Table Of ContentLogic in Asia: Studia Logica Library
Series Editors: Fenrong Liu · Hiroakira Ono · Kamal Lodaya
Peter van Emde Boas
Ghica van Emde Boas
Kaibo Xie
Bonan Zhao
Analyzing the
Logic of Sun Tzu in
“The Art of War”,
Using Mind Maps
Logic in Asia: Studia Logica Library
SeriesEditors
FenrongLiu,TsinghuaUniversityandUniversityofAmsterdam,Beijing,China
HiroakiraOno,JapanAdvancedInstituteofScienceandTechnology(JAIST),Ishikawa,Japan
KamalLodaya,Bengaluru,India
EditorialBoard
NatashaAlechina,UniversityofNottingham,Nottingham,UK
ToshiyasuArai,ChibaUniversity,ChibaShi,Inage-ku,Japan
SergeiArtemov,CityUniversityofNewYork,NewYork,NY,USA
MattiasBaaz,TechnicaluniversityofVienna,Austria,Vietnam
LevBeklemishev,InstituteofRussianAcademyofScience,Russia
MihirChakraborty,JadavpurUniversity,Kolkata,India
PhanMinhDung,AsianInstituteofTechnology,Thailand
AmitabhaGupta,IndianInstituteofTechnologyBombay,Mumbai,India
ChristophHarbsmeier,UniversityofOslo,Oslo,Norway
ShierJu,SunYat-senUniversity,Guangzhou,China
MakotoKanazawa,NationalInstituteofInformatics,Tokyo,Japan
FangzhenLin,HongKongUniversityofScienceandTechnology,HongKong
JacekMalinowski,PolishAcademyofSciences,Warsaw,Poland
RamRamanujam,InstituteofMathematicalSciences,Chennai,India
JeremySeligman,UniversityofAuckland,Auckland,NewZealand
KaileSu,PekingUniversityandGriffithUniversity,Peking,China
JohanvanBenthem,UniversityofAmsterdamandStanfordUniversity,TheNetherlands
HansvanDitmarsch,LaboratoireLorraindeRechercheenInformatiqueetsesApplications,
France
DagWesterstahl,StockholmUniversity,Stockholm,Sweden
YueYang,SingaporeNationalUniversity,Singapore
SyrayaChin-MuYang,NationalTaiwanUniversity,Taipei,China
LogicinAsia:StudiaLogicaLibrary
This book series promotes the advance of scientific research within the field of logic in
Asian countries. It strengthens the collaboration between researchers based in Asia with
researchersacrosstheinternationalscientificcommunityandoffersaplatformforpresent-
ingtheresultsoftheircollaborations.Oneofthemostprominentfeaturesofcontemporary
logic is its interdisciplinary character, combining mathematics, philosophy, modern com-
puterscience,andeventhecognitiveandsocialsciences.Theaimofthisbookseriesisto
provideaforumforcurrentlogicresearch,reflectingthistrendinthefield’sdevelopment.
The series accepts books on any topic concerning logic in the broadest sense, i.e., books
on contemporary formal logic, its applications and its relations to other disciplines. It
accepts monographs and thematically coherent volumes addressing important develop-
ments in logic and presenting significant contributions to logical research. In addition,
research works on the history of logical ideas, especially on the traditions in China and
India, are welcome contributions.
The scope of the book series includes but is not limited to the following:
(cid:129)
Monographs written by researchers in Asian countries.
(cid:129)
Proceedings of conferences held in Asia, or edited by Asian researchers.
(cid:129)
Anthologies edited by researchers in Asia.
(cid:129)
Research works by scholars from other regions of the world, which fit the goal of
“Logic in Asia”.
The series discourages the submission of manuscripts that contain reprints of previously
publishedmaterialand/ormanuscriptsthatarelessthan165pages/90,000wordsinlength.
Please also visit our webpage: http://tsinghualogic.net/logic-in-asia/background/
Relation withStudiaLogicaLibrary
ThisseriesispartoftheStudiaLogicaLibrary,andisalsoconnectedtothejournalStudia
Logica.ThisconnectiondoesnotimplyanydependenceontheEditorialOfficeofStudia
Logicaintermsofeditorialoperations,thoughtheseriesmaintainscooperativetiestothe
journal.
This book series is also a sister series to Trends in Logic and Outstanding Contributions
to Logic.
For inquiries and to submit proposals, authors can contact the editors-in-chief Fenrong
Liu at [email protected] or Hiroakira Ono at [email protected].
Peter van Emde Boas · Ghica van Emde Boas ·
Kaibo Xie · Bonan Zhao
Analyzing the Logic of
Sun Tzu in “The Art of War”,
Using Mind Maps
PetervanEmdeBoas GhicavanEmdeBoas
InstituteforLogic,LanguageandComputation Heemstede,TheNetherlands
UniversityofAmsterdam
Amsterdam,TheNetherlands BonanZhao
UniversityofEdinburgh
KaiboXie Edinburgh,UK
SchoolofHumanities
TsinghuaUniversity
Beijing,China
ISSN2364-4613 ISSN2364-4621 (electronic)
LogicinAsia:StudiaLogicaLibrary
ISBN978-981-19-6249-3 ISBN978-981-19-6250-9 (eBook)
https://doi.org/10.1007/978-981-19-6250-9
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSingaporePte
Ltd.2022
Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whetherthewhole
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Foreword
The book you have just opened is probably unlike anything you have ever
readsofar.Itoffersyouapathtodirectcontactwith“TheArtofWar”,the
masterpiece of Sun Tzu, a classical theorist of warfare in Ancient China. You
may even dimly know Sun Tzu quotes that have entered our cultural main-
stream, such as his famous claim that successful generals win their battles
before they even start.
Sun Tzu’s work was written in the middle of the first millennium BCE in
pre- unification China. In this period many vibrant states vied and fought
for power in a multi-centered political landscape that saw a proliferation of
creativephilosophicalschools,andofculturaldiversityandscientificachieve-
ment generally. But “The Art of War” also testifies to the elegant compact-
ness of classical Chinese, which pervaded and unified this diverse cultural
realm. The present book will introduce you to the content of Sun Tzu’s work
and the thinking behind it, bringing together military science, logic and lan-
guage, and to some extent, ancient Chinese culture.
War is a constant in human history, showing us at our most inhuman at
times, yet at other times in supreme acts of selfless courage, sacrifice, and
generosity. So much is at stake in war that a society learns by leaps and
bounds, and innovations emerge of every sort: from better technology to
better organization, and in Sun Tzu’s book: to deeper thinking. Thus,“The
ArtofWar”hasbeentranslatedtheworldover,makingitswayfromacademic
circles of scholars to the open competitive world of modern business. This
entry into a broader swath of society is not just a sideshow, since part of the
methodology of the present book comes precisely from the latter contact.
Sun Tzu’s book stands in a long tradition of thinking about the art of war.
Hellenistic and Roman authors wrote on the topic, so did medievals like
Machiavelli, and people like me even have their cherished Von Clausewitz on
their book-shelves, watching as I write the lines of this preface. But Sun Tzu
offers a unique perspective of reflection on the thinking behind warfare that
v
vi Foreword
adds a further dimension to this military literature. It stresses out-thinking
ratherthanoutfightingone’sopponents,presaging-withsomecreativepoetic
licence in reading the text - notions from epistemology and game theory that
only became clear in recent centuries.
Now over to the text lying before you. It was written by a unique team
consisting of a theoretical computer scientist, a practical computer scientist
operating in the business world, and two students of logic who also have
direct acquaintance with classical Chinese. I doubt that any such team has
ever attempted a task like this. The result of this collaboration is a striking
source book.
This book offers a totally new way of representing ancient texts, using ’mind
maps’. This visual tool for broad audiences, inspired by techniques in the
business world, highlights the main meaning structures of a text in a faith-
ful and illuminating manner. Using this method, the book then provides a
systematic compendium of the logical patterns of statement in the ancient
text (parallel, conditional, metaphorical, and so on) that reflect Sun Tzu’s
thinking. These are the building blocks for the further types of reasoning to
which“The Art of War”invites its readers. But there is more. You will also
find the approach taken in this book informative on the linguistic structure
of the classical Chinese language, since it contains careful discussions of how
to best fit the vocabulary of the Chinese text to the authors’ mind maps.
A word of explanation may be needed for the word ’logic’ in the title of this
book. This term has many meanings, from its ordinary language senses of
coherent structure and cogent argument to the technical senses of logicians
and computer scientists that involve formulas and sometimes run all the way
to automation and AI. In this book, ’logic’ mainly refers to the coherent
recurring patterns of statement identified by the authors in Sun Tzu’s text,
no mean task in itself. There is little further analysis in the book of the
reasoning that might be done with such patterns. The reason is that, on the
whole, “The Art of War”does not provide sustained chains of argument,
although the authors do identify where these might start.
Part I of this book explains the methodology employed by the authors, and
it is the part that you can read as a continuous narrative. I have not de-
scribed all its contents here, leaving you to discover other interesting themes
by yourself. Some game theory is brought to bear: the claim that Sun Tzu
discovered modern notions like higher levels of reasoning about others and
game-theoretic equilibria turns out to be under-supported by the text. Also,
a bit of embedding is provided of Sun Tzu’s thinking in the cultural outlook
oftheclassicalChinese,andsomenon-warfare-relatedtextualgemsin“The
Art of War”are highlighted. Parts II and III, containing the complete source
material, are a compendium of chapter-by-chapter analyses in parallel En-
glish and Chinese versions that you can consult as the interest or the need
strikes you. All parts taken together give a unique approach to Sun Tzu’s
Foreword vii
text, unlike existing translations or commentaries, bringing to life, as the au-
thors say, the rhythm and visual quality of the original. Thus, you will get
closetowhattheoriginaltextisactuallysaying,notobscuredbyacurtainof
stylistic adaptation, literary embellishment, or philosophical interpretation.
In laying out the material in this way, this book establishes a platform for
furtheruses.Youcanstrikeoutfromhereandengageindeeperlogicalanaly-
sis of the theory suggested by Sun Tzu’s work, make comparisons with other
historical authors on the art of war, link up with the linguistic study of clas-
sical Chinese, or, if none of these are your thing, apply the author’s mind
mapping and pattern search approach to other ancient texts than that of
Sun Tzu, and other topics than war.
The style employed in writing the present book is plain, direct and modest.
I think of it as partly academic, and partly speaking to common sense in
wider circles, in line with the outreach sought by the authors. Both academic
scholars in various fields and a more general audience should be able to get
something of value.
Finally, warfare reflects society and culture. I can only agree with what the
authorssaythemselves.Inbringingtheactualtextofthe“ArtofWar”closer
to us readers in their crisp new format, free from intrusive interpretations,
they do something more. They also bring us closer to the birth of reflective
thinking in ancient Chinese culture, which was to go on to produce so many
of the wonders of the world.
Netherlands, January 2022 Johan van Benthem
Johan van Benthem is University Professor, emeritus, University of Amsterdam,
Henry Waldgrave Stuart Professor, Stanford University (philosophy, CSLI),
Jin Yuelin Professor, Tsinghua University Beijing (philosophy)
and co-director, UvA-Tsinghua Joint Research Center in logic.
Preface
This is not a book about war. In this book we examine an ancient Chinese work on
strategy and warfare, written by Sun Tzu: The Art of War.
This famous work has been studied and translated many times before, from the per-
spectiveofhistory,militarystrategy,orbusinessstrategy.Somefamousquotesareeven
used for modern computer strategy games.
We look at Sun Tzu’s work from the perspective of logic, mathematics, and computer
science.Makinguseofcontemporarymindmapping methods,weshowhowlogiccanbe
extracted from this 2500 years old text. We believe that this has not been done before.
There are several reasons why you may be interested in this book. Perhaps you could
find some inspiration for new ways to look at old text. Maybe you want to have a fresh
look at the work of Sun Tzu from a new perspective: as a logician, as a linguist, as an
interested layman, or as a business person. We tried to make the methods we used to
be understandable and applicable to persons of many interests, and we tried to make
the diagrams that explain our methods as readable as possible. Nevertheless, you may
find that the fonts of some diagrams are almost too small to be readable. There is not
muchwecoulddoaboutit,beingboundtoasmallpapersize.Enlargedversionsofthe
major mind map diagrams can be found on our website [90].
What began as a not-so-serious exercise in mind mapping of chapter IV of The Art of
War for the purpose of preparing a chapter for the Handbook on the history of logic in
China [69],turnedouttobeaveryusefultooltodiscoverstructureandpatternsinthe
text. We developed the Text Tree Mind Map (TTMM) as a special kind of mind map,
whereawholesourcetextcanbeseenintwo-dimensionalform,andwhereitispossible
to preserve the order of the text.
Theoriginalgoalofthechapterinthehandbookwastoinvestigateconnectionsbetween
the ideas of Sun Tzu and (contemporary) logic, in particular, aspects related to game
theoryandtheoryofmind.Whenafirstdraftofthischapterwaspresentedatthethird
meetingontheHistoryofLogicalThoughtinChina,inapril2014inTianjin,oneofour
colleagues observed that Sun Tzu is actually a logic text.
At that time we considered this to be a curious observation. However, using the Mind
mappingtechniquesinthisproject,itbecameclearthatthetexthasalogicalstructure,
which is not well-preserved in the various translations. When we looked at the Chinese
text in addition to the English translation, as recommended by Prof. Fenrong Liu, it
turned out that the logical structure is even more prominent in the Chinese original.
ix
x Preface
This is the cause for the word logic in the title of this book. Of course there is more to
this title than that, we hope this will become clear later.
We continued our research for the first six chapters in The Art of War, which resulted
in a presentation at the conference The Making of the Humanities VII, 2018, and a
website, https://suntzu.squaringthecircles.com/, which shows all mind maps and
descriptions of the patterns for these chapters.
Thisbookexpandsontheworkfortheconferencein2018inseveralways.Itnowcovers
all chapters of Sun Tzu’s book. We made mind maps, not only of the English text, but
also of the Chinese text. We also did a thorough search for patterns, using the mind
maps. The Chinese mind maps were helpful in uncovering more patterns and finding
problems in the translation.
The major patterns we found using our mind mapping methods are: Enumerations,
Pairs of Opposites, and Metaphors. Conditional Sentences, or if-then-else type
sentences, can be categorized as a set of patterns.
Althoughwetriedtoconstructanexhaustivelistofthepatternsthatwefoundin“The
Art of War”, such an effort can never be complete and there can never be a complete
consensus about what we found. Especially, the area of Conditional Sentences could be
a subject of further scientific work.
The mind maps, which we defined and named as Text Tree Mind Maps, enable us to
bring back rhythm and visual structure of Sun Tzu’s book which is obscured in many
translations, because the translators tried to produce a narrative, instead of a literal
translation. We hope that mind mapping methods can inspire others to find new ways
of analyzing old text.
A new look at game theoretical aspects of Sun Tzu’s text is also part of this book,
although we consider this to be a good subject for further work, and therefore the
description is not complete.
Our work is based on a translation made by Lionel Giles [23] in 1910, and on compar-
isons with the original Chinese text [91] both taken from the Gutenberg project, which
provides old books and text without copyright to be freely used.
Thecreationofthisbookwasateameffortbyfourauthors,whereeachhadanessential
role:
Peteristhechief-scientistwhocontributedhisknowledgeaboutmathematics,theoretical
computer science, logic, and game theory.
Bonan contributed the idea of looking for patterns in the text of Sun Tzu, and she
described them. She also produced the Chinese versions of the mind maps.
Kaibo is responsible for topics related to ancient Chinese Logic and Linguistics. He
lookedatspecialChinesecharactersandthespeciallanguageconstructswheretheyare
used. Moreover, he contributed with a study about contradictions and its meaning in
Sun Tzu’s time.
WithBonan’sandKaibo’sknowledgeofclassicalChineseweuncoveredspeciallanguage
constructs and defined better translations.
TheideaofmakingmindmapsoriginatedfromGhica.ShealsoproducedtheLATEXsources
forthetextanddevelopedtoolsforcreatingauniformlookforthetextandmindmaps
in all chapters.
