In pursuing any kind of scientific activity, we pose a certain problems, and seek solution of them by various methods; as a result, we form our own judgements on the matter to which the given problem pertained, and finally make public this judgement, which is a solution of the problem posed, in conjunction with the relevant evidence. Freedom to pursue science thus requires freedom in each of the four fields mentioned above; that is the individual pursuing scientific activity must enjoy freedom to choose problems, freedom to choose a method, i.e., the means whereby he/she solves his/her problems, freedom of thought, and freedom of speech. Kazimierz Ajdukiewicz (1890–1963), a philosopher of science analyses here all these four “freedoms”, as well as considers both the extent to which each of them is indispensable to the successful advance of science and the extent to which a limitation on them can be justified on other grounds.
Ajdukiewicz's lectures, edited from extant stenographic records, are concerned with various types of semantic function. Lecture III explains the 'behavioural' and associative role of signs, introduces the notion of 'field of representation', and describes a special sort of representation based on isomorphism. Lectures IV and V discuss two theories of linguistic meaning: the 'expressivist' view, according to which an object is used as a linguistic expression if it is employed in order to convey information, and the 'associationistic' view, according to which a linguistic expression must be capable of evoking thoughts in the mind of the addressee. The criteria are regarded as both too broad and too narrow. Lectures VI-VIII present a more sophisticated semantic theory based on Husserl's distinction between 'presenting content' and intention. Ajdukiewicz points out that it does not take into account the compositional aspect of linguistic expressions.
During the first semester of the academic year 1930/31 in the John Casimir University in Lvov Kazimierz Ajdukiewicz delivered a series of lectures on logical semantics. In eight of them, now published for the first time, he presents - in the very clear manner - his fractional method of identifying syntactic categories, and he shows how to use this method to eliminate the antynomies of classes, relations and properties. The Ajdukiewiczian method had been appreciated among logicians and it is considered widely one of the starting points of so-called categorial grammars.
The main aim of the study - written by Ajdukiewicz in 1913 in order to fulfil the requirements for a teaching certificate - is to provide a clear classification of set-theoretic paradoxes (Russell's, Burali-Forti's, Richard's, König's, and Berry's) and to present a uniform way of framing them, which combines ideas put forward by Grelling, Nelson, and Russell. In the last part of the study, Ajdukiewicz surveys available solutions (Poincaré, Richard, Russell, Frege, Bernstein, Jourdain) and comments on their validity. The edition is based on a typescript.
The lectures recorded by Stefan Oleksiuk mainly concern the part of logic called, in Polish terminology, “logical semiotics” (application of formal logic to matters of natural language). Ajdukiewicz discusses several important philosophical issues, such as the problem of meaning, representation, the status of general names, the truth-value of sentences or propositions, and identity