Mathematical justification is still infallible.
In contemporary epistemology, fallibilism has become the universally presupposed stance. This trend is not confined to empirical knowledge; in recent years, it has also been extended to mathematical knowledge. In this paper, I argue against the fallibilist view on mathematical justification, and adv...
| Publicado en: | Synthese Vol. 205; no. 5; pp. 1 - 17 |
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| Formato: | Artículo |
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Springer Nature
May2025
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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=185719970&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 185719970 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: May2025 vid: 205 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 185719970 10.1007/s11229-025-05028-0 ppf: 1 ppct: 16 formats: fmt: – @attributes: type: T – @attributes: type: P size: 873KB tig: atl: Mathematical justification is still infallible. aug: au: Wu, YuTang affil: https://ror.org/05bqach95 Department of Philosophy, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, 10617, Taipei, Taiwan sug: keyword: Excuse Fallibilism Infallibilism Luminosity Mathematical justification ab: In contemporary epistemology, fallibilism has become the universally presupposed stance. This trend is not confined to empirical knowledge; in recent years, it has also been extended to mathematical knowledge. In this paper, I argue against the fallibilist view on mathematical justification, and advocate infallibilism. Specifically, I examine the fallibilist account offered by De Toffoli in Philosophical Quarterly, 7(4), 823-844, 2021, which is the most developed version in the literature. This account proposes a distinctive characterisation of mathematical justification, which is fallibilistic. To counter this, I will demonstrate that De Toffoli’s argument is unsuccessful. From the objections emerges the positive view that I go on to develop and defend, which is a bi-level theory of mathematical epistemology. In my theory, I distinguish between first-level justification, which concerns mathematical beliefs, and second-level justification, which pertains to judgments about the justificational states of those mathematical beliefs. I will argue that while second-level justification is fallible, first-level justification is infallible, and it is this first-level justification that constitutes mathematical justification. Based on my picture, I then advocate an infallibilist view of mathematical justification. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2025. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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