 LOGICAL AND HISTORICAL DETERMINATION OF THE ARROW AND SEN IMPOSSIBILITY THEOREMSBranislav Boričić Economic Annals, 2007, vol. 52, issue 172, 7-20 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. Keywords: impossibility theorem; (in)consistency (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:beo:journl:v:52:y:2007:i:172:p:7-20 Ordering information: This journal article can be ordered from Access Statistics for this article Economic Annals is currently edited by Will Bartlett More articles in Economic Annals from Faculty of Economics and Business, University of Belgrade Contact information at EDIRC. |
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