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 uberdie 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 Godel

1956 Sugaku Kisoron (Foundation of Mathematics)

1962 Professor, Tokyo University of Education1963 Moved to Univ Illinois (-1992)

1971 Gendai Shugoron Nyumon (Introduction to modern settheory)

1972 Sugaku Kisoron no Sekai (The world of foundation ofmathematics)




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 andQuantum 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 andPhysics)

1986 Godel

1988 Shomeiron Nyumon (Introduction to Proof Theory) withYasugi Mariko

1990 Godel no Yume (Godel’s dream)




Even after he moved to UIUC from Tokyo U of Education in 1963, hetrained 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 ofphil. of sci community. Polish logic. Mereology. translations

Hilbert-Ackermann Gruntzuge der theoretische Logik(with TakeoJi-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 tomath education.

1954 Sugaku Josetu (Introduction to Mathematics, with YoshidaYoichi)

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 Education1955- Tokyo TechAuthor of items ”Foundation of Mathematics” and ”Set theory”Encyclopedic Dictionary of Mathematics: The Mathematical Societyof Japan (Kiyoshi Ito (ed.))

1966 Suri Ronrigaku Josetsu (Introduction to MathematicalLogic)

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 ofMathematics) 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.)SituationTheory 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 ModalLogic)

1968 Translation of Tractatus Logico-Philosophicus

1968 Gendai Ronrigaku (Modern Logic) with SakamotoHyakudai.

1979 Nihongo no Bunpo to Ronri (Grammer and Logic ofJapanese). Montague grammer applied to Japanese withintroduction to higher-order logic.

Shimizu Yoshio

1984 Kigo Ronrigaku (Symbolic Logic). Up to incompletenesstheorem.



Early 1990s : social situation

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



Textbooks before 2000s: translations

Translated textbooks mainly for 100-200-level-equivalent logiccourses

Quine (1959) Methods of Logic (Japanese translation byNakamura 1961)

Lemmon (1965) Beginning Logic (Japanese translation by Takeoand Asano 1973, reprinted in 2001)

Nolt-Rohatyn (1988) Scham’s outline of logic. (Japanesetranslation by Kachi and Saito, 1995-1996)

Jeffrey (1991 Reprinted 2004) Formal Logic (Japanesetranslation by Todayama 1997)

Barwise-Etchemendy Language, Proof and Logic : translation byOsawa-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 underinfluence 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) Maehara1992 Hosoi

Intermediate

1977 (reprinted 2006) Maehara1989 Hayashi1994 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 Criticalthinking 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 justnominal 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 logicpositions 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 2metalogic as a semester course 14metalogic plus incompleteness 2metalogic, 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 nologic course (Arizona)Teaching assistantship usually include training of teaching criticalthinking 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 oneintroductory course which teaches the basic notions of logic. Allstudents should be encouraged to take such a course. Thesecourses should include the following:

The informal notion of ”logically correct argument”.Informal strategies for producing logically correct arguments andcounterexamples to fallacious arguments.The propositional calculus as an example of a formal language,formal proofs, and the formalization of natural languagearguments.



ASL guideline 2004

Recommendations for beginning post-secondary education (cont’d)

All post-secondary institutions should offer at least oneintroductory course which teaches the basic notions of logic. Allstudents should be encouraged to take such a course. Thesecourses should include the following:

A discussion of the relationship of proof, truth, andcounterexamples, including a discussion of the SoundnessTheorem.The predicate calculus extension of propositional logic.At least an informal discussion of the Completeness Theorem, iftime permits.



ASL guideline 2004

Recommendations for advanced post-secondary educationInstitutions of higher learning should, in addition, offer a courseor (sequence of courses) which cover the following logic-relatedtopics.

Elementary facts about sets (up through basic facts aboutbinary relations, the diagonal method, the proof thatuncountable sets exist, and the basic properties of countablesets).Basic facts about inductive definitions and proofs by induction,of the kind that permeate logic.Propositional and Predicate Calculus (The formalization ofinformal argument, the axiomatic method in mathematics andscience).Semantics (truth and validity, definability, the SoundnessTheorem, the notion of consistency, the Gdel CompletenessTheorem).An introduction to model theory (at least the CompactnessTheorem for countable languages with an application or two).The Gdel Incompleteness Theorems, their philosophical andfoundational consequences.



ASL guideline 2004

Recommendations for advanced post-secondary education (cont’d)The course’s format, the instructor’s field, and the interests ofthe students and instructor will all influence the tone, thepresentation, the emphasis, and the choice of additional topics.The basic concerns and results of logic listed here, however, arerelevant 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 asequence of two or more courseswould depend on manyparameters: the backgrounds and abilities of students, thelength of the course, and the depth one wanted to go into thevarious topics, for example. These are matters which will haveto be settled at the local level.Beyond this core material, there is additional material whichshould be made available to all students.



ASL guideline 2004

Recommendations for advanced post-secondary education (cont’d)

Institutions of higher learning should also offer courses whichinclude the following material within their scope.

An introduction to proof theory (Natural Deduction, theGentzen Hauptsatz, Herbrand’s Theorem, for example).Some additional model theory (e.g., the Lowenheim-Skolemtheorems for countable languages, the decidability of the theoryof dense linear orderings, the non-expressibility of variousmathematical notions in first-order logic, non-standard modelsof arithmetic).Some additional set theory (some cardinal and ordinalarithmetic, a discussion of the axiom of choice).An introduction to computability theory (some machine modelof effective computability, Church’s Thesis; absolutelyunsolvable problems; the undecidability of validity).



ASL guideline 2004

Recommendations for advanced post-secondary education (cont’d)

Institutions of higher learning should also offer courses whichinclude the following material within their scope.

An introduction to other kinds of logic. Just which woulddepend on the interests of the faculty in question.Some examples include intuitionistic logic, higher-order logic,modal logic, temporal logic, infinitary logic, and substructurallogics.An introduction to uses of logic in computer science (e.g.,unification and the resolution method and their connections toPROLOG, and the λ-calculus and its connections to LISP inparticular 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 neededfor 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 everyphilosophy student

Philosophy of science has same problems



workshop 2009

Comments from questionnaire, mostly from graduate students andpostdocsWant connections to philosophy

want to learn not just technical skills but also applications andhistory of logic

It is not clear which part of logic relates to my own specializedfield

like to study history of logic as well as non-hand-wavingmathematical logic

Philosophical logic and philosophy of logic

history and background philosophical discussion behind logic

training of symbolizatoin of philosophical arguments of myspecialization area may be of interest



workshop 2009

Faculty comment from questionnaireActive learning or practice sessions desired

In my student days, there were few logic textbooks. No practicesessions. I just took notes and at only some occations Ianswered questions when I was pointed. Homework every weekor practice sessions will train students more.



workshop 2009

Faculty comment from questionnaireCurriculum

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



workshop 2009

from questionnaireWorkshops 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 oflogic are involved in their own field



A response

Tutorial on non-classical logic by Graham Priest, Kyoto February15-17, 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 forPhilosophers” (2011-2014)

Aim. development of a teaching material of advanced logic inJapanese.

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 logicPhilosophy, 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 coinductionRyota Akiyoshi (Keio) Reconsidering Gentzen’s consistencyproofYuko Murakami (Tohoku) Development of non-classical logicTakeshi Yamada (Tokyo) Concept of evidence in anti-realismTakuro 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 ofGraham Priest’s Towards non-being

Minao Kukita (Kyoto) ambiguity of description phrasesNaoya Fujikawa (Kyoto) Intensional transitive verbs in TowardsNon-being



PhilLogMath 1

Afternoon session: Ambiguity

Tetsuji Iseda (Kyoto) Statistical model and subjectiveprobability of ambiguous predicatesKengo Okamoto (Tokyo Met) Transitions, contextual variables,ignorability—Ambiguity from the point of dynamic hybrid logicShunsuke Yatabe (AIST) Ambiguity and limits: definability ofcoinductive objects in constructive naive set theory and itsconsequences



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 RadicalInquisitive 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 Doctorthesis on proof theoretic semantics (session in Japanese)Daisuke Bekki and Hiroko Ozaki (Ochanomizu University)Sub-directional Combinatory Logic (SDCL) and CategorialGrammarChung-chieh Shan (Cornell Unversity/ Tsukuba University)Interpreting generic statements in topological spaces”



PhilLogMath 4

theoretical linguistics, metaphysics and non-classical logicContinued to be in English

July 16 2012, Seiryo Kaikan

Wataru Uegaki (MIT) scalar implicatureTakashi Yagisawa (SCUN) possibilities beyond possible worldsTetsuhiro Kamide (Cyber University) An embedding-basedmethod 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 graduatestudents 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 noronrigaku nyumon ippo mae (Advanced introduction to logic forphilosophers)



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: Nomath in written entrance examination for Tohoku philosophy.



Tohoku 2012(Murakami)

Goal: understand (1) Putnam’s twin earth (2) Kripke’s rigiddesignator

basic model theory toward homomorphism and isomorphism ofstructures

possible world semantics of quantified modal logic

Putnam seemed OK. Rigid designator might have well required awhole 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 algebraicsemantics

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 withoutdepartment-level organization, such as statistics.Lack of course numbering system: no standard curriculum, noprerequisite 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 innatural science/math

most students learn those areas only for university entranceexamination for humanities:

most national universities: multiple choice test of math up tohigh school Math II (without differentiation/integration butintroduction) and introductory natural science.Tokyo and Kyoto are better as they have written exams of matheven for humanities and social science.private universities: math is required only in exceptional casesfor humanities.



cf. Ishiguro’s comments on British education

system

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



no need of philosophers any more?

Naturalization of philosophy. Methodology of individual science,mostly experimentalLogic as a tool of mathematicization of philosophy: it was theprogram 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 thefirst-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 CriticalThinking Nagoya University, Japan, 16 February 2013


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Logic Education for Philosophers: A Case in Japan

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