Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus.
By way of a close reading of Boole and Frege's solutions to the same logical problem, we highlight an underappreciated aspect of Boole's work—and of its difference with Frege's better-known approach—which we believe sheds light on the concepts of 'calculus' and 'mechanization' and on their history....
| Publicado en: | Synthese Vol. 199; no. 5/6; pp. 11913 - 11944 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
Dec2021
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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=154480358&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 154480358 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Dec2021 vid: 199 iid: 5/6 pid: 237 pub: Springer Nature artinfo: ui: 154480358 10.1007/s11229-021-03318-x ppf: 11913 ppct: 31 formats: fmt: @attributes: type: P size: 451KB tig: atl: Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculus. aug: au: Waszek, David Schlimm, Dirk affil: Department of Philosophy, McGill University, Leacock Building, Room 414, 855 Sherbrooke St. W., H3A 2T7, Montreal, QC, Canada su: Mathematical notation Philosophy of mathematics Calculus sug: subj: Mathematical notation Philosophy of mathematics Calculus keyword: Boole Frege Logic Mechanization Notations ab: By way of a close reading of Boole and Frege's solutions to the same logical problem, we highlight an underappreciated aspect of Boole's work—and of its difference with Frege's better-known approach—which we believe sheds light on the concepts of 'calculus' and 'mechanization' and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege's Begriffsschrift, on the other hand, is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege's outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value—particularly in light of recent interest in the role of notations in mathematics and logic—in reviving Boole's idea of an intrinsic link between, as he put it, a 'calculus' and a 'directive method' to solve problems. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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