{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T02:40:15Z","timestamp":1773196815121,"version":"3.50.1"},"reference-count":79,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T00:00:00Z","timestamp":1638489600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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<jats:italic>nature<\/jats:italic>, rather than in<jats:italic>mathematics<\/jats:italic>. 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\u2013whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are<jats:italic>mentis fictiones<\/jats:italic>, 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<jats:italic>rerum natura<\/jats:italic>. Unlike infinite wholes, infinitesimals\u2014as well as imaginary roots and other well-founded fictions\u2014may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality.<\/jats:p>","DOI":"10.1017\/s1755020321000575","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T07:37:04Z","timestamp":1638517024000},"page":"36-66","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["LEIBNIZ ON BODIES AND INFINITIES:<i>RERUM NATURA<\/i>AND MATHEMATICAL FICTIONS"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3489-0158","authenticated-orcid":false,"given":"MIKHAIL G.","family":"KATZ","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7713-4782","authenticated-orcid":false,"given":"KARL","family":"KUHLEMANN","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9699-7762","authenticated-orcid":false,"given":"DAVID","family":"SHERRY","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3150-4346","authenticated-orcid":false,"given":"MONICA","family":"UGAGLIA","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,12,3]]},"reference":[{"key":"S1755020321000575_r76","unstructured":"[76] Toland, J. (1716). Remarques Critiques sur le Syst\u00eame de Mr. Leibnitz de l\u2019Harmonie pr\u00e9\u00e9tablie; o\u00f9 l\u2019on recherche, en passant, Pourquoi les Syst\u00eames Metaphysiques Des Mathematiciens Ont Moins de clart\u00e9 Que Ceux Des Autres: \u00e9crites Par Ordre de Sa Majest\u00e9 la feu\u00eb Reine de Prusse. Histoire Critique de la Republique Des Lettres, Tome XI, pp.\u00a0115\u2013133 (published anonymously)."},{"key":"S1755020321000575_r21","doi-asserted-by":"publisher","DOI":"10.1007\/s00407-005-0102-4"},{"key":"S1755020321000575_r20","volume-title":"The Early Mathematical Manuscripts of Leibniz","author":"Child","year":"1920"},{"key":"S1755020321000575_r77","volume-title":"Thinking and Calculating. Essays on Logic, Its History and Its Applications in Honor of Massimo Mugnai","author":"Ugaglia","year":"2022"},{"key":"S1755020321000575_r11","first-page":"849","article-title":"Leibniz on the indefinite as infinite","volume":"51","author":"Bassler","year":"1998","journal-title":"The Review of Metaphysics"},{"key":"S1755020321000575_r44","unstructured":"[44] Leibniz, G. W. (1695). Letter to l\u2019Hospital, June 14\/24, 1695, in Gerhardt [25], Vol. I, pp.\u00a0287\u2013289."},{"key":"S1755020321000575_r74","doi-asserted-by":"publisher","DOI":"10.1080\/000337999296373"},{"key":"S1755020321000575_r48","unstructured":"[48] Leibniz, G. W. (1701). Cum Prodiisset\u2026 mss Cum prodiisset atque increbuisset Analysis mea infinitesimalis\u2026. In Gerhardt [30], pp.\u00a039\u201350. Available from: http:\/\/books.google.co.il\/books?id=UOM3AAAAMAAJ."},{"key":"S1755020321000575_r13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-94-017-9664-4_2","volume-title":"Interrelations Between Mathematics and Philosophy","volume":"41","author":"Beeley","year":"2015"},{"key":"S1755020321000575_r32","doi-asserted-by":"publisher","DOI":"10.1007\/s10670-012-9370-y"},{"key":"S1755020321000575_r38","unstructured":"[38] Leibniz, G. W. (1672\/3. Confessio Philosophi. In Leibniz [55] (A.VI. 3. 115\u2013149)."},{"key":"S1755020321000575_r49","unstructured":"[49] Leibniz, G. W. (1702). Letter to Varignon, February 2, 1702. In Gerhardt [25], Vol. IV, pp.\u00a091\u201395."},{"key":"S1755020321000575_r30","volume-title":"Leibniz\u2019s Philosophy of Logic and Language","author":"Ishiguro","year":"1990"},{"key":"S1755020321000575_r54","unstructured":"[54] Leibniz, G. W. (1716). Letter to Samuel Masson. In Gerhardt [26], Vol. VI, pp.\u00a0624\u2013629. Translated in Ariew\u2013Garber\u2019s Leibniz [58], pp.\u00a0225\u2013230."},{"key":"S1755020321000575_r10","first-page":"117","article-title":"Leibniz versus Ishiguro: Closing a quarter century of syncategoremania","volume":"6","author":"Bascelli","year":"2016","journal-title":"HOPOS: The Journal of the International Society for the History of Philosophy of Science"},{"key":"S1755020321000575_r34","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3596-4_20"},{"key":"S1755020321000575_r40","unstructured":"[40] Leibniz, G. W. (1678). Letter to Elisabeth. A.2.12. 659\u2013666. Translated in [58]."},{"key":"S1755020321000575_r65","doi-asserted-by":"publisher","DOI":"10.1017\/CCOL0521365880.004"},{"key":"S1755020321000575_r5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-94556-9_10"},{"key":"S1755020321000575_r68","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00131-9_15"},{"key":"S1755020321000575_r12","doi-asserted-by":"crossref","unstructured":"[12] Beeley, P. (2008). Infinity, infinitesimals, and the reform of Cavalieri: John Wallis and his critics. In Goldenbaum\u2013Jesseph [27], pp.\u00a031\u201352.","DOI":"10.1515\/9783110211863.31"},{"key":"S1755020321000575_r17","first-page":"115","volume-title":"Kontinuum, Analysis, Informales\u2014Beitr\u00e4ge Zur Mathemathik Und Philosophie von Leibniz","author":"Breger","year":"2016"},{"key":"S1755020321000575_r69","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/978-94-017-9664-4_3","volume-title":"G. W. Leibniz, Interrelations Between Mathematics and Philosophy","volume":"41","author":"Rabouin","year":"2015"},{"key":"S1755020321000575_r62","volume-title":"Mathesis universalis. \u00c9crits sur la math\u00e9matique universelle","author":"Leibniz","year":"2018"},{"key":"S1755020321000575_r45","unstructured":"[45] Leibniz, G. W. (1695). Responsio ad nonnullas difficultates a Dn. Bernardo Niewentiit circa methodum differentialem seu infinitesimalem motas. Act. Erudit. Lips. In Gerhardt [25], Vol. V, pp.\u00a0320\u2013328. A French translation by Parmentier is in [56], pp.\u00a0316\u2013334]."},{"key":"S1755020321000575_r78","doi-asserted-by":"publisher","DOI":"10.5840\/leibniz199883"},{"key":"S1755020321000575_r41","unstructured":"[41] Leibniz, G. W. (1683). Elementa nova matheseos universalis. In Leibniz [55] (A.VI. 4A. 513\u2013524)."},{"key":"S1755020321000575_r75","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0114.1982.tb00097.x"},{"key":"S1755020321000575_r53","unstructured":"[53] Leibniz, G. W. (1706). Letter to Des Bosses, March 11, 1706. In Gerhardt [26], Vol. II, pp.\u00a0304\u2013308. Translated in Look and Rutherford\u2019s Leibniz [61], pp.\u00a030\u201339."},{"key":"S1755020321000575_r46","unstructured":"[46] Leibniz, G. W. (1695). Letter to Huygens, July 1, 1695. In Gerhardt [25], Vol. II, p.\u00a0205 and Briefwechsel, p.\u00a0757. Available from: https:\/\/dbnl.nl\/tekst\/ huyg003oeuv10_01\/huyg003oeuv10_01_0239.php."},{"key":"S1755020321000575_r27","doi-asserted-by":"publisher","DOI":"10.1515\/9783110211863"},{"key":"S1755020321000575_r31","doi-asserted-by":"publisher","DOI":"10.1007\/s00283-021-10140-3"},{"key":"S1755020321000575_r39","unstructured":"[39] Leibniz, G. W. (1676). Numeri Infiniti. In Leibniz [55] (A.VI. 3. 496\u2013504)."},{"key":"S1755020321000575_r35","doi-asserted-by":"publisher","DOI":"10.1007\/s004070050035"},{"key":"S1755020321000575_r72","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-28273-4","volume-title":"Conflicts Between Generalization, Rigor, and Intuition. Number Concepts Underlying the Development of Analysis in 17\u201319th Century France and Germany","author":"Schubring","year":"2005"},{"key":"S1755020321000575_r37","unstructured":"[37] Leibniz, G. W. (1669). Letter to Thomasius, April 20\u201330, 1669. In Leibniz [55] (A2.12. 23\u201338)."},{"key":"S1755020321000575_r42","first-page":"326","volume-title":"Act. Erudit. Lips","volume":"VII","author":"Leibniz","year":"1686"},{"key":"S1755020321000575_r1","doi-asserted-by":"publisher","DOI":"10.5840\/leibniz2015252"},{"key":"S1755020321000575_r16","first-page":"151","article-title":"\u00dcber Leibniz\u2019 Unendlichkeitstheorie","volume":"23","author":"Bosinelli","year":"1991","journal-title":"Studia Leibnitiana"},{"key":"S1755020321000575_r18","first-page":"64","volume-title":"\u2018F\u00fcr Unser Gl\u00fcck Oder das Gl\u00fcck Anderer\u2019 Vortr\u00e4ge Des X. Intemationalen Leibniz-Kongresses Hannover, 18\u201323 Juli 2016","author":"Breger","year":"2017"},{"key":"S1755020321000575_r43","unstructured":"[43] Leibniz, G. W. (1686). Discours de Metaphysique. In Leibniz [55] (A.VI. 4B2. 1529\u20131589)."},{"key":"S1755020321000575_r26","first-page":"1875","volume-title":"Die Philosophischen Schriften von Gottfried Wilhelm Leibniz","author":"Gerhardt"},{"key":"S1755020321000575_r22","doi-asserted-by":"publisher","DOI":"10.1007\/s00407-021-00277-0"},{"key":"S1755020321000575_r24","volume-title":"Historia et Origo Calculi Differentialis a G. G. Leibnitio Conscripta","author":"Gerhardt","year":"1846"},{"key":"S1755020321000575_r28","volume-title":"Leibniz\u2019s Science of the Rational","volume":"26","author":"Grosholz","year":"1998"},{"key":"S1755020321000575_r7","doi-asserted-by":"publisher","DOI":"10.1093\/philmat\/nky023"},{"key":"S1755020321000575_r15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00327456"},{"key":"S1755020321000575_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-25572-5_3"},{"key":"S1755020321000575_r8","doi-asserted-by":"publisher","DOI":"10.1007\/s10838-016-9334-z"},{"key":"S1755020321000575_r52","unstructured":"[52] Leibniz, G. W. (1704). Letter to de Volder, June 30, 1704. In Gerhardt [26], Vol. II, pp.\u00a0267\u2013272."},{"key":"S1755020321000575_r14","doi-asserted-by":"publisher","DOI":"10.1007\/s10699-015-9473-4"},{"key":"S1755020321000575_r50","unstructured":"[50] Leibniz, G. W. (1702). Letter to Varignon, April 14, 1702. In Gerhardt [25], Vol. IV, pp.\u00a097\u201399."},{"key":"S1755020321000575_r36","first-page":"89","article-title":"An anonymous criticism from Berlin to Leibniz\u2019s philosophy: John Toland against mathematical abstractions","volume":"16","author":"Lamarra","year":"1990","journal-title":"Studia Leibnitiana"},{"key":"S1755020321000575_r61","volume-title":"The Leibniz\u2013Des Bosses Correspondence","author":"Leibniz","year":"2007"},{"key":"S1755020321000575_r66","doi-asserted-by":"publisher","DOI":"10.1017\/CHOL9780521226059.031"},{"key":"S1755020321000575_r55","volume-title":"S\u00e4mtliche Schriften Und Briefe","author":"Leibniz","year":"1923"},{"key":"S1755020321000575_r73","doi-asserted-by":"crossref","first-page":"166","DOI":"10.25162\/sl-2012-0010","article-title":"Infinitesimals, imaginaries, ideals, and fictions","volume":"44","author":"Sherry","year":"2012","journal-title":"Studia Leibnitiana"},{"key":"S1755020321000575_r2","volume-title":"G. W. Leibniz. The Labyrinth of the Continuum. Writings on the Continuum Problem, 1672\u20131686","author":"Arthur","year":"2001"},{"key":"S1755020321000575_r23","doi-asserted-by":"crossref","unstructured":"[23] Garber, D. (2008). Dead force, infinitesimals, and the mathematicization of nature. In Goldenbaum\u2013Jesseph [27], pp.\u00a0281\u2013306.","DOI":"10.1515\/9783110211863.281"},{"key":"S1755020321000575_r56","volume-title":"La Naissance du Calcul diff\u00e9rentiel. 26 Articles Des Acta Eruditorum","author":"Leibniz","year":"1989"},{"key":"S1755020321000575_r19","first-page":"55","article-title":"Two papers by John Toland","volume":"IV","author":"Brown","year":"1999","journal-title":"I Castelli di Yale"},{"key":"S1755020321000575_r9","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1080\/26375451.2020.1851120","article-title":"Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks","volume":"36","author":"Bair","year":"2021","journal-title":"British Journal for the History of Mathematics"},{"key":"S1755020321000575_r79","volume-title":"Leibniz\u2019s \u2018New System\u2019 and Associated Contemporary Texts","author":"Woolhouse","year":"1997"},{"key":"S1755020321000575_r64","first-page":"123","volume-title":"The History of Continua: Philosophical and Mathematical Perspectives","author":"Levey","year":"2021"},{"key":"S1755020321000575_r58","volume-title":"Philosophical Essays","author":"Leibniz","year":"1989"},{"key":"S1755020321000575_r29","volume-title":"Varieties of Continua. From Regions to Points and Back. Chapter 3 with \u00d8ystein Linnebo","author":"Hellman","year":"2018"},{"key":"S1755020321000575_r33","first-page":"33","volume-title":"L\u2019infinito in Leibniz, Problemi e Terminologia","author":"Knobloch","year":"1990"},{"key":"S1755020321000575_r63","doi-asserted-by":"publisher","DOI":"10.2307\/2998315"},{"key":"S1755020321000575_r51","unstructured":"[51] Leibniz, G. W. (1702). Letter to Varignon, June 20, 1702. In Gerhardt [25], Vol. IV, pp.\u00a0106\u2013110."},{"key":"S1755020321000575_r3","first-page":"11","volume-title":"The Philosophy of the Young Leibniz","volume":"35","author":"Arthur","year":"2009"},{"key":"S1755020321000575_r60","unstructured":"[60] Leibniz, G. W. (2004). Confessio Philosophi: Papers Concerning the Problem of Evil, 1671\u20131678 (The Yale Leibniz Series), by G. W. Leibniz (author) and Robert C. Sleigh Jr. (translator). Available from: https:\/\/books. google.co.il\/books?id=Jj3Z0dHp6_MC."},{"key":"S1755020321000575_r4","doi-asserted-by":"publisher","DOI":"10.1007\/s00407-013-0119-z"},{"key":"S1755020321000575_r57","volume-title":"Philosophical Papers and Letters","volume":"2","author":"Leibniz","year":"1989"},{"key":"S1755020321000575_r47","unstructured":"[47] Leibniz, G. W. (1695). Specimen dynamicum, pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis, et ad suas causas revocandis. Acta Eruditorum. In Gerhardt [25], Vol. VI, pp.\u00a0234\u2013254. Translated in Loemker [57], pp.\u00a0435\u2013444 (Part I)."},{"key":"S1755020321000575_r71","doi-asserted-by":"publisher","DOI":"10.1007\/s00407-020-00249-w"},{"key":"S1755020321000575_r67","doi-asserted-by":"crossref","first-page":"109","DOI":"10.25162\/sl-2013-0007","article-title":"\u201cAnalytica Generalissima Humanorum Cognitionum\u201d. Some reflections on the relationship between logical and mathematical analysis in Leibniz","volume":"45","author":"Rabouin","year":"2013","journal-title":"Studia Leibnitiana"},{"key":"S1755020321000575_r59","volume-title":"Quadrature arithm\u00e9tique du cercle, de l\u2019ellipse et de l\u2019hyperbole","author":"Leibniz","year":"2004"},{"key":"S1755020321000575_r70","doi-asserted-by":"crossref","unstructured":"[70] Rabouin, D. (2021). Can one be a fictionalist and a platonist at the same time? Lessons from Leibniz.","DOI":"10.4000\/11xmc"},{"key":"S1755020321000575_r25","first-page":"1849","volume-title":"Leibnizens mathematische Schriften","author":"Gerhardt"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020321000575","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T17:48:03Z","timestamp":1726249683000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020321000575\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,3]]},"references-count":79,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S1755020321000575"],"URL":"https:\/\/doi.org\/10.1017\/s1755020321000575","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,3]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}