Alfred Tarski in Poland: New Translations and...

Joint Mathematics MeetingsAssociation for Symbolic Logic

Baltimore, Maryland17–18 January 2014

Alfred Tarski in Poland:New Translations and Background

James T. Smith, Professor EmeritusSan Francisco State University

Joint work with Andrew and Joanna McFarland, of Płock, Poland

Alfred Teitelbaum (1901–1983)

1924 PhD in logic,Warsaw University

Name changes:

1921—Tajtelbaum1924—Tarski

Jobs scarce, partic-cularly for Jews

Until 1939 Tarski was a

• full-time Warsaw high-schoolteacher, and simultaneously

• part-time University• researcher and• lecturer in general courses,

particularly for teachers.

Tarski attained worldwideattention as a logician.

Tarski was stranded on a lecturetour in the US when the Nazis in-vaded Poland in 1939.

After some hard years he becamea professor at Berkeley andfounded the world's leadingprogram of logic research.

He was the external examiner formy PhD at Regina in 1970.

New information willsoon be available foryou.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Three Goals

(1) Translate and provide background for some of Tarski'searly work on geometry.

With this, all his geometry is now in English.

(2) Translate and provide background for all Tarski's workthat remained only in Polish.

Now, all his work is available in English, French, or Ger-man.

(3) Update Steven Givant's 1986 Tarski bibliography.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Three Goals

(1) Translate and provide background for some of Tarski'searly work on geometry.

With this, all his geometry is now in English.

(2) Translate and provide background for all Tarski's workthat remained only in Polish.

Now, all his work is in English, French, or German. (Including his first paper on truth!)

(3) Update Steven Givant's 1986 Tarski bibliography.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Three Goals

(1) Translate and provide background for some of Tarski'searly work on geometry.

With this, all his geometry is now in English.

(2) Translate and provide background for all Tarski's workthat remained only in Polish.

Now, all his work is available in English, French, orGerman. (Including his first paper on truth!)

(3) Update Steven Givant's 1986 Tarski bibliography.

Our book doesn’t supplantthe Fefermans' wonderfulbiography of Tarski, but sup-plements it.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Part)))))))))

Contains))))))))))))))))))))))))))))))))))))

Debut 1st paper: axiomatics of well-ordering

Geometry Banach–Tarski paper, etc.

Teaching Materials for high-school students and teach-ers

Supplement Ch. 15 Twelve assorted contributionsCh. 16–18 Update of 1986 bibliography

Highlighted items discussed today.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Section))))))

For attention today))))))))))))))))))))))))))))))))))))))))

Ch. 2 Tarski 1921 . . . . . . . . Axiomatics of well-ordering

§15.1 Comment on . . . . . . . . . Understanding deductionŁukasiewicz 1925

§15.6 Tarski 1930–1931 . . . . . . . . . . . . Concept of truth

Ch.12–13

1931–1932 Problems . . . . . . . . . . Logic in educa-1935 Geometrja text tional materials

Cultural Tarski’s single axiom D for defining aremarks well-ordered set <Z, R>:–––––––

(œU f Z)( /= U | (›!a 0 U)(œu 0 U)¬ u R a)

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Section))))))

For attention today))))))))))))))))))))))))))))))))))))))))

Ch. 2 Tarski 1921 . . . . . . . . Axiomatics of well-ordering

§15.1 Comment on . . . . . . . . . Understanding deductionŁukasiewicz 1925

§15.6 Tarski 1930–1931 . . . . . . . . . . . . Concept of truth

Ch.12–13

1931–1932 Problems . . . . . . . . . . Logic in educa-1935 Geometrja text tional materials

8 December 1924WarsawPhilosophical Institute

Jan Łukasiewicz,

On a Certain Way ofUnderstanding theTheory of Deduction,

Przegląd filozoficzny 28

Listener’s notes?

(1935)

Game:

Construct Booleanformulas with tiles.

Construct proofsusing modus ponens

and substitution.

Łukasiewicz:• Deduction has to do with form,

not content.• Game should be expanded to

incorporate œ, ›.

Tarski:• This suggests the possibility

of "geometric" consistencyproofs.

Leśniewski:• Here is a recursive definition

of formula.• This shows ( ) not needed.

Some Impact

Łukasiewicz officiallyintroduced “Polish”

notation in 1929.

1962 Wff'n Proof game byLayman E. Allen basedon the 1929 idea.

Allen told me he hadn'tknown about the1924 game.

“Reverse Polish” notation now in common use.

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Section))))))

For attention today))))))))))))))))))))))))))))))))))))))))

Ch. 2 Tarski 1921 . . . . . . . . Axiomatics of well-ordering

§15.1 Comment on . . . . . . . . . Understanding deductionŁukasiewicz 1925

§15.6 Tarski 1930–1931 . . . . . . . . . . . . Concept of truth

Ch.12–13

1931–1932 Problems . . . . . . . . . . Logic in educa-1935 Geometrja text tional materials

1930–1931 Presentations by Tarski

Feb 20 Vienna University Basic concepts ofmetamathematics

Mar 27 Warsaw Society of Sci. [same]Oct 28 Warsaw Phil. Institute Concept of true

sentenceDec10–13

Lwów Polish Phil. Soc. Fund. concepts ofmethodology*

Dec 15 Lwów Polish Phil.Soc. Concept of truthDec 16 Lwów Polish Math. Soc. Definable sets f *Mar 21 Warsaw Society of Sci. Concept of truthApr 15 Warsaw Phil. Institute Gödel's incomplete-

ness theorem

Translated in the new book *previously accessible

18 December 1930 Lwów Polish Philosophical SocietyTarski’s First Publication on Truth

**

Alfred TarskiEarly Work in Poland: Geometry and Teaching

with a Bibliographic Supplement

Section))))))

For attention today))))))))))))))))))))))))))))))))))))))))

Ch. 2 Tarski 1921 . . . . . . . . Axiomatics of well-ordering

§15.1 Comment on . . . . . . . . . Understanding deductionŁukasiewicz 1925

§15.6 Tarski 1930–1931 . . . . . . . . . . . . Concept of truth

Ch.12–13

1931–1932 Problems . . . . . . . . . . Logic in educa-1935 Geometrja text tional materials

1930–1932 Tarski |14 exercises forexceptionally eagerstudents

Translated, partiallysolved in our new book

Emphases:• case-ridden arguments (9)• ›-elimination (5)

1935 Tarski coauthored

Geometry for the Third GimnazjumClass

Chwiałkowski, seniorSchayer: recent Tarski student

a translated here (44 pp.)

Notable: stress on closedsystems ( Hauber's Law),| Tarski's famous 1936 logic text.

If (A1 6 B1) & (A2 6 B2)& (A1 w A2) & ¬(B1 & B2)

then (A1 7 B1) & (A2 7 B2) .

Joanna & Andrew McFarlandWitold Kozlowski (1919– )Tarski’s high-school student

Thank you foryour interest!

James T. SmithProfessor EmeritusSan Francisco State University