We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically investigate the expressive power of these languages in causal team semantics, and we provide complete natural deduction calculi for each language. Furthermore, we introduce a generalized semantics which allows representing uncertainty about the causal laws, and we analyze the expressive power and proof theory of the causal-observational languages over this enriched semantics.

We put forth an account for when to believe causal and evidential conditionals. The basic idea is to embed a causal model in an agent’s belief state. For the evaluation of conditionals seems to be relative to beliefs about both particular facts and causal relations. Unlike other attempts using causal models, we show that ours can account rather well not only for various causal but also evidential conditionals.

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. This, we argue, (...) suggests that Pearl’s logic is either too weak or too strong. (shrink)

One family of maximizing act consequentialist theories are actualist direct theories. Indeed, historically there are at least three different forms of actualist direct consequentialism (due to Bentham, Moore, and contemporary consequentialists). This paper is about the logical differences between these three actualist direct theories and the differences between actualist direct theories and their competitors. Three main points emerge. First, the sharpest separation between actualist direct theories and their competitors concerns the so-called inheritance principle. Second, there are a myriad of other (...) logical differences among actualist direct theories. Third, one theory (Moore's theory) stands out among actualist direct theories because it entails a variety of logical principles. This fact may count in favor of that theory. (shrink)

The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9. (shrink)

Galles & Pearl (l998) claimed that s [possible-worlds] framework.s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they (...) viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all. (shrink)

This thesis studies Judea Pearl’s logic of counterfactuals derived from the causal modeling framework, in comparison to the influential Stanlnaker-Lewis counterfactual logics. My study focuses on a characteristic principle in Pearl’s logic, named reversibility. The principle, as Pearl pointed out, goes beyond Lewis’s logic. Indeed, it also goes beyond the stronger logic of Stanlnaker, which is more analogous to Pearl’s logic. The first result of this thesis is an extension of Stanlnaker’s logic incorporating reversibility. It will be observed that the (...) translation of reversibility from Pearl’s language to the standard language for conditional logic deserves some attention. In particular, a straightforward translation following Pearl’s suggestion would render reversibility incompatible with Stanlnaker’s logic. A new translation of reversibility will be proposed, and an extension of Stanlnaker’s logic with the inclusion of the translated reversibility will be investigated. More importantly, it will be shown that the extended Stanlnaker’s logic is sound and complete with respect to a modified Stanlnaker’s semantics. The extension of Stanlnaker’s logic has an interesting implication. Zhang, Lam, and de Clercq have shown that special case of reversibility, despite its name, actually states an important kind of irreversibility: counterfactual dependence between distinct events is irreversible. In other words, reversibility entails that there is no cycle of counterfactual dependence altogether generalizations of reversibility. However, as shown in Zhang et al., Pearls’ logic does not rule out cycles of counterfactual dependence altogether. It in fact allows cycles that involve three or more distinct events. This is peculiar because the status of cyclic counterfactual dependence seems no more metaphysically secure than that of mutual counterfactual dependence. This consideration leads to an exploration of logics that rule out all cycles of counterfactual dependence. A surprising result is that the extension of Stanlnaker’s logic is precisely a logic of this sort. (shrink)