Classical, Relativistic and Constructivist Ways of Asserting Theorems

Abstract

Most people who use formal systems, and in particular logical systems, feel that because these systems lack any connection with colloquial speech, they also lack the function of expressing beliefs, performed by ordinary language sentences uttered with a serious intent. Those systems become merely a technical tool for further technical scientific constructions. Thus, the whole of deductive science becomes largely a technique, i.e. a kind of creative activity, which consists not in discovering an objective reality, but rather in constructing one. It affords a rather subjective pleasure of constructing complicated entities out of simple elements. The only way to evaluate the construction objectively is to employ the criterion of its applicability to further constructions, or perhaps the criterion of the author’s ingenuity in devising an original and imaginative contrivance.