Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

**The limits of understanding and the understanding of limits : David Hume’s mathematical sources.** / Larvor, Brendan.

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Larvor, B 2022, The limits of understanding and the understanding of limits: David Hume’s mathematical sources. in *Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume.* Research in History and Philosophy of Mathematics, Springer International Publishing AG, Switzerland .

Larvor, B. (Accepted/In press). The limits of understanding and the understanding of limits: David Hume’s mathematical sources. In *Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume *(Research in History and Philosophy of Mathematics). Springer International Publishing AG.

Larvor B. The limits of understanding and the understanding of limits: David Hume’s mathematical sources. In Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume. Switzerland : Springer International Publishing AG. 2022. (Research in History and Philosophy of Mathematics).

@inbook{eea13a0c33a94e19a0f4c78ecb89d1ce,

title = "The limits of understanding and the understanding of limits: David Hume{\textquoteright}s mathematical sources",

abstract = "David Hume devoted a long section of his Treatise of Human Nature to an attempt to refute the indivisibility of space and time. In his later Enquiry Concerning Human Understanding, he ridiculed the doctrine of infinitesimals and the paradox of the angle of contact between a circle and a tangent. Following up Hume{\textquoteright}s mathematical references reveals the role that a handful of mathematical examples (in Hume{\textquoteright}s case, the indivisibility of space and the angle of contact) played in the work of philosophers who (like Hume) were not otherwise interested in mathematics, and who used them to argue for either fideist or sceptical conclusions. Such paradoxes were taken to mark the limit of rational mathematical enquiry, beyond which human thought should either fall silent or surrender to religious faith. The fideist argument occurs, for example, in Malezieu{\textquoteright}s {\'E}l{\'e}ments de G{\'e}ometrie, to which Hume refers indirectly in the Treatise. Hume did not seem to appreciate that while bringing rigour to the differential and integral calculus was a central problem for mathematics, the angle of contact was (by his time) a non-problem that arose in the first place only owing to the antique authority of Euclid. Following Hume{\textquoteright}s mathematical sources thereby shows us something about the role and significance of mathematics in the wider intellectual culture of his time. A small number of isolated and fossilized puzzles became emblematic of mathematics as both rational authority and inaccessible mystery. ",

keywords = "mathematics, HISTORY, philosophy, Hume",

author = "Brendan Larvor",

year = "2022",

month = apr,

day = "15",

language = "English",

series = "Research in History and Philosophy of Mathematics",

publisher = "Springer International Publishing AG",

booktitle = "Research in History and Philosophy of Mathematics",

address = "Switzerland",

}

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T1 - The limits of understanding and the understanding of limits

T2 - David Hume’s mathematical sources

AU - Larvor, Brendan

PY - 2022/4/15

Y1 - 2022/4/15

N2 - David Hume devoted a long section of his Treatise of Human Nature to an attempt to refute the indivisibility of space and time. In his later Enquiry Concerning Human Understanding, he ridiculed the doctrine of infinitesimals and the paradox of the angle of contact between a circle and a tangent. Following up Hume’s mathematical references reveals the role that a handful of mathematical examples (in Hume’s case, the indivisibility of space and the angle of contact) played in the work of philosophers who (like Hume) were not otherwise interested in mathematics, and who used them to argue for either fideist or sceptical conclusions. Such paradoxes were taken to mark the limit of rational mathematical enquiry, beyond which human thought should either fall silent or surrender to religious faith. The fideist argument occurs, for example, in Malezieu’s Éléments de Géometrie, to which Hume refers indirectly in the Treatise. Hume did not seem to appreciate that while bringing rigour to the differential and integral calculus was a central problem for mathematics, the angle of contact was (by his time) a non-problem that arose in the first place only owing to the antique authority of Euclid. Following Hume’s mathematical sources thereby shows us something about the role and significance of mathematics in the wider intellectual culture of his time. A small number of isolated and fossilized puzzles became emblematic of mathematics as both rational authority and inaccessible mystery.

AB - David Hume devoted a long section of his Treatise of Human Nature to an attempt to refute the indivisibility of space and time. In his later Enquiry Concerning Human Understanding, he ridiculed the doctrine of infinitesimals and the paradox of the angle of contact between a circle and a tangent. Following up Hume’s mathematical references reveals the role that a handful of mathematical examples (in Hume’s case, the indivisibility of space and the angle of contact) played in the work of philosophers who (like Hume) were not otherwise interested in mathematics, and who used them to argue for either fideist or sceptical conclusions. Such paradoxes were taken to mark the limit of rational mathematical enquiry, beyond which human thought should either fall silent or surrender to religious faith. The fideist argument occurs, for example, in Malezieu’s Éléments de Géometrie, to which Hume refers indirectly in the Treatise. Hume did not seem to appreciate that while bringing rigour to the differential and integral calculus was a central problem for mathematics, the angle of contact was (by his time) a non-problem that arose in the first place only owing to the antique authority of Euclid. Following Hume’s mathematical sources thereby shows us something about the role and significance of mathematics in the wider intellectual culture of his time. A small number of isolated and fossilized puzzles became emblematic of mathematics as both rational authority and inaccessible mystery.

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KW - HISTORY

KW - philosophy

KW - Hume

M3 - Chapter (peer-reviewed)

T3 - Research in History and Philosophy of Mathematics

BT - Research in History and Philosophy of Mathematics

PB - Springer International Publishing AG

CY - Switzerland

ER -