26/06/2024, 17:00 — 18:00 — Online
Bruno Dinis, Department of Mathematics, UÉvora
Nonstandard Analysis meets Philosophy
Nonstandard analysis (NSA), founded by Abraham Robinson in the 1960s, was to a great extent inspired by Leibniz’s ideas and intuitions towards the use of infinitesimal and infinitely large quantities. One of the greatest features of NSA is that, by allowing a correct formulation of infinitesimals, one is now able to reason using orders of magnitude. This means that one can give precise meaning, and reason formally, about otherwise vague terms such as "small" or "large". Recently, accounts of vagueness relying on NSA were introduced [2, 8, 4]. In particular, and unlike other accounts of vagueness, the so-called nonstandard primitivist account [4, 5] embraces transitivity for marginal differences (i.e. "small" differences), but not for large differences in a soritical series. Nonstandard primitivism also seems to be particularly adequate to deal with the ship of Theseus paradox [3, 6] and may also shed some light in doxastic reasoning by considering infinitesimal probabilities and associating them to infinitesimal credences [1, 7]. We aim at assessing the relative merits of nonstandard primitivism and to show some lines of future research regarding the connections between NSA and philosophy.
(This is joint work with Bruno Jacinto)
- Benci, Vieri and Horsten, Leon and Wenmackers, Sylvia. Infinitesimal Probabilities. The British Journal for the Philosophy of Science, 69 (2): 509–552, 2018.
- Walter Dean. Strict finitism, feasibility, and the sorites. Review of Symbolic Logic, 11 (2):295–346, 2018.
- Bruno Dinis. Equality and near-equality in a nonstandard world. Log. Log. Philos., 32 (1):105–118, 2023. ISSN 1425-3305,2300-9802.
- Bruno Dinis and Bruno Jacinto. A theory of marginal and large difference. Erkenntnis, 2023.
- Bruno Dinis and Bruno Jacinto. Marginality scales for gradable objects. (preprint), 2023.
- Bruno Dinis and Bruno Jacinto. Counterparts as Near-equals. (preprint), 2024.
- Kenny Easwaran. Regularity and Hyperreal Credences. Philosophical Review, 123 (1):1- 41, 2014.
- Yair Itzhaki. Qualitative versus quantitative representation: a non-standard analysis of the sorites paradox. Linguistics and Philosophy, 44:1013–1044, 2021.
