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Blurring Out Cosmic Puzzles

Published online by Cambridge University Press:  01 January 2022

Yann Benétreau-Dupin
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Abstract

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made in a Bayesian framework that represents credal states by single credence functions to avoid these conclusions, but none of them can do so for all versions of the Doomsday argument. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of ignorance and explains away these puzzles.

Type
Confirmation Theory
Information
Philosophy of Science , Volume 82 , Issue 5 , December 2015 , pp. 879 - 891
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

This article stems from discussions at the UCSC-Rutgers Institute for the Philosophy of Cosmology in summer 2013. I am grateful to Chris Smeenk and Wayne Myrvold for discussions and comments on earlier drafts. For helpful discussions, I thank participants at the Imprecise Probabilities in Statistics and Philosophy workshop at the Munich Center for Mathematical Philosophy in June 2014 and at the Graduate Colloquium series at Western University. I used excerpts and results from this article in a subsequent paper: “The Bayesian Who Knew Too Much.”

References

Augustin, Thomas, Coolen, Frank P. A., de Cooman, Gert, and Troffaes, Matthias C. M., eds. 2014. Introduction to Imprecise Probabilities. Hoboken, NJ: Wiley.10.1002/9781118763117CrossRefGoogle Scholar
Benétreau-Dupin, Yann. 2015. “The Bayesian Who Knew Too Much.” Synthese 192:1527–42.CrossRefGoogle Scholar
Bostrom, Nick. 2002. Anthropic Bias: Observation Selection Effects in Science and Philosophy. New York: Routledge.Google Scholar
Carroll, Sean. M. 2001. “The Cosmological Constant.” Living Reviews in Relativity 4:1–56.10.12942/lrr-2001-1CrossRefGoogle ScholarPubMed
Dawid, A. Philip, Stone, M., and Zidek, James V.. 1973. “Marginalization Paradoxes in Bayesian and Structural Inference.” Journal of the Royal Statistical Society B 35:189–233.Google Scholar
de Cooman, Gert, and Miranda, Enrique. 2007. “Symmetry of Models versus Models of Symmetry.” In Probability and Inference: Essays in Honour of Henry E. Kyburg Jr., ed. Harper, William L. and Wheeler, Gregory, 67–149. London: College.Google Scholar
de Cooman, Gert, Miranda, Enrique, and Quaeghebeur, Erik. 2009. “Representation Insensitivity in Immediate Prediction under Exchangeability.” International Journal of Approximate Reasoning 50:204–16.10.1016/j.ijar.2008.03.010CrossRefGoogle Scholar
Dieks, Dennis. 1992. “Doomsday; Or, The Dangers of Statistics.” Philosophical Quarterly 42:78–84.10.2307/2220450CrossRefGoogle Scholar
Dieks, Dennis 2007. “Reasoning about the Future: Doom and Beauty.” Synthese 156:427–39.CrossRefGoogle Scholar
Goodman, Steven N. 1994. “Future Prospects Discussed.” Nature 368:106–7.10.1038/368106b0CrossRefGoogle Scholar
Gott, J. Richard. 1993. “Implications of the Copernican Principle for Our Future Prospects.” Nature 363:315–19.CrossRefGoogle Scholar
Gott, J. Richard 1994. “Future Prospects Discussed.” Nature 368:108.CrossRefGoogle Scholar
Griffiths, Thomas L., and Tenenbaum, Joshua B.. 2006. “Optimal Predictions in Everyday Cognition.” Psychological Science 17:767–73.10.1111/j.1467-9280.2006.01780.xCrossRefGoogle ScholarPubMed
Hartle, James B., and Srednicki, Mark. 2007. “Are We Typical?” Physical Review D 75:123523.Google Scholar
Joyce, James M. 2010. “A Defense of Imprecise Credences in Inference and Decision Making.” Philosophical Perspectives 24:281–323.CrossRefGoogle Scholar
Kyburg, Henry E. 1978. “Subjective Probability: Criticisms, Reflections, and Problems.” Journal of Philosophical Logic 7:157–80.10.1007/BF00245926CrossRefGoogle Scholar
Leslie, John A. 1990. “Is the End of the World Nigh?” Philosophical Quarterly 40:65–72.10.2307/2219967CrossRefGoogle Scholar
Maor, Irit, Krauss, Lawrence, and Starkman, Glenn. 2008. “Anthropic Arguments and the Cosmological Constant, with and without the Assumption of Typicality.” Physical Review Letters 100:041301.10.1103/PhysRevLett.100.041301CrossRefGoogle ScholarPubMed
Martel, Hugo, Shapiro, Paul R., and Weinberg, Steven. 1998. “Likely Values of the Cosmological Constant.” Astrophysical Journal 492:29–40.CrossRefGoogle Scholar
Monton, Bradley, and Roush, Sherrilyn. 2001. “Gott’s Doomsday Argument.” Unpublished manuscript, PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/1205.Google Scholar
Neal, Radford M. 2006. “Puzzles of Anthropic Reasoning Resolved Using Full Non-indexical Conditioning.” Technical Report no. 0607, Department of Statistics, University of Toronto.Google Scholar
Norton, John D. 2010. “Cosmic Confusions: Not Supporting versus Supporting Not.” Philosophy of Science 77:501–23.CrossRefGoogle Scholar
Pogosian, Levon, Vilenkin, Alexander, and Tegmark, Max. 2004. “Anthropic Predictions for Vacuum Energy and Neutrino Masses.” Journal of Cosmology and Astroparticle Physics 7:1–17.Google Scholar
Richmond, Alasdair. 2006. “The Doomsday Argument.” Philosophical Books 47:129–42.CrossRefGoogle Scholar
Smith, Cedric A. B. 1961. “Consistency in Statistical Inference and Decision.” Journal of the Royal Statistical Society B 23:1–37.Google Scholar
Solà, Joan. 2013. “Cosmological Constant and Vacuum Energy: Old and New Ideas.” Journal of Physics: Conference Series 453:012015.Google Scholar
Syversveen, Anne Randi. 1998. “Noninformative Bayesian Priors: Interpretation and Problems with Construction and Applications.” Unpublished manuscript, Department of Mathematical Sciences, Norwegian University of Science and Technology. http://www.math.ntnu.no/preprint/statistics/1998/S3-1998.ps.Google Scholar
Tegmark, Max, and Bostrom, Nick. 2005. “Is a Doomsday Catastrophe Likely?” Nature 438:754.10.1038/438754aCrossRefGoogle ScholarPubMed
Troffaes, Matthias C. M. 2007. “Decision Making under Uncertainty Using Imprecise Probabilities.” International Journal of Approximate Reasoning 45:17–29.10.1016/j.ijar.2006.06.001CrossRefGoogle Scholar
Vilenkin, Alexander. 1995. “Predictions from Quantum Cosmology.” Physical Review Letters 74:846–49.10.1103/PhysRevLett.74.846CrossRefGoogle ScholarPubMed
Walley, Peter. 1991. Statistical Reasoning with Imprecise Probabilities. London: Chapman & Hall.CrossRefGoogle Scholar
Weinberg, Steven. 1987. “Anthropic Bound on the Cosmological Constant.” Physical Review Letters 59:2607–10.10.1103/PhysRevLett.59.2607CrossRefGoogle ScholarPubMed
Weinberg, Steven 2000. “A Priori Probability Distribution of the Cosmological Constant.” arXiv preprint. http://arxiv.org/abs/astro-ph/0002387.Google Scholar
Weinberg, Steven 2007. “Living in the Multiverse.” In Universe or Multiverse? ed. Carr, Bernard, 29–42. Cambridge: Cambridge University Press.10.1017/CBO9781107050990.004CrossRefGoogle Scholar
Wells, Willard. 2009. Apocalypse When? Calculating How Long the Human Race Will Survive. Chichester: Springer.10.1007/978-0-387-09837-1CrossRefGoogle Scholar