Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Deductive Reasoning Under Uncertainty Using a Water Tank Analogy

Abstract : This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds would commit themselves to executing physically impossible tasks.
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download
Contributor : Guy Politzer Connect in order to contact the contributor
Submitted on : Thursday, May 22, 2014 - 12:57:31 AM
Last modification on : Thursday, March 17, 2022 - 10:08:21 AM
Long-term archiving on: : Friday, August 22, 2014 - 11:21:05 AM


  • HAL Id : ijn_00867284, version 2



Guy Politzer. Deductive Reasoning Under Uncertainty Using a Water Tank Analogy. 2014. ⟨ijn_00867284v2⟩



Record views


Files downloads