The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland

235 Pages·2014·1.97 MB·English

by  Roman Murawski (auth.)

Science Networks
Historical Studies
48
Roman Murawski
The Philosophy
of Mathematics
and Logic in the
1920s and 1930s
in Poland
Science Networks. Historical Studies
Science Networks. Historical Studies
Founded by Erwin Hiebert and Hans Wußing
Volume 48
Edited by Eberhard Knobloch, Helge Kragh and Volker Remmert
Editorial Board:
K. Andersen, Amsterdam R. Halleux, Liège
H.J.M. Bos, Amsterdam S. Hildebrandt, Bonn
U. Bottazzini, Roma D. Kormos Buchwald, Pasadena
J.Z. Buchwald, Pasadena Ch. Meinel, Regensburg
K. Chemla, Paris J. Peiffer, Paris
S.S. Demidov, Moskva W. Purkert, Bonn
M. Folkerts, München D. Rowe, Mainz
P. Galison, Cambridge, Mass. Ch. Sasaki, Tokyo
I. Grattan-Guinness, London R.H. Stuewer, Minneapolis
J. Gray, Milton Keynes V.P. Vizgin, Moskva
Roman Murawski
The Philosophy of
Mathematics and Logic
in the 1920s and 1930s
in Poland
Translated from Polish by Maria Kantor
RomanMurawski
FacultyofMathematicsandComputerScience
AdamMickiewiczUniversity
Poznan´,Poland
Translator
Maria Kantor
Jagiellonian University
Kraków,Poland
ThetranslationhasbeenfundedbytheFoundationforPolishScience.
ISSN1421-6329 ISSN2296-6080(electronic)
ISBN978-3-0348-0830-9 ISBN978-3-0348-0831-6(eBook)
DOI10.1007/978-3-0348-0831-6
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Dedicated to
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.
Contents
1 Predecessors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 JanS´niadecki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Jo´zefMariaHoene-Wron´ski. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 HenrykStruve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 WładysławBiegan´ski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 SamuelDickstein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 EdwardStamm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 ThePolishSchoolofMathematics. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 WarsawSchoolofMathematics:Sierpin´ski,Janiszewski,
Mazurkiewicz. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 27
2.2 LvovSchoolofMathematics:Steinhaus,Banach,
Z˙ylin´ski,Chwistek. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Lvov-WarsawSchoolofPhilosophy. . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 KazimierzTwardowski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 JanŁukasiewicz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 ZygmuntZawirski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4 StanisławLes´niewski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5 TadeuszKotarbin´ski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.6 KazimierzAjdukiewicz. . .. . . . .. . . .. . . . .. . . .. . . . .. . . .. 101
3.7 AlfredTarski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.8 MariaKokoszyn´ska. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.9 CracowCircle(Bochen´ski,Drewnowski,Salamucha). . . . . . . . . 131
3.10 AndrzejMostowski.. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. 145
3.11 HenrykMehlberg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4 BenedyktBornstein.. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. 163
5 CracowCentre. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.1 JanSleszyn´ski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.2 StanisławZaremba. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.3 WitoldWilkosz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
vii
viii Contents
Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
BiographicalNotes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Introduction
Theaimofthisbookistopresentandanalyseanumberofphilosophicalconcepts
concerning mathematics and logic as formulated by Polish logicians, mathemati-
ciansandphilosophersintheinterwarperiod.Whywasthisperiodchosen?Itwasa
specialtimeinthehistoryofPolishscience,especiallyinthehistoryofPolishlogic
andmathematics.ThisperiodsawthedevelopmentoftheLvov-WarsawSchoolof
Philosophy and the Warsaw School of Logic, which was related to the former, as
well as the Polish School of Mathematics, which set the direction of advance of
mathematics, logic and philosophy (in particular, analytic philosophy) for many
years.Moreover,investigationsconductedintheseschoolsandtheresultsobtained
won world recognition and belong to the most important achievements in the
particular domains. Therefore, it is worth asking the question whether this devel-
opment of logic and mathematics was accompanied, and to what extent, by a
philosophical reflection. Specifically, it is worth formulating the following ques-
tions:(1)WastheresearchinmathematicsandlogicconductedininterwarPoland
connected with some philosophical concepts, more precisely methodological or
more generally epistemological ones, concerning mathematics and logic, or did
their sources have any philosophical motivations and convictions or were they
autonomous fields? (2) If they were autonomous domains what were the ‘private’
philosophicalpreferencesoftheirauthorsandwhydidtheynotexertanyinfluence
ontheresearchitselfinlogicandmathematics?(3)Ifthislogicandmathematical
research was based on certain philosophical assumptions then what were these
assumptions?(4)Didtheclose collaborationbetween philosophersandmathema-
ticiansininterwarPoland(infact,italsohadaninstitutionaldimensionapartfrom
thepersonalandprivateones)forcethelattertobecomeinterestedinphilosophical
issues?(5)Weretheachievementsandresultsinmathematics,andespeciallylogic,
the starting point of formulating some philosophical concepts concerning these
domains? (6) Were there any original concepts in the philosophy of mathematics
andlogicinPoland?(7)WhatwastheattitudeofPolishlogicians,mathematicians
andphilosopherstowardstheconceptsofthephilosophyofmathematicsandlogic,
which wereformulatedandintensivelydevelopedinthefirsthalfofthetwentieth
century,namelylogicism,intuitionismandformalism?
ix