  The way Leibniz applied his philosophy to mathematics has been the subject of
longstanding debates. A key piece of evidence is his letter to Masson on
bodies. We offer an interpretation of this often misunderstood text, dealing
with the status of infinite divisibility in nature, rather than in mathematics.
In line with this distinction, we offer a reading of the fictionality of
infinitesimals. The letter has been claimed to support a reading of
infinitesimals according to which they are logical fictions, contradictory in
their definition, and thus absolutely impossible. The advocates of such a
reading have lumped infinitesimals with infinite wholes, which are rejected by
Leibniz as contradicting the part-whole principle. Far from supporting this
reading, the letter is arguably consistent with the view that infinitesimals,
as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions
usable in mathematics, but possibly contrary to the Leibnizian principle of the
harmony of things and not necessarily idealizing anything in rerum natura.
Unlike infinite wholes, infinitesimals - as well as imaginary roots and other
well-founded fictions - may involve accidental (as opposed to absolute)
impossibilities, in accordance with the Leibnizian theories of knowledge and
modality.
