Probabilistic language in indicative and counterfactual conditionals

This paper analyzes indicative and counterfactual conditionals that have in their consequents probability operators: probable, likely, more likely than not, 50% chance and so on. I provide and motivate a unified compositional semantics for both kinds of probabilistic conditionals using a Kratzerian syntax for conditionals and a representation of information based on Causal Bayes Nets. On this account, the only difference between probabilistic indicatives and counterfactuals lies in the distinction between conditioning and intervening. This proposal explains why causal (ir)relevance is crucial for probabilistic counterfactuals, and why it plays no direct role in probabilistic indicatives. I conclude with some complexities related to the treatment of backtracking counterfactuals and subtleties revealed by probabilistic language in the revision procedure used to create counterfactual scenarios. In particular, I argue that certain facts about the interaction between probability operators and counterfactuals motivate the use of Structural Equation Models (Pearl 2000) rather than the more general formalism of Causal Bayes Nets.

Causal Models and Conditional Reasoning

There are deep intuitions that the meaning of conditional statements relate to probabilistic law-like dependencies. In this chapter it is argued that these intuitions can be captured by representing conditionals in causal Bayes nets (CBNs) and that this conjecture is theoretically productive. This proposal is borne out in a variety of results. First, causal considerations can provide a unified account of abstract and causal conditional reasoning. Second, a recent model (Fernbach & Erb, 2013) can be extended to the explicit causal conditional reasoning paradigm (Byrne, 1989), making some novel predictions on the way. Third, when embedded in the broader cognitive system involved in reasoning, causal model theory can provide a novel explanation for apparent violations of the Markov condition in causal conditional reasoning (Ali et al, 2011). Alternative explanations are also considered (see, Rehder, 2014a) with respect to this evidence. While further work is required, the chapter concludes that the conjecture that conditional reasoning is underpinned by representations and processes similar to CBNs is indeed a productive line of research.

Probabilistic Causation

This chapter will explore a variety of projects that aim to characterize causal concepts using probability. These are, somewhat arbitrarily, divided into four categories. First, a tradition within philosophy that has aimed to define, or at least constrain, causation in terms of conditional probability is discussed. Secondly, the use of causal Bayes nets to represent causal relations, to facilitate inferences from probabilities to causal relations, and to ‘identify’ causal quantities in probabilistic terms is discussed. Thirdly, efforts to measure causal strength in probabilistic terms are reviewed, with particular attention to the significance of these measures in the context of epidemiology. Finally, attempts are discussed to analyze the relation of ‘actual causation’ (sometimes called ‘singular causation’) using probability.

Causality

Causal knowledge is central to children’s understanding of the world, but there have been many different conceptions of how causal knowledge is represented and how it is learned. I outline four different approaches to causality that have influenced developmental research, stressing agency, mechanism, association, and probabilistic models, and give examples of theory and research in each area. I focus in more detail on the most recent probabilistic model accounts that stress the role of causation in inferences about possibilities. These include potential interventions to change the world and counterfactuals about alternate ways the world might be. These accounts also employ computational ideas about causal Bayes nets and Bayesian learning, and these ideas are outlined.

Norms and high-level cognition: Consequences, trends, and antidotes

We are neither as pessimistic nor as optimistic as Elqayam & Evans (E&E). The consequences of normativism have not been uniformly disastrous, even among the examples they consider. However, normativism won't be going away any time soon and in the literature on causal Bayes nets new debates about normativism are emerging. Finally, we suggest that to concentrate on expert reasoners as an antidote to normativism may limit the contribution of research on thinking to basic psychological science.