CaltechAUTHORS
  A Caltech Library Service

The Axiomatic Structure of Empirical Content

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

[img]
Preview
PDF - Published Version
See Usage Policy.

305Kb
[img]
Preview
PDF (Author's copy) - Updated Version
See Usage Policy.

314Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20101008-094039001

Abstract

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
Funders:
Funding AgencyGrant Number
NSFSES-0751980
Subject Keywords:Falsifiability; Empirical Content ; Revealed preference; Afriat's Theorem; First-order logic; Model Theory
Classification Code:JEL classication numbers: A10,D00
Record Number:CaltechAUTHORS:20101008-094039001
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101008-094039001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20349
Collection:CaltechAUTHORS
Deposited By: Shirley Johnson
Deposited On:08 Oct 2010 17:07
Last Modified:26 Dec 2012 12:30

Repository Staff Only: item control page