Ordóñez Angulo, Emmanuel;
(2018)
Seeing the infinite.
Masters thesis (M.Phil.Stud), UCL (University College London).
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Abstract
Against the consensus in the epistemology of mathematics, this thesis argues that knowledge of infinity by acquaintance is possible. Even if knowledge of small cardinal numbers by acquaintance or via experience is possible, the consensus goes, knowledge of large numbers, and importantly of infinite numbers, is only possible by description or via theory. The thesis starts by taking up Stewart Shapiro’s view that cardinal numbers can be understood in terms of structures, and hence that knowledge of small cardinals by experience may be understood as experience of small structures, to suggest that a purported experience of the first infinite cardinal, ℵ0, may be understood as an experience of the corresponding infinite structure. This suggestion is reached obliquely by focusing on a particular puzzling case concerning knowledge of infinity: a subject’s perceptual report of ‘encountering’ it. The main hurdle in explaining this puzzle will be that infinities are widely understood in both philosophy and mathematics to exist actually rather than potentially, such that in a framework of perceptual experience requiring both relata of the perceptual relation to be co-present, actual infinities can of course not be. Unlike mathematical abstracta, however, perceptual experience is not placeless and timeless but perspectival and extended in time. Hence, an account of the subject’s mental state in terms of potential infinity needn’t entail anything about the (actually infinite) structure purportedly perceived. I develop such a modal-logic-based account drawing on Shapiro and Øystein Linnebo’s explication of potential infinity and on a version of Jaakko Hintikka’s explication of knowledge modified for knowledge by acquaintance. The broader consequences of making sense of the possibility of acquaintance with infinity are sketched in terms of Fraser MacBride’s ‘access’ challenge against Shapiro’s epistemology.
| Type: | Thesis (Masters) |
|---|---|
| Qualification: | M.Phil.Stud |
| Title: | Seeing the infinite |
| Event: | UCL |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2018. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL SLASH UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10062365 |
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