Plausible deductive reasoning using a water tank analogy

The diagrammatic representation by "square-and-strips" used to illustrate and solve problems linked to conditional probability distributions is reinterpreted exclusively in terms of liquids in water tanks and applied to a new domain, namely deductive inferences under uncertainty. The isomorphism between the physical constraints on the capacity of the tank and its subdivisions and elementary laws of conditional probability is shown. Then, the analogy is exploited to qualitatively determine, and quantitatively compute, the limits in probability of the conclusion of basic deductive arguments (such as Modus Ponens, the Hypothetical Syllogism, Contraposition, etc.) that are used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. It is shown that the probability bounds imposed by the premises on the conclusion and their respect by reasoners, stem from, and amount to, respecting trivial principles such as "a part of the tank cannot contain more than the whole tank's capacity", or "if a part is empty, the other part contains all the liquid", etc., suggesting a physical counterpart of Dutch book arguments to assess individuals' rationality.