A philosopher, a medical doctor, and a statistician talk about causality. They discuss the relationships between causality, chance, and statistics, resorting to examples from medicine to develop their arguments. This debate gives rise to an original trialogue, a tribute to the famous conversation between d'Alembert and Diderot, two great French thinkers of the Enlightenment. The trialogue notably offers an introduction to the philosophy of causality and an initiation to statistics, including recent developments that should prove interesting to specialists and laypeople alike.Otros cien pasos serían los que anduvieron, cuando al doblar de una punta pareció descubierta y patente la misma causa, sin que pudiese ser otra, de aquel horrísono y para ellos espantable ruido, que tan suspensos y medrosos toda la noche les había tenido; y eran (si no lo has, ! oh lector! por pesadumbre y enojo) seis mazos de batán que con sus alternativos golpes aquel estruendo formaban.They went it might be a hundred paces farther, when on turning a corner the true cause, beyond the possibility of any mistake, of that dread-sounding and to them awe-inspiring noise that had kept them all the night in such fear and perplexity, appeared plain and obvious; and it was (if, reader, thou art not disgusted and disappointed) six fulling hammers which by their alternate strokes made all the din.
M. de Cervantes, El Ingenioso Hidalgo de Don Quijote de la Mancha (English translation by J. Ormsby)In relating what follows I must confess to a certain chronological vagueness. The events themselves I can see in sharp focus, and I want to think they happened that same evening, and there are good reasons to suppose they did. In a narrative sense they present a nice neat package, effect dutifully tripping along at the heels of cause. Perhaps it is the attraction of such simplicity that makes me suspicious, that along with the conviction that real life seldom works this way.R. Russo, The risk pool Notation -9, existential quantifier, mathematical symbol meaning "there exists." -), mathematical symbol meaning "implies" (or, equivalently, "if (…) then (…)").-0-1, mathematical notation meaning "0 or 1." -f0; 1g, set consisting of the two numbers 0 and 1. -½a; b, interval consisting of all the real numbers equal to or larger than a and equal to or smaller than b.*Corresponding author: Antoine Chambaz, Modal'X (EA 3454), Université Paris Ouest Nanterre, 200 av de la République, From this follows a counterfactual model for reality, where what happens in the real world is the projection of what concomitantly occurs in parallel, counterfactual worlds. Used for the sake of approaching causality, this induces a conceptual difficulty: there may be something more, or something else, in effects and causes than what actually takes place in our world. Or not, since a puzzling twist allows the statistician to build counterfactual worlds inducing by projection the actual world based on the observation of the sole actual world.The aforementioned projection is driven by possibl...