Logic Education for Philosophers: A Case in Japan

Logic education for philosophers: a case in Japan

Logic education for philosophers: a case in
Japan

Yuko Murakami
Tohoku University

December 13, 2012

Yuko Murakami (Tohoku University) December 13, 2012 1 / 69

Logic education for philosophers: a case in Japan Backgrounds

Logic tradition in Japan: Ono Katudi

Ono Katudi (1909-2001)
Ono wrote the ﬁrst logic paper as Japanese: Untersuchungen uber
¨
die Grundlagen der Mathematik, J. Fac. Sci. Univ. Tokyo, Sect. I 3,
329-389 (1938).
It was reviewed by Gentzen and MacLane.
taught at Shizuoka and Nagoya: still strong in logic



Logic tradition in Japan: Takeuti Gaishi

Takeuti Gaishi (1926-): colleague and friend of G¨del
o
1956 Sugaku Kisoron (Foundation of Mathematics)
1962 Professor, Tokyo University of Education
1963 Moved to Univ Illinois (-1992)
1971 Gendai Shugoron Nyumon (Introduction to modern set
theory)
1972 Sugaku Kisoron no Sekai (The world of foundation of
mathematics)




1975 Proof Theory
1978 So, Ken, Topos (Sheaf, Category, and Topos)
1980 Chokkan shugi teki Shugoron (Intuitionistic set theory)
1981 Senkei Daisu to Ryosirikigaku (Linear algebra and
Quantum Mechanics)




More philosophical?
1982 Sugaku teki Sekai Kan (A mathematical worldview)
1983 Lee daisu to Soryusiron (Lee algebra and Particle theory)
1985 Mugen Sho Kaiseki to Butsurigaku (Inﬁnitesimal and
Physics)
1986 G¨del
o
1988 Shomeiron Nyumon (Introduction to Proof Theory) with
Yasugi Mariko
1990 G¨del no Yume (G¨del’s dream)
o o




Even after he moved to UIUC from Tokyo U of Education in 1963, he
trained many Japanese logicians, including
Takahashi (Horai) Masako
Yasugi Mariko
Okada Mitsuhiro (Mitsu)
Proof theory became the mainstream of logic in Japan



Logic tradition in Japan: Ishimoto Arata

Ishimoto Arata (1917-) Tokyo Tech. (1968-1991) Logic leader of
phil. of sci community. Polish logic. Mereology. translations
Hilbert-Ackermann Gruntz¨ge der theoretische Logik(with Takeo
u
Ji-ichiro)
Reichenbach Elements of symbolic logic
Lemmon Introduction to axiomatic set theory
1965 Kyoto U. part-time lecturer.



Logic tradition in Japan: Seki Setsuya
Seki Setsuya (1926-) One of early logicians in Japan. later shifted to
math education.
1954 Sugaku Josetu (Introduction to Mathematics, with Yoshida
Yoichi)
1955 Kisoron (Foundation)
1956 Kori (Axioms)
1957 Shugo-ron Nyumon (Introduction to Set Theory)
1958 Kakuritu ron Nyumon (Introduction to Probability theory)
Yoshida Natsuhiko (1928-) Hokkaido U, Tokyo Tech.
One of importers of logical positivism
1955 Translation of Ayer Language, Truth and Logic
1958 Ronrigaku (Logic)



Logic tradition in Japan: Maehara Shoji
Maehara Shoji (1927-1992)
1938- Tokyo University of Education
1955- Tokyo Tech
Author of items ”Foundation of Mathematics” and ”Set theory”
Encyclopedic Dictionary of Mathematics: The Mathematical Society
of Japan (Kiyoshi Ito (ed.))
1966 Suri Ronrigaku Josetsu (Introduction to Mathematical
Logic)
1967 Kigo Ronri Nyumon (Introduction to Symbolic Logix)
Reprinted in 2005
1968-1969 Translation of Bourbaki Set Theory
1973 Suri Ronrigaku (Mathematical Logic)
1977 Sugaku Kisoron Nyumon (Introduction to Foundation of
Mathematics) Reprinted in 2006


Logic tradition in Japan: Algebraic and Relevant
logic

Relevant logics, logical operations: Hirokawa Sachio (Kyushu),
Komori Yuichi (Chiba)
Modal logic: Sugihara Takeo (Fukui U), Suzuki (Shizuoka)



Stanford Connection

not just philosophy but linguistics and cognitive science
Japanese visiting scholars at CSLI: Nakatogawa, Tutiya, Harada,
Ishikawa, Irifuji...
Researcher Kameyama
Ph.D.s Kanazawa (NII) Shirahata (Keio)
publication Barwise-Gawron-Plotkin-Tutiya (eds.)Situation
Theory and its Applications: Volume 2 (1991)


Logic education for philosophers: a case in Japan Textbooks and curriculums

logic textbooks in late 1980s
Sakai Hidehisa (1934-1994): active until mid-1980s
1965 Yoso Ronri ni kansuru Ichi Kosatu (An Essay on Modal
Logic)
1968 Translation of Tractatus Logico-Philosophicus
1968 Gendai Ronrigaku (Modern Logic) with Sakamoto
Hyakudai.
1979 Nihongo no Bunpo to Ronri (Grammer and Logic of
Japanese). Montague grammer applied to Japanese with
introduction to higher-order logic.
Shimizu Yoshio
1984 Kigo Ronrigaku (Symbolic Logic). Up to incompleteness
theorem.



Early 1990s : social situation

Cliche: that Japanese are not logical. Such a claim was heard almost
every day on major newspapers
Hide Ishiguro and Mitsu Okada came back to Tokyo (Keio U)



Textbooks before 2000s: translations
Translated textbooks mainly for 100-200-level-equivalent logic
courses
Quine (1959) Methods of Logic (Japanese translation by
Nakamura 1961)
Lemmon (1965) Beginning Logic (Japanese translation by Takeo
and Asano 1973, reprinted in 2001)
Nolt-Rohatyn (1988) Scham’s outline of logic. (Japanese
translation by Kachi and Saito, 1995-1996)
Jeﬀrey (1991 Reprinted 2004) Formal Logic (Japanese
translation by Todayama 1997)
Barwise-Etchemendy Language, Proof and Logic: translation by
Osawa-Nakagawa-Nakatogawa (Hokudai group) 2006



Textbooks in 1990s-2000s: original textbooks

Ono, H. (1994) Joho Kagaku ni okeru Ronri (Logic in Informatics)
One of the best logic textbook.
Ono, H. (1994) Joho Daisu (Algebra for Informatics)



Textbooks in 1990s-2000s: original textbooks

Noya(1997) Ronri training
exercise book (2001), new version (2006)
Flow chart analysis of logical connections of a paragraph under
inﬂuence of Nolt-Rohatyn



Textbooks in 1990s-2000s

Todayama Ronrigaku wo Tsukuru (To make logic)
focuses on FoL, but mentions modal and intuitionistic logic
(frustrated by other textbooks?)



Textbooks in 1990s-2000s

List of textbooks of mathematical logic (Kamo Hiroyasu)
Introductory
1967 (reprinted 2005) Maehara
1992 Hosoi
Intermediate
1977 (reprinted 2006) Maehara
1989 Hayashi
1994 Ono
Advanced
1988 (reprinted 2010) Takeuti-Yasugi Shomeiron Nyumon
(Introduction to Proof Theory)



Logic in other communities

Critical thinking in English education as well as debate Critical
thinking in psychology
Critical Shinkaron (comics)
Logic in jurisprudence; Need communication. (e.g. Faculty of Law,
Kanazawa U.)


Logic education for philosophers: a case in Japan activities in academic associations

logic education workshops, PSSJ

Philosophy of Science Society, Japan (Katetsu)
Organizers: Nakatogawa, Iida
1993 Overview of logic education
1994 Logic in ﬁrst-year
1995 Logic education software
1999 Japanese language and logic


Logic education for philosophers: a case in Japan activities in academic associations

Murakami (1998)

Why importing American logic education is irrelevant in Japan
System in higher education: lack of practice sessions due to just
nominal TA system
Number of faculty members in a single philosophy department


Logic education for philosophers: a case in Japan Social factors

higher education policy change

1992 Liberal art education became non-mandatory, while logic
positions were mostly in liberal art

Logic positions in philosophy departments.
National U: only in Hokkaido U. Fujimoto, Noya, Nakatogawa.
Public: Tokyo Metropolitan U
Private: Keio, Waseda


Logic education for philosophers: a case in Japan Social factors

2000s: under economic depression

Social demands to higher education
reasoning skills, communication skills
non-subject examinations
PISA
Critical thinking courses became popular


Logic education for philosophers: a case in Japan ASL questionnaire

ASL report (Zach 2004)

37 answers from top 50 US universities
average number of faculty members w AOS logic: 3.83
average number of logic courses (regularly oﬀered): 4.81



Curriculum contents

crithical thinking: UG 9, G 0
formalization (no metalogic) UG 18, G 11
metalogic (up to completeness) UG 0, G21
formalization and completeness 2
metalogic as a semester course 14
metalogic plus incompleteness 2
metalogic, incompleteness, computability as a semester course 3
modal logic G5
set theory G1
formal semantics G3
seminar G1



notes

Only one university can obtain a degree in philosophy with taking no
logic course (Arizona)
Teaching assistantship usually include training of teaching critical
thinking and formalization



US standard of minimal logic skills of philosophers

introductory metalogic
pedagogy of critical thinking and formalization



ASL guideline 2004

Recommendations for beginning post-secondary education
All post-secondary institutions should oﬀer at least one
introductory course which teaches the basic notions of logic. All
students should be encouraged to take such a course. These
courses should include the following:
The informal notion of ”logically correct argument”.
Informal strategies for producing logically correct arguments and
counterexamples to fallacious arguments.
The propositional calculus as an example of a formal language,
formal proofs, and the formalization of natural language
arguments.



ASL guideline 2004

Recommendations for beginning post-secondary education (cont’d)
All post-secondary institutions should oﬀer at least one
introductory course which teaches the basic notions of logic. All
students should be encouraged to take such a course. These
courses should include the following:
A discussion of the relationship of proof, truth, and
counterexamples, including a discussion of the Soundness
Theorem.
The predicate calculus extension of propositional logic.
At least an informal discussion of the Completeness Theorem, if
time permits.



ASL guideline 2004
Recommendations for advanced post-secondary education
Institutions of higher learning should, in addition, offer a course
or (sequence of courses) which cover the following logic-related
topics.
Elementary facts about sets (up through basic facts about
binary relations, the diagonal method, the proof that
uncountable sets exist, and the basic properties of countable
sets).
Basic facts about inductive definitions and proofs by induction,
of the kind that permeate logic.
Propositional and Predicate Calculus (The formalization of
informal argument, the axiomatic method in mathematics and
science).
Semantics (truth and validity, definability, the Soundness
Theorem, the notion of consistency, the Gdel Completeness
Theorem).


ASL guideline 2004
Recommendations for advanced post-secondary education (cont’d)
The course’s format, the instructor’s ﬁeld, and the interests of
the students and instructor will all inﬂuence the tone, the
presentation, the emphasis, and the choice of additional topics.
The basic concerns and results of logic listed here, however, are
relevant and applicable to many areas of science and scholarship,
and should be considered within the core of logic.
Whether this core material should be covered in one course or a
sequence of two or more courseswould depend on many
parameters: the backgrounds and abilities of students, the
length of the course, and the depth one wanted to go into the
various topics, for example. These are matters which will have
to be settled at the local level.
Beyond this core material, there is additional material which
should be made available to all students.


ASL guideline 2004
Institutions of higher learning should also offer courses which
include the following material within their scope.
An introduction to proof theory (Natural Deduction, the
Gentzen Hauptsatz, Herbrand’s Theorem, for example).
Some additional model theory (e.g., the L´wenheim-Skolem
o
theorems for countable languages, the decidability of the theory
of dense linear orderings, the non-expressibility of various
mathematical notions in first-order logic, non-standard models
of arithmetic).
Some additional set theory (some cardinal and ordinal
arithmetic, a discussion of the axiom of choice).
An introduction to computability theory (some machine model
of effective computability, Church’s Thesis; absolutely
unsolvable problems; the undecidability of validity).


ASL guideline 2004

Institutions of higher learning should also offer courses which
include the following material within their scope.
An introduction to other kinds of logic. Just which would
depend on the interests of the faculty in question.
Some examples include intuitionistic logic, higher-order logic,
modal logic, temporal logic, infinitary logic, and substructural
logics.
An introduction to uses of logic in computer science (e.g.,
unification and the resolution method and their connections to
PROLOG, and the λ-calculus and its connections to LISP in
particular and computation in general).



notes

Category theory and other contents may be adequate nowadays
uniﬁed approach to substructural logics are necessary
More background knowledge in mathematics absolutely needed
for philosophy students


Logic education for philosophers: a case in Japan toward current project

A proposal and trials

Murakami (2009) proposal on logic in philosophy education
critical thinking
formalization
introductory metalogic
Turing machine, incompleteness
proof theory
non-classical logics
remedial of mathematics



workshop 2009

Workshop (2009): How to train philosophers as heavy users of logic?
What about logic should philosophers know in 2030?



workshop 2009

From discussion
PSSJ should encourate information sharing
A roadmap needed: what to learn before grad school admission
Career paths of philosophers and logicians should be discussed
Critical thinking should become a required course for every
philosophy student
Philosophy of science has same problems



workshop 2009
Comments from questionnaire, mostly from graduate students and
postdocs
Want connections to philosophy
want to learn not just technical skills but also applications and
history of logic
It is not clear which part of logic relates to my own specialized
ﬁeld
like to study history of logic as well as non-hand-waving
mathematical logic
Philosophical logic and philosophy of logic
history and background philosophical discussion behind logic
training of symbolizatoin of philosophical arguments of my
specialization area may be of interest


workshop 2009

Faculty comment from questionnaire
Active learning or practice sessions desired
In my student days, there were few logic textbooks. No practice
sessions. I just took notes and at only some occations I
answered questions when I was pointed. Homework every week
or practice sessions will train students more.



workshop 2009

Faculty comment from questionnaire
Curriculum
There is no connection between logic education and math
education. We should have been taught ﬁrst-order logic before
analysis in the ﬁrst-year of college [i.e. real-number analysis,
which requires the ϵ − δ argument]



workshop 2009

from questionnaire
Workshops and tutorials
72 percent (34) of answers want tutorials.
26 like non-classical logics, 21 like set theory
3-day intensive session a year is popular



workshop 2009

Observations
Graduate students have little idea which skills and knowledge of
logic are involved in their own ﬁeld



A response

Tutorial on non-classical logic by Graham Priest, Kyoto February
15-17, 2010
Day 1. Modal logic.
Day 2. Conditionals and Intuitionistic logic
Day 3. Many-valued logic.



PJ: advanced logic for philosophers

JSPS Grant-in-aid Project ”Promotion of Advanced Logic for
Philosophers” (2011-2014)
Aim. development of a teaching material of advanced logic in
Japanese.
review trends in logic via colloquium
test runs of advanced logic courses


Logic education for philosophers: a case in Japan Kaken project: PhilLogMath

PhilLogMath

Aim: Trend review of logic
Philosophy, Logic and Mathematics (Linguistics too)
Day-long seminars on logic in Tokyo and Kyoto



PhilLogMath 0

As a satellite workshop of PSSJ
November 11 2011, Osaka University
Shunsuke Yatabe (AIST) Yablo’s paradox and coinduction
Ryota Akiyoshi (Keio) Reconsidering Gentzen’s consistency
proof
Yuko Murakami (Tohoku) Development of non-classical logic
Takeshi Yamada (Tokyo) Concept of evidence in anti-realism
Takuro Onishi (Kyoto) How to ﬁnd logical rules



PhilLogMath 1

First workshop in Tokyo
November 21 2011, Seiryo Kaikan
Morning session: celebrating publication of the translation of
Graham Priest’s Towards non-being
Minao Kukita (Kyoto) ambiguity of description phrases
Naoya Fujikawa (Kyoto) Intensional transitive verbs in Towards
Non-being



PhilLogMath 1

Afternoon session: Ambiguity
Tetsuji Iseda (Kyoto) Statistical model and subjective
probability of ambiguous predicates
Kengo Okamoto (Tokyo Met) Transitions, contextual variables,
ignorability—Ambiguity from the point of dynamic hybrid logic
Shunsuke Yatabe (AIST) Ambiguity and limits: deﬁnability of
coinductive objects in constructive naive set theory and its
consequences



PhilLogMath 2

Shift to an international workshop
March 14, 2012, Seiryo Kaikan
Takuro Onishi (Kyoto) ”BHK-interpretation and Bilateralism”
Katsuhiko Sano (JAIST) ”An ‘Impossibility’ Theorem in Radical
Inquisitive Semantics”
Masahiko Sato (Kyoto) ”Bootstrapping Mathematics”
Richard Dietz (Tokyo) ”Comparative Concepts”
Conrad Asmus (JAIST) ” Vagueness and Revision Sequences”



PhilLogMath 3

Linguistics included
May 17 2012, Seiryo Kaikan
”Author meets Critics” meeting on Takuro Onishi’s Doctor
thesis on proof theoretic semantics (session in Japanese)
Daisuke Bekki and Hiroko Ozaki (Ochanomizu University)
Sub-directional Combinatory Logic (SDCL) and Categorial
Grammar
Chung-chieh Shan (Cornell Unversity/ Tsukuba University)
Interpreting generic statements in topological spaces”



PhilLogMath 4

theoretical linguistics, metaphysics and non-classical logic
Continued to be in English
July 16 2012, Seiryo Kaikan
Wataru Uegaki (MIT) scalar implicature
Takashi Yagisawa (SCUN) possibilities beyond possible worlds
Tetsuhiro Kamide (Cyber University) An embedding-based
method for non-classical logics



Lessons so far from PhilLogMath

The workshop series has its model— Logic seminar in Indiana
Presentation or attendance should give one of goals for graduate
students in the related areas?
Linguistics should be emphasized more?
Philosophical talks?


Logic education for philosophers: a case in Japan Kaken project: Course practice

advanced undergraduate and graduate

Kyoto (Yatabe)
Tohoku 2011 (Murakami)
Tohoku 2012 (Murakami)
Kyoto CAPE seminar 2012 (Yatabe and Murakami)



Kyoto(Yatabe)

One-year course covering
Proof theory
Minimal logic
Getting popular!



Tohoku (Murakami)

Based on ideas outlined in Murakami (2010) Tetsugaku no tame no
ronrigaku nyumon ippo mae (Advanced introduction to logic for
philosophers)



Tohoku 2011(Murakami)

Goal: To understand Ishiguro’s inﬁnitesimal interpretation of Leibniz
FOL completeness
Skolem theorem
existence of non-standard model
Result: spent too much time on remedial mathematics. FOUND: No
math in written entrance examination for Tohoku philosophy.



Tohoku 2012(Murakami)

Goal: understand (1) Putnam’s twin earth (2) Kripke’s rigid
designator
basic model theory toward homomorphism and isomorphism of
structures
possible world semantics of quantiﬁed modal logic
Putnam seemed OK. Rigid designator might have well required a
whole semester...



Kyoto CAPE

Short course: 1.5-hour lectures, 4 times
Yatabe 1 proof theory: substructural logic and hypersequents
Yatabe 2 theory of truth on non-classical logics
Murakami 1 modal logic: from relational semantics to algebraic
semantics
Murakami 2 algebraic logic



ﬁndings

Need a full-semester or year-long course even for a single topic
No prerequisite system.
How to make it teacher-proof?
Kyoto students have better math skills?



Next plans

Credit-awarding course at Kyoto
Kyoto CAPE 2013: graduate-level logic course (Yatabe,
Murakami)
Possibilities of other forms
Open University, Tokyo Met U.: Matsuzaka et al.



analysis

Institutional problems
budgetary-personnel problems
academic problems



institutional problems and budgetary problems

Such problems are not specific to logic but common to fields without
department-level organization, such as statistics.
Lack of course numbering system: no standard curriculum, no
prerequisite description. Transfer is exceptional.
Few universities offer sound classes of logic.



Logic speciﬁc problems?

Training of philosophers of science has common problems
interdisciplinary area which requires knowledge and skills in
natural science/math
most students learn those areas only for university entrance
examination for humanities:
most national universities: multiple choice test of math up to
high school Math II (without diﬀerentiation/integration but
introduction) and introductory natural science.
Tokyo and Kyoto are better as they have written exams of math
even for humanities and social science.
private universities: math is required only in exceptional cases
for humanities.



cf. Ishiguro’s comments on British education
system

”I am sorry for those excellent philosophers not to have a chance to
learn mathematics after they chose their subjects when they were 11
years old in a grammar school. They did not even know much about
elementary calculus. I really appreciate Japanese education after
WWII, where even girls learnt mathematics!”



no need of philosophers any more?

Naturalization of philosophy. Methodology of individual science,
mostly experimental
Logic as a tool of mathematicization of philosophy: it was the
program of analytic philosophy


Logic education for philosophers: a case in Japan Situation changing

online

massive open online course (MOOC).
COURSERA does not oﬀer a transcript in Japanese for courses of the
ﬁrst-year courses, but it is possible in a few years.
English as teaching language?



who should oﬀer basic training for professionals?

University or academic associations?
can the organization oﬀer advanced courses?
sustainability of part-time lecturer system



Should logic stay in philosophy? If yes, how?

Already shifted to CS/mathematics?
What research areas of philosophy require logic?
historical investigation of philosophy of logic and others, i.e.
analytic philosophy of the 20th century
philosophical logic
foundation of mathematics, or philosophy of mathematics
any others?



Future of philosophers with logical skills

academic writing centers: a possible career option of philosophers?
International Symposium on Academic Writing and Critical
Thinking Nagoya University, Japan, 16 February 2013


Logic Education for Philosophers: A Case in Japan

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