Comparative infinite lottery logic

Studies in History and Philosophy of Science Part A 84:28-36 (2020)
  Copy   BIBTEX


As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models based on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets.



    Upload a copy of this work     Papers currently archived: 92,283

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Reflecting on finite additivity.Leendert Huisman - 2015 - Synthese 192 (6):1785-1797.
Potential infinite models and ontologically neutral logic.Theodore Hailperin - 2001 - Journal of Philosophical Logic 30 (1):79-96.
Logic Semantics with the Potential Infinite.Theodore Hailperin - 2010 - History and Philosophy of Logic 31 (2):145-159.
Ultralarge and infinite lotteries.Sylvia Wenmackers - 2012 - In B. Van Kerkhove, T. Libert, G. Vanpaemel & P. Marage (eds.), Logic, Philosophy and History of Science in Belgium II (Proceedings of the Young Researchers Days 2010). Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten.
Infinity and a Critical View of Logic.Charles Parsons - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):1-19.
Infinite chains and antichains in computable partial orderings.E. Herrmann - 2001 - Journal of Symbolic Logic 66 (2):923-934.


Added to PP

51 (#313,850)

6 months
13 (#200,551)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Matthew Parker
London School of Economics

Citations of this work

Add more citations

References found in this work

Counterpart theory and quantified modal logic.David Lewis - 1968 - Journal of Philosophy 65 (5):113-126.
Fair infinite lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
The Axioms of Subjective Probability.Peter C. Fishburn - 1986 - Statistical Science 1 (3):335-358.

View all 9 references / Add more references