Logic of Science

in the particular sense, a discipline that applies the concepts and technical apparatus of modern logic to the analysis of systems of scientific knowledge. The term is also often used in reference to the laws by which a science develops (the logic of scientific development), the rules and procedures of scientific investigation (logic of investigation), and the study of the psychological and methodological presuppositions of scientific discoveries (the logic of scientific discovery).

The logic of science began developing as a specialized discipline in the second half of the 19th century and took definitive form in the first quarter of the 20th, under the influence of the ideas of G. Frege, B. Russell, and L. Wittgenstein. The members of the Vienna Circle, under M. Schlick, as well as H. Reichenbach and the members of the Berlin Society for Scientific Philosophy and other philosophers, naturalists, and mathematicians (K. Popper, V. Dubislav), undertook intensive study of the logic of science. Since the starting point of the overwhelming majority was neopositivism, the opinion became widespread over the years that the logic of science is a specifically positivist approach to the philosophical and methodological analysis of scientific knowledge. In fact, however, the neopositivist approach is only one of the ways in which the logic of science might be interpreted.

Along with the representatives of neopositivism, pragmatism, neo-Thomism, and the philosophy of linguistic analysis, philosophers and logicians who have taken the position of dialectical materialism have also participated actively in the development of the modern logic of science. Intensive investigations in the logic of science have been conducted in the USSR, the USA, Poland, Great Britain, the German Democratic Republic, the Federal Republic of Germany, and Italy.

The sphere of problems encompassed by the logic of science includes the study of the logical structures of scientific theories; the study of the manner in which the artificial (formalized) languages of science are constructed; the investigation of the various types of deductive and inductive inferences used in the natural, social, and technical sciences; the analysis of the formal structures of fundamental and derived scientific concepts and definitions; the examination and perfection of the logical structures of research procedures and operations and the development of logical criteria to test their heuristic effectiveness; and the investigation of the logicoepistemological and logicome-thodological content of the reduction of the scientific theories (and such processes as abstraction, explanation, prediction, and extrapolation) most often used in all spheres of scientific activity.

The application of formalization methods is an important tool in the logical analysis of systems of scientific knowledge. One advantage of the formalization method is that it makes it possible to elucidate logical connections and relationships and fixes strict rules to guarantee the deduction of the most reliable knowledge from the initial premises of a given theory. These premises emerge after their logical treatment as axioms of the formalism under consideration. In the case of deductive theories, this is a matter of the rules of necessary inference. The deductive construction of a theory is most often encountered in mathematics, theoretical physics, and theoretical biology and in scientific disciplines that rest on them.

The rules of inductive theories characterize various forms of probabilistic inference. Inductive theories are typical of most empirical sciences in which, for various reasons, indeterminacy situations arise that are associated with incomplete information about the connections, properties, and relationships of the objects of investigation.

The creation of formalized systems makes it possible to investigate a number of the most important logical properties of the meaningful theories reflected in a given formalism. These properties especially include the consistency, completeness, and independence of the initial postulates of the particular theory.

The discovery of the commonality of the logical structures of scientific theories that differ in content has opened up great possibilities for transferring the concepts and methods of one theory to the field of another, for substantiating the possibility of reducing one theory to another, and for elucidating the common conceptual and methodological presuppositions of different theories. This has particular importance in unifying and simplifying systems of scientific knowledge, especially under the conditions created by the rapid emergence and development of new scientific disciplines.

A special place in the logic of science is occupied by problems related to the empirical substantiation and verification of the theories and hypotheses of the natural sciences and sociology. Intensive investigations in this sphere have demonstrated the unsoundness both of the early neopositivist principle of complete verifiability and of the criterion of falsifiability. The difficulties that arose in the neopositivist logic of science drew the attention of many logicians and philosophers to the problem of the connection and interaction of logical structures with the structures of objective and experimental practical activity. This results in a whole series of new approaches to the logic of science and explains to a considerable degree the growing interest among foreign logicians in the principles of the theory of knowledge of dialectical materialism.

Of particular interest is logical semantics, which deals with the study of the sense and meaning of theoretical and empirical terms in the language of different sciences. A whole series of complex problems has arisen with the discovery that predicates—by means of which concepts are expressed and the rules of given scientific theories are formulated—do not reduce exhaustively to observation predicates that fix the results of direct scientific observations and experiments. Among the most important of these are the problems of the logical analysis of the vocabularies of various sciences, the rules by which the language of theory is translated into that of observation, and the investigation of the interactions and interrelationships between natural languages and artificial ones. Studies in the semantics of general scientific terms, such as “system,” “structure,” “model,” “measurement,” “probability,” “fact,” and “theory,” have taken on particular importance here. Multiplicity of meaning and the different methods in which these words are used, which have been revealed with the rapid development of cybernetics, structural linguistics, systems theory, and other fields, have made logicomethodological analysis the most important prerequisite for the effective reorganization and heuristic use of such concepts.

The most recent period (since the late 1950’s) has proved to be a turning point in the development of the logic of science, not only because of the recognition of the essential limitations of the neopositivist interpretation but also because extremely significant progress has been made in the spread of the ideas and methods of logical analysis to the social sciences. Intensive investigations have been conducted in the study of the language, structure, and rules of argument of legal, ethical, and, in part, sociological theories. Notable results have been obtained in the logic of decisions, the logic of norms and valuations, and the logic of systems. The technical and conceptual tools of those aspects of symbolic logic referred to as nonclassical (various aspects of polysemantic logics, modal logics, and the logic of probabilistic and statistical reasoning) have become common in these areas. The application of the logic of science to a number of sociological disciplines, however, has met with considerable difficulties, related, on the one hand, to the complexity of the laws and theoretical structures of these sciences and, on the other, to the insufficient development or complete absence of an adequate mathematical apparatus. Further development of the logic of science, therefore, requires more intense inquiry into symbolic logic, in all of its varieties.

In the USSR, the study of the logic of science is conducted most intensively at the institutes of philosophy of the Academy of Sciences of the USSR, the Academy of Sciences of the Ukrainian SSR, and the Academy of Sciences of the Georgian SSR and at the departments of philosophy of Moscow, Leningrad, and Tbilisi universities.