This text extends our analysis of the Leibnizian heritage pursued in and elsewhere. In Section 6 we present the conclusions of our contextualisation of the letter to Masson. Here we show that, while infinite wholes contradicting the part–whole principle are absolute impossibilities, imaginary roots and infinitesimals are only accidental impossibilities, even if their definitions are taken to be only nominal. In Section 5 we analyze the meaning of infinity, fiction, and well- founded fiction in Leibniz. unbounded infinity in Leibniz, as well as his comparison of the hornangle and inassignables. In Section 4 we analyze the distinctions infinite number vs. In Section 3 we analyze RA’s reading and show that the 1716 comments on the calculus not only provide no support for an Ishiguro-syncategorematic reading, but support a rather different interpretation of his infinitesimals: they are well-founded ‘fictions of the mind’ ( mentis fictiones, Footnote 5 Leibniz to des Bosses ). We analyze the Leibnizian exposition on the philosophy of nature and its historical and theological context in Section 2, where we also deal with the meaning of his comments on the calculus. Contextualizing the letter will help evaluate such claims. Bassler, Arthur, and Rabouin and Arthur (RA) have appealed to one such comment in support of the claim that Leibnizian infinitesimals are syncategorematic (in the sense detailed in Section 3). The letter deals with issues of the philosophy of nature and also comments briefly upon the infinitesimal calculus. In the same year (his last), Leibniz penned a response in a detailed letter Footnote 4 to editor Samuel Masson. The critique was apparently written already in 1703 Footnote 3 but only published in a 1716 volume of Histoire Critique de la Republique des Lettres. Toland accused Leibniz of allowing his calculus to infect his metaphysics. The critic has by now been definitively identified as John Toland Footnote 2 (1670–1722) see. Mais de s’imaginer, qu’ils pourront rendre compte de la nature des choses par de tels Calculs, c’est là precisement que consiste leur erreur. 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. 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. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part–whole principle. 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. In line with this distinction, we offer a reading of the fictionality of infinitesimals.
We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. A key piece of evidence is his letter to Masson on bodies. The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates.