Chambers, Christopher P. and Echenique, Federico and Shmaya, Eran (2010) The Axiomatic Structure of Empirical Content. Social Science Working Paper, 1317. California Institute of Technology , Pasadena, CA. http://resolver.caltech.edu/CaltechAUTHORS:20101008-094039001
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In this paper, we provide a formal framework for studying the empirical content of a given theory. We define the falsifiable closure of a theory to be the least weakening of the theory that makes only falsifiable claims. The falsifiable closure is our notion of empirical content. We prove that the empirical content of a theory can be exactly captured by a certain kind of axiomatization, one that uses axioms which are universal negations of conjunctions of atomic formulas. The falsifiable closure operator has the structure of a topological closure, which has implications, for example, for the behavior of joint vis a vis single hypotheses. The ideas here are useful for understanding theories whose empirical content is well-understood (for example, we apply our framework to revealed preference theory, and Afriat's theorem), but they can also be applied to theories with no known axiomatization. We present an application to the theory of multiple selves, with a fixed finite set of selves and where selves are aggregated according to a neutral rule satisfying independence of irrelevant alternatives. We show that multiple selves theories are fully falsifiable, in the sense that they are equivalent to their empirical content.
|Item Type:||Report or Paper (Working Paper)|
|Additional Information:||Author's copy: Date: August 20, 2010. We thank Nageeb Ali, Yaron Azrieli, Bettina Klaus, Tomasz Strzalecki, and Leeat Yariv for comments. Chambers and Echenique acknowledge support from the NSF through grant SES- 0751980.|
|Group:||Social Science Working Papers|
|Subject Keywords:||Falsifiability; Empirical Content ; Revealed preference; Afriat's Theorem; First-order logic; Model Theory|
|Classification Code:||JEL classication numbers: A10,D00|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Katherine Johnson|
|Deposited On:||08 Oct 2010 17:07|
|Last Modified:||26 Dec 2012 12:30|
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