Measure, Topology and Probabilistic Reasoning in Cosmology

Abstract

I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes is finite-dimensional, and so admits a measure of the relevant sort, however, it is always the case that the family is not a compact topological space, and so does not admit a physically significant, well behaved probability measure. Problems of a different but still deeply troubling sort plague arguments about likelihood in that context, which I also discuss. I conclude that most standard forms of argument used in cosmology to estimate the likelihood of the occurrence of various properties or behaviors of spacetimes have serious mathematical, physical and conceptual problems.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,594

External links

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

Through your library

  • Only published works are available at libraries.

Similar books and articles

Admissible Representations for Probability Measures.Matthias Schröder - 2007 - Mathematical Logic Quarterly 53 (4):431-445.
Measure, Randomness and Sublocales.Alex Simpson - 2012 - Annals of Pure and Applied Logic 163 (11):1642-1659.
Gunk, Topology and Measure.Frank Arntzenius - 2004 - In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press.
Computability of Measurable Sets Via Effective Topologies.Yongcheng Wu & Decheng Ding - 2006 - Archive for Mathematical Logic 45 (3):365-379.
Quantum Covers in Quantum Measure Theory.Sumati Surya & Petros Wallden - 2010 - Foundations of Physics 40 (6):585-606.
Finite Powers of Strong Measure Zero Sets.Marion Scheepers - 1999 - Journal of Symbolic Logic 64 (3):1295-1306.
Should We Care About Fine-Tuning?Jeffrey Koperski - 2005 - British Journal for the Philosophy of Science 56 (2):303-319.
Infinite Lotteries, Perfectly Thin Darts and Infinitesimals.Alexander R. Pruss - 2012 - Thought: A Journal of Philosophy 1 (2):81-89.
Characterizing Common Cause Closedness of Quantum Probability Theories.Yuichiro Kitajima & Miklós Rédei - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (B):234-241.

Analytics

Added to PP
2015-09-07

Downloads
42 (#276,140)

6 months
2 (#278,494)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Erik Curiel
Ludwig Maximilians Universität, München

Citations of this work

A Primer on Energy Conditions.Erik Curiel - 2017 - In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. Birkhäuser. pp. 43-104.
Categories and the Foundations of Classical Field Theories.James Owen Weatherall - forthcoming - In Elaine Landry (ed.), Categories for the Working Philosopher. Oxford, UK: Oxford University Press.
Does Inflation Solve the Hot Big Bang Model׳s Fine-Tuning Problems?C. McCoy - 2015 - Studies in History and Philosophy of Modern Physics 51:23-36.

View all 14 citations / Add more citations

References found in this work

The Anthropic Cosmological Principle.John D. Barrow - 1986 - Oxford University Press.
Philosophy of Cosmology.Chris Smeenk - 2013 - In Robert Batterman (ed.), Oxford Handbook of Philosophy of Physics. Oxford: Oxford University Press. pp. 607-652.
The Anthropic Cosmological Principle.J. J. C. Smart - 1987 - Philosophical Quarterly 37 (149):463-466.
Similarity, Topology, and Physical Significance in Relativity Theory.Samuel C. Fletcher - 2016 - British Journal for the Philosophy of Science 67 (2):365-389.

View all 7 references / Add more references