How to Frame a Mathematician

Fisseni, Bernhard; Sarikaya, Deniz; Schmitt, Martin; Schröder, Bernhard

doi:10.1007/978-3-030-15655-8_19

Cited by 8 publications

(2 citation statements)

References 5 publications

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“…Once those intuitions are internalized we can encounter them in mathematical contexts just like we can encounter familiar or prototypical situations in our everyday life. This consideration has led to a frame approach to mathematics; see Fisseni et al (2019) and Carl et al (2021).…”

Section: On the Metaphorical Viewmentioning

confidence: 99%

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: On the Metaphorical Viewmentioning

confidence: 99%

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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“…Being experimental ethics a young discipline, it is possible that it will see deep methodological change over time. 12 SeeKant and Sarikaya (2020) for a study of these iterated acts of mathematization, andCarl et al (2021) andFisseni et al (2019) for a study of the idea of learning mathematical objects via familiarizing with prototypical situations. 13 The reader does not have to be familiar with the details on L. Actually, this is exactly what we claim, that only mathematicians are sufficiently familiar with the details on L to have stable intuitions.…”

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confidence: 99%

Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free

Kant

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Sarikaya

2021

KRITERION – Journal of Philosophy

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This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians (since they are sometimes hard to grasp even for mathematicians). This consideration is supported by a case study in set theory.

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A Plea for Research-Based Teaching in Mathematics Education (Due to Ethical Reasons)

Sarikaya

2024

Advances in Mathematics Education

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How to Frame a Mathematician

Cited by 8 publications

References 5 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

Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free

A Plea for Research-Based Teaching in Mathematics Education (Due to Ethical Reasons)

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