TY - JOUR

T1 - Leibniz on Bodies and Infinities

T2 - Rerum Natura and Mathematical Fictions

AU - Katz, Mikhail G.

AU - Kuhlemann, Karl

AU - Sherry, David

AU - Ugaglia, Monica

PY - 2024/3

Y1 - 2024/3

N2 - 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.

AB - 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.

KW - Aristotle

KW - Bernoulli

KW - body

KW - des Bosses

KW - Huygens

KW - inassignable quantities

KW - infinitesimal calculus

KW - infinitesimals

KW - infinity

KW - Leibniz

KW - Leibnizian metaphysics

KW - magnitude

KW - Masson

KW - monad

KW - multitude

KW - substance

KW - Thomasius

KW - useful fiction

KW - Varignon

KW - Wallis

UR - http://www.scopus.com/inward/record.url?scp=85120861723&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2112.08155

DO - 10.48550/arXiv.2112.08155

M3 - Article

AN - SCOPUS:85120861723

VL - 17

SP - 36

EP - 66

JO - Review of Symbolic Logic

JF - Review of Symbolic Logic

SN - 1755-0203

IS - 1

ER -