LOGICAL AND HISTORICAL DETERMINATION OF THE ARROW AND SEN IMPOSSIBILITY THEOREMS

Abstract

General classification of mathematical statements divides them into universal, those of the form ∀xA, and existential  ones ∃xA. Common formulations of impossibility theorems of K. J. Arrow and A. K. Sen are represented by the statements of the form ‘there is no x such that A’. Bearing in mind logical equivalence of formulae ¬∃xA and ∀x¬A, we come to the conclusion that the corpus of impossibility theorems, which appears in the theory of social choice, could make a specific and recognizable subclass of universal statements. In this paper, on the basis of the established logical and methodological criteria, we point to a sequence of extremely significant ‘impossibility theorems’, reaching throughout the history of mathematics to the present days and the famous results of Arrow and Sen in field of mathematical economics. We close with specifying the context which makes it possible to formulate the results of Arrow and Sen accurately, presenting a new direct proof of Sen’s result, with no reliance on 
the notion of minimal liberalism.