Details
| Original language | English |
|---|---|
| Pages (from-to) | 36-66 |
| Number of pages | 31 |
| Journal | Review of Symbolic Logic |
| Volume | 17 |
| Issue number | 1 |
| Early online date | 3 Dec 2021 |
| Publication status | Published - Mar 2024 |
Abstract
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.
Keywords
- Aristotle, Bernoulli, body, des Bosses, Huygens, inassignable quantities, infinitesimal calculus, infinitesimals, infinity, Leibniz, Leibnizian metaphysics, magnitude, Masson, monad, multitude, substance, Thomasius, useful fiction, Varignon, Wallis
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
- Arts and Humanities(all)
- Philosophy
- Mathematics(all)
- Logic
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In: Review of Symbolic Logic, Vol. 17, No. 1, 03.2024, p. 36-66.
Research output: Contribution to journal › Article › Research › peer review
}
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 -