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An Impossibility Theorem for Verisimilitude

Sjoerd D. Zwart and Maarten Franssen
Synthese
Vol. 158, No. 1 (Sep., 2007), pp. 75-92
Published by: Springer
Stable URL: http://www.jstor.org/stable/27653575
Page Count: 18
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An Impossibility Theorem for Verisimilitude
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Abstract

In this paper, we show that Arrow's well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow's requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements of "Unanimity, Independence of irrelevant alternatives and Non-dictatorship" at the level of sentence variables. By giving a formal account of the incompatibility of the considerations of content and likeness, our impossibility result makes it possible to systematize the discussion about verisimilitude, and to understand it in more general terms.

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