This paper offers a refutation of P. Duhem's thesis that the falsifiability of an isolated empirical hypothesis H as an explanans is unavoidably inconclusive. Its central contentions are the following: 1. No general features of the logic of falsifiability can assure, for every isolated empirical hypothesis H and independently of the domain to which it pertains, that H can always be preserved as an explanans of any empirical findings O whatever by some modification of the auxiliary assumptions A in conjunction (...) with which H functions as an explanans. For Duhem cannot guarantee on any general logical grounds the deducibility of O from an explanans constituted by the conjunction of H and some revised non-trivial version R of A: the existence of the required set R of collateral assumptions must be demonstrated for each particular case. 2. The categorical form of the Duhemian thesis is not only a non-sequitur but actually false. This is shown by adducing the testing of physical geometry as a counterexample to Duhem in the form of a rebuttal to A. Einstein's geometrical articulation of Duhem's thesis. 3. The possibility of a quasi a priori choice of a physical geometry in the sense of Duhem must be clearly distinguished from the feasibility of a conventional adoption of such a geometry in the sense of H. Poincare. And the legitimacy of the latter cannot be invoked to save the Duhemian thesis from refutation by the foregoing considerations. (shrink)