Open AccessLogical and historical determination of the Arrow and Sen impossibility theorems
Author(s) -
Branislav R. Boričić
Publication year - 2007
Publication title -
economic annals/ekonomski anali
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.148
H-Index - 12
eISSN - 1820-7375
pISSN - 0013-3264
DOI - 10.2298/eka0772007b
Subject(s) - impossibility , arrow , arrow's impossibility theorem , mathematical economics , equivalence (formal languages) , social choice theory , mathematics , context (archaeology) , logical conjunction , logical equivalence , field (mathematics) , sequence (biology) , epistemology , computer science , discrete mathematics , pure mathematics , philosophy , law , paleontology , genetics , biology , political science , programming language
General classification of mathematical statements divides them into universal, those of the form xA , and existential ЭxA ones. 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 ¬ЭxA 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.