1. ON THE METHOD OF PRESENTATION OF LOGIC
As any other science, logic is immersed in a certain cultural and linguistic medium without which it cannot exist as a science. This fact manifests itself, in particular, in that in logic one constantly has to use certain intuitively obvious and easily understandable considerations, to make use of simple examples and explanations in ordinary language. While all this is outside of the sphere of logical laws, without this material the latter cannot be formulated and understood. And it is not a retreat from the methods of logic. On the contrary, it is a necessary element of the methodology of every science if the latter is interpreted as a whole, and not as a collection of its individual problems that may, to a certain extent, acquire an individual existence and produce an impression of independence of the above medium. As the presentation of logic becomes more and more detailed, the need for such a common medium increases. One of the reasons for this is that logic comes closer to the surface of linguistic practice, where one has to take into account a considerable number of circumstances that violate the purity of logical norms; another reason is that logic deals with linguistic expressions that by their very nature represent a product of numerous and varied sources and function in a complex system of linguistic connections. Of the elementary purity of logical constructions which can be seen, for instance, at the level of the propositional calculus, very little is left here. In this situation, the complexities associated with deduction are replaced by those related to the necessity of coordinating a great number of various analytical factors. Because of this, the method of presentation of logic changes. At present, a presentation based on supplementary addition of new definitions and assertions, in no way affecting the previous discussion, is already impossible. A situation arises now when we have to consider at once a whole combination of problems, conceptions and statements. But it is impossible to speak about everything at once. A consistent analysis of one kind of problem implies abstraction from the others, acceptance as given of a whole number of terms and statements which in further discussion become a subject of special study. As a result of this, the presentation of material no longer corresponds with the notion of the presentation of logic formed on the basis of observation of the logic of propositions and predicates in contemporary courses of logic. In what follows we shall from the very beginning have to make use of expressions which later will become a subject of our analysis. There is no vicious circle here at all, since we shall mean the explication of linguistic expressions that is necessarily accompanied by their 'doubling'.
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