Introduction: Infinity in Early Modern Philosophy

Nachtomy, Ohad; Winegar, Reed

doi:10.1007/978-3-319-94556-9_1

Cited by 2 publications

(14 citation statements)

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“…Below, I present a proposal that builds upon several ideas reviewed above, to revise Onof and Schulting’s (2015; hereafter OS2015) proposal, so as to address the worry that it presents the unity of space as that of a brute given (e.g. Messina 2014; Williams 2018; Guyer 2018), which would be problematic for the B-TD. In that proposal, space tout court characterized by its unicity and topological features is said to define the unity which ‘precedes all concepts’ (B161n.).…”

Section: The Footnote and Its Compatibility With The Taementioning

confidence: 99%

“…Indeed, the unity of the consciousness unifying a manifold is a concept (A103); this implies that when the same synthesis is carried out again, its product falls under the same concept, but need not be the same particular. It has thus been argued that independent geometric representations are not in the same space (Guyer 2018). PUI: The claim that the unity of space presupposes a synthesis is seemingly incompatible with the claim that it is an infinite given magnitude because such a magnitude cannot be synthesized by finite beings (Guyer 2018).…”

Section: Introductionmentioning

confidence: 99%

“…It has thus been argued that independent geometric representations are not in the same space (Guyer 2018). PUI: The claim that the unity of space presupposes a synthesis is seemingly incompatible with the claim that it is an infinite given magnitude because such a magnitude cannot be synthesized by finite beings (Guyer 2018).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…PUI: The claim that the unity of space presupposes a synthesis is seemingly incompatible with the claim that it is an infinite given magnitude because such a magnitude cannot be synthesized by finite beings (Guyer 2018).…”

Section: Introductionmentioning

confidence: 99%

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The Unicity, Infinity and Unity of Space

Onof

2023

Kantian rev.

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The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions.

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Section: The Footnote and Its Compatibility With The Taementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Unicity, Infinity and Unity of Space

Onof

2023

Kantian rev.

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LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

Katz

Kuhlemann²,

Sherry³

et al. 2021

The Review of Symbolic Logic

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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.

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Introduction: Infinity in Early Modern Philosophy

Cited by 2 publications

References 0 publications

The Unicity, Infinity and Unity of Space

The Unicity, Infinity and Unity of Space

LEIBNIZ ON BODIES AND INFINITIES:RERUM NATURAAND MATHEMATICAL FICTIONS

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