jordan philosophy and ideology 1963

8/17/2019 JORDAN Philosophy and Ideology 1963

1/542

1

JORDAN, Z. A. Philosophy and Ideology TheDevelopment of Philosophy and Marxism-Leninism inPoland since the Second World War, D. ReidelPublishing Company, Dordrecht-Holland, Copyright

1963http://www.marxistsfr.org/archive/jordan/ideology/index.htm

First published: by D. Reidel Publishing Company, Dordrecht-Holland, Copyright1963 by D. Reidel Publishing Company, Dordrecht, Holland No part of this bookmay be reproduced in any form, by print, photoprint, microfilm, or any othermeans without permission from the publisher. Printed in The Netherlands by D.Reidel, Dordrecht;Transcribed: by Sam Berner.

From the Editor: The present volume of the ‘Sovietica’ series is part of theresults of an extensive research program, undertaken by the Institute of East-European Studies of the University of Fribourg (Switzerland) with the help ofthe Rockefeller Foundation. I would like to express here my thanks.

Yet, I think, my good sir, that it would be better for me to have a musicalinstrument or a chorus which I was directing in discord and out of tune, betterthat the mass of mankind should disagree with me and contradict me than thatI, a single individual, should be out of harmony with myself and contradictmyself.Plato, Gorgias 482 bce

To my Teachers and Friends in Poland with Respect and Affection


2/542

2

ContentsPreface

PART I / PHILOSOPHY BETWEEN THE TWO WARSIntroduction.

Chapter 1. The Lwów SchoolChapter 2. The Warsaw SchoolThe Philosophers Chapter 3. Other Schools and Other PhilosophersChapter 4. Marxian TraditionChapter 5. Sociology and Social Philosophy

PART II. The Period of Reconstruction and the Rise of Marxism-LeninismIntroduction.Chapter 6. The Philosophical RevivalFormal and Mathematical Logic Chapter 7. The Beginning of Marxist-Leninist PhilosophySome Peculiar Characteristics of the Polish Version of Marxist-LeninistPhilosophy Historical Materialism

PART III. The Years of MilitancyIntroduction. Chapter 8. The Road to AscendancyChapter 9. The Instrumentalist Conception of PhilosophyChapter 10. Criticism of the Warsaw SchoolChapter 11. Phenomenology from the Marxist-Leninist StandpointChapter 12. Criticism of Znaniecki’s Sociology and the Decline of Social Inquiry

PART IV. Formal Logic and DialecticsIntroduction.Chapter 13. The Superiority of DialecticsChapter 14. Change, Motion, and ContradictionChapter 15. The Abandonment of the Logic of Contradiction

PART V. The Materialistic Theory of Knowledge, Theories of Truth andof UniversalsIntroduction. Chapter 16. Engels’ Representative Realism and Lenin’s Theory of PerceptionChapter 17. The Causal Theory of Knowledge

Chapter 18. Anthropological RealismChapter 19. The Materialist Conception of TruthChapter 20. The Truths of Logic and MathematicsChapter 21. Absolute and Relative Truth and the Relativity of KnowledgeChapter 22. The Doctrine of Partiality of TruthsChapter 23. The Doctrine of Concreteness of TruthsChapter 24. The Relevance of the Problem of Universals and the Rejection ofthe Three Classic DoctrinesChapter 25. The Marxist-Leninist Theory of UniversalsChapter 26. The Danger of Platonism

PART VI. Marxist-Leninist Historicism and the COncept of Ideology

Introduction.Chapter 27. The Methodological ApproachChapter 28. The Nature of Historical Laws


3/542

3

Chapter 29. The Technological Conception of HistoryChapter 30. The Empirical Meaning of Historical MaterialismChapter 31. Prediction in the Social SciencesChapter 32. The Revision of the Theoretical Framework of Historical MaterialismChapter 33. Two Interpretations of the Role of IdeologyChapter 34. The Reappraisal of the Dual Theory of IdeologyChapter 35. The New Principles of the History of the Philosophy and theirRevisionThe New Principles. The Revisionist Trend. The Revaluation.

Conclusions.

Bibliography.

Abbreviations used in the BibliographyBibliography

Notes.


4/542

4


5/542

5

Preface

The purpose of this study is to describe the development of philosophy inPoland since the end of the Second World War and the development of Marxist-

Leninist philosophy which, owing to international political events, has assumedan important role in the intellectual life of contemporary Poland. This task couldnot have been accomplished without relating post-war developments to thoseof the interwar period. Consequently, the period studied covers the years 1918-1958.

Yet another extension was necessary. Marxism-Leninism regards sociology as apart of philosophy. Moreover, Marxism-Leninism often resorts to sociology tosupport or justify some of its philosophical views. Finally, its criticism of ‘bourgeois philosophy’ is often concerned with social philosophy and sociologicaltheories which supposedly are implicit or explicit in ‘bourgeois philosophy’. Forthis reason it was desirable to consider in this study some theoretical andmethodological problems of the social sciences. They are taken into accountwhen they illuminate philosophical controversies or the evolution of Marxist-Leninist philosophy.

Marxism-Leninism is not only a new line of development but also a new point ofdeparture in Polish philosophy. It provides a striking contrast with theestablished philosophical tradition which originated roughly at the time when G.E. Moore and Bertrand Russell initiated the analytical trend in Englishphilosophy. The contrast can be epitomised by the contradistinction ofphilosophy and ideology, chosen as the title of this study.

To make this point clear, it was necessary to inquire more closely into some ofthe philosophical theories of Marxism-Leninism. In view of the fact that themore specifically philosophical parts of Marxism-Leninism are little known. thisdetailed inquiry might hold some intrinsic interest. It considerably enlarged thescope and length of this study, but also revealed some new facts which shedlight on the changes wrought in Marxism-Leninism under the impact of itsencounter with academic philosophy.

Considering the ideological nature of Marxism-Leninism, its rise in Poland wasbound to lead to sharp clashes of philosophical attitudes and opinions. Owing topolitical circumstances, these clashes turned into an internecine war, whichMarxism-Leninism declared upon the existing philosophical tradition, itsmethods and techniques, its general programme and particular views. The warwas not waged solely by intellectual means and did not respect the proceduresnecessary in the search for truth. Yet the outcome of this conflict was not thedestruction of philosophy by ideology. On the contrary, it was ideology whichslowly changed its initial position, reducing its claims, revising its points of view,modernising its outlook, and discovering the value of objectivity, logicalconsistency and free inquiry.

This dénouement might have been of more general significance were it not forcertain restrictive circumstances peculiar to Poland which are to be found in thevigour of the native philosophical tradition. It is no exaggeration to say that the

outcome might have been different, if Polish philosophy had not been steeledfor generations against any form of irrationalism by a systematic cultivation of


6/542

6

logical and other scientific procedures and if it could not draw upon theseresources to maintain its steadfastness of purpose and its power of attraction.

Although the Polish case may not admit of any easy generalisation, it seems toprompt some general reflections on the importance of philosophical thinking, itsrelevance to man’s life, and its social function. The controversies andarguments to be recounted and analysed in the following pages transcend apurely theoretical approach to problems of philosophy. If Polish philosophershad failed to bring to bear the whole force of their knowledge upon theproblems at issue or to take the utmost advantage of the persuasive power oflogical procedures, if they had yielded to the extra-logical pressure or ceased tooppose confused thinking and fallacious reasoning, something more than anabstract argument would have been lost. Conversely, the sustained andsuccessful effort to maintain a certain kind of philosophical inquiry or a certainway of exercising intelligence had repercussions outside the restricted field ofphilosophy. It undermined and helped to dispel irrational beliefs in the widerarea of social life. Although philosophical controversies in Poland were in some

respects a contest of specialised skills and knowledge, they were notexclusively such, for they carried risks and implications from which a debatepursued in academic seclusion is usually free. For this reason the developmentsin Poland seem to have a universal significance.

It is sometimes said that the philosophy of to-day, having become specialisedand technically refined, has lost relevance to that with which the common manis concerned. The development of events in Poland does not confirm thisopinion. The prevailing philosophical tradition was professional as well as beingtechnically advanced. Its vision, which, to quote Friedrich Waismann, inspiresany philosophy worth the name, was derived from science and logic. Yet it hasshown itself to have implications for the perplexities and conflicts of the times.The vision not only secured the survival of philosophical thinking, but alsohelped the general public by providing it with standards of rationality andobjectivity as well as by inspiring confidence in the fruitfulness of criticaldiscussion as a means of liberating the mind from errors and prejudices. Thephilosopher’s consistency, persistence and reasonableness were clearly relevantto ordinary opinions and left their imprint on the course of social and politicalevents.


7/542

7

PART ONEPHILOSOPHY BETWEEN THE TWO WARS

INTRODUCTION

The last sixty years have perhaps constituted the most remarkable period inthe history of philosophy in Poland. Never before were so many talents andabilities attracted to philosophy to make valuable contributions in itsdevelopment. Poland, after the First World War, having hardly regained its ownstatehood and organised its institutions of teaching and research, became oneof the internationally important centres of philosophical studies. Polish logiciansand philosophers promoted new trends and opened fresh fields of research. Thefame of the Warsaw School was widely known to some because of itsmathematicians and to others because of its logicians and philosophers.

When the Second World War broke out some thought that this was the end of a

bright but short interlude. Among them was E.T. Bell, the distinguishedhistorian of mathematics. Recalling Alfred North Whitehead’s tribute of 1934 toH. M. Sheffer and ‘the great school of Polish mathematicians, concluding withthe statement: “there is continuity in the progress of ordered knowledge’, Bellwrote: ‘Five years less one month later, ‘the great school of Polishmathematicians’ was being bombed from the air in the progress of orderedignorance, that is, in the general progress of European civilisation. What hadtaken twenty years to gather was dispersed and in part obliterated in abouttwenty days. ‘The great school of Polish mathematicians’ followed the ViennaCircle into death or exile’ [1].

Bell’s prophecy turned out to be only partly true and Whitehead’s faith in thecontinuity of the progress of ordered knowledge has been vindicated. Shortlyafter the end of hostilities of the Second World War the survivors resumed theinterrupted development. The losses in human lives and research facilities,suffered by want on destruction and systematic extermination, were grievousbut not fatal. First to recover were mathematics and mathematical logic; thefirst post-war volume of Fundamenta Mathematicae appeared in 1945 and theregular publication of this periodical was recommenced in 1947. About thesame time mathematical logic resumed its place in the world of learning. At theInternational Congress of Philosophy in Amsterdam (1948) Polish philosophersdid not appear in person, but their contributions were numerous and of thesame quality as previously. By the side of the older generation of philosophers

there appeared the younger one, which made a promising start and justifiedtrust in the future. Important works, some of them of outstanding value, werepublished. There was no reason to feel apprehensive that the present would notequal and even improve upon the past.

Just then, however, the course of development was again interrupted bypolitical interference, suppression of free thought and speech, and theimposition of an oracular philosophy, enforced by decrees and administrativemeasures. The protracted struggle for the rights of reason, intellectual integrity,respect for facts, even the validity of logical thinking, began in earnest. A greatamount of mental energy and spiritual resources was spent in the defence ofthe elementary and well-established truths. The struggle was desperate,philosophical thinking appeared to be doomed. Its outcome in 1956, suddenand decisive, again proved all the apprehensions to be exaggerated. The


8/542

8

submerged determination to search for truth and abide by its verdict has re-asserted itself with a renewed strength. If one looks back at the Polishphilosophical scene in the years since 1945, one thing stands out in clear relief.The modern philosophical tradition, which commenced in Poland at thebeginning of this century and gathered strength during the following decades,has survived all the disasters and upheavals and contributed to shape themethods and ways of philosophical thinking in the postwar period. It hascontinued unobtrusively even at times when a different tradition seemed tohave won the day and proclaimed its decisive victory over the past and itsdiscovery of the ultimate truth.

This power of survival is probably due to many factors, of which one, however,is of direct interest to the purpose of this study. It should be looked for in thepersistence and vigour of the modern Polish philosophical tradition which gaveto its followers in the post-war era the strength of deep-rooted beliefs noteasily misled or affected by pressure and other more extreme measures. Thistradition must be traced back to its source, for it has provided the background

of post-war developments and has constituted their formative force andinfluence.


9/542

9

Chapter 1. THE LWÓW SCHOOL

The beginning of modern philosophy in Poland can be given a precise date. Itwas in 1895 that Kazimierz Twardowski (1866-1938) was appointed to thechair of philosophy at Lwów University and became the founder of modern

Polish philosophy[2].

Twardowski belonged to the so-called Austrian school whose head was FranzBrentano. The large circle of Brentanists included psychologists andphilosophers of a world-wide reputation: Alexius Meinong, Alois Höfler, OskarKraus, Christian Ehrenfels, Carl Stumpf. Twardowski’s contributions to theteaching of the school considered to be the most important are contained in hisbook Zur Lehre vum Inhalt und Gegenstand der Vorstellungen. Einepsychologische Untersuchung, published in 1894. They provided a link in thedevelopment of thought which, on the one side, led from Brentano’s descriptivepsychology to Meinong ontology (Gegenstandstheorie), and to Husserl’sphenomenology, on the other. Husserl recognised the importance ofTwardowski contribution and, after the publication of Logische Untersuchungen,Twardowski’s reputation was established in Austrian and German philosophy[3].

When Twardowski arrived in Lwów, he came to a philosophical wilderness.There was much interest in philosophy, but it was taught and pursued in thetraditional, somewhat amateurish manner. Twardowski clearly faced the choiceof either continuing his own work and returning to Vienna as soon as possible,or staying in Lwów, giving up his own studies, and devoting his life to teaching.He decided upon the latter course. This decision must have been a momentousone for him. If constituted the decisive turning point in the history of philosophyin Poland.

Twardowski’s teaching was based on Brentano’s philosophy and on its furtherdevelopment, to which other Brentanists and himself contributed. In a certainsense Brentano was a supporter of psychologism; he saw in psychology thebasic science of all science. Psychology, as he conceived it, was an empiricaldiscipline, although its empiricism was not of the kind familiar to naturalscientists. It did not make any use of experiments and very little ofobservation; it did not try to reduce psychological phenomena to physiologicalprocesses, as was done by G. T. Fechner and W. M. Wundt. Moreover, Brentanoagreed with Comte that psychological phenomena cannot be really observed byintrospection. Instead, we can directly apprehend them and, by a careful andminute description of what there is before our mind, acquire the knowledge ofthe phenomena involved. Brentano’s psychology is a descriptive science, basedon direct apprehension of its subject matter and thus superior, in his opinion, tonatural science, which is barred from direct access to what it investigates. Inthis sense, psychology provides fundamental knowledge for all science.Brentano returned to the thesis of the French rationalist thinkers of theseventeenth century that we know the mind better than we shall ever knowmatter.

Brentano’s descriptive psychology provides a basis for a general method ofphilosophical investigations. When we perceive a tree outside the window, wecannot be aware of its being there without being aware at the same time of the

act of seeing it. This distinction between an act and its object, which althoughdistinct are never given separately and might thus be confused, is fundamental


10/542

10

for Brentano’s philosophy. Only the act of a representation – and by this termBrentano refers to anything that is apprehended by or is before the mind –constitutes a psychological phenomenon. The object of an act is often aphysical thing and cannot be, therefore, a constituent of a mental phenomenon.

Besides the act and object, there is still a third element, which must bedistinguished in every mental phenomenon – the content of the act. Brentanodid not keep the object and the content of the act clearly apart and the sharpdistinction between them is Twardowski’s important contribution. The contentof the act is the latter’s ‘quality’, by virtue of which the act is directed towardsits object and not to something else, as well as that by which it presents theobject to the mind in one manner rather than another. To this distinctionbetween content and object Twardowski added two further theses. First, that toevery representation there corresponds an object and, second, that there is anecessary relation between a representation and its object. The latter thesis,which for Twardowski was a psychological statement, might have ultimatelypaved the way for Husserl’s transcendental idealism.

Brentano’s conception of mental phenomena contained the nucleus of ideasthat led far beyond his initial point of departure. They could lead in the directionwhich Husserl took, or to conceptual analysis and formal logic, to logicalanalysis of language, to syntax and semantics. The choice of roads dependedon what was given paramount attention: the descriptive psychology which dealtwith the mental act and its content, or the objects apprehended in the act ofrepresentation. This duality in Brentano’s initial position became morepronounced owing to Twardowski’s distinction. Twardowski took the secondcourse and made extensive excursions, beyond the bounds of descriptivepsychology, into the field of logic and the theory of knowledge.

In Poland Brentano’s philosophy was thus given a distinctly realistic orientation.While his descriptive psychology provided the means for specificallypsychological investigations, carried on by Twardowski himself and by a largenumber of his pupils, it also constituted a starting point for a wide range ofepistemological and ontological research, which undermined and finallydestroyed the last vestiges of psychologism, in the above-defined sense,common to Brentano and Twardowski.

Only the acts are immanent to and constituents of the consciousness; theobjects, given by means of representations, are outside the consciousness andtranscendent to it. The analysis of psychological phenomena, carried by means

of descriptive psychology, revealed a whole realm of objects independent fromthe experiencing subject – of things, meanings, concepts, logical laws, whichare neither immanent to the mind nor mere genemlisations of the mind’sactivity. To describe these objects, to differentiate between them, to revealtheir structure and relations, became the proper task of philosophy. They arefound by the mind, and psychology only helps to establish their realityempirically. Twardowski’s writings abound in suggestive psychologicaldescriptions and thorough philosophical analysis, in clarifications and definitionsof the philosophical conceptual framework used in the discussion of thequestions of psychology, logic and the theory of knowledge (the different kindsof representations, concepts, judgements, sentences, propositions, and thenotion of truth). This move forward, away from psychologism, is unmistakable

and pronounced in the whole activity of Twardowski. He laid the foundations forthe logical conception of science and for epistemology in the etymological sense


11/542

11

of this term. Twardowski called his method by a name now very familiar – theanalytical method[4].

In his lectures, Twardowski dealt approvingly with the reform of formal logic,initiated at that time, paid much attention to logic and encouraged his pupils todo so. But in an article widely read in Poland at that time, he pronouncedhimself against the ‘symbolomania’ in which one of his pupils (Jan Łukasiewicz– unnamed in the article) indulged, so Twardowski thought, too much.Łukasiewicz not only agreed with his teacher that logic had been led astray bypsychologism, but was also convinced that it was exact logical analysis thatshould replace psychological examinations of the origin of concepts as themethod of philosophical investigations. Twardowski rejected this suggestion.Logic is not a self-sufficient, autonomous discipline. It is, rather, an instrumentto be carefully used for the solution of definite problems. Its concepts cannot beassumed; they must be critically examined and applied in accordance with theresults of philosophical analysis. This was the attitude which Husserl took withrespect to modern formal logic and to logical investigations on the foundations

of mathematics, and which was represented by Roman Ingarden in Poland inthe ‘thirties. Twardowski’s views also influenced Stanislaw Leśniewski, who hadbegun his studies under Hans Cornelius in Germany, but completed them inLwów. It perhaps explains Leśniewski’s initial distrust of formalism which helater abandoned when he found a way of his own to combine Twardowski’sstandpoint with formal techniques.

However much Twardowski might have been opposed to the traditionalphilosophy in Poland and abroad – its lack of a method, its terminologicalconfusions and conceptual ambiguities, its failure to find ‘empirical’ foundations– he was no admirer of scientism. He believed that philosophy could work out amethod of its own, appropriate to its subject matter and fully satisfying therequirements of scientific procedure. Philosophy was to him an autonomousscience and not a discipline to be made scientific by parcelling out its variousproblems to particular sciences. He was only a severe critic of the traditionalphilosophy, and not its liquidator. He was ready to undertake work of reform,and he practised it throughout his life. But his programme was limited and didnot include the drastic measures which his former pupils were later to advocate.

The direction in which Twardowski led his followers in Poland required them toundertake painstaking analysis of specific problems which were rich inconceptual and terminological distinctions, and directed rather to theclarification than to the solution of the problems involved. Philosophy, as he

conceived and taught it, was unlike its popular conception, impressed upon thepopular mind by Poland’s romantic poets and messianic philosophers, who moreor less identified it with flights of imagination and poetical inspiration.Philosophy became a pedestrian affair, an elaborate and highly specialisedtechnique of thinking, which, being closer than ever before to the hard groundof everyday experience and common sense, could not be followed, as was thecase in the past, by educated but philosophically untrained amateurs. A sharpline of division emerged between the old and poetic and the new and scientificphilosophy, the division line being concerned rather with the standards ofperformance than the subject-matter of what was considered to be aphilosopher’s proper study. Twardowski’s school, wrote Tadeusz Czeżowski, wasa hard one. It made great demands on the beginner and at first offered little

reward[5].


12/542

12

What is known under the name of the Lwów school had thus little in commonwith a philosophical school of thought; it was a school of philosophical methodand thinking. Its members were not linked with each other and with theirteacher by a common body of philosophical assumptions and beliefs; theydiffered widely in this respect. The unity was forged by the common formalstandards of clear thinking, precision of conceptual analysis, and by theterminological distinctions and mode of expression.

Twardowski did not proclaim these standards, but practised them himself in hislectures and seminars which covered a great variety of subjects – psychology,logic, history of philosophy, ethics – and thus showed that the methodadvocated by him admitted of universal application. He sharply differentiatedbetween what can be accepted as a body of philosophical knowledge – thevarious problems, their different solutions, the arguments for and against them,the basic philosophical trends and schools of thought – and theWeltanschauung, the world outlook, which goes beyond what can be known andwhich accepts certain tentative solutions as final on the basis of global value

judgements. He did not reject them altogether, recognising their practical utility,at the same time denying them scientific value. Twardowski’s vast knowledgeof classical philosophical literature made him abhor all onesidedness born ofignorance or contempt for the achievements of the past and excessive claims ofbeing in possession of the whole truth[6].

The secret of Twardowski’s influence and achievement as a teacher lay not onlyin the power of his mind, his vast and varied knowledge, his didactic talentsand efficiency, but also in the Socratic quality of his personality, to which all hispupils testify unanimously. There was an atmosphere of uncompromisingintegrity about him. His demands for precision and exactitude in philosophicalthinking which he practised himself and inculcated in others, sprang from hisdeep sense of intellectual honesty, and were a reflection of his unremittentconcern and respect for truth. To choose a philosopher’s life was to him tofollow an exacting calling which demanded an effort both of mind and will.

Twardowski taught as much by example as by his lectures and seminars. Heleft an inheritance which is not measurable in purely intellectual values, aninvisible power which once created pervades the minds of those who have beenaffected by it and who in turn pass it on multiplied to the others.

Finally, Twardowski was the organiser of philosophical activities in Poland. Hedevised and tried out the university curriculum and didactic methods of

teaching philosophy, which, with minor changes, have been followed ever since.He organised the first psychological laboratory in Poland (1901) and set up inLwów the first Philosophical Society (1904). He actively supported the decisionto start the first Polish philosophical periodical, Przeglą d Filozoficzny founded byWładysław We ryho in Warsaw in 1898, and he founded in 1911 and editeduntil his death Ruch Filozoficzny, a bibliographical philosophical publicationunique of its kind at that time, which kept Polish philosophers informed aboutphilosophical developments at home and abroad. He initiated the translationinto Polish of classical philosophical literature and encouraged others to followhis example.

When Twardowski died in 1938, his life work as founder of the school, asteacher and organiser of philosophical activities, had already brought ampleresults. The philosophical scene in Poland was completely transformed and


13/542

13

philosophy flourished. Philosophy became an academic, scientific discipline,taught by his former pupils, at all the Polish universities. The philosophicalactivities were well organised. There were national philosophical congressesevery few years, (the first was held in 1923), philosophical societies meetingregularly in every university centre, and four philosophical periodicals of a highstandard were published. There was above all a thriving school of philosophicalthinking, vigorous and confident, with an established reputation for its variousachievements. The memory of Twardowski was a living force and the record ofhis achievements an inspiration for further sustained work by all. It was widelyfelt that Twardowski found the best way to combine abstract pursuit and searchfor truth with service to the community, or, to use the fashionable expressionof the post-war period, he found how science can best serve life.

Twardowski had numerous pupils and followers displaying a wide range ofabilities and interests. Between the oldest and youngest among them there wasan age difference of more than a generation. Jan Łukasiewicz (1878-1956) andWładysław Witwicki (1878-1948) were Twardowski’s oldest pupils. The first

excelled in abstract reasoning, the second, a leading Polish psychologist andPlato’s masterful translator, displayed a great power of observation and wasunsurpassed in subtle and detailed descriptions of psychic phenomena,especially of emotions. The fact that these two men, so different in what theystrived for and achieved, came from the same school is telling evidence ofTwardowski’s breadth of mind and tolerance.

To the same generation as Łukasiewicz and Witwicki belong KazimierzAjdukiewicz (born 1890), Stefan Baley (1885-1952), Stefan Błachowski (born1889), Władysław Borowski (1879-1938), Tadeusz Czeżowski (born 1889),Daniela Gromska, Salomon Igel (1889-1942), Stanisław Kaczorowski (born1889), Tadeusz Kotarbiński (born 1886), Mieczysław Kreutz (born 1892),Stanisław Leśniewski (1886-1939), Kazimierz Sośnicki (born 1883) andZygmunt Zawirski (1882-1948). But besides these thinkers, who later becameprominent in psychology, formal logic and philosophy, there were also otherswho were either Twardowski’s pupils or came under his influence, though theirmain interest lay outside philosophy. Among them were Ryszard Gansiniec(1888-1958), a classical scholar, Julian Kleiner (1886-1957), a historian ofliterature, Zygmunt Łempicki (1886-1943), a German philologist and historianof culture of many accomplishments, Ostap Ortwin (1873-1942), a literary critic,Władysław Szumowski (1875-1954), the holder of the first chair of history andphilosophy of medicine at the University of Cracow[7], Bogdan Nawroczyński(born 1882), a professor of pedagogy, and Mieczysław Treter (1883-1944), an

art historian and theorist.

The second generation of Twardowski’s pupils included Walter Auerbach,Eugenia Blaustein (1905-1944), Leopold Blaustein (1905-1944), IzydoraDą mbska, Maria Kokoszyńska, Seweryna Łuszczewska-Romahnowa, HenrykMehlberg, Zygmunt Schmierer, Helena Słoniewska, Tadeusz Witwicki. They tooktheir degrees after the First World War, were taught by Twardowski andAjdukiewicz, and, with some exceptions, belong to a different philosophicalformation known as the Warsaw school.

Until recently Twardowski’s school was referred to, at least in Poland, as theLwów-Warsaw school. This was an apt description in view of the continuity in

the philosophical development and of the persistence of certain characteristictraits in the philosophical method that have been apparent from the time


14/542

14

Twardowski came to Lwów up to the present day. This continuity, which bothits supporters and opponents rightly and strongly emphasise[8], is best testifiedto by the fact that all or practically all the leaders of the new philosophicalorientation that emerged in Poland after the First World War were at some timeor other Twardowski’s pupils and followers. The Lwów-Warsaw school was alsoa convenient name, because it helped to differentiate the philosophical schoolfrom the Warsaw school of mathematicians, led by Zygmunt Janiszewski (1888-1920), Wacław Sierpiński (born 1882), Kazimierz Kuratowski (born 1896) andStefan Mazurkiewicz (1888-1945), which shortly after the First World Waracquired a world-wide reputation, as well as from the Warsaw school of logic,whose undisputed leaders were Leśniewski, Łukasiewicz and Alfred Tarski. Boththe mathematical and the logical school were often called, particularly abroad, ‘the Warsaw school’ without any further qualification.

There is no doubt, however, that Twardowski’s conception of philosophy, whichhe imparted to his pupils and which they at first espoused, differed in many andimportant respects from that which they evolved in their maturity. The

differences are real, deep, and sometimes fundamental, and the passage oftime put into relief what in the past was only vaguely seen and understood.Kotarbiński, one of the protagonists in the development of ideas originated byTwardowski, rightly emphasised that it is more correct to speak of the Lwów(Twardowski’s) and the Warsaw school than to class them together[9].

To put it concisely, the Lwów school can be described as a period ofpsychologism and the Warsaw school as that of ‘logicism’. By psychologism inthis context should not be understood the well known historical trend whichtried to reduce philosophy to psychology, the laws of logic or sociology topsychological laws, and historical and cultural events to the state ofconsciousness of the contemplating mind. As it was indicated above,psychologism stands here for the opinion that whatever is studied by anyscience must be first given in the representation (in Brentano’s sense) and theexamination of what is given is the task of psychology.

The pupils who remained most faithful to their teacher and who could still bedescribed as members of Twardowski’s school when the Warsaw school cameinto being, were those whose interests were psychological. Some of them, likeBlachowski and Baley, became experimental psychologists; they extended thescope, but adhered to Twardowski’s teaching in letter and spirit[10]. Others, andthese included perhaps the most original psychologists among Twardowski’sfollowers, contributed to the expansion of descriptive psychology and to the

improvement of the methodology of psychology in general. To this groupbelonged Władysław Witwicki, Igel, Kreutz, and, among the younger, Auerbachand Blaustein, whose life of great promise and high achievements was cut shortat an early age in a concentration camp.

Those of Twardowski’s pupils who were interested in philosophy followed a pathof their own rather than deviating from the road paved by him. Their methodwas continuation of, but it also differed from, Twardowski’s approach both inmanner and content. Philosophy in Poland took its now familiar modern formonly in the Warsaw school.

If attention is concentrated on the differences, the contrast between the Lwówand Warsaw schools is considerable. They can be differentiated in a fourfoldway. The Lwów school represented the pre-logistic stage of development; it


15/542


16/542

16

łukasiewicz’s first papers, published in Przeglą d Filozoficzny (1903, 1907), dealtwith the problems of induction and with the notion of cause. Notes and reviews,which he wrote at that time, show the interest with which he followed thecriticism of psychologism in logic launched by Husserl, Meinong and Höfler. Hisfirst major publication was On the Principle of Contradiction in Aristotle,followed three years later by Die logischen Grundlagen derWahrscheinlichkeitsrechnung. This period might be considered closed with twoessays – On Science and The Concept of Magnitude[13].

Philosophically his most important contributions of that period were probablyOn the Principle of Contradiction in Aristotle and On Science. The latter wastwice reprinted twenty years later and its description and classification ofdifferent kinds of reasoning were until recently universally accepted inPoland[14]. The former is a historical and systematic study of the principle ofnon-contradiction in Aristotle, still of a considerable value for a historian of logic,in which with an exemplary clarity the distinction between the ontological,logical and sychological principles of non-contradiction was made and their

respective validity discussed. This distinction has also turned out to be ofpermanent value and has provided the basis from which every discussion – andthey became frequent in recent years in Poland – on the status of the principleof noncontradiction used to start. The ontological and the logical principles ofnoncontradiction are equivalent, but neither of them is equivalent to thepsychological principle. The latter states that two beliefs expressed incontradictory sentences cannot exist in one mind. It is clear that this statementis an empirical probability law and not a principle at all.

łukasiewicz rejected the claim that the principle of non-contradiction in itsontological or logical formulation is a ‘first principle’ or, as it was put at thattime, a ‘fundamental law of thought’. It is a logical theorem, whose validity maybe doubted. It must be proved, therefore, but such a proof cannot be foundeither in Aristotle or anywhere else. If the principle of non-contradiction isneither a ‘first principle’ nor a proved theorem, we must recognise that weaccept it for its important extra-logical reasons, of practical and moral nature,namely as a means to guard us against falsehood and lies[15]. Apart from otherreasons, striking at that time, but no longer valid today, by which he supportedhis opinions, Łukasiewicz used Couturat’s algebra of logic to show that theprinciple of non-contradiction is a theorem and not an axiom, a theoremprovable in this system. It should be added that Łukasiewicz never againreturned to the view on the principle of non-contradiction expounded in his firstmajor work. He recognised that the metalogical principle of non-contradiction

must be assumed as an absolute principle, if logic and science in generil is tomake sense [16].

The study On the Principle of Contradiction in Aristotle is memorable foranother reason. It made a reference to the Aristotelian doctrine on contingentpropositions, which were to play a considerable role in the discovery ofmanyvalued logics, mentioned the possibility of constructing a non-Aristotelianlogic, and shortly discussed the relation between time and the validity of theprinciple of non-contradiction with respect to the world of experience. The ideaof a nonAristotelian logic took firmer roots in Die logischen Grundlagen derWahrscheinlichkeitsrechnung, where he came to the conclusion that theprinciple of bivalence is not absolute. There are sentences which are neither

true nor false and to reject them on the ground of Aristotle’s principle ofbivalence is to transform that principle into a prejudice[17].


17/542

17

All these contributions contained many original ideas, they excelled in clarity ofthought, in precision and simplicity of language. They made Łukasiewicz arising philosophical star in Poland, but not an explorer of new lands.Philosophically he moved well within the area familiar to Twardowski’s schooland he did not deny its assumptions. Before he became completely absorbed informal logic, he considered that effective philosophical methods for solvingphilosophical problems could be found. He changed his opinion only with hisfirst logical discoveries, which convinced him of the inventive and explanatorypower of formal logic. His demand for the reconstruction of philosophy bymeans of formal logic probably began emerging in his mind at the same time asthe idea of many-valued logics was born, to solve, as he then thought, some ofthe philosophical problems which haunted him[18] and to prompt furtherdiscoveries in formal logic. This opened a new period in the development ofphilosophy in Poland.

The differences between the Lwów and the Warsaw school grew up slowly andalmost imperceptibly, to become accentuated only in the late ‘twenties. By

1930 Leśniewski’s system of the foundations of logic and mathematics, whichwas to avoid the shortcomings of Principia Mathematica, was emerging fromthe privacy of lectures, seminars, and personal contacts into print[19].Łukasiewiczs investigations on the propositional calculus, Aristotle’s syllogistic,many-valued logics, and history of logic, were summarised in a number ofarticles and reports[20]. Two important text-books of formal logic were published,which, as it were, codified various discoveries made in Poland and abroad,incorporated them into the body of common philosophical knowledge, and set apattern for teaching of and research in logic[21]. Tarski, who since 1923 made anumber of important contributions, clearly joined his teachers as the thirdleader of the logical school and became responsible for initiating systematicstudies in rectalogic and semantics[22]. Kotarbiński Elements of the Theory ofKnowledge, Formal Logic and Methodology of Science was just published andshowed how the general assumptions of the school were applied in practice andwhat they could achieve[23]. The leading logicians, Leśniewski, Łukasiewicz, andTarski, and the most prominent philosophers, Kotarbiński and Ajdukiewicz,were by that time surrounded by a large number of young assistants andfollowers who had already made their mark in logic or philosophy. The schoolalso had adherents outside Warsaw, in Lwów, Poznań, and Wilno, Kraków jealously guarding its independence both in logic and philosophy, and exerciseda considerable influence on the minds of the younger generation studying atthe universities or starting their own research. The Warsaw school was clearlythe dominant force in academic philosophy and a powerful stimulus in the

intellectual life of the country.

The Warsaw school had its logical and its philosophical wing without losing itsunity. The unity was the manifestation of a personal union of logic andphilosophy, represented by Leśniewski and Łukasiewicz, reinforced by themutual influence which the pure logicians and the philosophers were exercisingon each other. In this respect Tarski, who is a logician and mathematician,represented a new departure which, in the course of time, was to assert itselfincreasingly in the development of the school. While the older generation oflogicians represented the alliance of philosophy and formal logic, the youngergeneration of logicians combined logic and mathematics, drew away fromphilosophy and were becoming more and more absorbed in and by the

mathematical school. This trend has become very pronounced after the Second


18/542

18

World War. Although its origin could be traced already in the ‘thirties, it did notaffect the unity of the Warsaw school at that time.


19/542

19

Chapter 2. THE WARSAW SCHOOL

The first distinguishing characteristic of the Warsaw School to appear, was thespectacular rise to prominence of formal and mathematical logic. This was dueto Leśniewski and Łukasiewicz who jointly share the honour of being the

founders of the Warsaw school. Its achievements have by now become widelyknown, even outside the narrow circle of professional logicians. Some of theirworks have been translated or rewritten in one of the world-languages, othershave been competently summarised and reviewed, particularly in the columnsof Journal of Symbolic Logic. The most important results have beenincorporated, after the Second World War, in all contemporary textbooks oflogic. There is no need, therefore, to give here another survey of itsachievements. For the purpose of this study it is enough to indicate the mostoutstanding of them and to emphasise those of their features which werephilosophically important and became a point at issue in the post-war period.

THE LOGICIANS

From this viewpoint Leśniewski’s system still holds its high rank of importanceand philosophical significance[24]. In the inter-war period he was a powersecond to none and he influenced deeply both the logicians, includingŁukasiewicz, and the philosophers, among the latter Kotarbifiski, who eversince has emphatically recognised his indebtedness to Leśniewski[25]. Tarski,through whom, one may almost say, Leśniewski became known internationally,has also repeatedly testified to Leśniewski’s inspiration in his own research[26].Kotarbiński’s and Tarski’s tribute could be extended to others. In fact, hardlyanyone who spent his formative or mature years at that time in Warsaw

escaped being influenced, in sonic way or other, by this extraordinary mind,extreme in whatever views he held, and whose combined power of criticism andof invention caused both admiration and fear.

Leśniewski’s position was based rather on personal contacts than on what hepublished. For he published little during his Warsaw period and what he did waswritten in a highly condensed manner; some parts of it could be followed onlyby those fully acquainted with Leśniewski’s ideas and methods. He was aperfectionist for whom nothing, either in his own or other people’s work, wasgood enough. Leśniewski died prematurely and during the war his manuscriptswere destroyed. The efforts to reconstruct Leśniewski’s system are being made

both in Poland and abroad

[27]

.

Leśniewski seemed to have influenced the philosophy of the Warsaw school bysome of his philosophical views and by his practice. His practice was an almostruthless, radical formalism, to which he adhered not for its own sake, but as aninstrument of conveying meanings and intuitions otherwise doomed, as he felt,to ambiguities and distortions. Formalism was to him the only effective methodof making unequivocal philosophical statements and of consistent reasoning,free from the pitfalls of contradictions. He was thus one of the decisiveinfluences in accepting the view, hotly contested by traditionalistic philosophers,that there is in formalism a creative power that liberates the mind from manyevils which beset philosophy in the past.


20/542

20

Leśniewski was able to arouse and to establish respect for formalism by hisunusual technical inventiveness and by his deep philosophical insight which hetried to express in a formalised language. During his philosophicalapprenticeship in Twardowski’s school he was converted to the absoluteconception of truth, and became a staunch opponent of any kind of relativismwhich, following Twardowski, he thought to be prompted by confusion ofthought or terminological ambiguities. Formal theories which he constructedwere to provide an exact and adequate description of the structure of the world.This prompted the utmost care which he took in every aspect of theconstruction – semantical categories, axioms, formation and transformationrules, definitions – and the attention which he paid to the deduction oftheorems or to the perfecting of matters of detail. Mere formalism of theHilbertian type or Russell’s logicism were of no interest to him. They could beand were interpreted as a play with meaningless symbols or a game of chess[28].A formalised deductive theory consisted for him of clearly meaningful,intuitively valid propositions. The most important of them were those involvingthe word ‘is’ (ontology) and ‘part of’ (mereology), or involving the concept of

class in its distributive and collective sense. Leśniewski’s ontology andmereology are deductive theories of objects and relations that hold amongthem, and correspond in their content to the traditional ontology. They are notmetaphysical theories in the sense that they do not make any assumptionsabout the nature of those objects. For what we know, they might be or mightnot be material. The axiom of ontology remains true irrespective of whethernames of concrete entities, universal or empty names are substituted for itsvariables (on this account ontology is a more general theory than Aristotle’ssyllogistic). But the meaning which the axiom ascribes to the term ‘is’ (‘∈’) in

its main sense makes the propositional function ‘x ∈ y’ a true expression

provided that ‘x’ does not admit empty or universal names as its value, or,affirmatively expressed, provided that only names of individual objects can be

substituted for ‘x’. Similarly in mereology the name of a part of an objectclearly cannot be objectless. Consequently, ontology and mereology areparticularly suited for what is known as nominalism or rather the programme ofa nominalistic reconstruction of logic and science. Leśniewski is a precursor,perhaps still unsurpassed, of what later was undertaken by Chwistek, Goodmanand Quine.

Leśniewski’s examinations of antinomies were of high philosophical importanceand exercised a powerful influence in the development of philosophy in Poland.Little of them has been left in writing and they constituted part of the ‘oraltradition’ of the Warsaw school, based on Leśniewski’s lectures and on personal

contacts[29]

. They inspired the distinction between an object-language andmetalanguage, a theory and metatheory, and prompted the emergence ofphilosophical and theoretical semantics.

In the examinations of antinomies, Leśniewski’s starting point was therecognition of the basic difference between an antinomy and an ordinarycontradiction. The latter results from an error, from the failure to formulatefully and precisely all our premisses and directives of transformation; it can be,therefore, removed by purely technical means. This cannot be done with theformer. Leśniewski criticised the way in which antinomies were eliminated inPrincipia Mathematica, because the theory of types was a kind of a police-theory or of prophylactic, as Tarski put it, to guard the deductive sciences

against the known and other possible antinomies. It cured the symptomswithout touching the cause of the disease.


21/542

21

An antinomy differs from a contradiction in that the former does not result froman error or imprecision, but follows in a valid manner from the premisses andrules of inference, which we believe to be true. The elimination of antinomies,of any possible antinomy, requires, therefore, a re-examination of thesepremisses and rules of inference. Leśniewski’s system of logic and foundationsof mathematics was such a re-examination (it has been shown convincinglythat the logical antinomies cannot be reproduced in Leśniewski’s ontology)[30].It included the theory of semantical categories which, technically speaking,corresponds to the role played by Russell’s theory of types, but otherwisediffers from it. The theory of semantical categories was not added to thesystem of logic, but the system itself grew out of the theory and owes to itmany of its peculiar characteristics. Moreover, the theory of semanticalcategories is not concerned with logical objects such as individuals, classes,relations; it classifies and orders logical constituents of language, hence itsname and immediate philosophical relevance. In concrete applications the signsand expressions belonging to different semantical categories are madeapparent by being enclosed in different kinds of brackets, the use of which is as

much restricted and fixed as that of other expressions. In Leśniewski’s words,the theory of semantical categories did not replace the hierarchy established bythe simplified theory of types, which for him lacked intuitive justification, but ‘intuitively undermined’ such assumptions and consequence relations thattogether lead to contradictions. As Leśniewski said, he would feel bound toaccept the theory of semantical categories, if he wished to speak sense, werethere no antinomies whatsoever in the world[31].

After his Lwów period Leśniewski hardly ever said anything on philosophicalsubjects. Unlike Leśniewski, Łukasiewicz spoke often on these matters.Compared with Leśniewski, Łukasiewicz enjoyed the reputation of being alogician with pronounced philosophical interest. This opinion cannot be accepted

without qualification.

łukasiewicz admired formalistic methods irrespective of what philosophicalpurpose and intentions they served. Formal logic was not to him a method oran instrument, but an autonomous discipline, to be studied for its own sake.The importance of this discipline was increased in his eyes by the fact that itcarried philosophical implications and provided useful techniques formathematics. But if that were not the case, formal logic would still possess anintrinsic value. Łukasiewicz was critical of Hilbert’s formalism, because itdeprived formal logic of its independent status, subordinated it to mathematicsand transformed it into some kind of mechanical device for getting results[32].

This criticism was prompted by the consideration that formal logic has achieveda degree of precision which mathematics cannot emulate and that by making offormal logic a maid-servant of mathematics the standards of precision achievedby formal logic are being debased. In fact, however, Łukasiewicz sharedHilbert’s approach to formalistic methods; he valued them because they did getresults. He was fascinated by what can be done with symbols once theappropriate techniques are worked out and he did not spurn any of them, asLeśniewski did, since they were considered in some sense or otherphilosophically unsound. Łukasiewicz rejected the assumption of the Lwówschool which required that basic logical concepts should be philosophicallyexamined before they are accepted and made use of. In a discussion with Adam

Żółtwski, representing the traditional trend in philosophy, he said plainly thatthis was an unfounded presumption of philosophy.


22/542

22

This attitude was probably responsible for the influence Łukasiewicz exercisedon the mathematicians in Poland; he provided them with methods that theyfound useful in their own work. While Leśniewski, who became a mathematicianand devoted his life to the task of securing a safe and consistent foundation formathematics was more or less ignored by the mathematician, Łukasiewicz, inspite of not being a mathematician sensu stricto, did play a considerable role inthe development of mathematical thought in Poland. He was particularlyinfluential with the Warsaw mathematical school grouped round the editors ofFundamenta Mathematicae[33].

Within classical logic Łukasiewicz’s work was concentrated on the propositionalcalculus and the theory of A-I-E-O relations (Aristotle’s syllogistic), of which hewas recognised an undisputed master and to which he gave their modern form,unsurpassed in simplicity, clarity and formal precision. The publication ofElements of Mathematical Logic established his authority in very wide circles inPoland and the appearance of Untersuchungen

ber den Aussagenkalk

l,written together with Tarski, marked the beginning of his international

reputation. But the full recognition abroad came later, not until the yearsfollowing the end of the Second World War, when the Republic of Eiregenerously offered him hospitality in Dublin. His creative power remainedalmost unaffected by the progress of age and he died like Euler, working andmaking plans for future work[34].

łukasiewicz became acquainted with the modern propositional calculus probablythrough Frege and there is no doubt whatsoever that Frege influenced himdeeply, both by his logical and philosophical ideas. Under Frege’s influence hebecame a Platonist in logic, the position which he rejected as ‘mythology’ in hislater years, and to which he again returned later still 35[35]. He also thoughtFrege’s calculus to be superior to that of Russell-Whitehead and perfected itconsiderably, in particular by reducing the number of axioms from six to three(compared with four axioms of Principia Mathematica after one had been founddeducible from the others by Bernays and Łukasiewicz working independentlyof each other). He devised a symbolism of his own, based upon a suggestion ofChwistek, the now widely known CN calculus, making it possible to dispensewith dots and brackets, and, consequently, constituting an essential stepforward in the strict formalisation of logic. He constructed other propositionalcalculi and their subsequent investigation greatly contributed to theunderstanding of the structure of formal theories. Łukasiewicz’s interest in thepropositional calculus was based on the belief that the calculus of propositionsis the fundamental logical discipline and the ‘deepest foundation’ of all

deductive sciences. The whole structure of logic rests on it and mathematicsrests on logic. If there are different logics of propositions, irreducible to eachother – and manyvalued logics have established this fact – there must bedifferent calculi of predicates, and, consequently, different theories of sets anddifferent arithmetics[36].

Apart from the axiomatic method, he worked out with Tarski’s assistance thematrix method as a general method of constructing formal calculi, investigatedthe consistency, independence, and completeness of logistic system, anddevised new methods of providing proofs to this effect. He initiated a vast bodyof investigations on the extended and restricted propositional calculi, as well ason calculi with single axioms (based on Sheffer’s stroke, equivalence or

implication as primitive terms), and himself achieved important results in thisfield. While some of his discoveries should be credited to Łukasiewicz himself,


23/542

23

others could have been made only because he worked with a team of logiciansof great brilliance. One of them was Tarski. Others were Stanisław Jaśkowski(born 1906), Adolf Lindenbaum (1909-1941), Andrzej Mostowski (born 1913),Mojżesz Presburger, Jerzy Slupecki (born 1904), Bolesław Sobociński (born1906), Mordchaj Wajsberg, all of whom left their mark and contributed to theachievements of the logical school as a whole. The team work was an essentialand characteristic feature of the school and one of the secrets of its success.The collaboration was so close and intimate that it is often hard, if notimpossible, to say, who should be credited with what. The team spirit withoutdepreciating individual merits, those of Łukasiewicz and Tarski in particular, is atribute to the disinterestedness and purposiveness of all[37].

The rich crop of particular and general results not only enriched our knowledgeof formal structures but also constituted a prerequisite of the emergence ofmetalogic. This term occurs already in On the Principle of Contradiction inAristotle (1910). Łukasiewicz used it to refer to investigations on the relationsbetween logical principles which may lead, as he suggested, to various logical

systems, including non-Aristotelian ones, in a similar fashion as theinvestigations on the parallel axiom had led to the construction of non-Euclidean geometries 38[38].

The choice of the term ‘metalogic’ might have been also prompted by thedistinction between ‘mathematics’ and ‘metamathematics’ made a few yearsearlier in Germany to differentiate between two parts of Hilbert’s programme.Hilbert tried to show: firstly, that the whole of mathematics can be presentedas a system of formulae derived from axioms according to some fixed rules;secondly, that this system is consistent. ‘Metamathematics’ was the name givento the investigations and arguments which were expected to secure the proof ofconsistency. As Hilbert conceived it, metamathematics was to make use – apartfrom other restrictions – only of the very simplest logical operations. Metalogicwas conceived differently. Some of its seminal ideas can be traced toLeśniewski’s lectures at the University of Warsaw from the early ‘twentiesonwards and to the stimulus which he provided in scientific discussions.Metalogic grew out of the critical examination of the principles and methodsused in the construction of deductive systems, which also includedinvestigations on the consistency of these systems as one of its important tasks.In view of the generality of these examinations they were known at first by thename of ‘methodology of deductive sciences’. In the course of time thisconception turned out to be too narrow. On the one hand, there arose the needto differentiate between the language of the systems considered and the

language in which the methodological investigations were carried out (thelanguage and meta-language); on the other, various special concepts, createdfor the purpose of investigating the construction and structure of deductiveformalised systems, called for critical examination and systematisation (thetheory and the meta-theory). In the late ‘twenties these facts were widelyrecognised. The appearance of Łukasiewicz Elements of Mathematical Logicmade them more pronounced and the publication of Łukasiewicz"s and TarskiUntersuchungen

ber den Aussagenkalk

l showed the metalogic in the processof its creation by the sheer weight and number of results and efforts at theirsystematisation.

The decisive step was taken by Tarski, who, from the evaluation of methods

applied in the construction of deductive theories, passed to investigating themtheories as wholes and to the elaboration of concepts necessary for this task. In


24/542

24

his papers Tarski avoided the expression ‘metalogic’ and used instead that of ‘metatheory’ or ‘metamathematics’. This was prompted by his conviction thatevery deductive theory, and consequently also every logical system, is amathematical discipline. ‘Metamathematics’ was, therefore, a more generalterm than ‘metalogic’. As to its meaning, ‘metamathematics’ in Tarski’s sensediffered considerably from that in Hilbert’s[39].

łukasiewicz’s second major contribution to logic was his research into its historyand the encouragement which he gave to others to follow suit. Łukasiewicz’sinterest in the history of logic dated from the time when he was still a followerof the Lwów school. His acquaintance with modern formal logic constituted,however, a decisive turning point; only then did he realise that the existingworks on the history of logic had no scientific value[40]. His most importantcontributions concern the logic of the Stoics, which he rescued fromcontemptuous oblivion restoring it to its true greatness, and Aristotle’ssyllogistic, which he liberated from its distorting accretions accumulatedthrough centuries, and presented in its original formal and modern formalised

form. The interest in Aristotle’s logic, which had occupied his mind since theearly ‘twenties, was brought to its fruition in the first edition of Aristotle’sSyllogistic. He died before the second edition, supplemented by an exposition ofAristotle’s modal logic, appeared in print. His life-long concern with Aristotle’slogic was closely bound with many of his own discoveries and testified to thefact that historical research is fruitful in more than one respect.

łukasiewicz found followers and collaborators in Poland, among whom JanSalamucha (1903-1944) and J. M. Bocheński (born 1902) were the mostdistinguished. The first examined the concept of deduction in Aristotle andThomas Aquinas, St. Thomas’ proof ex motu for the existence of God,Ockham’s propositional calculus, and the problems of antinomies in medievallogic[41]. Before the war the second published several contributions on ancientand medieval logic, to become in the post-war period an internationallyrecognised authority on the subject[42]. Other contributions which wereprompted or influenced by Łukasiewicz’s historical research, came fromZbigniew Jordan, Maria Kokoszyńska, and Konstanty Michalski[43].

łukasiewicz conceived the idea that means should be provided to equip an ableyoung man, willing to undertake the task, with the necessary knowledge inclassical philology, history and formal logic in order that he might devote hisentire life to the rewriting of the history of logic. This idea was not and couldnot be implemented; the task clearly overreaches at present the strength of

body and mind of any single man[44]

. But however unfeasible Łukasiewicz’s ideawas, his insistence and efforts have achieved wonders. Since he spoke for thefirst time on the logic of the Stoics in 1923, a steady output of studies began tofollow, first a trickle in Poland and Germany, later, in particular after theSecond World War, a gathering stream all over the world. Many contributorsrecognised their indebtedness to Łukasiewicz and hardly anyone can ignorewhat he had to say on the subject[45]. In Poland after the Second World War theinterest in the history of logic revived, but little work, based on the study oforiginal sources, has been done so far.

łukasiewicz’s greatest achievement, as is now widely recognised, is thediscovery of many-valued logics. The fact that they do arouse considerable

controversies -concisely and suggestively summarised in the Introduction to J.B. Rosser and A. R. Turquette Many-Valued Logics – perhaps only enhances the


25/542

25

audacity not so much of the idea itself, entertained before Łukasiewicz, but ofworking it out and of establishing many-valued logics as consistent formalstructures[46]. The main facts concerning the logical discovery are easy toascertain. The L3 was established by Łukasiewicz by the matrix method in1920[47], that is, before E. L. Post’s celebrated paper was published. The Ln followed in 1922, according to Łukasiewicz’s own statement, but was notpublished until 1929, that is after Post’s generalisation[48]. The mutualindependence of Post and Łukasiewicz is evident from their respectivepublications, from the differences in the approach, formal in the case of Post,philosophical in that of Łukasiewicz, as well as in their respective treatment ofthe designated truth-values. In its abstract form the Ln system was presentedin Łukasiewicz and Tarski Untersuchungen fiber den Aussagenkalk l, itsphilosophical origin and implications were examined in ŁukasiewiczPhilosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalk

ls.A primitive base of L3 was established by Wajsberg in 1929 and the axioms of afull L3 were given by Słupecki in 1936

[49]. Finally, in the ‘fifties Łukasiewiczexamined L4 more closely by the matrix method in Aristotle’s Syllogistic and A

System of Modal Logic[50]

.

The idea prompting Łukasiewicz to construct L3 originated from his studies ofAristotle’s logic and his interest in providing a consistent basis for the thesis ofindeteminism. The latter interest is apparent from first to last in his attempts toformulate a theory of contingency which would allow the acceptance of theexistence of true contingent propositions[51]. Probably already in 1910, when hewrote On the Principle of Contradiction in Aristotle, he came to the conclusionthat the thesis of indeteminism and the principle of bivalence, or rather that ofthe excluded middle, as he then saw it, were incompatible. He stated this viewin an address delivered at Warsaw University in 1918 and again in a much fullerform in 1922; the former was recently reprinted, the latter was never published

and perished during the Warsaw rising[52]. Besides his indeterministicconvictions, at the source of the discovery of L3 was Łukasiewicz’s concern withmodal logic. He was prompted by the intuition, which has turned out to be right,that a system of modal logic cannot be accommodated within L3.

łukasiewicz’s conviction concerning the incompatibility of indeterminism and ofthe principle of bivalence was strengthened by one of Kotarbiński’s studies, firstpublished in 1913. In fact Kotarbiński went further than that and came veryclose to the idea of a three-valued logic. If a man is free, Kotarbiński argued,i.e. is able to make choices and bring about what without his action would notmaterialise, there must be things in the Universe which may or may not happen,

an ‘ambivalent possibility’, as he described it. A statement about an ambivalentpossibility cannot, therefore, be either true or false; it constitutes a ‘third kindof propositions’, different from those which are true or false. Kotarbińskirejected expressly the principle of bivalence, that a ‘given proposition is eithertrue or false’, which ‘unlawfully passes off for the principle of the excludedmiddle’. The latter is valid only in so far as it states that contradictorystatements cannot be false together, from which it does not follow, however,that one of them must be true. Kotarbiński argued in a Brouwerian manner thatif a proposition is proved not to be false, this does not entail that it is true. Heconcluded: ‘Every proposition is either true or false or neither true nor false andquartum non datur’ [53]. He was not certain, however, whether this assumptiondoes not lead to contradictions and whether the quartum non datur principle is

not absurd[54]. Kotarbiński’s essay was known to Łukasiewicz and according tohis own confession strongly influenced his thoughts on the subject[55]. The


26/542

26

seeds of L3 were sown in the Lwów school and more than one mind participatedin their cultivation.

As is well known, these seeds go back to Aristotle. Łukasiewicz’s discoverycarries, above all, the Aristotelian imprint and was prompted by his studies ofAristotle’s logic guided by his knowledge of formal modern logic. Aristotleaccepted the view that particular statements referring to some future events,e.g. the statement ‘there will be a sea-battle to-morrow’, when pronounced to-day can be neither true nor false. Łukasiewicz drew the conclusion therefromthat they must have a third value different from truth and falsehood. Let usassume, in accordance with Aristotle’s suggestion, that: it is contingent that p(symbolically: Tp) if and only if it is possible that p and it is possible that not p.In Łukasiewicz’s notation this definition can be written as the equivalence (Q):

Q T p K M p M N p.

Now, if a statement is either true or false, there is no true value of p for which

Tp is true. The right-hand side of the equivalence is a conjunction which forboth truth-values of p must become falsehood. A consistent theory ofcontingency requires that the principle of bivalence of our intuitive and classiclogic is replaced by a more general principle. There is nothing to prevent usfrom doing it in view of the fact that the statement: ‘for every p, p is either trueor false’, is not a theorem but a principle of logic and can be replaced by adifferent principle, provided that certain conditions are satisfied. On this basisŁukasiewicz proceeded to the construction of L3, an interpretation of which wasto be modal logic, the third value standing for possibility. This attempt failedand Łukasiewicz was the first to see and to recognise it. L3 can be constructedand proved to be a consistent and complete formal system, but modal logic isnot its interpretation. If we consider the theorems of L3 as those of modal logic,some theorems of L3 turn out to be inconsistent with the accepted meaning ofmodal functors, some others could not be interpreted in terms of modal logic.In particular, the theory of contingency cannot be accommodated within athree-valued modal system. If Tp is equivalent to KMpMNp and KMpMNp is truefor some values of p, say ?, then we can assert both M? and MN?. However,from these assertions and a theorem due to Leśniewski follows that we havethen to assert Mp, or, in other words, to admit that all problematic propositionsare true. This destroys what Łukasiewicz called basic modal logic, a set ofassumptions which must be included in any system of modal logic, if it is tomake sense. The rejection of the expression Mp, which has to be asserted in athree-valued modal logic is a constituent of the basic modal logic[56].

Twenty years after this failure Łukasiewicz returned to his original idea and bydefining certain four-valued matrices he succeeded in constructing a fourvaluedsystem of modal logic that renders faithfully, in his opinion, our intuitionsassociated with modal functors and includes a consistent theory of contingentpropositions[57]. The theory of contingency is very ingenious but requires purelysymbolical treatment. It assumes the distinction of two kinds of possibility andcontingency, for which an appropriate terminology does not exist in ordinaryspeech (they can perhaps be described and expressed as different degrees ofassertibility, associated with respective problematic and contingent statements).By means of a four-valued modal system and two kinds of possibility andcontingency the existence of true contingent propositions in Aristotle’s sense:

Q T p K M N p,


27/542

27

can be asserted, with the functor ‘M’ denoting different possibilities.

There were some other attempts, all made outside Poland – in France, theUnited States, and the USSR – to find an interpretation or to make use of the Ln in the calculus of probability, quantum mechanics, set theory, and the theoryof electronic circuits. Neither was fully successful and neither contributedsubstantially to the development of the branch of science which was to benefitfrom it[58]. Thus, at present, the interpretation of L4 in terms of modal logic isthe only example of L n being something else but a purely formal structure.Moreover, this instance is not yet safely established. Hence some logicians lookaskance at the many-valued logics, as Leśniewski did. Leśniewski considered asuseless such consistent deductive theories as enable us to prove an everincreasing number of theorems which are irrelevant in view of their beingunrelated to reality. But the history of science provides numerous examples ofabstract theories which had been developed long before any use was found forthem. Moreover, there can be little doubt that Łukasiewicz’s performance of a ‘bold experiment’ has fundamentally changed our conception of logic and

provided a new insight into the nature of formal structures, including thosebased on the intuitive bivalent logic.

łukasiewicz became a logician through search in philosophy for exactitude andprecision in speech and thought. In the propositional calculus, greatly improvedby his own achievements, he found the unsurpassed model of perfection whichevery science should strive for and try to emulate. Mathematics was noexception to this rule. As he saw it, modern formal logic was no branch ofmathematics, but an autonomous science which set up a new ideal of scientificprecision even for mathematicians. Compared with this function any otherservice that formal logic may render to mathematics, for instance by helping tosolve otherwise very important questions of the consistency and completenessof mathematics (written 1929), has a secondary value. By raising still higherthe standards of scientific procedure, formal logic makes every branch ofknowledge exert itself to raise its own standards and to approximate the idealmodel of formal logic. This was in Łukasiewicz’s opinion the highest contributionof formal logic to science and philosophy[59].

To train one’s mind in the methods of formal logic, wrote Łukasiewicz, is toallow scales to fall from one’s eyes. ‘One notices distinctions where there isnone to the others and one sees nonsense where others look for deepmysteries’. Then comes the realisation that one has not learnt to think logically,precisely, consistently, thoroughly, neither in philosophy nor in science, neither

in public nor in personal life[60]

. Certain conclusions follow inevitably. Much thathas been done in the past in philosophy has no scientific value and to continuein the old habits of thought is simply a waste of time and mental energy.

This evaluation of formal logic made Łukasiewicz despair of philosophy. In anaddress delivered at the Second Polish Congress of Philosophy (Warsaw, 1927)Łukasiewicz gave the advice to the audience that they should forget the pastand start everything again from scratch. If all human disciplines were orderedaccording to the scientific precision of their methods, philosophy would have tobe placed at the bottom. Philosophical systems of the past might have someaesthetic and moral value, they might occasionally have made a true andintuitively justifiable observation, but scientific value they have none. The

philosophers’ failure to make of philosophy a science results from their neglectof logic. They do not adhere to and do not follow the logical procedure or they


28/542

28

base their views on wrong theories of logic. Philosophy has thus fallen into theabyss of vain speculations from which only formal logic, and the axiomaticmethod in particular, can rescue it.

Not all philosophical problems could be examined in the suggested manner, butnot all philosophical problems have a definite sense. Those which are concernedwith the essences of the world, with the mythological entities like Plato’s ideasor Kant Dinge an sich, cannot be formulated in a comprehensible, clear, andunambiguous manner. Questions concerning the structure of the world – time,space, causality, determinism, indeterminism, teleology – are a differentmatter; to these questions the axiomatic method can be applied. While theaxiomatic method provides an instrument by means of which scientificphilosophical theories can be constructed, experience and natural scienceswould be used to verify them and to revise continually the basic concepts andassumptions of these theories. The latter would pave the way for aphilosophical synthesis, a truly scientific and formally sound view of the world,to guide us in our efforts to improve ourselves and the world we live in[61].

This makes it clear that Łukasiewicz’s conception of philosophy substantiallydiffered from that advocated by the Vienna Circle. Łukasiewicz spokeapprovingly of Moritz Schlick’s and his followers’ efforts to revise philosophicalmethod by making use of formal logic, but he emphatically rejected Carnap’sreduction of philosophy to logic of science. He was inclined to agree withCarnap that metaphysical propositions are meaningless, if they claim to conveyknowledge about something which is over and beyond all experience (theessence of things, or things in themselves). But this is the Kantianunderstanding of metaphysics; there remain factual problems concerning thestructure of the world which are metaphysical, whether they are so termed ornot. The latter are not syntactical questions, as Carnap suggested. It is hard tosee at all, how by investigating the structure of language, its formation andtransformation rules, the problems as to whether the world is or is not finite inspace can be solved. The same applies to the question of causality,determinism, and many others. These are questions of fact and their solution isnot a matter of language. One can again agree with Carnap that there is aformal mode of speech correlated to a material mode and that some errorsmight be avoided by translating sentences expressed in the material mode intothose clearly syntactical. But to say that by such a translation we get rid of themisleading impression, inherent in the material mode of speech, that a ‘material’ sentence refers to some extra-linguistic reality where no reference ofthis kind is in fact involved, is a dogmatic, unjustifiable statement. The

sentence: ‘the evening star and the morning star are identical’ is correlatedwith: “the words ‘evening star’ and ‘morning star’ are synonymous”; theirmeaning, however, is quite different. The former refers to the extra-linguistic,the latter to the linguistic reality. The matter of fact involved in the former wasresolved after long years of observations and could not have been decided uponby an examination concerned with the usage or by the reflections upon themeaning of the words referred to in the latter.

Finally, Carnap’s view that logical and mathematical sentences are tautologieswhich do not say anything about the world cannot be accepted either. There arevarious systems of geometry and logic but one and only one of them doesapply to the outside world, irrespective of the fact whether we are at present

able to state which of them does. When a formal a priori structure is applied toreality it must be treated as any other hypothesis, i.e. to be verified by


29/542

29

experience. When this is achieved, a geometrical or logical system does conveysome knowledge about the outside world. Carnap’s logic of science and theWiener Kreis doctrine in general, Łukasiewicz stated, were risky philosophicalspeculations which would soon become obsolete[62].

The critical attitude to the logical positivism of the Vienna Circle waspresumably reinforced by Łukasiewicz’s return to Platonism in logic. Łukasiewiczdiscovered that formal logic displays certain paradoxical features. On the onehand, formal logic is neutral; it does not commit anyone to any particular viewin ontology or in the theory of knowledge, and it can be combined withempiricism or rationalism, with realism or idealism. On the other hand, a formallogician accepts, in practice, the nominalist viewpoint. The expressions andsentences with which he deals, are considered to be names of man-madeinscriptions. This should commit him to finitism; only a finite number ofinscriptions can be given at any time. Finitism makes, however, the validity oflogic dependent on certain empirical facts, which is unacceptable, and isactually incompatible with the logician’s practice. There is no longest logical

thesis, as there is no largest natural number. Moreover, it can be easily shownthat in the two-valued propositional calculus the class of all theorems is infinitein Dedekind’s sense. The nominalistic outward appearances of formal logicmask metaphysical problems concealed in the foundations of logic[63]. Howshould they be solved?

The answer belongs to philosophy and not to logic. Łukasiewicz never said thatit is either too complex or impossible to give a theory which would do withoutpostulated abstract entities, but he was inclined to accept their existence on theground of what is implied by logical constructions and by the insight theyprovide. We believe that there are shortest possible axioms of various calculiwhich are to be found. In general, the logician only discovers formal structures.They appear to his mind ‘as if they were a concrete and palpable object, madeof the strongest material, a hundred times stronger than concrete and steel’.Nothing can be changed, created, arbitrarily decided by the logician, who by hisefforts gains the knowledge of ‘permanent and lasting truths’. PersonallyŁukasiewicz believed that they were the thoughts of God[64].

łukasiewicz was a man of few philosophical ideas and those which he held inone period of his life seem to have differed sharply from those expounded byhim in another. The one exception was his unshakeable conviction in the truthof the thesis of indeterminism. In other respects he oscillated between theextremes. Philosophically Łukasiewicz was influential inconsiderably

strengthening certain tendencies. He has done much to inspire the respect forthe use of formal logic in philosophical investigations, implying somerestrictions on the range of problems discussed and a sharp distinction betweenwhat can be scientifically examined and what does not lend itself to suchtreatment. He also strengthened the methodological orientation of Polishphilosophy and its absorption in the problems of science. He was a moderatesupporter of scientism; he believed and inspired trust in the methods andachievements of science, both in their theoretical and practical aspects. Ingeneral, he seems to have been a power in so far as some intellectual trendswere concerned and to have exercised little influence in matters concerning thephilosophical programme and methodological procedures. What he wishedphilosophers to accomplish was not feasible. He underrated the difficulties of

reducing philosophical problems to the form which would provide a possibility oftheir solution by a purely deductive method, and also those connected with the


30/542

30

verification of axiomatised philosophical systems. Practically nobody tried to putthese ideas into effect. What was widely accepted was Łukasiewicz’s criticism ofthe state of philosophy, his diagnosis of its causes and his belief that muchcould be improved by sharpening the philosopher’s tools with the assistance offormal logic.

Tarski (born 1902) from the beginning enjoyed the advantages anddisadvantages of his intellectual background. Unlike his teachers he was bytraining a mathematician and logician, and only afterwards a philosopher[65]. Inhis philosophical views he was influenced by Kotarbiński, to whom the collectionof his pro-war papers, translated into English, is dedicated. But what he tookfrom philosophy he repaid with interest.

Already his first contribution[66], in which he showed that, granted the use offunctions with propositional variables and of the universal quantifier, all thepropositional functors can be defined i

jordan philosophy and ideology 1963

Documents