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

A Survey of Contrastive and Counterfactual Explanation Generation Methods for Explainable Artificial Intelligence

A number of algorithms in the field of artificial intelligence offer poorly interpretable decisions. To disclose the reasoning behind such algorithms, their output can be explained by means of socalled evidence-based (or factual) explanations. Alternatively, contrastive and counterfactual explanations justify why the output of the algorithms is not any different and how it could be changed, respectively. It is of crucial importance to bridge the gap between theoretical approaches to contrastive and counterfactual explanation and the corresponding computational frameworks. In this work we conduct a systematic literature review which provides readers with a thorough and reproducible analysis of the interdisciplinary research field under study. We first examine theoretical foundations of contrastive and counterfactual accounts of explanation. Then, we report the state-of-the-art computational frameworks for contrastive and counterfactual explanation generation. In addition, we analyze how grounded such frameworks are on the insights from the inspected theoretical approaches. As a result, we highlight a variety of properties of the approaches under study and reveal a number of shortcomings thereof. Moreover, we define a taxonomy regarding both theoretical and practical approaches to contrastive and counterfactual explanation.S

The Intriguing Relation Between Counterfactual Explanations and Adversarial Examples

The same method that creates adversarial examples (AEs) to fool image-classifiers can be used to generate counterfactual explanations (CEs) that explain algorithmic decisions. This observation has led researchers to consider CEs as AEs by another name. We argue that the relationship to the true label and the tolerance with respect to proximity are two properties that formally distinguish CEs and AEs. Based on these arguments, we introduce CEs, AEs, and related concepts mathematically in a common framework. Furthermore, we show connections between current methods for generating CEs and AEs, and estimate that the fields will merge more and more as the number of common use-cases grows

Similarity Structure on Scientific Theories

I review and amplify on some of the many uses of representing a scientific theory in a particular context as a collection of models endowed with a similarity structure, which encodes the ways in which those models are similar to one another. This structure, which is related to topological structure, proves fruitful in the analysis of a variety of issues central to the philosophy of science. These include intertheoretic reduction, emergent properties, the epistemic connections between modeling and inference, the semantics of counterfactual conditionals, and laws of nature. The morals are twofold: first, the further adoption of formal methods for describing similarity (and related topological) structure has the potential to aid in decisive progress in philosophy of science; and second, the selection and justification of such structure is not a matter of technical convenience, but rather often involves great conceptual and philosophical subtlety. I conclude with various directions for future research

In Defense of a Contextualized Suppositional Account of Conditional Credence

Conditional credence is an important concept in many areas of philosophy. However, little consensus has been achieved regarding its semantics and ontology. In this thesis I shall sketch a contextualist suppositional account of conditional credence by drawing insights from two seemingly disjoint debates: the foundational debate on the relationship between conditional and unconditional probabilities, and the semantic debate on the relationship between conditional probability and probabilities of conditionals. I argue that, for a given pair of propositions A and B, the conditional credence one ought to have for B given that A - P(B|A) - may depend on contextual parameters like the way in which we mentally represent the extensions of as well as the stochastic relationships between A and B

Book Symposium: David Albert, After Physics

On April 1, 2016, at the Annual Meeting of the Pacific Division of the American Philosophical Association, a book symposium, organized by Alyssa Ney, was held in honor of David Albert’s After Physics (Harvard University Press, 2015). All participants agreed that it was a valuable and enlightening session. We have decided that it would be useful, for those who weren’t present, to make our remarks publicly available. Please bear in mind that what follows are remarks prepared for the session, and that on some points participants may have changed their minds in light of the ensuing discussion