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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T11:19:39Z","timestamp":1721301579106},"reference-count":48,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-by\/4.0"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,3]]},"abstract":"Abstract<\/jats:title>In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects of predicativism, we explore some approaches to predicativity within the modal framework for potentiality developed in Linnebo (2013) and Linnebo and Shapiro (2019). This puts predicativism into a more general framework and helps to sharpen some of its key theses.<\/jats:p>","DOI":"10.1017\/s1755020321000423","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T08:47:21Z","timestamp":1637657241000},"page":"1-32","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["PREDICATIVISM AS A FORM OF POTENTIALISM"],"prefix":"10.1017","volume":"16","author":[{"given":"\u00d8YSTEIN","family":"LINNEBO","sequence":"first","affiliation":[]},{"given":"STEWART","family":"SHAPIRO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"S1755020321000423_r34","first-page":"294","volume-title":"Revue de M\u00e9taphysique et de Morale","volume":"14","author":"Poincar\u00e9","year":"1906"},{"key":"S1755020321000423_r44","unstructured":"[44] Weaver, N. (2005). Predicativity Beyond $\\Gamma $ 0. Available from: https:\/\/www.math.wustl.edu\/nweaver\/gamma0.pdf."},{"key":"S1755020321000423_r7","volume-title":"From Kant to Hilbert: A Sourcebook in the Foundations of Mathematics","volume":"2","author":"Ewald","year":"1996"},{"key":"S1755020321000423_r5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(01)00083-5"},{"key":"S1755020321000423_r10","first-page":"590","volume-title":"The Oxford Handbook of Philosophy of Mathematics and Logic","author":"Feferman","year":"2006"},{"key":"S1755020321000423_r20","first-page":"123","volume-title":"The Philosophy of Bertrand Russell","volume":"2","author":"G\u00f6del","year":"1951"},{"key":"S1755020321000423_r14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139626279.006"},{"key":"S1755020321000423_r27","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020313000014"},{"key":"S1755020321000423_r41","volume-title":"Foundations Without Foundationalism: A Case for Second-Order Logic","author":"Shapiro","year":"1991"},{"key":"S1755020321000423_r24","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1554"},{"key":"S1755020321000423_r42","volume-title":"Time, Creation and the Continuum: Theories in Antiquity and the Early Middle Ages","author":"Sorabji","year":"2006"},{"key":"S1755020321000423_r45","volume-title":"The Continuum: A Critical Examination of the Foundations of Analysis","author":"Weyl","year":"1918"},{"key":"S1755020321000423_r46","doi-asserted-by":"publisher","DOI":"10.1007\/BF02102305"},{"key":"S1755020321000423_r47","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199552078.001.0001"},{"key":"S1755020321000423_r48","first-page":"29","volume-title":"Fundamenta Mathematicae","volume":"16","author":"Zermelo","year":"1930"},{"key":"S1755020321000423_r21","doi-asserted-by":"crossref","first-page":"295","DOI":"10.3917\/rip.229.0295","article-title":"Predicativism as a philosophical position","volume":"3","author":"Hellman","year":"2004","journal-title":"Revue Internationale de Philosophie"},{"key":"S1755020321000423_r8","doi-asserted-by":"publisher","DOI":"10.2307\/2269764"},{"key":"S1755020321000423_r11","first-page":"169","article-title":"Conceptions of the continuum","volume":"51","author":"Feferman","year":"2009","journal-title":"Intellectica"},{"key":"S1755020321000423_r16","first-page":"117","volume-title":"Between Logic and Intuition: Essays in Honor of Charles Parsons","author":"Feferman","year":"2021"},{"key":"S1755020321000423_r28","unstructured":"[28] Linnebo, \u00d8. (2004). Plural quantification. Stanford Internet Encyclopedia of Philosophy. 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(2017). Predicativity and Parametric Polymorphism of Brouwerian Implication. Available from: https:\/\/arxiv.org\/pdf\/1710.07704.pdf."},{"key":"S1755020321000423_r31","doi-asserted-by":"publisher","DOI":"10.2307\/2273327"},{"key":"S1755020321000423_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.indag.2019.01.004"},{"key":"S1755020321000423_r3","unstructured":"[3] Crosilla, L. M. (2016). Constructivity and Predicativity: Philosophical Foundations. Ph.D. Dissertation, University of Leeds."},{"key":"S1755020321000423_r15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01052728"},{"key":"S1755020321000423_r13","unstructured":"[13] Feferman, S. (2012). Is the Continuum Hypothesis a Definite Mathematical Problem. 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Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http:\/\/creativecommons.org\/licenses\/by-nc-by\/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}