Screening off generalized:Reichenbach’s legacy

Eells and Sober proved in 1983 that screening off is a sufficient condi- tion for the transitivity of probabilistic causality, and in 2003 Shogenji noted that the same goes for probabilistic support. We start this paper by conjecturing that Hans Reichenbach may have been aware of this fact. Then we consider the work of Suppes and Roche, who demonstrated in 1986 and 2012 respectively that screening off can be generalized, while still being sufficient for transitivity. We point out an interesting difference between Reichenbach’s screening off and the generalized version, which we illustrate with an example about haemophilia among the descendants of Queen Victoria. Finally, we embark on a further generalization: we develop a still weaker condi- tion, one that can be made as weak as one wishes

Probability Functions, Belief Functions and Infinite Regresses

In a recent paper Ronald Meester and Timber Kerkvliet argue by example that infinite epistemic regresses have different solutions depending on whether they are analyzed with probability functions or with belief functions. Meester and Kerkvliet give two examples, each of which aims to show that an analysis based on belief functions yields a different numerical outcome for the agent's degree of rational belief than one based on probability functions. In the present paper we however show that the outcomes are the same. The only way in which probability functions and belief functions can yield different solutions for the agent's degree of belief is if they are applied to different examples, i.e. to different situations in which the agent finds himself

"Till at last there remain nothing":Hume's <i>Treatise</i> 1.4.1 in contemporary perspective

In A Treatise of Human Nature, David Hume presents an argument according to which all knowledge reduces to probability, and all probability reduces to nothing. Many have criticized this argument, while others find nothing wrong with it. In this paper we explain that the argument is invalid as it stands, but for different reasons than have been hitherto acknowledged. Once the argument is repaired, it becomes clear that there is indeed something that reduces to nothing, but it is something other than what, according to many, Hume had in mind. Thus two views emerge of what exactly it is that reduces. We surmise that Hume failed to distinguish the two, because he lacked the formal means to differentiate between a rendering of his argument that is in accordance with the probability calculus, and one that is not

"The worst ever conceived by a man of genius":Hume's probability argument in A Treatise

The probability argument in Hume’s A Treatise of Human Nature (Section 1.4.1) has been widely criticized, with David Stove calling it “the worst [argument] ever conceived by a man of genius”. We explain that the argument is open to two interpretations: one that is in accordance with probability theory and one that is not. We surmise that Hume failed to distinguish between the two, and that this contributed to the confusion surrounding the argument