Jan Wolenski

The semantic theory of truth, formulated by Alfred Tarski in the 1939s, is primarily a mathematical theory. On the other hand, it also has a considerable philosophical content. This paper presents the second aspect of this theory. It can be shown that several traditional philosophical issues pertaining to the concept of truth can be illuminated by Tarski’s account of truth. It concerns, for instance, the idea of correspondence, the relation of truth and logic, the problem of the relativity/absoluteness of truth, etc.

The Polish School of Logic flourished in the period 1920-1939. Philosophically, it was influenced by Kazimierz Twardowski, professor at the University of Lwow (now Lviv in Ukraine), who established the Lwow-Warsaw School, to which the mentioned logical group belonged. Twardowski claimed that logic is very important in every kind of human activity, professional as well as private. Hence, every argument should be clearly formulated and proceed by correct inferential rules. These postulates involved semiotics, formal logic, and methodology of science — that is, logica sensu largo. This position was accepted by Twardowski’s most distinguished students, such as Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz, and Tadeusz Kotarbiński, who graduated before 1914, as well as the next generation of logicians and philosophers, particularly by Alfred Tarski. Although all these people considered logic, philosophy, and science as completely neutral with respect to politics and ideology, they treated logical skills as indispensable in political activities. In philosophical specialized terminology, Polish logicians regarded logic as a weapon against irrationalism. This position was also represented by Polish logicians who did not belong to the group of Twardowski’s students.

This paper provides an interpretation of Father Bocheński’s saying “Beyond logic there is only nonsense.” He considered the battle against superstitions of various kinds as one of the most important intellectual and social duties. The phrase in itself suggests that logic is a weapon in the mentioned battle. Logic is understood broadly, that is, as semantics, formal logic and the methodology of science, and was considered by Bocheński as the main instrument of rational philosophy. Hence, the formula under discussion has an explicit metaphilosophical significance, although Bochenski’s understanding of the concept of differs from that of the Vienna Circle.

The view I defend here is that ought cannot be logically derived from is. This can be justified at the level of very elementary deontic logic, as captured by the generalized logical square. This logical fact can be stated as the Hume thesis. However, the inspection of a given normative order may suggest that something exists. On the other hand, such conclusions can be fallible. In order to argue that ought is derivable from is, one must use extralogical elements and, in particular, definitions. Such strategies are in fact employed by Searle and Conte.

The book is a collection of the author¿s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner.

Tadeusz Kotarbinski is one of towering figures in contemporary Polish philosophy. He was a great thinker, a great teacher, a great organizer of philosophical and scientific life, and, last but not least, a great moral authority. He died at the age of 96 on October 3, 1981. Kotarbinski was active in almost all branches of philosophy. He made many significant contributions to logic, semantics, ontology, epistemology, history of philosophy, and ethics. He created a new field, namely praxiology. Thus, using an ancient distinction, he contributed to theoretical as well as practical philoso~hy. Kotarbinski regarded praxiology as his major philosophical "child". Doubtless, praxiology belongs to practical philosophy. This collection, howewer, is mainly devoted to Kotarbinski' s theoretical philosophy. Reism - Kotarbinski' s fundamental idea of ontology and semantics - is the central topic of most papers included here; even Pszczolowski' s essay on praxiology considers its ontological basis.,Only two papers, namely that of Zarnecka-Bialy and that of Wolenski, are not linked with reism. However, both fall under the general label "Kotarbinski: logic, semantics and ontology". The collection partly consists of earlier published papers.

The problem of induction belongs to the most controversial issues in philosophy of science. If induction is understood widely, it covers every fallible inference, that is, such that its conclusion is not logically entailed by its premises. This paper analyses so-called reductive induction, that is, reasoning in which premises follow from the conclusion, but the reverse relation does not hold. Two issues are taken into account, namely the definition of reductive inference and its justification. The analysis proposed in the paper employs metalogical tools. The author agrees with the view that a quantitative account of degree of confirmation for universal theories via logical probability is problematic. However, prospect for a qualitative approach look as more promising. Using the construction of maximally consistent sets allows to distinguish good and worthless induction as well as shows how to understand induction in a semantic way. A closer analysis of deductivism in the theory of justification shows that it is a hidden inductivism.

According to the received view formal semantics applies to natural language to some extent only. It is so because natural language is inherently indefinite, in particular, its expressions are ambiguous, vague and admits departures from syntactic rule. Moreover, intensional contexts occur in ordinary language—it results in limitations of the principle of compositionality. The ordinary conversation appeals to various principles, for instance, Grice’s maxims which exceed logical formalism. Thus, ordinary language cannot be fully formalized. On the other hand, if L is a formal language, its metalanguage ML, must be partially informal—for instance, it contains, terms of ordinary mathematics, especially set theory. Even, if, for instance, due to the technique of aritmetization, ML can be represented in L, such a representation is only local. In fact, this view can be derived from some Tarski’s remarks on the role played by natural language. It is usually assumed that the universality of natural language, is the source of troubles associated with antinomies. It is so this circumstance requires a solution, for example by distinguishing levels of language. However, even if antinomies are excluded, what is informal is prior with respect to what is formal. It shows that formal semantics has limitations even with respect to formalized languages.

This paper describes the story of the German translation of Tarski’s seminal work The Concept of Truth in Fomalized Languages, originally published in Polish in 1933; the German translation was published in 1935 and became a sensation in logic and philosophy. The story is based on the letters exchanged mostly between Tarski and Kazimierz Twardowski (other persons were involved as well); this collection was discovered 3 years ago. The letters clarify some terminological points, changes in Tarski’s views, participation of other people (Kazimierz Ajdukiewicz, Rudolf Carnap, Maria Kokoszyńska and Karl Popper) in doing translation as well as the ways of the early influence of Tarski’s work.

This paper discusses the concept of metalogic, its methods and the role in logic. The problem of how logic is used in metalogic is also a topic of the author’s considerations. Metalogic is understood here as that part of metamathematics which is restricted to logical systems, and refers to studies of logical systems by mathematical methods. The scope of metalogic depends on the range of the concept of logic. The paper focuses on classical first-order logic, but some remarks concern other systems as well.Metalogic exhibits various properties of logics via definitions and metatheorems, concerning completeness, consistency, etc. It is argued that attributes of logical systems without formal use in metalogic would be very vaguely understood. These methods cover an amount of mathematics as well as of logic itself. Hence the question of how strong metalogic should be in order to prove metalogical theorems. Any answer has to delimit the repertoire of logic used in metalogic. This leads to the problem of circularity of metalogic and the question concerning the source of meaning for logical constants.