Screening off generalized: Reichenbach’s legacy

Eells and Sober proved in 1983 that screening off is a sufficient condition 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 condition, one that can be made as weak as one wishes.

Challenging the 'hidden' assumption in J. L. Schellenberg's hiddenness argument: an exploration into the nature of divine love

In recent years, J. L. Schellenberg has developed and defended a forceful argument for atheism. He argues that the existence of inculpable nonbelief, together with the (a priori) claim that this is not what we would expect if a perfectly loving God exists, provides probabilistic support for atheism. In response, most critics have focused on either denying the existence of inculpable nonbelief offering reasons why it is compatible with the existence of a perfectly loving God. I propose a new strategy for responding to Schellenberg's argument, however, which focuses on clarifying what perfect love entails. I claim that since Schellenberg employs perfect being theology in formulating his argument, he is thereby committed to the assumption that perfect love entails infinite love. I argue, however, that this assumption is unwarranted, and that if it can be shown that God's love is possibly not infinite, then Schellenberg's argument fails.

Challenging the 'hidden' assumption in J. L. Schellenberg's hiddenness argument: an exploration into the nature of divine love

In recent years, J. L. Schellenberg has developed and defended a forceful argument for atheism. He argues that the existence of inculpable nonbelief, together with the (a priori) claim that this is not what we would expect if a perfectly loving God exists, provides probabilistic support for atheism. In response, most critics have focused on either denying the existence of inculpable nonbelief offering reasons why it is compatible with the existence of a perfectly loving God. I propose a new strategy for responding to Schellenberg's argument, however, which focuses on clarifying what perfect love entails. I claim that since Schellenberg employs perfect being theology in formulating his argument, he is thereby committed to the assumption that perfect love entails infinite love. I argue, however, that this assumption is unwarranted, and that if it can be shown that God's love is possibly not infinite, then Schellenberg's argument fails.

A New Condition for Transitivity of Probabilistic Support

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity.

Inpainting forgery detection using hybrid generative/discriminative approach based on bounded generalized Gaussian mixture model

We propose in this paper a novel reliable detection method to recognize forged inpainting images. Detecting potential forgeries and authenticating the content of digital images is extremely challenging and important for many applications. The proposed approach involves developing new probabilistic support vector machines (SVMs) kernels from a flexible generative statistical model named “bounded generalized Gaussian mixture model”. The developed learning framework has the advantage to combine properly the benefits of both discriminative and generative models and to include prior knowledge about the nature of data. It can effectively recognize if an image is a tampered one and also to identify both forged and authentic images. The obtained results confirmed that the developed framework has good performance under numerous inpainted images.