Indeterminacy, coincidence, and “Sourcing Newness” in mathematical research.
Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías (J Cult Econ 10(5):434–449, 2017). I argue here that...
| Publicado en: | Synthese Vol. 200; no. 1; pp. 1 - 24 |
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| Formato: | Artículo |
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Springer Nature
Feb2022
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=155390269&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 155390269 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Feb2022 vid: 200 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 155390269 10.1007/s11229-022-03493-5 ppf: 1 ppct: 23 formats: fmt: – @attributes: type: T – @attributes: type: P size: 398KB tig: atl: Indeterminacy, coincidence, and “Sourcing Newness” in mathematical research. aug: au: Martin, James V. affil: Western Michigan University, Kalamazoo, MI, USA sug: keyword: Indeterminacy Mathematical coincidence Mathematical practice ab: Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías (J Cult Econ 10(5):434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical facts (merely) a coincidence is roughly to suggest that the investigation of connections between these facts isn’t worthwhile. To say of this pair, “That’s no coincidence!” is to suggest just the opposite. I further argue that this perspective on mathematical coincidence, which pays special attention to what mathematical coincidences do, may provide us with a better view of what mathematical coincidences are than extant accounts. I close by reflecting on how understanding mathematical coincidences as generating indeterminacy accords with a conception of mathematical research as ultimately aiming to reduce indeterminacy and complexity to triviality as proposed in Rota (in: Palombi (ed) Indiscrete thoughts, Birkhäuser, 1997). pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2022. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2022 holdings: @attributes: islocal: N |
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