## A Two-Sided Ontological Solution to the Sleeping Beauty Problem

Preprint 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.

## 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.

## A Dichotomic Analysis of the Surprise Examination Paradox

English translation of a paper appeared in French in Philosophiques 2005, vol. 32, pages 399-421 (with minor changes with regard to the published version).

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine’s solution and Hall’s reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure.

## A Dichotomic Analysis of the Surprise Examination Paradox

I shall present in what follows a new conceptual framework to solve the surprise examination paradox (henceforth, SEP), in the sense that it reorganizes, by adapting them, several elements of solution described in the literature. The solution suggested here rests primarily on the following elements: (i) a distinction between a monist and a dichotomic analysis of the paradox; (ii) the introduction of a matrix definition, which is used as support with several variations of the paradox; (iii) the distinction between a conjoint and a disjoint definition of the cases of surprise and of non-surprise, leading to two structurally different notions of surprise.

## An Introduction to Analytic Philosophy

In this book, Paul Franceschi provides us with an introduction to analytic philosophy. In a concrete way, he chooses to describe forty paradoxes, arguments or philosophical issues that represent so many challenges for contemporary philosophy and human intelligence, for some paradoxes of millennial origin—such as the Liar or the sorites paradox—are still unresolved in the present day. Some other philosophical puzzles, however—such as the Doomsday argument—appeared only recently in the literature. The author strives to introduce us clearly to each of these problems as well as to major attempts that have been formulated to solve them.

“I’m really impressed by this very neat and stimulating book. I highly recommend it both to students for pedagogy and general culture (prisoner’s dilemma, twin-earth, etc.), and to professionals as well for the reference tool and even more generally to those who like to think.”

Julien Dutant, Philotropes, Philosophical blog

The Kindle version is also available.