Deductive Reasoning Under Uncertainty: A Water Tank Analogy

Erkenntnis 81 (3):479-506 (2016)
Download Edit this record How to cite View on PhilPapers
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 of coherence intervals would commit themselves to executing physically impossible tasks.
(categorize this paper)
Reprint years
PhilPapers/Archive ID
Revision history
Archival date: 2019-03-18
View upload history
References found in this work BETA
Indicative Conditionals.Stalnaker, Robert

View all 19 references / Add more references

Citations of this work BETA
Bayesian Reasoning with Ifs and Ands and Ors.Cruz, Nicole; Baratgin, Jean; Oaksford, Mike & Over, David E.
Widening Access to Bayesian Problem Solving.Cruz, Nicole; Desai, Saoirse Connor; Dewitt, Stephen; Hahn, Ulrike; Lagnado, David; Liefgreen, Alice; Phillips, Kirsty; Pilditch, Toby & Tešić, Marko

Add more citations

Added to PP index

Total views
129 ( #29,039 of 50,201 )

Recent downloads (6 months)
15 ( #33,940 of 50,201 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.