Alfred Tarski in Poland: New Translations and Background

Transcription

1 Joint Mathematics Meetings Association for Symbolic Logic Baltimore, Maryland January 2014 Alfred Tarski in Poland: New Translations and Background James T. Smith, Professor Emeritus San Francisco State University Joint work with Andrew and Joanna McFarland, of Płock, Poland

2 Alfred Teitelbaum ( ) 1924 PhD in logic, Warsaw University Name changes: 1921 Tajtelbaum 1924 Tarski Jobs scarce, particcularly for Jews

3 Until 1939 Tarski was a full-time Warsaw high-school teacher, and simultaneously part-time University researcher and lecturer in general courses, particularly for teachers. Tarski attained worldwide attention as a logician.

4 Tarski was stranded on a lecture tour in the US when the Nazis invaded Poland in After some hard years he became a professor at Berkeley and founded the world's leading program of logic research. He was the external examiner for my PhD at Regina in 1970.

5 New information will soon be available for you.

6 Three Goals Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement (1) Translate and provide background for some of Tarski's early work on geometry. With this, all his geometry is now in English. (2) Translate and provide background for all Tarski's work that remained only in Polish. Now, all his work is available in English, French, or German. (3) Update Steven Givant's 1986 Tarski bibliography.

7 Three Goals Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement (1) Translate and provide background for some of Tarski's early work on geometry. With this, all his geometry is now in English. (2) Translate and provide background for all Tarski's work that 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.

8 Three Goals Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement (1) Translate and provide background for some of Tarski's early work on geometry. With this, all his geometry is now in English. (2) Translate and provide background for all Tarski's work that remained only in Polish. Now, all his work is available in English, French, or German. (Including his first paper on truth!) (3) Update Steven Givant's 1986 Tarski bibliography.

9 Our book doesn t supplant the Fefermans' wonder ful biography of Tarski, but supplements it.

10 Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement Part ))))))))) Debut Geometry Teaching Contains )))))))))))))))))))))))))))))))))))) 1st paper: axiomatics of well-ordering Banach Tarski paper, etc. Materials for high-school students and teachers Supplement Ch. 15 Twelve assorted contributions Ch Update of 1986 bibliography Highlighted items discussed today.

11 Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement Section )))))) Ch. 2 For attention today )))))))))))))))))))))))))))))))))))))))) Tarski Axiomatics of well-ordering 15.1 Comment on...understanding deduction Łukasiewicz Tarski Concept of truth Ch Problems... Logic in educa Geometrja text tional materials

12 Cultural remarks Tarski s single axiom D for defining a well-ordered set <Z, R> : ( œ U f Z) ( =/ U (!a 0 U)(œ u 0 U) u R a )

13 Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement Section )))))) Ch. 2 For attention today )))))))))))))))))))))))))))))))))))))))) Tarski Axiomatics of well-ordering 15.1 Comment on...understanding deduction Łukasiewicz Tarski Concept of truth Ch Problems... Logic in educa Geometrja text tional materials

14 8 December 1924 Warsaw Philosophical Institute Jan Łukasiewicz, On a Certain Way of Understanding the Theory of Deduction, Przegląd filozoficzny 28 Listener s notes? (1935)

15 Game: Construct Boolean formulas with tiles. Construct proofs using 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" consistency proofs. Leśniewski: Here is a recursive definition of formula. This shows ( ) not needed.

16 Some Impact Łukasiewicz officially introduced Polish notation in Wff'n Proof game by Layman E. Allen based on the 1929 idea. Allen told me he hadn't known about the 1924 game. Reverse Polish notation now in common use.

17 Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement Section )))))) Ch. 2 For attention today )))))))))))))))))))))))))))))))))))))))) Tarski Axiomatics of well-ordering 15.1 Comment on...understanding deduction Łukasiewicz Tarski Concept of truth Ch Problems... Logic in educa Geometrja text tional materials

18 Presentations by Tarski Feb 20 Vienna University Basic concepts of metamathematics Mar 27 Warsaw Society of Sci. [same] Oct 28 Warsaw Phil. Institute Concept of true sentence Dec Lwów Polish Phil. Soc. Fund. concepts of methodology* Dec 15 Lwów Polish Phil.Soc. Concept of truth Dec 16 Lwów Polish Math. Soc. Definable sets f * Mar 21 Warsaw Society of Sci. Concept of truth Apr 15 Warsaw Phil. Institute Gödel's incompleteness theorem Translated in the new book *previously accessible

19 18 December 1930 Lwów Polish Philosophical Society Tarski s First Publication on Truth **

20 Alfred Tarski Early Work in Poland: Geometry and Teaching with a Bibliographic Supplement Section )))))) Ch. 2 For attention today )))))))))))))))))))))))))))))))))))))))) Tarski Axiomatics of well-ordering 15.1 Comment on...understanding deduction Łukasiewicz Tarski Concept of truth Ch Problems... Logic in educa Geometrja text tional materials

21 Tarski 14 exercises for exceptionally eager students Translated, partially solved in our new book Emphases: case-ridden arguments (9) - elimination (5)

22 1935 Tarski coauthored Geometry for the Third Gimnazjum Class Chwiałkowski, senior Schayer: recent Tarski student a translated here (44 pp.) Notable: stress on closed systems ( 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).

23 Thank you for your interest! Joanna & Andrew McFarland Witold Kozlowski (1919 ) Tarski s high-school student James T. Smith Professor Emeritus San Francisco State University