{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T11:10:03Z","timestamp":1756120203377,"version":"3.44.0"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T00:00:00Z","timestamp":1712880000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl, and Brouwer, argued that a line is not composed of points but rather a matrix of a continued insertion of points. In spite of this disagreement on the structure of the continuum, they did distinguish the <jats:italic>temporal line<\/jats:italic> from the <jats:italic>spatial line<\/jats:italic>. In this paper, we argue that there is indeed a difference between the intuition of the spatial continuum and the intuition of the temporal continuum. The main primary aspect of the temporal continuum, in contrast with the spatial continuum, is the notion of <jats:italic>orientation<\/jats:italic>.<\/jats:p><jats:p>The continuum has usually been mathematically modeled by <jats:italic>Cauchy<\/jats:italic> sequences and the <jats:italic>Dedekind<\/jats:italic> cuts. While in the first model, each point can be approximated by rational numbers, in the second one, that is not possible constructively. We argue that points on the temporal continuum cannot be approximated by rationals as a temporal point is a <jats:italic>flow<\/jats:italic> that sinks to the past. In our model, the continuum is a collection of constructive <jats:italic>Dedekind<\/jats:italic> cuts, and we define two topologies for temporal continuum: 1. <jats:italic>oriented<\/jats:italic> topology and 2. the <jats:italic>ordinary<\/jats:italic> topology. We prove that every total function from the <jats:italic>oriented<\/jats:italic> topological space to the <jats:italic>ordinary<\/jats:italic> one is continuous.<\/jats:p>","DOI":"10.1017\/s1755020324000078","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T03:03:57Z","timestamp":1712891037000},"page":"420-438","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["THE TEMPORAL CONTINUUM"],"prefix":"10.1017","volume":"18","author":[{"given":"MOHAMMAD","family":"ARDESHIR","sequence":"first","affiliation":[{"name":"SHARIF UNIVERSITY OF TECHNOLOGY"}]},{"given":"RASOUL","family":"RAMEZANIAN","sequence":"additional","affiliation":[{"name":"UNIVERSITY OF LAUSANNE"}]}],"member":"56","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"year":"2000","author":"Martel","key":"S1755020324000078_r15"},{"key":"S1755020324000078_r18","first-page":"177","volume-title":"Perspectives on Negation","author":"Veldman","year":"1995"},{"key":"S1755020324000078_r11","volume-title":"From Kant to Hilbert: A Source Book in the Foundations of Mathematics","volume":"2","author":"Ewald","year":"1996"},{"volume-title":"On the Foundation of Mathematics","year":"1907","author":"Brouwer","key":"S1755020324000078_r5"},{"key":"S1755020324000078_r17","volume-title":"Constructivism in Mathematics: An Introduction","volume":"1","author":"Troelstra","year":"1988"},{"volume-title":"Brouwer Meets Husserl. On the Phenomenology of Choice Sequences","year":"2006","author":"van Atten","key":"S1755020324000078_r3"},{"key":"S1755020324000078_r1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710094"},{"key":"S1755020324000078_r6","volume-title":"Collected Works","volume":"1","author":"Brouwer","year":"1975"},{"key":"S1755020324000078_r12","volume-title":"The Thirteen Books of Euclids Elements","volume":"1","author":"Heath","year":"1956"},{"key":"S1755020324000078_r4","doi-asserted-by":"publisher","DOI":"10.1093\/philmat\/10.2.203"},{"volume-title":"The Continuum: A Critical Examination of the Foundation of Analysis","year":"1994","author":"Weyl","key":"S1755020324000078_r19"},{"key":"S1755020324000078_r7","unstructured":"[7] Cantor, G. (1883). Foundations of a General Theory of Manifolds: A Mathematico-Philosophical Investigation into the Theory of the Infinite, in [11]."},{"key":"S1755020324000078_r13","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171283000265"},{"key":"S1755020324000078_r16","doi-asserted-by":"publisher","DOI":"10.1063\/1.3059791"},{"year":"2004","author":"Kuiper","key":"S1755020324000078_r14"},{"key":"S1755020324000078_r8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2010.09.001"},{"volume-title":"Physics","year":"1999","key":"S1755020324000078_r2"},{"key":"S1755020324000078_r9","doi-asserted-by":"publisher","DOI":"10.1515\/9783110226133.147"},{"key":"S1755020324000078_r10","doi-asserted-by":"publisher","DOI":"10.2307\/2183661"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020324000078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T10:47:47Z","timestamp":1756118867000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020324000078\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,12]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["S1755020324000078"],"URL":"https:\/\/doi.org\/10.1017\/s1755020324000078","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"subject":[],"published":{"date-parts":[[2024,4,12]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. 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"}}]}}