GARDNER'S PARADOX AND THEORY OF DESCRIPTIONS
Article Sidebar
Main Article Content
Abstract
Martin Gardner's two-children paradox posits two scenarios, in one we know that of two children one is a girl, and in the other we know that of two children the older one is a girl. The chances of the other child being a girl is not the same in these two scenarios, in the first being 1 in 3 while in the second they are 1 in 2. Gardner himself believed that the problem of this paradox lies in the ambiguous way the scenarios are articulated. However, it is possible to show that the original version of the paradox provides sufficient content for a meaningful explanation of these unexpected results. Inspired by comments by Leonard Mlodinow, we attempt to provide a comprehensible explanation for this counterintuitive change with help of Bertrand Russell's theory of descriptions. The difference between the two scenarios then boils down to the difference between indefinite and definite descriptions.
Article Details
References
Khovanova, Tanya, "Martin Gardner's Mistake" in: The College Mathematics Journal, Vol. 43, No. 1, 2012.
Marks, Stephen and Smith, Gary, "The Two-Child Paradox Reborn?" in: Chance, Vol. 24, No. 1, 2011.
Mlodinow, Leonard, The Drunkard's Walk, Pantheon Books, New York, 2008.
Parramore, Keith and Stephens, Joan, "Two girls - the value of information" in: The Mathematical Gazette,Vol. 98, No. 542, 2014.
Russell, Bertrand, "On Denoting" in: Mind, Vol. 14, No. 56, 1905.