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In the famous thought experiment studied in this article, Galileo attemptedto refute the Aristotelian hypothesis that heavier bodies should fall morequickly than lighter ones. After pointing out some inconsistencies in Galileo'sapproach, we show, through the design of two alternative but equivalentexperiments, that from his imaginary experiment, it is not possible to reachthe conclusion that all bodies fall simultaneously. We show why, to explain theresult of this type of experience, it is necessary to establish the equivalencebetween inertial and gravitational masses derived exclusively from experience.

A critique of one of Galileo's mental experiments and an explanation on why bodies fall with equal acceleration through the vacuum