge from mathemat-
ics. Moreover, Zhu mainly ascribed its advantages to the advances in modern 
mathematics; in particular, its use of symbols and formulae, which endowed log-
ic with a capacity to attain completeness, consistency, and a greater analytical 
capacity. Even though his short overview of the history of mathematical logic 
mentioned all the important contributors to the field, from Leibniz to Russell, 
Zhu’s focus remained with Hilbert, who, according to Zhu, was able to include 
the most advanced principles of mathematics into his logic. While Zhu did not 
explicitly indicate this, the content of the article derived heavily from Hilbert’s 
and Ackermann’s Grundzüge der theoretischen Logik (1928).14 As a matter of fact, 
some parts of Zhu’s “Essentials of Mathematical Logic” correspond entirely to 
individual sections of the 1928 edition of Hilbert’s and Ackermann’s Grundzüge 
der theoretischen Logik. Thus, Zhu’s introduction to mathematical logic was in fact 
an introduction to the early Hilbert-Ackermann system of mathematical logic. 
Zhu’s article from 1933 covered the following aspects of the Hilbert-Ackermann 
system of logic: Propositional logic (lunduan luoji 論斷邏輯),15 which included: 
a) the definition of proposition; b) methods of elementary connectives (jiben jiehe 
基本結合);16 c) equivalence (dengshi 等式); d) a further discussion on the elemen-
tary connective methods (including the Sheffer stroke, Russell, etc.); e) elementary 
forms (of logical expressions) (jiben xingshi 基本形式);17 f ) tautological (always true) 
14 The first (1928) and second (1938) editions of the book differ considerably from each other. The 
first book builds upon Hilbert’s formalistic first-order logic and still included the Entsheidungs-
problem and the question of completeness of logic as a system, which were ultimately left out of the 
later edition. The second edition was also translated into English and given the title Principles of 
Mathematical Logic (1950).
15 Here the term lunduan 論斷, otherwise meaning “inference” or “judgment”, stands for “proposition” 
or German Aussage, as in Hilbert’s Aussagenkalkül.
16 Zhu’s term jiehe 結合 is semantically motivated after the original German term Verknüpfung as in 
“logische Grundverknüpfungen” as used in Hilbert’s and Ackermann’s mathematical logic. 
17 The original title of the section was “Normalform für die logischen Ausdrücke” (i.e. Section 1, 
Chapter 3 of the 1928 edition).
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224 Jan VRHOVSKI: Between Philosophy and Mathematics...
connections of propositions (yongzhen zhi jiehe 永真之結合);18 g) the theorem of 
reciprocity (huyixing zhi dingli 互易性之定理);19 h) the ever-false connections of 
propositions (yongmiu zhi jiehe 永謬之結合);20 i) special elementary propositions 
(teshu zhi jiben xingshi 特殊之基本形式);21 j) a further discussion on the question 
of conjunction (always true) and disjunction (always false); k) the problem of how 
to draw conclusions (ruhe xia duan’an zhi wenti 如何下斷案之問題).
As indicated above, the structure and content of Zhu’s presentation of the essential 
features of mathematical logic corresponds to that of Hilbert’s and Ackermann’s 
book from 1928. As Zhu himself also noted in the 1933 version of the article, 
his source material was his notes from Hilbert’s lectures, taken when he was still 
a student at Göttingen. Maybe the only parts of the text which Zhu decided to 
modify were the examples of propositions, which Zhu adapted to fit the Chinese 
socio-political context. The same article was reprinted in 1934 in the Quarterly 
Journal of Science of the National Wuhan University (Guoli Wuhan daxue like jikan 
國立武漢大學理科季刊), which also happened to be one of the central means 
through which the group of mathematicians at Wuhan University promulgated 
their research, which in 1934 also encompassed set theory and the foundational, 
mathematical, and mathematico-logical theories of David Hilbert.22 
Two years later, in 1936, Zhu published another article, “An Introduction to 
Mathematical Logic (Shuli luoji daolun 數理邏輯導論)”, which represented a 
continuation of the article from 1933, where Zhu introduced the content of the 
remaining few chapters of the book by Hilbert and Ackermann. In this new arti-
cle, however, Zhu’s attitude towards logic changed slightly, at least in his manner 
of expression. This time, he compared mathematical logic to the method of “ex-
hausting the principles” or “qiongli 窮理”, a Neo-Confucian term which used to 
be linked to the Western concept of science. Zhu claimed that through logic one 
can extend already known laws to individual physical entities and distil the most 
fundamental principles of nature from known facts. In this context, mathematical 
logic represented the most advanced such method. He also remarked that math-
ematical logic takes the most elementary laws of science and translates them into 
relations between subjects and predicates, and between propositions. 
18 Originally: “Charakterisierung der immer richtigen Aussagenverbindungen.” 
19 The original title of the section was “Das Prinzip der Dualität [The Principle of Duality]”. 
20 Originally “Die disjunktive Normalform für logische Ausdrücke.” 
21 This section appears to summarize chapter 7 of the first section in the original book, “Mannigfaltigkeit 
der Aussagenverbindungen, die aus gegebene Grundaussagen gebildet werden können.” 
22 Volumes 4 and 5 of the above-mentioned journal saw the publications of a Chinese translation of 
Hilbert’s The Theory of Algebraic Number Fields by Hua Luogeng, a series of articles on “Set Theory” 
( Jihelun 集合論) by Xiao Wencan etc. 
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225Asian Studies X (XXVI), 2 (2022), pp. 209–241
The 1936 sequel introduced two new chapters from Hilbert’s and Ackermann’s 
book. It was divided into two main chapters: “The Axioms of Propositional Log-
ic (Lunduan luoji zhi yuanli 論斷邏輯之原理)” and “Main Ideas of Predicate 
Logic (Weici luoji zhong zhi zhuyao sixiang 謂詞邏輯中之主要思想)”. In the 
first chapter Zhu summarized the content of chapters 10 and 11 of the first part 
of Hilbert’s and Ackermann’s Grundlagen.23 At the same time, Zhu seems to have 
slightly departed from their original line of thought, for in his description the ax-
ioms from the Principia Mathematica are given the main role. He even added his 
own thoughts about the relationship between axioms of other branches of science 
and mathematical logic, where he maintained that mathematical logic represented 
a meta-scientific view of the axiomatic system, for it takes logical method as its 
main subject of enquiry. By being a meta-systemic science, it would thus be exempt 
from the rest of sciences, which must adhere strictly to the principles of the logical 
method and depend upon the consistency of their axiomatic fundaments (Zhu 
Yanjun 1936b, 85). The second part of Zhu’s article summarized the introductory 
parts of the second section of Hilbert’s and Ackermann’s Grundlagen (1928).24 
Gao Xingjian—“ABC of Mathematical Logic” 
Significant contributions to the popularization of mathematical logic in 1930s 
China were also made by Gao Xingjian 高行健, a graduate in chemistry from 
the Central University (Zhongyang daxue 中央大學), a member of the National 
Institute for Compilation and Translation (Guoli bianyi guan 國立編譯館), and 
a professor of mathematics at Guiyang Medical University (–1948). As a prolific 
contributor to the journal World of Science (Kexue shijie 科學世界) he composed a 
series of articles on different topics from mathematics, mathematical games (youxi 
shuxue 游戲數學), interesting mathematical problems (shuxue wenti 數學問題), 
and new records of the most recent developments in mathematics (jinnian shuxue 
zhi xin jilu 近年數學之新紀錄), to more specific topics from the most fashion-
able branches of mathematics, such as mathematical logic. Gao also contributed a 
few articles to the famous Kexue journal, such as a short article on the Goldbach 
conjecture and some shorter articles on number theory.
For the present discussion, the most relevant of Gao’s articles from the 1930s was 
his “ABC of Mathematical Logic (Shuli luoji ABC 數理邏輯ABC)” from 1936. 
The article aims to introduce the main concepts from mathematical logic to a 
23 “Die Axiome des Aussagenkalküls” and “Beispiele für die Ableitung von Formeln aus den 
Axiomen.” 
24 Such as, for example, “Methodische Grundgedanken des Funktionenkalküls” etc. 
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226 Jan VRHOVSKI: Between Philosophy and Mathematics...
more general readership. Most importantly, it attempts to do so by treating math-
ematical logic as a branch of mathematics. Gao was well-aware of previous intro-
ductions to Hilbert’s and Ackermann’s mathematical logic made by Zhu Yanjun. 
The main source of Gao’s guide to the principles of mathematical logic was prob-
ably J. S. Turner’s Mathematical Logic from 1928. A further interesting feature of 
the above-mentioned article was Gao’s notion of mathematical logic, which he 
called the science of sciences, and science as such as an example of materialized 
logic. And a rather natural corollary to that position was that  mathematical logic 
was the most advanced and modern example of this method. As the most impor-
tant contemporary mathematical logicians Gao listed Russell and Hilbert, and 
enumerated the numerous synonyms for mathematical logic which were in use 
at the time. Otherwise, Gao’s article was extremely concise and simple. The first 
part25 covered three main topics: 1) Elementary Symbols, 2) Elementary Equa-
tions, and 3) Proofs of Elementary Equations.
Introduction of the Principles of Mathematical Logic into the 
National System of Education
Another important aspect of the establishment of mathematical logic in Republi-
can China, and one of the most substantial direct outcomes of the developments 
described above, was its gradual inclusion into the new standardized secondary 
school, normal school, and university curricula. The beginnings of this inclusion 
can be traced back to the first bundle of reforms of the national system of edu-
cation promulgated by the Nationalist government, whose aim was to unify and 
standardize education at Chinese schools and universities. Not long after the cen-
tral government had moved to Nanjing (April 1927), the new Nationalist Minis-
try of Education began devising new plans for large-scale reforms of the national 
system of education. In so doing, it consulted various Western models, from the 
American “pragmatic” model of education, propagated by Hu Shi and his adher-
ents, to French and German models of education. Subsequently, the first drafts of 
reforms were issued in the aftermath of the first national congress on questions 
of education in May 1928. The collection of documents issued following the Na-
tional Congress on Education was epitomized in one titled “Reorganization of 
School System of the Republic of China (Zhengli Zhonghua renmin xuexiao 
xitong an 整理中華人民學校系統案)”. In 1929, further documents stipulating 
new sets of regulations for institutes of higher education were issued—such as the 
25 According to its title, Gao also planned to publish further parts of the article in the Kexue shijie. 
However, I was not able to ascertain the existence of any sequels to the 1936 article. 
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227Asian Studies X (XXVI), 2 (2022), pp. 209–241
“Regulations for Universities (Daxue guicheng 大學規程)”, “Organizational Law 
for Universities (Daxue zuzhifa 大學組織法)” and so on. These plans were re-
vised at the Second National Congress on Education in 1930. Finally, new school 
laws for secondary, normal, and vocational education were promulgated again in 
1932. The education system reforms in the Nanjing period of the Republic were 
not the first enterprise of this kind. In some respects, the first set of reforms, 
promulgated in 1922, were only continuing previous plans for modernization and 
standardization of the Chinese system of education26 (see Pepper 1996).
Curricular changes, proposed in the framework of the National Congresses on 
Education of 1929 and 1930, were outlined in the Curricular Standards for Junior 
and Senior Secondary Schools (Chuji gaoji zhongxue kecheng biaozhun 初級高級中
學課程標準 (1932)), and Curricular Standards for Normal Colleges (Shifan xuexiao 
kecheng biaozhun 師範學校課程標準 (1934)). These were published in several 
consecutive publications from 1932 on, and the manuals were revised in the early 
1940s. For university curricula, there further existed a series of documents issued 
by the Ministry of Education entitled List of University Courses (Daxue kemu biao 
大學科目表 (1940)). These started to appear in 1933, when an original draft ver-
sion of the publication was published by the Commercial Press in Shanghai (Da-
xue kemu caoan 大學科目草案 (A Draft of University Courses)). In this draft 
document, the list of proposed standard courses at universities was supplemented 
by a list of prescribed literature.
Mathematical Logic in Senior Secondary Schools
The Curricular Standards for Junior and Senior Secondary Schools from 1932, which 
were based on the reform plans drafted and ratified by the Ministry of Education 
in 1929, stipulate that an introductory course on logic was to be taught in the 
final years of the senior secondary schools.27 The prescribed content of the course 
“Logic (Lunli 論理)” covered the following topics:
• The Scope of Logic (essential characteristics, classification of logic, 
the relationship between logic and “other sciences”).
• Analysis of Human Thought (the relationship between thought 
and life, the origin and development of thinking, organization of 
26 For developments related to teaching of logic, see, for example, Zhai 2016, 59–63; He 1989, 
75–106. 
27 The chapter of the manual, entitled “Gaoji zhongxue lunli kecheng biaozhun 高級中學論理課程
標準 (Standard Curriculum in Logic for Senior Secondary Schools)”, was later also issued as an 
independent document.
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228 Jan VRHOVSKI: Between Philosophy and Mathematics...
thought, the difference between true and false thought, the differ-
ence between simple and complex thinking, the relationship between 
thought and writing).
• Essentials of Scientific Method (comparison between common sense 
and science, the aims and attributes of science, etc.).
• Induction (the concept of causality and critical review of the simple 
“five methods of induction”, observation, analysis, conjecture, experi-
ment and probability, the meaning and effect of scientific laws).
• Deduction (the new and old fields of induction (“old” refers to Ar-
istotelian logic (lunlixue 論理學) and “new” refers to mathematical 
logic (luoji 邏輯), propositions (ci 辭) and propositional forms, rela-
tionships between propositions (kinds of immediate inferences and 
mediate inferences, syllogism), criticism of the old method of de-
duction, an exposition of the new method of deduction (analytical 
structure of thought, symbolist reformation of thought, strict form 
of thinking).
• System of Science (empirical science and pure science, natural sci-
ence and social science, science and art, science, and philosophy).
As we can observe in the above outline of the content of the course on logic, at 
least in relation to the field of logic, the curricular reforms of the late 1930s em-
bodied an extremely ambitious attempt to equip future university level students 
with basic knowledge about the scientific method on the one hand, and science of 
logic on the other. Furthermore, the new standard curriculum, which was drafted 
in the late 1920s and promulgated in the 1930s, was devised in a manner similar 
to the propaedeutic writings of Wang Dianji 汪奠基 which had been published 
in the first two years of the Nanjing period. As a matter of fact, the introduction of 
“new” mathematical logic into the curriculum might also have been indirectly fa-
cilitated by Wang’s contributions to logic education and his ideas about how logic 
and the scientific method ought to be taught at different levels of education in 
China. Aside from that, the secondary school course on logic, as stipulated by the 
new standardized curriculum, conveys a certain evolutionary image of Western 
logic, where mathematical logic was not only treated as the only extant upgrade 
of the classic Aristotelian logic, but also a new version of logic, which ought to be 
used in everyday life. Because, through the relationship between old and new, the 
significance and usefulness of logic was not believed to shift from the quotidian to 
the scientific sphere, but rather to retain the same sense of universality throughout 
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229Asian Studies X (XXVI), 2 (2022), pp. 209–241
the entire process. This implied a view that knowledge about the patterns of the 
universe was also seen as pertaining to the sphere of its practical use in everyday 
life. Maybe the only feature of the curriculum which was critically aligned to the 
native discourse on the relationship between Western and Eastern thought was its 
strong emphasis on providing a clear delimitation between rational thought and 
the view on life. 
The standard curriculum described above remained unaltered throughout the fol-
lowing decade,28 until in the Revised Curricular Standards for Junior and Senior 
Middle Schools from 1942, when for some unknown reason the course “Logic” 
for senior middle schools was abolished in favour of more extensive courses on 
physics and chemistry (Ministry of Education 1942). Following the curricular re-
forms at secondary level of education, from 1928 on, a series of new standardized 
textbooks on logic started to emerge. In accordance with the new model, these 
textbooks apportioned a considerable part of their content to mathematical log-
ic—usually referred to as shuxue (de) lunlixue 數學(的)論理學. The first such sec-
ondary school textbook emerged in 1925. The book Logic (Lunlixue 論理學) was 
written by Wang Zhenxuan 王振瑄 (1928), a teacher at Peking Women’s Higher 
Normal College (Beijing nüzi gaodeng shifan xuexiao 北京女子高等師範學校). 
It was included in the semi-official series New Education System Senior Secondary 
School Textbooks (Xin xuezhi gaozhong jiaokeshu 新學制高中教科書), published by 
the Commercial Press. At this stage, the textbook had not yet offered an overview 
of the content mathematical logic, nor did it mention any results of Russell’s 
mathematical logic in the section on deduction. Nevertheless, mathematical log-
ic had already been included in the historical overview of development of both 
Western and Eastern logics (Chinese and Indian logic). A substantial step for-
ward was made in the standardized secondary school textbooks in the early 1930s. 
Thus, in 1935, Zhang Xizhi’s (張希之, ?) book Essentials of Logic (Lunlixue gang-
yao 論理學綱要) from 1932 was abridged and upgraded into a textbook, Senior 
Secondary School Logic (Gaozhong lunlixue 高中論理學). In 1935 it was reissued 
under the title Gaozhong xin biaozhun lunlixue 高中新標準論理學 (New Stand-
ard Logic for Senior Secondary Schools). Although Zhang’s earlier book had only 
briefly mentioned mathematical logic, the new one, published just three years lat-
er, already included an entire chapter devoted to the “contributions of new deduc-
tive method”. Aside from a historical introduction to the concept of mathematical 
logic, Zhang’s textbook also introduced the elementary concepts from Russell’s 
Introduction to Mathematical Philosophy and Principia Mathematica, in particular 
a few elementary notions from relational and propositional calculi, propositional 
functions, the Sheffer stroke and so on (Zhang Xizhi 1935, 198–221). Apart from 
28 In the 1933, 1936, and 1937 editions the structure and content of the course remained unaltered.
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230 Jan VRHOVSKI: Between Philosophy and Mathematics...
these concepts and principles, Zhang also extensively introduced Shen Youqian’s 
沈有乾 interpretation of Ladd-Franklin’s theory of syllogism together with his 
bagua-based notation. Zhang’s book was published in the New Standard Senior 
Secondary School Textbooks series with the Wenhua xueshe 文化學社 in Peking. 
Zhang’s introduction to mathematical logic for secondary schools was not su-
perseded by any new generation of Chinese textbooks. As a matter of fact, in the 
following years the trend to introduce mathematical logic slowly declined. In the 
new generation of textbooks, starting with Zhu Zhangbao’s 朱章寳 New Edition 
Senior Secondary School Logic (Xinbian gaozhong lunlixue 新編高中論理學) from 
1940, even though mathematical logic was still mentioned in the historical over-
view of logic, the section on “new deductive method” (yanyi xin fa 演繹新法) was 
reduced to a less technical introduction of contemporary symbolic logic. 
Normal Colleges and Universities
The implementation of early education system reforms in early 1930s brought 
similar curricular modifications to the general course on logic in the framework 
of national normal colleges. The document Curricular Standards for Normal Col-
leges from 193429 provides the following outline of the prescribed content of the 
course on logic (called “Lunlixue 論理學”): a) Analysis of Thought (with an em-
phasis on the ability to identify fallacies and the so-called truth-standards etc.); 
b) Essentials of the Scientific Method; c) Induction; d) Deduction: i) Deductive 
Systems; ii) Terms and Classes; iii) Propositions and Propositional Forms; iv) 
Exposition of Formal Deduction: 1) Aristotelian Logic and 2) New Method 
of Mathematical Logic (shuxue luoji 數學邏輯): (Calculus of Classes, Calculus 
of Propositions, Calculus of Propositional Functions (ci zhi hanshu 辭之函數). 
The course on logic was also cancelled from the basic curriculum for normal 
colleges, only a few years after it was removed from the secondary school cur-
ricula in 1946. In the early 1930s, introductory courses on logic (usually called 
“Lunlixue 論理學”) became a common component of the general curriculum 
for the first-year undergraduate students. Initially, these were elective courses, 
usually conducted by members of the departments of philosophy. As in the case 
of Qinghua University, the course of logic was offered as a part of a bundle of 
elective courses in science or humanities. Later, the status of logic at universities 
rose, as it became an independent mandatory course for all first-year students at 
national universities. 
29 See the Editorial Committee for Elementary and Secondary School Curricular Standards of the 
Ministry of Education (1934). 
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231Asian Studies X (XXVI), 2 (2022), pp. 209–241
Consequently, logic also became a topic of entrance exams, as well as general 
exams at the end of each academic year. The growing presence of logic in univer-
sity curricula also entailed a growing need for standard elementary and advanced 
textbooks on the subject. Following the reforms of the late 1920s, there was also 
an increase in the number of translations of Western textbooks on logic as well as 
textbooks written by various Chinese authors. Moreover, because mathematical 
logic became a synonym for contemporary logic, in the 1930s there was also a 
growing need for Chinese textbooks which would include mathematical or con-
temporary symbolic logic. Beside the most important textbooks, such as those 
written by Wang Dianji and Jin Yuelin, the late 1930s and early 1940s saw the 
publication of further textbooks written by young Chinese philosophers, which 
included at least a section devoted to modern logic. The first such noteworthy 
book was Shen Youqian’s short overview of Modern Logic (Xiandai luoji 現代邏
輯) from 1933, and the other was Mou Zongsan’s Logical Paradigms (Luoji di-
anfan 邏輯典範) from 1940.30 Throughout the 1920s and 1930s, translations of 
foreign works in modern logic kept emerging at a relatively steady pace. Even 
though already from the 1920s on a relative abundance of new Chinese publica-
tions on modern logic was available to Chinese readers and scholars, the evolution 
of standard material prescribed for elementary courses in logic at Chinese uni-
versities seems not to have followed the same developmental trajectory. Instead, 
lecturers in logic at more marginal universities kept prescribing already outdated 
Western textbooks, which did not include symbolic or mathematical logic at all. 
Often these universities tended to retain the earlier pragmatist approach towards 
teaching logic. Even at Qinghua, in 1933 the textbook on logic, which was pre-
scribed for the entrance examination and the general exam at the end of the year, 
was Wolf ’s Essentials of Logic from 1926.31 
On the other hand, the content of basic university courses on logic depended 
largely on the lecturers. A general view of Chinese universities in early 1930s 
reveals that sometimes the modern outlook of the course on logic was correlated 
to the lecturer’s affiliation with the Qinghua School of Philosophy. A solid exam-
ple of this would be Peking University, where Zhang Shenfu lectured on mathe-
matical logic. Another example was the newly founded Wuhan University, where 
contemporary logic was taught by Wan Zhuoheng 萬卓恆 a former student of 
Qinghua College (class of 1923) and the holder of a master’s in philosophy from 
Harvard. In 1930s and 1940s Wuhan University was known as one of the few 
Chinese universities where mathematical logic was taught both in the framework 
of the general course on logic and as a specialized course (advanced logic) at 
30 On Mou Zongsan’s early work related to modern logic, see Suter (2017); Vrhovski (2020).
31 See Qinghua daxue (1933).
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232 Jan VRHOVSKI: Between Philosophy and Mathematics...
the Department of Philosophy.32 Sometimes, however, the most important factor 
behind the development of more advanced courses on logic was, quite naturally, 
the lecturer’s familiarity with the subject, mostly through first-hand experience 
gained at Western universities. 
The educational background of lecturers also greatly influenced the selection of 
specialized elective courses, both at undergraduate and graduate levels, within 
the curricula at departments of philosophy across the country. Thus, for example, 
Qinghua’s status as the centre for mathematical logic in China was inextricably 
linked to Jin Yuelin’s pedagogical and scientific work as well as Zhang Shenfu’s 
intensive propagation of the notion of mathematical logic. In other words: a broad 
selection of lectures on logic was the first condition of development of the dis-
cipline of modern logic at the department, and more than on anything else this 
depended on the pedagogical effort of the lecturers and their efforts at the broader 
dissemination or popularization of this new subject of learning. 
According to documentary evidence and biographical material, by the early 1930s 
Chinese logicians’ efforts to popularize the notion of mathematical logic in China 
were extremely fruitful. Various indications speak in favour of this assumption, 
the most important of which was, of course, the inclusion of mathematical logic 
into secondary and normal curricula. At the university level, the education system 
reforms of the early 1930s materialized mainly in the establishment of a man-
datory general course in logic for all freshmen at universities. Apart from that 
mathematical logic became gradually recognized as an integral part of curricula at 
national philosophy departments. Although the levels of inclusion varied between 
historical overviews and concrete theoretical introductions, mathematical logic 
also became a specialized, selective course at some philosophical departments. 
However, this change did not occur overnight, because in the early 1930s math-
ematical logic was actually taught only at an extremely small number of Chinese 
universities, considerable efforts were needed to achieve its broader presence in 
Chinese academia. Thus the draft version of the document University Cours-
es (Daxue kemu 大學科目) from 1933, which enumerated the basic mandatory 
courses, still mentioned only the course “Logic” (Lunlixue).33 The original content 
32 Wan Zhuoheng is also mentioned in He Lin’s book Modern Chinese Philosophy (1947) as one of 
only a handful of Chinese experts in the field of mathematical logic. He’s recognizing Fan as a 
mathematical logician probably rested on his reputation as one of only few professors of logic, who 
attached great importance to the mathematical logic of Russell’s Principia Mathematica (see He 
Lin 1947, 31).
33 The booklet Draft of the University Courses (Daxue kemu caoan 大學科目草案), issued by the Chi-
nese Ministry of Education in 1933, also prescribed the basic literature for the course, namely 
the following two books: Josiah Royce’s “The Principles of Logic” (1913) and J. E. Creighton’s 
Azijske_studije_2022_2_FINAL.indd   232 5. 05. 2022   15:46:48
233Asian Studies X (XXVI), 2 (2022), pp. 209–241
was extended and upgraded in the revised version of the List of University Courses 
from 1940, which provided a list of both obligatory and selective courses. In this 
document (or possibly even earlier) “Mathematical Logic” was listed as the stand-
ard selective course for undergraduate programs in philosophy, prescribed to be 
taught in the fourth year of study (Ministry of Education 1940, 48).
Concluding Remarks
The above analysis reveals that the advances in Chinese studies of mathematical 
logic were represented, above all, by the so-called “Qinghua School of (Mathe-
matical) Logic”. In its earliest years, as the central Chinese platform for research 
on Russell’s philosophy and his Principia Mathematica, the Department of Phi-
losophy at Qinghua University defined the state of Chinese knowledge of the 
topic and at the same time assumed the role of the main disseminator of the 
Russellian notion of mathematical logic. To a certain degree, this early period of 
mathematical logic at Qinghua was epitomized by Jin Yuelin’s work Logic, while 
at the same time it also marked an important transition of the research interest of 
the members of the school towards developments in the framework of the Har-
vard School of Logic on one side, and trends in European mathematical logic on 
the other. Similarly, in the late 1930s the new generation of logicians at Qinghua 
University also assumed the leading role in raising Chinese research into the dis-
cipline to a new level. This final chapter of mathematical logic at Qinghua was 
defined by the introduction of more recent advances in European mathematical 
logic into the curriculum at the department. 
However, in the framework of the school of logic at Qinghua University math-
ematical logic was still deeply immersed in the context of philosophical studies, 
and consequently also generally explicated in a profoundly philosophical manner. 
Secondly, as a school of thought, the development of the Qinghua School was also 
strongly inclined towards particular theories and currents in mathematical logic, 
and therewith also more or less disassociated from specific other such theories. 
Thus, one example of a theory which was not at the centre of inquiries at Qin-
ghua was Hilbert’s formalist project, which also offered its own solution to the 
foundations of mathematical logic. The task of introducing Hilbertian formalism, 
Cantorian set theory and other topics from mathematical logic to Chinese schol-
ars was later assumed by a group of Chinese mathematicians headed by Tang 
Zaozhen, a professor at Wuhan University, and Zhu Gongjin, a mathematician 
An Introductory Logic (1919 edition). Both were also available in Chinese, and the translators were 
Tang Bohuang 唐擘黃 (Tang Yue 唐鉞, 1891–1987) and Liu Qi 劉奇, respectively. 
Azijske_studije_2022_2_FINAL.indd   233 5. 05. 2022   15:46:48
234 Jan VRHOVSKI: Between Philosophy and Mathematics...
who studied under Hilbert. The related developments which took place at Wuhan 
University and in the framework of the popularization and introduction of math-
ematical logic in mathematical journals can be described as a step in the direction 
of the mathematization of the notion of mathematical logic in China. Moreover, 
the research conducted by the leading figures in this movement, such as Tang 
Zaozhen and Xiao Wencan at Wuhan University, was profoundly different from 
the that conducted at Qinghua School, since the notion of mathematical logic 
as well as its content were regarded within the context of mathematics, and as a 
branch of mathematics closely related to the problems of its foundations. Based 
on its different conceptualization, the notion of mathematical logic produced 
through this important turn can be described as the current of the “mathematical 
notion” of mathematical logic. 
Finally, the degree of the establishment of the notion of mathematical logic in the 
more general intellectual discourse in late 1920s and 1930s China is further at-
tested by the inclusion of its content into the new, standardized secondary school 
and university curricula. In the context of the standardization and modernization 
of the logical curricula, the integration of content from mathematical logic as a 
most highly developed form of deductive logic reached its peak in the first half 
of the 1930s, when several new standard textbooks for secondary schools already 
included elementary concepts from Principia Mathematica and related works by 
Russell and others. Together with the rise of the notion of mathematical logic as 
the newest form of deductive logic a new terminology started to form, which pos-
sessed a strongly modern undertone. Although this distinction originated in the 
earliest introduction of the notion in the early 1920s, by the 1930s the difference 
between traditional and modern logic became expressed more uniformly in the 
terminology used to describe these two developmental stages in Western logic. 
On the other hand, the use of terminology in the 1930s also revealed an indirect 
influence of broader philosophical and political trends on logical terminology. 
An important influence was that of cultural relativism, which created the urge to 
differentiate the universal idea of logic from “culturally conditioned” evolutionary 
versions of logic, such as Indian, Chinese or Greek Aristotelian logic. When this 
first concerted attempt at standardizing logical terminology was completed in 
1939, some of these distinctions were still retained, while in the actual literature 
the terminological gaps remained considerable. For these as well as other reasons, 
a focused study of the shifts and changes in Chinese logical terminology in the 
1920s and 1930s is needed. 
Unfortunately, the development of mathematical logic in the years following the 
outbreak of the Sino-Japanese war is, due to circumstances of the time, very 
poorly documented. As a consequence, there is a wide and unsurmountable gap 
Azijske_studije_2022_2_FINAL.indd   234 5. 05. 2022   15:46:48
235Asian Studies X (XXVI), 2 (2022), pp. 209–241
in our understanding of the later parts of the trends and developments described 
above. In the end, however, with the profound changes that took place at the 
establishment of the PRC in 1949 the majority of these developments were 
brought to an abrupt end. In this way, our treatment of these early developments 
will serve as a basis for assessing the degree of discontinuity and change rather 
than the main basis for describing a general continuity in Chinese studies of 
mathematical logic. Moreover, a deeper insight into the developments of math-
ematical logic at Chinese universities during wartime, which probably brought 
the foremost experts in the field closer together than ever before and thus pro-
vided very favourable circumstances for the development of a more unitary or 
even interdisciplinary developmental trajectory, would also provide the missing 
narrative link between the period under examination in this article and the pro-
foundly disparate developments in the late 1940s and early 1950s. Since we are 
still unable to provide an adequate insight into the development in mathematical 
logic that took part under the fog of war which enveloped China between 1937 
and 1945, the present study represents the last still historically attainable fraction 
of its developmental path. 
Last but not least, perhaps the most indisputable dimension of continuity was 
retained through the key agents who contributed to the re-formation of math-
ematical logic in the first decade of the PRC, such as Hu Shihua, who obtained 
their basic training in the milieu of the Qinghua School (in the late 1920s and 
early 1930s its members lectured at all other leading Chinese universities), and 
whose work in mathematical logic was not sanctioned in the framework of the 
ideological transition that took place in Chinese academia in the early 1950s. 
Acknowledgment
The author acknowledges the financial support from the Slovenian Research 
Agency (ARRS) in the scope of the research project N6-0161 (Complementary 
scheme) Humanism in Intercultural Perspective: Europe and China.
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