Did Euler found continuum mechanics on balance laws? “ Argumentum ab auctoritate est infirmissimum ”

Abstract

The content of this paper is not a historiographical reconstruction. Instead, it intends to give a documented opinion, based also on historical considerations, about the postulation scheme which must be preferred in formulating novel mechanical models. Truesdell has claimed that his own preferred postulation to continuum mechanics, which builds the theory based on local integral balance laws, is historically grounded in the work of Leonhard Euler. Is this position, so strongly advocated by Truesdell, tenable? In the present paper, based on circumstantial evidence and by using the technique of logical reconstruction of “lacking” mathematical details in a “corrupted” flow of mathematical reasonings, as proposed by dell’Isola and Spagnuolo, we conjecture that, most likely, Euler’s preferred postulation of mechanics was based on variational principles. This conjecture will need to be further substantiated, as, unfortunately, the greatest part of the corpus of Euler’s works (mainly published in Latin only or even not completely printed yet) is not easily accessible; therefore, the careful philological analysis needed to fully confirm the proposed conjecture is, at the moment, impossible. In the literature, one finds two argumenta ab actoritate: the first, used by Truesdell, claims that balance laws postulation must be accepted because Euler is assumed to have chosen it; the second, used by Truesdellians, claims that such a postulation must be accepted because Truesdell has shown us the light. However, it is well-known that argumenta ab auctoritate sunt infirmissima (The arguments based on the authority of a “bigger” thinker are the weakest).