Basic Rules of Arithmetic.
Inferential expressivism makes a systematic distinction between inferences that are valid qua preserving commitment and inferences that are valid qua preserving evidence. I argue that the characteristic inferences licensed by the principle of comprehension, from $x$ x is $P$ P to $x$ x is in the ext...
| Publicado en: | Australasian Journal of Philosophy Vol. 104; no. 3; pp. 654 - 673 |
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| Formato: | Artículo |
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Taylor & Francis Ltd
Sep2026
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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=197009536&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 197009536 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00048402 BHK jtl: Australasian Journal of Philosophy issn: 00048402 maglogo: N pubinfo: dt: Sep2026 vid: 104 iid: 3 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 197009536 10.1080/00048402.2025.2521739 ppf: 654 ppct: 19 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1005KB tig: atl: Basic Rules of Arithmetic. aug: au: Schloeder, Julian J. affil: University of Connecticut, Storrs sug: keyword: comprehension Frege inferential expressivism logicism Russell's paradox ab: Inferential expressivism makes a systematic distinction between inferences that are valid qua preserving commitment and inferences that are valid qua preserving evidence. I argue that the characteristic inferences licensed by the principle of comprehension, from $x$ x is $P$ P to $x$ x is in the extension of $P$ P and vice versa, fail to preserve evidence, but do preserve commitment. Taking this observation into account allows one to phrase inference rules for unrestricted comprehension without running into Russell's paradox. In the resulting logic, one can derive full second-order arithmetic. Thus, it is possible to derive classical arithmetic in a consistent logic with unrestricted comprehension. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Australasian Journal of Philosophy is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Australasian Journal of Philosophy holder: Taylor & Francis Ltd dt: @attributes: year: 2026 holdings: @attributes: islocal: N |
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