The Difficulty of Being Simple: On Some Interactions Between Mathematics and Philosophy in Leibniz’s Analysis of Notions

Rabouin, David

doi:10.1007/978-94-017-9664-4_3

Cited by 4 publications

(9 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Referring to possible connections between mathematics and philosophy in Leibniz and the interpretation that puts differential calculus at the core of Leibniz’ philosophy, Rabouin solo writes: Leibniz was … very explicit about some connections which he resisted making —although modern commentators tend to put a lot of emphasis on them. [69, note 47, p. 69] (emphasis on ‘resisted making’ ours)…”

Section: Syncategorematics Vs Keeping Bodies and Calculus Separatementioning

confidence: 99%

“…Leibniz was … very explicit about some connections which he resisted making —although modern commentators tend to put a lot of emphasis on them. [69, note 47, p. 69] (emphasis on ‘resisted making’ ours)…”

Section: Syncategorematics Vs Keeping Bodies and Calculus Separatementioning

confidence: 99%

“… 63 Meanwhile, Rabouin solo [69] expressed a more cautious position with regard to the 1716 letter; see Section 3.4, item 3. …”

mentioning

confidence: 99%

See 2 more Smart Citations

LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

Katz

Kuhlemann²,

Sherry³

et al. 2021

The Review of Symbolic Logic

View full text Add to dashboard Cite

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.

show abstract

Section: Syncategorematics Vs Keeping Bodies and Calculus Separatementioning

confidence: 99%

Section: Syncategorematics Vs Keeping Bodies and Calculus Separatementioning

confidence: 99%

See 1 more Smart Citation

LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

Katz

Kuhlemann²,

Sherry³

et al. 2021

The Review of Symbolic Logic

View full text Add to dashboard Cite

show abstract

“…[Nieuwentijt] me fait une objection sur un point qui m'est commun avec Messieurs Fermat, Barrow, Newton et tous les autres, 63 Meanwhile, Rabouin solo [69] expressed a more cautious position with regard to the 1716 letter; see Section 3.4, item 3.…”

Section: Discussionunclassified

Leibniz on bodies and infinities: rerum natura and mathematical fictions

Katz,

Kuhlemann,

Sherry

et al. 2021

Preprint

View full text Add to dashboard Cite

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 partwhole 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.

show abstract

“…One locus classicus is Couturat (1901). More modern interpretations can be found in Antognazza (2009), Arthur (2014), Rabouin (2015) and Rabouin (2024).…”

Section: From the Young Project To The Logical Primacy Of Propositionsmentioning

confidence: 95%

Definitions by abstraction and Leibniz's notion of quantity

Costantini

2024

Theoria

View full text Add to dashboard Cite

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an ‘alphabet of human thought’. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract objects, we should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz.

show abstract

The Difficulty of Being Simple: On Some Interactions Between Mathematics and Philosophy in Leibniz’s Analysis of Notions

Cited by 4 publications

References 3 publications

LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

Leibniz on bodies and infinities: rerum natura and mathematical fictions

Definitions by abstraction and Leibniz's notion of quantity

Contact Info

Product

Resources

About