APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

I argue elsewhere (Roche 2014) that evidence of evidence is evidence under screening-off. Tal and Comesaña (2017) argue that my appeal to screening-off is subject to two objections. They then propose an evidence of evidence thesis involving the notion of a defeater. There is much to learn from their very careful discussion. I argue, though, that their objections fail and that their evidence of evidence thesis is open to counterexample.

The author argues for the importance of non-Markovian causality in the social sciences because Markovian conditions often cannot be satisfied. Two theorems giving conditions for non-Markovian causes to be transitive are proved. Applications of non-Markovian causality in psychology and economics are outlined.

ABSTRACT This article aims to achieve two things: to identify the conditions for transitivity in probabilistic support in various settings, and to uncover the components and structure of the mediated probabilistic relation. It is shown that when the probabilistic relation between the two propositions, x and z, is mediated by multiple layers of partitions of propositions, the impact x has on z consists of the purely indirect impact, the purely bypass impact, and the mixed impact. It is also shown that (...) although mediated confirmation as a whole is not transitive, the indirect part of mediated confirmation is transitive. _1_ Introduction _2_ The Structure of the Mediated Probabilistic Relation _3_ Transitivity and Anti-transitivity _4_ Bypass Disconfirmation _5_ Horizontal Generalization _6_ Coarse Screens _7_ Vertical Generalization _8_ Conclusion Appendix. (shrink)

It is well known that probabilistic support is not transitive. But it can be shown that probabilistic support is transitive provided the intermediary proposition screens off the original evidence with respect to the hypothesis in question. This has the consequence that probabilistic support is transitive when the original evidence is testimonial, memorial or perceptual (i.e., to the effect that such and such was testified to, remembered, or perceived), and the intermediary proposition is its representational content (i.e., to the effect that (...) the such and such occurred). (shrink)

Probabilistic support is not transitive. There are cases in which x probabilistically supports y , i.e., Pr( y | x ) > Pr( y ), y , in turn, probabilistically supports z , and yet it is not the case that x probabilistically supports z . Tomoji Shogenji, though, establishes a condition for transitivity in probabilistic support, that is, a condition such that, for any x , y , and z , if Pr( y | x ) > Pr( y (...) ), Pr( z | y ) > Pr( z ), and the condition in question is satisfied, then Pr( z | x ) > Pr( z ). I argue for a second and weaker condition for transitivity in probabilistic support. This condition, or the principle involving it, makes it easier (than does the condition Shogenji provides) to establish claims of probabilistic support, and has the potential to play an important role in at least some areas of philosophy. (shrink)

This article examines Simpson's paradox as applied to the theory of probabilites and percentages. The author discusses possible flaws in the paradox and compares it to the Sure Thing Principle, statistical inference, causal inference and probabilistic analyses of causation.

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (shrink)

As every philosopher knows, “the design argument” concludes that God exists from premisses that cite the adaptive complexity of organisms or the lawfulness and orderliness of the whole universe. Since 1859, it has formed the intellectual heart of creationist opposition to the Darwinian hypothesis that organisms evolved their adaptive features by the mindless process of natural selection. Although the design argument developed as a defense of theism, the logic of the argument in fact encompasses a larger set of issues. William (...) Paley saw clearly that we sometimes have an excellent reason to postulate the existence of an intelligent designer. If we find a watch on the heath, we reasonably infer that it was produced by an intelligent watchmaker. This design argument makes perfect sense. Why is it any different to claim that the eye was produced by an intelligent designer? Both critics and defenders of the design argument need to understand what the ground rules are for inferring that an intelligent designer is the unseen cause of an observed effect. (shrink)

After clarifying the probabilistic conception of causality suggested by Good (1961-2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.