New Psychological Paradigm for Conditionals and General de Finetti Tables

International audienceThe new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called 'defective', but should be termed the de Finetti table. We show how to study general de Finetti truth tables for negations, conjunctions, disjunctions, and conditionals

Betting on conditionals

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B, and conditional bets, I bet you that if A then B. The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional – true, false, or void for indicative conditionals and win, lose or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgments in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis

Learning, conditionals, causation

This dissertation is on conditionals and causation. In particular, we (i) propose a method of how an agent learns conditional information, and (ii) analyse causation in terms of a new type of conditional. Our starting point is Ramsey's (1929/1990) test: accept a conditional when you can infer its consequent upon supposing its antecedent. Inspired by this test, Stalnaker (1968) developed a semantics of conditionals. In Ch. 2, we define and apply our new method of learning conditional information. It says, roughly, that you learn conditional information by updating on the corresponding Stalnaker conditional. By generalising Lewis's (1976) updating rule to Jeffrey imaging, our learning method becomes applicable to both certain and uncertain conditional information. The method generates the correct predictions for all of Douven's (2012) benchmark examples and Van Fraassen's (1981) Judy Benjamin Problem. In Ch. 3, we prefix Ramsey's test by suspending judgment on antecedent and consequent. Unlike the Ramsey Test semantics by Stalnaker (1968) and Gärdenfors (1978), our strengthened semantics requires the antecedent to be inferentially relevant for the consequent. We exploit this asymmetric relation of relevance in a semantic analysis of the natural language conjunction 'because'. In Ch. 4, we devise an analysis of actual causation in terms of production, where production is understood along the lines of our strengthened Ramsey Test. Our analysis solves the problems of overdetermination, conjunctive scenarios, early and late preemption, switches, double prevention, and spurious causation -- a set of problems that still challenges counterfactual accounts of actual causation in the tradition of Lewis (1973c). In Ch. 5, we translate our analysis of actual causation into Halpern and Pearl's (2005) framework of causal models. As a result, our analysis is considerably simplified on the cost of losing its reductiveness. The upshot is twofold: (i) Jeffrey imaging on Stalnaker conditionals emerges as an alternative to Bayesian accounts of learning conditional information; (ii) the analyses of causation in terms of our strengthened Ramsey Test conditional prove to be worthy rivals to contemporary counterfactual accounts of causation

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Conditionals, Causal Claims and Objectivity

In my thesis, I develop two distinct themes. The first part of my thesis is devoted to indicative conditionals and approaching them from an empirically informed perspective. In the second part, I am developing classical topics of philosophy of science, specifically, scientific objectivity and the role of values in science, in connection to recent methodological developments, revolving around the Replication Crisis