On the heuristic power of mathematical representations.
I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation (a) introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and (b) how it...
| Publicado en: | Synthese Vol. 200; no. 5; pp. 1 - 24 |
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| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Oct2022
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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=159284200&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 159284200 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Oct2022 vid: 200 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 159284200 10.1007/s11229-022-03883-9 ppf: 1 ppct: 23 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1.4MB tig: atl: On the heuristic power of mathematical representations. aug: au: Ippoliti, Emiliano affil: Sapienza University of Rome, Rome, Italy sug: ab: I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation (a) introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and (b) how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem. In addition, I defend an ‘inferential’ approach to the heuristic power of representations by arguing that these representations draw on ampliative inferences such as analogies and inductions. In effect, in order to construct a representation, we have to ‘assimilate’ diverse things, and this requires identifying similarities between them. These similarities form the basis for ampliative inferences that gradually build hypotheses to solve a problem. To support my thesis, I analyse two examples. The first one is intra-field (intra-mathematical), that is, the construction of an algebraic representation of 3-manifolds; the second is inter-fields, that is, the construction of a topological representation of DNA supercoiling. 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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