Here we shall employ the term "classical" to denote situations in science in which all propositions satisfy all the laws of classical logic, including that of excluded middle. This means that if x is a proposition of a given field of science, then the following statements will be true in regard to it: "either x or non-x," "either x is true or non-x is true," "x is either true or false." The emphasis here upon the law of excluded middle is (...) associated with the fact that criticism of this law is the basic content of nonclassical criticism of classical logic. (shrink)

I. Mathematical logic has long since come into use in the solution of individual problems of interest in the methodology of science. In this connection the question arises as to how effective this use is, and what its prospects are. Before formulating any general and categorical judgments on that score, it would be useful to discuss special cases of the application of mathematical logic to the methodology of science. In the present article we shall deal with one case of this (...) order, to wit, the utilization of mathematical logic in investigating the problem of possibility and necessity. (shrink)

The distinctive features of the properties and conditions of research into phenomena of the microworld relative to investigations into phenomena of the macroworld created so strong an impression in important circles that people have even begun to speak of a special logic of the microworld differing fundamentally from that familiar logic which came into being on the basis of the study of phenomena of the macroscopic world. The reader can find information about this in the works of Kuznetsov , Piatnitsyn (...) , and the present author. (shrink)

Various interrelationships between two-valued and many-valued logics are examined in . In the present article we propose to discuss questions bearing on these interrelations which have either not been clearly identified as philosophical in that book, were not given sufficiently detailed explanation, or were not touched upon at all.