1. Main assumptions, objectives and conditionings 1.1. The present book is concerned with certain problems in the logical philosophy of language . It is written in the the Polish logical, philosophical, and semiotic spirit of syntax of tradition, and shows two conceptions of the categorial languages : the theory of simple languages, i.e ., languages which do not include variables nor the operators that bind them (for instance, large fragments of natural languages, calculi, the language of languages of well-known sentential Aristotle's traditional syllogistic, languages of equationally definable algebras), and the theory of w-languages, i.e., languages which include operators and variables bound by the latter

No discipline has been more praised or more criticized than the writing of history. Cioero claimed that history teaches men how to live. Aris totle denied it the very name of science and regwded poetry as the higher wisdom. At various times history has been assigned a command ing or a demeaning statIUs in the hierarchy of sciences. Today one can admire the increasing precision and sophistication of the methods used by historia: ns. On the other hand, Thucydides' History of the PeZo ponesian War still serves as the ideal model of how to reconstruct the historical past. Even those who deny the possibility of an objective reconstruction of the past would themselves likie to be recorded by historians, "objectively" or not. Dislike of history and fear of its verdict are not incompatible with reverence and awe for its practitioners, the historians. So man's attitude to history is ambiguous. The controversy about history continues. Widely differing issues are at stake. Historians themselves, however, are the least engaged in the struggle. Rarely does a historian decide to open the door of his study and join in the melee about the meaning of history. More often he slams it shut and returns to his studies, oblivious of the fact that with the passage of thne the gap between his scientific work and its audience might widen. The historian does not shun the battle, he merely chooses his own battleground."

In the Introduction to the Polish-language version of the present book I expressed the hope that Polish studies in semiotics would before long be numerous enough to make possible another anthology on semiotics in Poland containing material published since 1970. That hope has in fact come true. The fact that semiotic research has been gaining momentum in this country is reflected in the growing interest in the discipline, in expanding international contacts, and in the steady increase in the number of publications. Thus, 1972 saw the setting up of the Department of Logical Semiotics, headed by the present writer, at Warsaw University Institute of Phi losophy. The seminar on semiotics, which I started in 1961, had met more than two hundred times by the end of 1976; since 1968, meetings have been held jointly with the Polish Semiotic Society. Another semi nar, confined to university staff and concerned with logical semiotics, which was inithted in 1970, had met more than fifty times by the end of 1976. The former seminar often plays host to foreign visiting pro fessors; so far scholars from Australia, Belgium, Britain, Canada, Czechoslovakia, France, the German Democratic Republic, Italy, the Netherlands, the Soviet Union, and the United States have attended."

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G."

When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers."

No discipline has been more praised or more criticized than the writing of history. Cioero claimed that history teaches men how to live. Aris totle denied it the very name of science and regwded poetry as the higher wisdom. At various times history has been assigned a command ing or a demeaning statIUs in the hierarchy of sciences. Today one can admire the increasing precision and sophistication of the methods used by historia:ns. On the other hand, Thucydides' History of the PeZo ponesian War still serves as the ideal model of how to reconstruct the historical past. Even those who deny the possibility of an objective reconstruction of the past would themselves likie to be recorded by historians, "objectively" or not. Dislike of history and fear of its verdict are not incompatible with reverence and awe for its practitioners, the historians. So man's attitude to history is ambiguous. The controversy about history continues. Widely differing issues are at stake. Historians themselves, however, are the least engaged in the struggle. Rarely does a historian decide to open the door of his study and join in the melee about the meaning of history. More often he slams it shut and returns to his studies, oblivious of the fact that with the passage of thne the gap between his scientific work and its audience might widen. The historian does not shun the battle, he merely chooses his own battleground.

When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers."