The Lvov – Warsaw School

THE LVOV – WARSAW SCHOOL AND CONTEMPORARY PHILOSOPHY

Jerzy Perzanowski

ed. by Katarzyna Kijania – Placek and Jan Woleński Synthese Library, vol. 273, Kluwer Academic Publishers, Dordrecht/Boston/London, 1998, pp. 399

About one hundred years ago, in 1902/3 Bertrand Russell tried, but unfortunately failed, to establish – first in England and next in other countries – a school of mathematical philosophy, i. e. philosophy dealing with real philosophical problems by means of serious mathematical methods. The are several reasons for the failure of the project. The most important are the following three: 1. that Russell himself during the I World War and just after it stopped, for several years, his brilliant philosophical work, passing instead to political and moral activity. Also, during this time he lost his intimate connection with his coworker A. N. Whitehead. 2. During the same period of time his a most gifted pupil Ludwig Wit­tgenstein, after finishing his “Tractatus Logico – Philosophicus”, also lost interest in philosophy, believing quite falsely that in the “Tractus” he was able to solve all important philosophical questions (What a pleasure indeed to be a young genius!). Next, after returning to philosophy in the 30-ties he eventually became the most influential critic and devastator of the Russellian program, introducing instead the fashion for linguistic philosophy (which fortunately is also over). 3. And, last but not least, the premature death of Frank Ramsey should also be mentioned here, for his genius and enthusiasm for real philosophy was so promising for the future. However he had time to mark only the first steps of a giant.

But Russell succeeded in several other countries: in Austria and Germany (Vienna Kreis), in Scandinavia, in USA, and also in Poland.

The case of Poland is quite interesting in itself. The Polish School of scientific, anti-irrationalistic philosophy, better known under its popular, though partly misleading name “the Lvov – Warsaw School”, is indeed, as the title of Władysław Krajewski’s essay rightly says: the first School of Non-Positivist, Scientific and Analytic Philosophy. It is an offspring of the two great traditions: the Brentanian and the Russellian ones. The Brentanian tradition was introduced by Kazimierz Twardowski, the founder of the school, one of the three most distinguished pupils of Brentano (A. Meinong and E. Husserl are two others). The Russellian line, on the other hand, was introduced by the first three Polish modern logicians, followers of Russell and Frege: Leon Chwistek from Kraków (and next Lwów), co-inventor of the simple theory of types; Jan Łukasiewicz the first doctor with habilitation (so called Private Dozent) of Kazimierz Twardowski, inventor of multi-valued logics, and probably the most original (at least as a person) of them – Stanisław Leśniewski, famous for his great contributions to logical philosophy and for his rather unsuc­cessful try to rebuilt the very foundations of mathematics in a nominalistic way.

The Lvov-Warsaw School was especially well-known from the thirties by its intimate connection with logic – Warsaw Logical School – which was transferred in part during the World War II, by its chief figure Alfred Tarski, to California.

The book under review contains essential part of the proceedings of the International Congress commemorating the starting point of the School. It was the first lecture given on November 15, 1895 to the audience of Lvov University by a very young at that time professor Kazimierz Twardowski, who earned the name by his famous Habillitationschrift “Zur Lehre vom Inhalt und Gegenstand der Vorstellun­gen”. In this memorable day, Kazimierz Twardowski started his forty years long career as the great (and very successful) teacher of Polish philosophers and other people of learning. Just one hundred years later, more than one hundred philoso­phers from ca. 20 countries took part in the Anniversary Congress. It was held in two places connected with the school: in Lvov (15 – 17 of November, 1995) and in Warsaw (19 – 21, 1995).

The book contains 31 papers divided into six parts with one general paper of introduction. The ntroductory paper “The Reception of the Lvov – Warsaw School” was given by Jan Woleński of Jagiellonian University, nearly an official historian of the School. In his 16 pages long essay Woleński describes very briefly the main points of the School’s history and the chief persons involved.

Part I, “History and Comparisons” contains nine essays. The first one, by Johannes L. Brandl of Salzburg University “Twardowski’s Distinction Between Actions and Products” discusses in a careful way the chief distinction made by Twardowski in his paper from 1912. Usually, it is treated as Twardowski’s farewell to his teacher Franz Brentano’s psychologism, at least in the case of logic and theory of language. The distinction, I think, is an ontological one, made at the very basic level. In his essay, the author is of a rather different opinion. He is involved in discussion of a serious problem in interpreting Twardowski’s distinction: is it indeed an ontological distinction between two kinds of entities (which is my own position), or is it made on a conceptual level, as a distinction between two ways of conceiving of just one kind of entity (which seems to be preferred by the author)?

Following the patterns of modern semantical analysis, Brandl becomes rather doubtful whether Twardowski’s distinction is clear enough and is arguing for conceptual interpretation of the distinction. One of its merits, according to Brandl, is that it gives the language much more prominent role than the ontological interpreta­tion. Is it really a merit? Is not the time to treat language only as a weapon, not as the final and basic subject of analysis?

Tadeusz Czarnecki of Cracow University of Technology his short paper “On Ajdukiewicz’s Empirical Meaning -Rule and Wittgenstein’s Defining Criterion” devotes to comparison of the two, in a sense, similar philosophies of language. They are especially similar in accounting for the role of sentences in the specification of meaning. In particular, the postulate of intersubjectivity of meaning, common for both philosophers is scrutinized in the paper. First, the security measures Aj­dukiewicz takes to make his empirical meaning – rule intersubjective are inquired. Next, Ajdukiewicz’s paradigm of the empirical meaning rule are compared with Wit­tgenstein’s criterion for intersubjectivity. In conclusion, Ajdukiewicz’s measures are insufficient, according to the author, at least if confronted with Wittgenstein’s requirements for intersubjectivity.

Late Professor Ryszard Jadczak of N. Copernicus University of Toruń, whose premature death in June 1998 left his friends and colleagues in a deep sorrow, deserved fully to be named an official historiographer and biographer of the School. His short paper “Inspirations and Controversies: From the letters between K. Twardowski and A. Meinong” is quite typical for his style relying on the search through archives and finding there several documents, published next with a brief, but essential commentary. In the reported paper, Professor Jadczak gave us a summary of correspondence between the two great Brentanian scholars from the period 23th December, 1893 till 13th February, 1907. Most of the correspondence concerns questions of Twardowski and advises of Meinong concerning establishing a Psychological Laboratory at the Lvov University, following the example of the so famous in a near future Laboratory at Graz University, as well as quite typical university matters concerning promotions, opinions, etc. In two cases the correspon­dence became more essential and dealt with some problems concerning the theory of objects as well as some doubts regarding Brentanian psychologism.

In an extremely short, two pages long, paper “The Lvov – Warsaw School: The First School of Non-Positivist Scientific and Analytic philosophy” Władysław Krajewski of Warsaw University, after defining the notions of “scientific philosophy” and “analytic philosophy” is arguing for the title’s thesis, with which I fully agree.

Elżbieta Pakszys of Poznań University in her essay “Women’s Contributions to the achievements of the Lvov – Warsaw School: A Survey” is giving a valuable survey of the women’s presence and contributions to the Lvov – Warsaw School. The list includes: Maria Kokoszyńska – Lutmanowa, Seweryna Łuszczewska – Rohmanowa, Dina Sztejnbarg (after marriage with Tadeusz Kotarbiński – Janina Kotarbińska), Janina Hosiasson – Lindenbaum, Daniela Gromska, Eugenia Ginsburg – Blaustein, Halina Słoniewska, Irena Filozofówna and several other persons. And, last but not least, the two most important of them: Professor Izydora Dąmbska i Professor Maria Ossowska. By the way, being a pupil of Professor Dąmbska I must say that she did not like male – female distinction in the case of philosophers.

A short summary of the activity of persons mentioned above is also included.

In his short and very clearly written paper “Truth-Bearers from Twardowski to Tarski” Artur Rojszczak of Jagiellonian University is discussing two basic question concerning Tarski’s theory of formal languages and semantics for them: 1. What are truth – bearers for Tarski? Generally speaking they are sentences. But, is Tarski using the concept of a sentence univocally? The answer is not!

Rojszczak distinguishes 8 variants of the notion at least, each of them very nominalistic in spirit, treating a sentence as an utterance or an inscription, or a formula in one of the three general variants: as psycho-physical entities, abstract psycho-physical entities and physical entities. Main part of the essay is devoted to a confrontation of this nominalistic position, shared by Tarski, Leśniewski and Kotarbiński, with a more common, classical position of Brentano and Twardowski (as well as of Frege) saying that truth-bearers are judgments. The reviewer is a bit surprised that the author in his discussion omitted the dependence of Tarski’s analysis on its set-theoretical background, which plays for Tarski’s theory the role of its ontological framework, and that the author is not considering at all the fact that the same formula can be written both by Rojszczak and by Perzanowski, hence the notion of a sentence (formula) must be closed on similarity relation, which is its abstract component.

In the 16 pages long essay “Twardowski and Husserl on Wholes and Parts” Marek Rosiak of Łódź University is dealing with the basic difficulty of any mereology of wholes based on the notion of relation treated as a part of a given whole. He starts with difficulties of Twardowski’s analysis of wholes given in its Habilitation­schrift. It leads immediately to so-called “queer analysis” in the terminology of Husserl, quite similar to the problem of “relation’s nexus” in the terminology of F. Bradley and B. Russell: The relation which unifies parts into one whole has already as its relatum something which it just constitute.

This leads the analysis into a sort of a regressus ad infinitum or introduces “looping” of a relation with its own argument. In his famous “III Unter­suchungen” Husserl rejects this regressus, for a unity, according to him, is conferred on the “moments” in the connected pieces. To this end, Husserl considers a very basic notion of foundation, which is immediate and basic, say primitive, without any further reduction. Foundations are things which unite a whole, which itself is not a part of a whole but only a connection of wholes. Next, after scrutinization, the author also criticizes Husserlian notion of a whole based on its foundation. The notion is too wide and depends on the notion of exclusion as more basic and fundamen­tal.

Evgeni G. Vinogradov of Lviv State University in a very short paper “The Rationalistic Paradigm of Franz Brentano and Kazimierz Twardowski” made comments on a historiophilosophical ideas of Brentano and Twardowski, recalling Twardowski’s dictum that we must be very careful “to use philosophy with goals alien to it”.

Urszula Żegleń of N. Copernicus University of Toruń in her 6 pages long essay “Łukasiewicz’s Interpretation of Aristotle’s Concept of Possibility” discusses Jan Łukasiewicz’s life – long interest in Aristotle’s notion of possibility. It started in a short lecture read by Łukasiewicz on 5 June 1920 at Lvov University and finished in well known papers on Ł – modal logic and modal syllogistic published by Łukasiewicz in the fifties. As can be shown, Aristotle is somewhat misleading about the notion of possibility. He tried to distinguish a pure notion of possibility and two notions of contingency. Łukasiewicz’s analysis is compared with the analysis of Czeżowski, and is explained chiefly by means of Łukasiewicz’s 3 – valued logics: possibility is interpreted as something indeterminate.

The II Part of the book is devoted to achievements and influence of Stanisław Leśniewski. It contains 4 papers.

It starts with 22 pages long essay “De Veritate: Another Chapter of Bolzano – Leśniewski Connection” by Arianna Betti of Florence University. The paper is devoted to confrontation of views of B. Bolzano and St. Leśniewski on truth and other basic logical notions. The author is successfully arguing that Leśniewski was strongly influenced, either immediately or through, say, writings and lessons of Husserl and Twardowski, by Bolzano learning. The main theses of the paper are as follows: 1. in his prelogistic writings the early Leśniewski defines truth of sentences in such a way that truth conditions are the same as Bolzano’s; 2. From this point of view the links between some parts of Leśniewski’s early writings and some aspects of Ontology are closer than it is commonly taken, 3. It can be shown that some of Bolzano’s views come close to Leśniewski’s Ontology.

The paper is based on a fairly careful description of Bolzano’s logical universe and his theory of meaning (which is rather complex) as compared with Leśniewski’s early semantics (which is not so simple either). Truth -makers are quite similar: they are relationships for Bolzano and relation of inherence for Leśniewski. The chief difference concerns truth-bearers. In Bolzano’s writings they are lektological objects, propositions composed of ideas, whereas for Leśniewski they are linguistic entities, sentences composed of terms. Under this distinction we can see the difference between the Platonic position of Bolzano and a nominalistic position of Leśniewski. On the other hand, both philosophers shared the same truth conditions, expressing the classical definition of truth. In the final part of the essay, the author discusses truth conditions for sentences in Leśniewski’s Ontology, including its well-known existence assumptions. The last paragraph of the paper contains quite informative historical remarks concerning common dependence between philosophers in Austro-Hungariam Empire.

“Leśniewski’s Conception of Logic” is discussed in a paper by Roberto Poli and Massimo Libardi of Trento University. It is well-known that Leśniewski based his idea of logic on a paradigm different to the common paradigm of modern mathematical logic, namely on the paradigm of traditional logic. Clearly, he changed it a bit. But the kernel ideas of traditional logic remains untouched. In particular, his basic calculi: Ontology and Mereology can and should be understood as calculi of names using quantifiers, introduced by Leśniewski’s Protothetic. Relying on these clues he defined logic as the discipline that investigates the question which propositions are true and which false. But the form of propositions under con­sideration is quite traditional.

In the paper “Non-Elementary Exegesis of Twardowski’s Theory of Presen­tation” Vladimir L. Vasyukov of Russian Academy of Science, Moscow is trying to interpret Twardowski’s theory of presentation into the framework of his own system of non-elementary Formal Phenome­nology, partly based on Leśniewski’s systems. Special emphasis is put on quantifying names into the framework of Twardowskian formal phenomenology, which is next formalized as a version of applied Protothetic.

Finally, Toshiharu Waragai of Tokyo Institute of Technology in his essay “On Some Essential Subsystems of Leśniewski’s Ontology and the Equivalence Between the Singular Barbara and the Law of Leibniz in Ontology” introduces and studies three natural subsystems of Leśniewski’s Ontology, obtained by suitable weakening of its basic axiom. The systems are shown to have a natural semantics and several natural equivalents. In particular, the position of Leibniz’s Law in the new system is investigated and shown to be equivalent to the singular Barbara figure.

Part III “Philosophy of Language” contains 5 papers.

The first one is the paper “The Paradox of Grelling and Nelson Presented as a Veridical Observation Concerning Naming” by Andrzej Grzegorczyk of Polish Academy of Science, Warsaw. The main enemy of the paper is antipsychologism. According to Grzegorczyk this strongly rationalistic attitude to logic and mathematics is responsible, at least in part, for the fact that the new semantical antinomies have appeared. Antipsycholgism is, in fact, an idealistic simplification.

In the paper the author, trying to overcome antipsychologism, is sketching in the paper rudiments of a semantics based on a psychological anthropology, which is quite similar to the old psychologism. But the rules of the new semantics are now strict. Semantics and logic, according to Grzegorczyk, deal with human utterances. Logic is a set of rules which are tools of the mind.

To illustrate his approach, the old master of Polish Logic is presenting a new solution to the Grelling-Nelson antinomy. The basic theory behind is a theory of naming. After introducing the full apparatus the old antinomy becomes a proof of a theorem showing a limitation of human mind. The main theorem says: There is a methodologically correctly defined empirical notion such that no human being accurately uses this notion.

I fully agree with the main thesis of Grzegorczyk’s work. I think, however, that he uses a rather old-fashioned distinction and a way to see the question. The old psycholo­gism is over. What we have instead, and what is the topic of Grzegorczyk’s discussion, is a new field of interdisciplinary domain of cognitive sciences. Logic is one of them. What Grzegorczyk is doing is simply transferring the old semantical paradoxes into Kantian in spirit theorems about limitations of human mind.

In a short article “Dąmbska, Quine, and empty names” Michele Marsonet of the University of Geneva, after comparing Dąmbska’s classic piece “Concerning the so-called Empty Names” with distinctions and considerations made by Kotarbiński and Quine shows quite clearly to what extent Dąmbska’s approach was a very early anticipation of the modern debates concerning names. “Going back now to Dąmbska’s article on empty names, we find there a clear understanding (as early as 1948) of the untenability of the neopositivist and purely linguistic approach, along with some clear anticipations that are today widespread following the post-empiricist turn. She recognized, for example, that the extension of the term ’empty name’ varies according to our Weltanschaung ….her short 1948 article is a very interesting anticipation of the current debate on conceptual schemes as well.”

Krystyna Misiuna of Warsaw University in her paper “Truth and Time” presents one of the chief polemic of the School: Is Truth time dependent or not? I.e., are statements concerning future true eternally, or they are true with suitable time relativization? In this important for the history of the School discussion took part such scholars as Twardowski himself, Kotarbiński, Łukasiewicz and Leśniewski.

The author in her paper is particularly devoted to famous Jan Łukasiewicz’s paper “On Determinism”.

Marian Przełęcki of Warsaw University in his paper “The Postulate of Precision: Its Sense and Its Limits” is trying to precise precision itself and to show their limits. He decided to put out of scientific precision’s domain reasoning with vague concepts, therefore quite a lot of philosophy, including most of metaphysics, and, of course, most of religious claims. The position of the author is rather moderate, however: “Absolute precision is unattainable. We must then learn to live with imprecision – to think and to speak rationally in spite of its all-pervasive presence.”

In 20 pages long essay “Polish Logic, Language, and Philosophy of Language” by Ryszard Zuber of CNRS, Paris a quite clear survey of the title’s subject is given. Some features and characteristic points of Polish Logic (like Leśniewski’s Systems) are clearly connected with special features of the Polish Language (lack of definite or indefinite articles, etc.).

The author starts with a short discussion of some Polish contribution to the study of the structure of a natural language, like Ajdukiewicz’s work on the categorization of linguistic expressions or also Ajdukiewicz’s work concerning the problem of intensionality of sentential operators formed from the verbs of propositional attitudes. The author stresses here Tarski’s famous criterion of the finite axiomatizability of deductive systems, for they imply, inter alia, the axiomatiza­bility of extended categorial grammars and, on the other hand, such unaxiomazi­bility of several other systems (for example, Grice’s implicature, Tokarz 1994). Particular emphasis is put on Polish works on the Extended Categorial Grammar (Buszkowski, Zuber, Kandulski and others). Also, the work on noun construction should be mentioned here, particularly the general work on determiners and generalized quantifiers initiated by the famous paper of Mostowski 1957.

Part IV of the book contains 4 papers and it entitled “Logic and the Foundations of Mathematics”. It is the kernel of the book indeed.

Wojciech Buszkowski of Poznań University in 11 pages long essay “The Ajdukiewicz Calculus, Polish Notation and Hilbert – Style Proofs” considers the question of a generalization of Ajdukiewicz’s parsing procedure to a broad class of languages written in Polish notation. Some gap in Ajdukiewicz’s justification of the unambiguity of Polish notation is pointed out and corrected. A general theorem which characterizes MP – reductions is given. Further, other links between Hilbert -style systems and formal grammar are also discussed, namely unification based learning algorithms and a grammatical consequence operation.

Andrzej Indrzejczak of Łódź University in a paper “Jaśkowski and Gentzen Approaches to Natural Deduction and Related Systems” compares, in a careful and very detailed way, the two approaches to Natural Deduction mentioned in the paper’s title. The author compares two systems of Natural Deduction: one due to Jaśkowski (1929, 1934) and another one due to Gentzen (1934). Next he confronts them with the sequent calculus of Gentzen (1934), and finally he adds a few words on Natural Deduction system introduced by Gentzen in 1936. Similarities and differences between systems compared are especially emphasized. Finally, the author is providing the reader with a very short, but informative, history of different lines of development Natural Deduction systems, including Tableaux ones.

“The Contribution of Polish Logicians to Recursion Theory” by Roman Murawski of Poznań University is a very well-written history of appropriate works of A. Tarski, A. Mostowski, A. Grzegorczyk (with his famous hierarchy of the primitive recursive functions), A. Janiczak and others. A special attention deserves the work of Andrzej Mostowski in investigation so-called Kleene – Mostowski hierarchy of arithmetical notions. Computable functionals, after introducing by K. Gödel and S. C. Kleene, were also investigated in Poland by Andrzej Grzegorczyk in the sixties. From work concerning constructive foundation of mathematics the Banach – Mazur’s computable analysis deserves a special attention. In this connection, the reviewer is a bit surprised that the work of Leon Chwistek and his coworkers is completely omitted by the author.

Ewa Orłowska of the Institute of Telecommunications, Warsaw in 18 pages long essay “Studying Incompleteness of Information: A Class of Information Logics” explores possible foundations for reasoning about knowledge discovered from incomplete information. Her basic idea is to explore of usual Kripke’s definition of satisfaction , with the notion of structure made more specific, however. Structures are derived directly from data provided by a user. Several logical systems for reasoning about such structures are developed. It is assumed that the user’s data consist of descriptions of some objects as explicit information in terms of their properties. Relations of structures are determined by subsets of properties of the respective objects.They reflect some aspects on incompleteness of the respective objects.

Two major groups of frames are considered: frames with indiscernibility – type relations and frames with orthogonality – type relations. The logics introduced in the paper are of a kind of modal logics with multiple modal operators. The paper ends with consideration of two kinds of a plain calculus of information (including implicit information only) and by showing that the system of Aristotelian syllogistic is a formal system adequate for reasoning about these relations.

Part V of the book “Ontology, Epistemology, Philosophy of Science” contains 5 papers.

The first one, “On Łukasiewicz’ Theory of Probability” by Timothy Childers and Onrej Majer from the Institute of Philosophy, Czech Republic Academy of Science, Prague is chiefly devoted to Łukasiewicz’s theory of probability from 1909-13, which despite its early occurrence, is rater neglected. The authors, after restating and clarifying theory in modern terms, are paying special attention to the theory itself. Both Łukasiewicz’s original motivations as well as historical reasons are taken into account.

Łukasiewicz identifies probability with “the truth value of an indefinite proposition” which is “the ratio between the number of values of the variables for which the proposition yields true judgments and the total number of values of variables”. It is not clear, what Łukasiewicz meant by “indefinite proposition”. The bulk of the paper is devoted to clarification of this rather obscure notion. The basic idea of the authors is to take an indefinite proposition as a prescription for forming sets of closed formulas, i. e., as prescription for taking set of models, which depends on a priori restriction (Łukasiewicz’s well-definite finite range). Some puzzles concerning Łukasiewicz’s notion of probability are next considered and partially answered. The authors show, in conclusion, that it is possible to explicate Łukasiewicz’s conception of probability in modern terms (done by de Finetti and
von Mises), and that the theory is workable, but with different motivations and goals.

Jan Czerniawski of Jagiellonian University, Cracow, in his short, 3 pages long paper “On What There Is – A Vindication of Reism” tries to revive and vindicate ontology saying that only concrete objects, called things, exist. To this end he decided to broke connections between a semantical thesis under discussion and the ontological one. He also believes that if somebody claims that the only objects that exist are things, but is interested in negative theses of Reism rather than in positive ones, he or she does not need any definition of a thing (what the reviewer fond to be just amusing oversimplification). The author advice is to rely on free logics rather than on Leśniewskian Ontology and to take more seriously some claims of phenomenology as the basic for a “new reism”.

Short paper “On the Concept of a Subject of Cognition in Ajdukiewicz’s Philosophy” by Anna Kanik of Jagiellonian University, Cracow, is a very clear discussion of the title’s question in strict connection, as Ajdukiewicz did, with the notion of science in at least three meanings, and its dependence on the connected notion of language.

“Induction and Probability in the Lvov – Warsaw School” is investigated by Ilkka Niiniluoto of Helsinki University. In his 12 pages long paper the author not only reports the work concerning the title’s subject done by the members of the School, but also compares it with the similar work done by people not belonging to it. As a matter of fact, the reader is provided with a short history of the subject.

Induction and probability were, in fact, not among the strongest areas of scientific interest of the School. In its early period Łukasiewicz did important work on probability and induction, presented in the above mentioned paper of Childers and Majer. However, the most important studies in the field of induction and confirmation theory were made by Janina Hosiasson (after marriege: Hosiasson – Lindenbaum) in the late 1920’s. She started the logical interpretations of probabilities as special values of sentences. The investigation was continuated after World War II by, among others, Jerzy Łoś.

The main approach in the School, since Łukasiewicz till Łoś, to the theory of induction was probabilistic. The chief work in this direction was done by Janina Hosiasson, however. She defended the view that inductive inference is justifiable, if its conclusion is not the hypothesis itself but the assignment of a degree of confirmation to the hypothesis. Finally, Ajdukiewicz’s work on inductive acceptance has to be also mentioned in this short summary.

The 4 – pages long piece “Łukasiewicz’s Logical Probilities and a Puzzle About Condinalization” Tomasz Placek of Jagiellonian University concerns some puzzles arising in Łukasiewicz’s theory. If you are ready to accept the rule of simple conditionalization: p'(A) = p(A/B) = = p(A and B) / p(B), and the idea that for a given intermediate sentence its probability is the ratio of the number of all true corresponding sentences to the number of all corresponding sentences you can immediately produce paradoxes connected with estimations of probabilities of a real events (like tomorrow travel). Conditionalist’s answer is namely different than determinist’s one.

Part VI, the last part of the book entitled “Logic and Philosophy” contains 4 papers.

It starts with 10 pages long essay by one of the book co-editor, Katarzyna Kijania – Placek of Jagiellonian University “Truth as Consensus. A Logical Analysis”. She follows some ideas of well – known philosophers of science, Edmund Poznański and Aleksander Wundheiler from their classic paper “The concept of truth in physics” (1934), taking that the notion of truth, at least in the case of physics, is operationalist one. Their proposal contains two proposals together: the coherence criterion and the common agreement criterion. The last criterion is just the one treated in the paper.

In the paper under discussion the author proposes to treat common agreement as a special case of majority argument. The idea is next executed in the framework of the first-order predicate logic with the generalized quantifier “most of x” added to its usual vocabulary. Partial models for such a calculus are analyzed in a fairly detailed and careful way and usual completeness theorems are provided.

Avenir I. Uyemov of Odessa University, Ukraine, in a short essay entitled “The Lvov – Warsaw School and the Problem of a Logical Formalism for General Systems Theory” compares the approach to analysis common for Lvov – Warsaw School with much more modern approach of the General Systems Theory. Some of the results of the School are occurred to be quite precursory from the modern point of view.

The 12 pages long essay “From Closure – Operating Deductive Methodology to Non – Standard Alternatives” by Stanisław J. Surma of Auckland University, New Zealand, is a generalization of the classical Tarski’s methodology of formal systems, done in a spirit of the Warsaw Logical School, and generalizing it into direction of abstract logic in Suszko’s style. The author distinguishes two classical Tarski’s operators: Cn – being a usual consequence (or closure) operator and Th – operator which for a given consequence relation defines its theories (i.e., closed on Cn systems) plus three new. They are: Cons, Ln and Max denoting respectively (and rather informally) all consistent sets of formulas, the family of all Lindenbaum oversystems of a given system, and the property of maximality, e. g. that of deductive completeness which is characterized as a non-trivial and regular family of subsets of a set of all formulas. The reader should be warned that the exact definitions of the notions under investigation needs much more care. The author of the paper is successfully looking for counterparts, for five notion introduced, of the well – known duality condition of J. Schmidt (1952): Cn(Th(Cn)) = Th(Cn(Th)).

Last but not least, is the paper “Forgotten and Neglected Solutions of Problems in Philosophical Logics” by Paul Weingartner of Salzburg University. It includes quite interesting and illuminating discussion of several questions of classical philosophy, like: Aristotle’s question – Is being a most compressive class or predicate? The modern answer is not! A solution to the Liar Paradox proposed by Paulus Venetus, or non modal intensions as the way from Aristotle to de Morgan are also discussed. Relevance implicit in Syllogistic is also studied as well as, for example, Anselm’s Ontological Argument interpreted with Intuitionistic Logic, etc. Weingertner essay is a nice contribution to logical philosophy, and probably the best choice to finish the book, for finis coronat opus.

The book under review contains nearly half of papers read at the Conference. The most important results of the School, like Tarski’s semantics, his Theory of Models, or Wajsberg and Łoś’s work on logical matrices, are omitted or only mentioned in it.

Despite these shortcomings, the book is quite informative collection of clearly written papers, convincing the reader about fairly high position of the School in
XX Century, not only analytical, philosophy.

Editors should be congratulated for the fine job they did, and for its fruits.

Jerzy Perzanowski