Intended and Unintended Mathematics: The Case of the Lagrange Multipliers

Molinini, Daniele

doi:10.1007/s10838-019-09483-5

Cited by 1 publication

(3 citation statements)

References 21 publications

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“…For Maddy's Wittgenstein, "use" means something along the lines of "direct extramathematical application", what we consider here a first layer of meaning as use. Dawson's Wittgenstein extends the meaning of this notion to include "indirect application" as well (for instance, "bridging" mathematical techniques), constituting a second layer of meaning as use (unintended applications in general, in the sense of Molinini (2019) may belong to this layer, as we argued in section 5). 14 Moreover, Dawson's extension of meaning as use also includes aesthetic purposes which, we think, represents the first step of a shift from what modern readers may consider technical uses to what they may regard non-technical uses.…”

Section: A Three-layer Meaning As Use Perspective Of the Pure/applied...mentioning

confidence: 99%

“…Famous examples are number theoretic considerations concerning prime numbers that turned out to be useful for cryptography, and group theory being developed long before the physical theories that use it nowadays. For a broader, very recent discussion on intended vs unintended applications, we refer the reader to Molinini (2019), who in turn refers to the distinction as "when mathematics is introduced and developed in the context of a particular scientific application" vs "when mathematics is used in the context of a particular scientific application but it has been developed independently from that application". 4 An anonymous reviewer raised the interesting comment that the sociological division of pure and applied mathematicians could be well understood from Wittgenstein's notion of language games: the division reflects different games being played.…”

Section: Bridging From the Applied Perspectivementioning

confidence: 99%

“…Hence, even if pure mathematics had no indirect or unintended uses (in the sense meant by Dawson (2014) and Molinini (2019) respectively), it would still have uses in this "mundane" sense. This adds to the consideration that pure mathematics cannot be just "pruned away" on the ground that it is meaningless because it has no uses.…”

Section: A Three-layer Meaning As Use Perspective Of the Pure/applied...mentioning

confidence: 99%

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Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy

Pérez-Escobar

Sarikaya

2021

Euro Jnl Phil Sci

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In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake.

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Section: A Three-layer Meaning As Use Perspective Of the Pure/applied...mentioning

confidence: 99%

Section: Bridging From the Applied Perspectivementioning

confidence: 99%

Section: A Three-layer Meaning As Use Perspective Of the Pure/applied...mentioning

confidence: 99%

See 1 more Smart Citation

Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy

Pérez-Escobar

Sarikaya

2021

Euro Jnl Phil Sci

View full text Add to dashboard Cite

show abstract

Intended and Unintended Mathematics: The Case of the Lagrange Multipliers

Cited by 1 publication

References 21 publications

Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy

Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy

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