What is an experiment in mathematical practice? New evidence from mining the Mathematical Reviews.
From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathema...
| Publicado en: | Synthese Vol. 203; no. 2; pp. 1 - 22 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Feb2024
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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=175152026&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 175152026 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Feb2024 vid: 203 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 175152026 10.1007/s11229-023-04475-x ppf: 1 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 630KB tig: atl: What is an experiment in mathematical practice? New evidence from mining the Mathematical Reviews. aug: au: Sørensen, Henrik Kragh Mathiasen, Sophie Kjeldbjerg Johansen, Mikkel Willum affil: Section for History and Philosophy of Science, Department of Science Education, University of Copenhagen, Niels Bohr Building, Universitetsparken 5, 2100, København Ø, Denmark Independent Scholar, Copenhagen, Denmark sug: keyword: Experimental mathematics Experiments Philosophy of mathematical practice Qualitative corpus studies ab: From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathematical practice, experiments are now conducted and used in a much broader range of epistemic practices such as concept formation, validation, and communication. In this article, we combine corpus studies and qualitative analyses to assess and categorize the epistemic roles experiments are seen—by mathematicians—to have in actual mathematical practice. We do so by text-mining a corpus of reviews from the Mathematical Reviews, which include the indicator word “experiment”. Our qualitative, grounded classification of samples from this corpus allows us to explore the various roles played by experiments. We thus identify instances where experiments function as references to established knowledge, as tools for heuristics or exploration, as epistemic warrants, as communication or pedagogy, and instances simply proposing experiments. Focusing on the role of experiments as epistemic warrants, we show through additional sampling that in some fields of mathematics, experiments can warrant theorems as well as methods. We also show that the expressed lack of experiments by reviewers suggests concordant views that experiments could have provided epistemic warrants. Thus, our combination of corpus studies and qualitative analyses has added a typology of roles of experiments in mathematical practice and shown that experiments can and do play roles as epistemic warrants depending on the mathematical field. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2024. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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