Some machine learning models, in particular deep neural networks, are not very well understood; nevertheless, they are frequently used in science. Does this lack of understanding pose a problem for using DNNs to understand empirical phenomena? Emily Sullivan has recently argued that understanding with DNNs is not limited by our lack of understanding of DNNs themselves. In the present paper, we will argue, contra Sullivan, that our current lack of understanding of DNNs does limit our ability to understand with DNNs. (...) Sullivan’s claim hinges on which notion of understanding is at play. If we employ a weak notion of understanding, then her claim is tenable, but rather weak. If, however, we employ a strong notion of understanding, particularly explanatory understanding, then her claim is not tenable. (shrink)

Explainable artificial intelligence (XAI) aims to help people understand black box algorithms, particularly of their outputs. But what are these explanations and when is one explanation better than another? The manipulationist definition of explanation from the philosophy of science offers good answers to these questions, holding that an explanation consists of a generalization that shows what happens in counterfactual cases. Furthermore, when it comes to explanatory depth this account holds that a generalization that has more abstract variables, is broader in (...) scope and/or more accurate is better. By applying these definitions and contrasting them with alternative definitions in the XAI literature I hope to help clarify what a good explanation is for AI. (shrink)

The first part of this paper argues that if Craver’s ([2007a], [2007b]) popular mutual manipulability account (MM) of mechanistic constitution is embedded within Woodward’s ([2003]) interventionist theory of causation--for which it is explicitly designed--it either undermines the mechanistic research paradigm by entailing that there do not exist relationships of constitutive relevance or it gives rise to the unwanted consequence that constitution is a form of causation. The second part shows how Woodward’s theory can be adapted in such a way that (...) (MM) neither undermines the mechanistic paradigm nor reduces constitution to causation. However, it turns out that this modified theoretical embedding of (MM) makes it impossible to produce empirical evidence for constitutive relations. The paper ends by suggesting an additional criterion, the fat-handedness criterion, which, when combined with (MM), generates indirect empirical evidence for constitutive relevance. (shrink)

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

What is understanding? My goal in this paper is to lay out a new approach to this question and clarify how that approach deals with certain issues. The claim is that understanding is a matter of compressing information about the understood so that it can be mentally useful. On this account, understanding amounts to having a representational kernel and the ability to use it to generate the information one needs regarding the target phenomenon. I argue that this ambitious new account (...) can accommodate much of the data that has motivated theories of understanding in philosophy of science, and can also be generally applicable in epistemology and daily life as well. (shrink)

In this paper, I argue that explanations just ARE those sorts of things that, under the right circumstances and in the right sort of way, bring about understanding. This raises the question of why such a seemingly simple account of explanation, if correct, would not have been identified and agreed upon decades ago. The answer is that only recently has it been made possible to analyze explanation in terms of understanding without the risk of collapsing both to merely phenomenological states. (...) For the most part, theories of explanation were for 50 years held hostage to the historical accident that they far outstripped in sophistication corresponding accounts of understanding. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealisedexplanation gamein which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of (...) variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Simple idealized models seem to provide more understanding than opaque, complex, and hyper-realistic models. However, an increasing number of scientists are going in the opposite direction by utilizing opaque machine learning models to make predictions and draw inferences, suggesting that scientists are opting for models that have less potential for understanding. Are scientists trading understanding for some other epistemic or pragmatic good when they choose a machine learning model? Or are the assumptions behind why minimal models provide understanding misguided? In (...) this paper, using the case of deep neural networks, I argue that it is not the complexity or black box nature of a model that limits how much understanding the model provides. Instead, it is a lack of scientific and empirical evidence supporting the link that connects a model to the target phenomenon that primarily prohibits understanding. (shrink)

There is considerable agreement among epistemologists that certain abilities are constitutive of understanding-why. These abilities include: constructing explanations, drawing conclusions, and answering questions. This agreement has led epistemologists to conclude that understanding is a kind of know-how. However, in this paper, I argue that the abilities constitutive of understanding are the same kind of cognitive abilities that we find in ordinary cases of knowledge-that and not the kind of practical abilities associated with know-how. I argue for this by disambiguating between (...) different senses of abilities that are too often lumped together. As a consequence, non-reductionists about understanding—those that claim that understanding-why is not reducible to knowledge-that—need to find another way to motivate the view. In the end, the fact that abilities are constitutive of understanding-why does not give us reason to conclude that understanding is a kind of know-how. (shrink)

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl to formalize a causal notion (...) of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman and Kratzer will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl (2000) to formalize a causal (...) notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman (1976) and Kratzer (1979) will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)

Explainable artificial intelligence (XAI) is an emerging, multidisciplinary field of research that seeks to develop methods and tools for making AI systems more explainable or interpretable. XAI researchers increasingly recognise explainability as a context-, audience- and purpose-sensitive phenomenon, rather than a single well-defined property that can be directly measured and optimised. However, since there is currently no overarching definition of explainability, this poses a risk of miscommunication between the many different researchers within this multidisciplinary space. This is the problem we (...) seek to address in this paper. We outline a framework, called Explanatory Pragmatism, which we argue has two attractive features. First, it allows us to conceptualise explainability in explicitly context-, audience- and purpose-relative terms, while retaining a unified underlying definition of explainability. Second, it makes visible any normative disagreements that may underpin conflicting claims about explainability regarding the purposes for which explanations are sought. Third, it allows us to distinguish several dimensions of AI explainability. We illustrate this framework by applying it to a case study involving a machine learning model for predicting whether patients suffering disorders of consciousness were likely to recover consciousness. (shrink)

For nearly as long as the word “correlation” has been part of statistical parlance, students have been warned that correlation does not prove causation, and that only experimental studies, e.g., randomized clinical trials, can establish the existence of a causal relationship. Over the last few decades, somewhat of a consensus has emerged between statisticians, computer scientists, and philosophers on how to represent causal claims and connect them to probabilistic relations. One strand of this work studies the conditions under which evidence (...) accumulated from non-experimental (observational) studies can be used to infer a causal relationship. In this paper, I compare the typical conditions required to infer that one variable is a direct cause of another in observational and experimental studies. I argue that they are essentially the same. (shrink)

The goal of this paper is to develop a counterfactual theory of explanation. The CTE provides a monist framework for causal and non-causal explanations, according to which both causal and non-causal explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I argue that the CTE is applicable to two paradigmatic examples of non-causal explanations: Euler’s explanation and renormalization group explanations of universality.

Duncan Pritchard argues that a feature that sets understanding-why apart from knowledge-why is that whereas (I) understanding-why is a kind of cognitive achievement in a strong sense, (II) knowledge-why is not such a kind. I argue that (I) is false and that (II) is true. (I) is false because understanding-why featuring rudimentary explanations and understanding-why concerning very simple causal connections are not cognitive achievements in a strong sense. Knowledge-why is not a kind of cognitive achievement in a strong sense for (...) the same reason knowledge-that is not. The latter thesis requires showing that having (p because q) information is not equivalent to having information about facts or principles that establish the explanatory connections between the phenomena in question. I make a positive case for this claim and defend it against objections. Based on this argument, I identify an alternative feature that sets understanding-why apart from knowledge-why: The minimal condition for understanding-why and knowledge-why with respect to their contents is not identical. Knowing why p merely requires information that some explanatorily relevant dependency obtains. Understanding why p additionally requires information about facts or principles that establish the explanatory connections between the phenomena in question. (shrink)

I argue that understanding why p involves a kind of intellectual know how and differsfrom both knowledge that p and knowledge why p (as they are standardly understood).I argue that understanding, in this sense, is valuable.

As is well-known, David Lewis’ counterfactual theory of causation is subject to serious counterexamples in ‘exceptional’ cases. What has not received due attention in the literature so far is that Lewis’ theory fails to provide necessary and sufficient conditions for causation in ‘ordinary’ cases, too. In particular, the theory suffers from the ‘problem of large causes’. It is argued that this problem may be fixed by imposing a minimization constraint, whilst this solution brings along substantial costs as well. In particular, (...) a precise formulation of minimization requires defining an ‘essential part of an event’ and/or an ‘essential subevent’. Although the possibility of such a definition is ultimately left open, some doubts are raised on whether the counterfactualists’ resources are fit for this purpose, and whether the challenge can be met without substantially departing from Lewis’ intention, which was to provide a reductive account of causation. (shrink)

Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations :483–496, 2009; Morrison in Philos Stud 143:33–57, 2009), the nature of computer data Computer simulations and the changing face of scientific experimentation, Cambridge Scholars Publishing, Barcelona, 2013; Humphreys, in: Durán, Arnold Computer simulations and the changing face of scientific experimentation, Cambridge Scholars Publishing, Barcelona, 2013), and the explanatory power of (...) computer simulations :277–292, 2008; Durán in Int Stud Philos Sci 31:27–45, 2017). The aim of this article is to show that these authors are right in assuming that results of computer simulations are to be trusted when computer simulations are reliable processes. After a short reconstruction of the problem of epistemic opacity, the article elaborates extensively on computational reliabilism, a specified form of process reliabilism with computer simulations located at the center. The article ends with a discussion of four sources for computational reliabilism, namely, verification and validation, robustness analysis for computer simulations, a history of successful implementations, and the role of expert knowledge in simulations. (shrink)

Extant counterfactual accounts of causation (CACs) still cannot handle preemptive causation. I describe a new variety of preemption, defend its possibility, and use it to show the inadequacy of extant CACs. Imagine that it is a law of nature that the first spell cast on a given day match the enchantment that midnight.

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.