Antirealism and the conditional fallacy : the semantic approach

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Conditionals and modularity in general logics

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics

Breaking de Morgan's law in counterfactual antecedents

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal

Counterfactuals 2.0 Logic, Truth Conditions, and Probability

The present thesis focuses on counterfactuals. Specifically, we will address new questions and open problems that arise for the standard semantic accounts of counterfactual conditionals. The first four chapters deal with the Lewisian semantic account of counterfactuals. On a technical level, we contribute by providing an equivalent algebraic semantics for Lewis' variably strict conditional logics, which is notably absent in the literature. We introduce a new kind of algebra and differentiate between local and global versions of each of Lewis' variably strict conditional logics. We study the algebraic properties of Lewis' logics and the structure theory of our newly introduced algebras. Additionally, we employ a new algebraic construction, based on the framework of Boolean algebras of conditionals, to provide an alternative semantics for Lewisian counterfactual conditionals. This semantic account allows us to establish new truth conditions for Lewisian counterfactuals, implying that Lewisian counterfactuals are definable conditionals, and each counterfactual can be characterized as a modality of a corresponding probabilistic conditional. We further extend these results by demonstrating that each Lewisian counterfactual can also be characterized as a modality of the corresponding Stalnaker conditional. The resulting formal semantic framework is much more expressive than the standard one and, in addition to providing new truth conditions for counterfactuals, it also allows us to define a new class of conditional logics falling into the broader framework of weak logics. On the philosophical side, we argue that our results shed new light on the understanding of Lewisian counterfactuals and prompt a conceptual shift in this field: Lewisian counterfactual dependence can be understood as a modality of probabilistic conditional dependence or Stalnakerian conditional dependence. In other words, whether a counterfactual connection occurs between A and B depends on whether it is "necessary" for a Stalnakerian/probabilistic dependence to occur between A and B. We also propose some ways to interpret the kind of necessity involved in this interpretation. The remaining two chapters deal with the probability of counterfactuals. We provide an answer to the question of how we can characterize the probability that a Lewisian counterfactual is true, which is an open problem in the literature. We show that the probability of a Lewisian counterfactual can be characterized in terms of belief functions from Dempster-Shafer theory of evidence, which are a super-additive generalization of standard probability. We define an updating procedure for belief functions based on the imaging procedure and show that the probability of a counterfactual A > B amounts to the belief function of B imaged on A. This characterization strongly relies on the logical results we proved in the previous chapters. Moreover, we also solve an open problem concerning the procedure to assign a probability to complex counterfactuals in the framework of causal modelling semantics. A limitation of causal modelling semantics is that it cannot account for the probability of counterfactuals with disjunctive antecedents. Drawing on the same previous works, we define a new procedure to assign a probability to counterfactuals with disjunctive antecedents in the framework of causal modelling semantics. We also argue that our procedure is satisfactory in that it yields meaningful results and adheres to some conceptually intuitive constraints one may want to impose when computing the probability of counterfactuals

Reactive preferential structures and nonmonotonic consequence

We introduce information bearing systems (IBRS) as an abstraction of many logical systems. We define a general semantics for IBRS, and show that IBRS generalize in a natural way preferential semantics and solve open representation problems

Metaphysical Dependence and Set Theory

In this dissertation, I articulate and defend a counterfactual analysis of metaphysical dependence. It is natural to think that one thing x depends on another thing y if had y not existed, then x wouldn\u27t have existed either. But counterfactual analyses of metaphysical dependence are often rejected in the current literature. They are rejected because straightforward counterfactual analyses fail to accurately capture dependence relations between objects that exist necessarily, like mathematical objects. For example, it is taken as given that sets metaphysically depend on their members, while members do not metaphysically depend on the sets they belong to. The set {0} metaphysically depends on 0, while 0 does not metaphysically depend on {0}. The dependence is asymmetric. But if counterfactuals are given a possible worlds analysis, as is standard, then the counterfactual approach to dependence will yield a symmetric dependence relation between these two sets. Because the counterfactual analysis fails to accurately capture dependence relations between sets and their members, most reject this approach to metaphysical dependence. To generate the desired asymmetry, I argue that we should introduce impossible worlds into the framework for evaluating counterfactuals. I review independent reasons for admitting impossible worlds alongside possible worlds. Once we have impossible worlds at our disposal, we can consider worlds where, e.g., the empty set does not exist. I argue that in the worlds that are ceteris paribus like the actual world, where 0 does not exist, {0} does not exist either. And so, according to the counterfactual analysis of dependence, {0} metaphysically depends on 0, as desired. Conversely, however, there is no reason to think that every world that is ceteris paribus like the actual world, where {0} does not exist, is such that 0 does not exist either. And so 0 does not metaphysically depend on {0}. After applying this extended counterfactual analysis to several set-theoretic cases, I show that it can be applied to account for dependence relations between other mathematical objects as well. I conclude by defending the counterfactual analysis, extended with impossible worlds, against several objections

Anti-exceptionalism and methodological pluralism in logic

According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria (such as fit to data, simplicity, fruitfulness, or consistency). In this paper, I analyze some important discussions in the philosophy of logic (intuitionism versus classical logic, semantic paradoxes, and the meaning of conditionals), and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. I argue that, rather than having a specific methodology such as abductivism, logic can be characterized by methodological pluralism. This position can also be seen as the application of scientific pluralism to the realm of logic