A Two-Sided Ontological Solution to the Sleeping Beauty Problem

eub-sbPreprint published on the PhilSci archive.

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the hyper-entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the hyper-entanglement urn. I draw then the consequences of considering that some balls in the hyper-entanglement urn have ontologically different properties from normal ones. In this context, drawing a red ball (a Monday-waking) leads to two different situations that are assigned each a different probability, depending on whether one considers “balls-as-colour” or “balls-as-object”. This leads to a two-sided account of the Sleeping Beauty problem.

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A Two-Sided Ontological Solution to the Sleeping Beauty Problem

1. The hyper-entanglement urn

Let us consider the following experiment. In front of you is an urn. The experimenter asks you to study very carefully the properties of the balls that are in the urn. You go up then to the urn and begin to examine its content carefully. You notice first that the urn contains only red or green balls. By curiosity, you decide to take a sample of a red ball in the urn. Surprisingly, you notice that while you pick up this red ball, another ball, but a green one, also moves simultaneously. You decide then to replace the red ball in the urn and you notice that immediately, the latter green ball also springs back in the urn. Intrigued, you decide then to catch this green ball. You notice then that the red ball also goes out of the urn at the same time. Furthermore, while you replace the green ball in the urn, the red ball also springs back at the same time at its initial position in the urn. You decide then to withdraw another red ball from the urn. But while it goes out of the urn, nothing else occurs. Taken aback, you decide then to undertake a systematic and rigorous study of all the balls in the urn.

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A Third Route to the Doomsday Argument

DA-figureA paper published (2009) in English in the Journal of Philosophical Research, vol. 34, pages 263-278 (with significant changes with regard to the preprint).

In this paper, I present a solution to the Doomsday argument based on a third type of solution, by contrast with, on the one hand, the Carter-Leslie view and on the other hand, the Eckhardt et al. analysis. I begin by strengthening both competing models by highlighting some variations of their ancestors models, which renders them less vulnerable to several objections. I describe then a third line of solution, which incorporates insights from both Leslie and Eckhardt’s models and fits more adequately with the human situation corresponding to the Doomsday argument. I argue then that the resulting two-sided analogy casts new light on the reference class problem. This leads finally to a novel formulation of the argument that could well be more consensual than the original one.

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A Third Route to the Doomsday Argument

In what follows, I will endeavor to present a solution to the problem arising from the Doomsday argument (DA). The solution thus described constitutes a third way out, compared to, on the one hand, the approach of the promoters of DA (Leslie 1993 and 1996) and on the other hand, the solution recommended by its detractors (Eckhardt 1993 and 1997, Sowers 2002).i

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Probabilistic Situations for Goodmanian N-universes

image22A paper appeared (2006) in French in the Journal of Philosophical Research, vol. 31, pages 123-141, under the title “Situations probabilistes pour n-univers goodmaniens.”

I proceed to describe several applications of the theory of n-universes through several different probabilistic situations. I describe first how n-universes can be used as an extension of the probability spaces used in probability theory. The extended probability spaces thus defined allow for a finer modelling of complex probabilistic situations and fits more intuitively with our intuitions related to our physical universe. I illustrate then the use of n-universes as a methodological tool, with two thought experiments described by John Leslie. Lastly, I model Goodman’s paradox in the framework of n-universes while also showing how these latter appear finally very close to goodmanian worlds.

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Probabilistic Situations for Goodmanian N-universes

The n-universes were introduced in Franceschi (2001, 2002) in the context of the study of the probabilistic situations relating to several paradoxes which are currently the object of intensive studies in the field of analytical philosophy: Goodman’s paradox and the Doomsday Argument. The scope of the present article is twofold: on one hand, to describe how modelling within the n-universes allows to extend the properties of the classical probability spaces used in probability theory, by providing at the same time a finer modelling of some probabilistic situations and a better support for intuition; on the other hand, to show how the use of n-universes allows to simplify considerably the study of complex probabilistic situations such as those which appear in the study of paradoxes.

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The Doomsday Argument and Hempel’s Problem

hempelPosprint in English (with additional illustrations) of a paper published in French in the Canadian Journal of Philosophy Vol.29, July 1999, pp. 139-56 under the title “Comment l’Urne de Carter et Leslie se Déverse dans celle de Hempel”.
I begin by describing a solution to Hempel’s Problem. I recall, second, the solution to the Doomsday Argument described in my previous Une Solution pour l’Argument de l’Apocalypse (Canadian Journal of Philosophy 1998-2) and remark that both solutions are based on a similar line of reasoning. I show thirdly that the Doomsday Argument can be reduced to the core of Hempel’s Problem.

This paper is cited in:

Koji Sawa, Junki Yokokawa and Tatsuji Takahashi (2013) Logical Equivalence: Symmetric and Asymmetric Features, Symmetry: Culture and Science, Vol. 24, No. x.

Milan M. Cirkovic, A Resource Letter on Physical eschatology, Am.J.Phys. 71 (2003) 122-133

Nick Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy, Routledge (2002)

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