Comparative Infinite Lottery Logic

Parker, Matthew (2020) Comparative Infinite Lottery Logic. In: UNSPECIFIED.

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Official URL: https://www.sciencedirect.com/science/article/abs/...

Abstract

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 infinite sets.

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Item Type:

Conference or Workshop Item (UNSPECIFIED)

Creators:

Creators	Email	ORCID
Parker, Matthew	W	0000-0002-7436-2149

Keywords:

Material theory of induction Qualitative probability Comparative probability Regular probability Infinite lottery Inductive logic Cosmology Eternal inflation Measure problem

Subjects:

General Issues > Confirmation/Induction
Specific Sciences > Physics > Cosmology
Specific Sciences > Probability/Statistics

Depositing User:

Dr. Matthew Parker

Date Deposited:

06 Feb 2021 21:11

Last Modified:

06 Feb 2021 21:11

Item ID:

18678

Official URL:

https://www.sciencedirect.com/science/article/abs/...