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Knowledge, Belief, and GodNew Insights in Religious Epistemology$
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Matthew A. Benton, John Hawthorne, and Dani Rabinowitz

Print publication date: 2018

Print ISBN-13: 9780198798705

Published to Oxford Scholarship Online: March 2018

DOI: 10.1093/oso/9780198798705.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 12 November 2019

Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments

Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments

Chapter:
(p.103) 5 Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments
Source:
Knowledge, Belief, and God
Author(s):

Isaac Choi

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198798705.003.0006

This chapter deals with two different problems in which infinity plays a central role. It first responds to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and it argues that we should use the subset principle for measuring knowledge. The chapter then turns to the normalizability and coarse tuning objections to fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, the chapter hopes to blunt much of the force of these objections to fine-tuning arguments.

Keywords:   fine-tuning arguments, infinity, measuring knowledge, multiverse, existence of God

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