Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory (...) asymmetry, and fails to specify why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power. (shrink)

We reassess Woodward’s counterfactual account of explanation in relation to regularity explananda. Woodward presents an account of causal explanation. We argue, by using an explanation of Kleiber’s law to illustrate, that the account can also cover some noncausal explanations. This leads to a tension between the two key aspects of Woodward’s account: the counterfactual aspect and the causal aspect. We explore this tension and make a case for jettisoning the causal aspect (...) as constitutive of explanatory power in connection with regularity explananda. (shrink)

An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide (...) a counterfactual account of DME, the Narrow Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory. (shrink)

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal (...) class='Hi'>explanation. This paper argues that several recent accounts Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations. (shrink)

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger :239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea (...) is supported by recent work on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations. (shrink)

In this paper, I explicate desiderata for accounts of explanation in historiography. I argue that a fully developed account of explanation in historiography must explicate many explanation-related notions in order to be satisfactory. In particular, it is not enough that an account defines the basic structure of explanation. In addition, the account of explanation must be able to explicate notions such as minimal explanation, complete explanation, historiographical explanation, explanatory depth, (...) explanatory competition, and explanatory goal. Moreover, the account should also tell how explananda can be chosen in a motivated way. Furthermore, the account should be able to clarify notions that are closely connected with explanation such as historical contingency. Finally, it is important that the account is able to recognize when explanation-related notions and issues are so closely intertwined that we are in danger of not seeing the differences between them. In other words, I argue that a satisfactory account of explanation in historiography must have the power to explicate central explanation-related notions and to clarify discussions where the differences between the notions are obscure. In order to explicate these desiderata, I formulate a counterfactual account of explanation and show how that account is able to explicate explanation-related notions and clarify issues that are connected with historiographical explanations. The success of the counterfactual account suggests that historiographical explanations do not differ fundamentally from explanations in many other fields. (shrink)

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

von Fintel and Gillies : 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker and Lewis. Von Fintel’s view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. More recently Moss :561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far the (...) small amount of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss’s view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it. (shrink)

This essay develops an inferential account of model explanation, based on Mauricio Suárez’s inferential conception of scientific representation and Alisa Bokulich’s counterfactual account of model explanation. It is suggested that the fact that a scientific model can explain is essentially linked to how a modeler uses an established model to make various inferences about the target system on the basis of results derived from the model. The inference practice is understood as a two-step activity, with (...) the first step involving making counterfactual statements about the model itself and the second step involving making hypothetical statements transferring over claims derived from the model onto the target. To illustrate how this two-step activity proceeds, an agent-based simulation model is discussed. (shrink)

This paper presents a counterfactual account of what a mechanism is. Mechanisms consist of parts, the behavior of which conforms to generalizations that are invariant under interventions, and which are modular in the sense that it is possible in principle to change the behavior of one part independently of the others. Each of these features can be captured by the truth of certain counterfactuals.

Extra-mathematical explanations explain natural phenomena primarily by appeal to mathematical facts. Philosophers disagree about whether there are extra-mathematical explanations, the correct account of them if they exist, and their implications (e.g., for the philosophy of scientific explanation and for the metaphysics of mathematics) (Baker 2005, 2009; Bangu 2008; Colyvan 1998; Craver and Povich 2017; Lange 2013, 2016, 2018; Mancosu 2008; Povich 2019, 2020; Steiner 1978). In this discussion note, I present three desiderata for any account of extra-mathematical (...) explanation and argue that Baron’s (2020) U-Counterfactual Theory fails to meet each of them. I conclude with some reasons for pessimism that a successful account will be forthcoming. (shrink)

We offer a novel theory of information that differs from traditional accounts in two respects: (i) it explains information in terms of counterfactuals rather than conditional probabilities, and (ii) it does not make essential reference to doxastic states of subjects, and consequently allows for the sort of objective, reductive explanations of various notions in epistemology and philosophy of mind that many have wanted from an account of information.

A theory of necessary and sufficient conditions is presented, as well as a theory of necessary and sufficient causes and effects, viewed as a particular case of the former. Ambiguities of the terms 'condition' and 'necessary condition' are explored, and a neutral meaning for 'condition' is favoured. The relation between necessary and sufficient conditions and implicative conditionals (including counterfactuals) is also discussed. Two problems of counterfactual theories of causal explanation are indicated, concerning (i) how to account for (...) causes that are not necessary and (ii) how to interpret the counterfactual from the negation of the effect to the negation of the cause. Application of the theory of necessary and sufficient conditions to Euler’s explanation of the Königsberg bridge problem is discussed. The theory of necessary and sufficient causes and effects is then applied to the flagpole shadow explanation and to two biological explanations, one involving a sufficient but not necessary cause and the other a necessary but not sufficient cause. Causes that are neither sufficient nor necessary are also recognized. Finally, a probabilistic approach to causes that are either not sufficient or not necessary is explored, including its application to examples of such cases. (shrink)

Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 1-16) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to non-vacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true.

On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual 'If it had been the case that p, then it would have been the case that q' is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in (...) the paper is which weights attach to different respects of similarity. I start by considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details. (shrink)

Many explanations rely on identity facts. In this paper, I propose an account of how identity facts explain: roughly, the fact that A is identical to B explains another fact whenever that other fact depends, counterfactually, on A being identical to B. As I show, this account has many virtues. It avoids several problems facing accounts of explanatory identities, and when precisified using structural equations, it can be used to defend interventionist accounts of causation against an objection.

On a Molinist account of creation and providence, not only is there is a complete set of truths about what every possible person would freely do in any possible set of circumstances, but these conditional truths are part of the very explanation of our existence. Robert Adams has recently argued that the explanatory priority of these conditionals undermines libertarian freedom. In the present essay, I take at close look at Adams’ argument and at the Molinist response of Thomas (...) Flint. After showing that Flint’s response is inadequate, I develop what I believe to be a more successful Molinist response to Adams’ argument. Along the way, I seek to provide some insight into the nature of libertarian freedom and the proper interpretation of the much discussed “principle of alternate possibilities.”. (shrink)

In this paper I examine a recent argument that regularity approaches to causation can easily solve the problem of pre-emption. If this argument were successful it would neatly solve the problem of pre-emption—a problem that many still consider to be a central unsolved problem for accounts of causation. The argument is surprising in that the conclusion goes against the common consensus that regularity accounts of causation cannot solve the problem of pre-emption, at least without major amendments. This consensus was one (...) of the reasons for the decline in popularity of the regularity approach and the rise in popularity (for a few decades at least) of the counterfactual approach. In its fullest form the recent argument is due to Strevens (Causation and explanation, topics in contemporary philosophy. MIT Press, Cambridge, MA, 2007). He claims, "Mackie's account supplies, without any of the complex amendments now standard in counterfactual theories, a completely satisfactory treatment of the standard cases of pre-emption". This paper examines this argument and refutes it. I argue that Mackie's account really does fail to solve the problem of pre-emption; it fails to account for even the standard cases of pre-emption in the literature. (shrink)

Philosophers who take rationality to consist in the satisfaction of rational requirements typically favour rational requirements that govern mental attitudes at a time rather than across times. One such account has been developed by Broome in Rationality through reasoning. He claims that diachronic functional properties of intentions such as settling on courses of actions and resolving conflicts are emergent properties that can be explained with reference to synchronic rational pressures. This is why he defends only a minimal diachronic requirement (...) which characterises forgetting as irrational. In this paper, I show that Broome’s diachronically minimalist account lacks the resources to explain how a rational agent may resolve incommensurable choices by an act of will. I argue that one can solve this problem by either specifying a mode of diachronic deliberation or by introducing a genuinely diachronic requirement that governs the rational stability of an intention via a diachronic counterfactual condition concerning rational reconsideration. My proposal is similar in spirit to Gauthier’s account in his seminal paper ‘Assure and threaten’. It improves on his work by being both more general and explanatorily richer in its application with regard to diachronic phenomena such as transformative choices and acts of will. (shrink)

Here I consider the relative merits of two recent models of explanation, James Woodward's interventionist-counterfactual model and the model model. According to the former, explanations are largely constituted by information about the consequences of counterfactual interventions. Problems arise for this approach because countless relevant interventions are possible in most cases and because it overlooks other kinds of equally relevant information. According the model model, explanations are largely constituted by cognitive models of actual mechanisms. On this approach, explanations (...) tend not to represent any of the aforementioned information explicitly but can instead be used to produce it on demand. The model model thus offers the more plausible account of the information of which we are aware when we have an explanation and of the ratiocinative process through which we derive many kinds of information that are relevant to the evaluation of explanations. (shrink)

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum (...) and the explanans. I support this claim by illustrating that CTE is applicable to Euler’s explanation (an example of a non-causal scientific explanation) and Loewer’s explanation (an example of a non-causal metaphysical explanation). (shrink)

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and (...) the explanans. I support this claim by illustrating that CTE is applicable to Euler’s explanation and Loewer’s explanation. (shrink)

In this paper I critically examine the notion of explanation used in Artificial Intelligence in general, and in the theory of belief revision in particular. I focus on two of the best known accounts in the literature: Pagnucco’s abductive expansion functions and Gärdenfors’ counterfactual analysis. I argue that both accounts are at odds with the way in which this notion has historically been understood in philosophy. They are also at odds with the explanatory strategies used in actual scientific (...) practice. At the end of the paper I outline the desiderata for an epistemologically motivated, scientifically informed belief revision model for explanation. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE (...) to mathematical explanations requires us to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

In order to determine whether a particular course of conduct is ethically permissible it is important to have a concept of what it means to be harmed. The dominant theory of harm is the counterfactual account, most famously proposed by Joel Feinberg. This determines whether harm is caused by comparing what actually happened in a given situation with the ‘counterfacts’ i.e. what would have occurred had the putatively harmful conduct not taken place. If a person's interests are worse (...) off than they otherwise would have been, then a person will be harmed. This definition has recently faced challenges from bioethicists such as John Harris, Guy Kahane and Julian Savulescu who, believing it to be severely flawed, have proposed their own alternative theories of the concept. In this article I will demonstrate that the shortcomings Harris, Kahane and Savulescu believe are present in Feinberg's theory are illusory and that it is their own accounts of harm that are fraught with logical errors. I maintain that the arguments presented to refute Feinberg's theory not only fail to achieve this goal and can be accommodated within the counterfactual account but that they actually undermine the theories presented by their respective authors. The final conclusion will be that these challenges are misconceived and fail to displace the counterfactual theory. (shrink)

Relationships of counterfactual dependence have played a major role in recent debates of explanation and understanding in the philosophy of science. Usually, counterfactual dependencies have been viewed as the explanantia of explanation, i.e., the things providing explanation and understanding. Sometimes, however, counterfactual dependencies are themselves the targets of explanations in science. These kinds of explanations are the focus of this paper. I argue that “micro-level model explanations” explain the particular form of the empirical regularity (...) underlying a counterfactual dependency by representing it as a physical necessity on the basis of postulated microscopic entities. By doing so, micro-level models rule out possible forms the regularity could have taken. Micro-model explanations, in other words, constrain empirical regularities and their associated counterfactual dependencies. I introduce and illustrate micro-level model explanations in detail, contrast them to other accounts of explanation, and consider potential problems. (shrink)

This paper defends a counterfactual account of explanation, according to which successful explanation requires tracing patterns of counterfactual dependence of a special sort, involving what I call active counterfactuals. Explanations having this feature must appeal to generalizations that are invariant--stable under certain sorts of changes. These ideas are illustrated by examples drawn from physics and econometrics.

I argue that David Lewis’s attempt, in his ‘Counterfactual Dependence and Time’s Arrow’, to explain the fixity of the past in terms of counterfactual independence is unsuccessful. I point out that there is an ambiguity in the claim that the past is counterfactually independent of the present (or, more generally, that the earlier is counterfactually independent of the later), corresponding to two distinct theses about the relation between time and counterfactuals, both officially endorsed by Lewis. I argue that (...) Lewis’s attempt is flawed for a variety of reasons, including the fact that his own theory about the evaluation of counterfactuals requires too many exceptions to the general rule that the past is counterfactually independent of the present. At the end of the paper, I consider a variant of Lewis’s strategy that attempts to explain the fixity of the past in terms of causal, rather than counterfactual, independence. I conclude that, although this variant avoids some of the objections that afflict Lewis’s account, it nevertheless seems to be incapable of giving a satisfactory explanation of the notion of the fixity of the past. (shrink)

Marc Lange objects to scientific essentialists that they can give no better account of the counterfactual invariance of laws than Humeans. While conceding this point succeeds ad hominem against some essentialists, I show that it does not undermine essentialism in general. Moreover, Lange's alternative account of the relation between laws and counterfactuals is - with minor modification - compatible with essentialism.

This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...) debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists. (shrink)

This thesis investigates the nature of psychiatric disorders, and to what extent they can form a basis for classification, explanation, and treatment interventions. These questions are important in the light of the “crisis of validity” in psychiatry, according to which current diagnostic categories do not pick out real disorders. I address the questions by defending an account of psychiatric disorders that can better accommodate social aspects and non-epistemic values than the symptom-based model of the Diagnostic and Statistical Manual (...) of Mental Disorders (DSM) and the brain disease model of the biomedical approach, including the Research Domain Criteria (RDoC). I concentrate on three ways that psychiatric disorders can differ from prototypical natural kinds, such as biological species and chemical elements. First, the concept of psychiatric disorder or mental disorder is partly value-laden and cannot be defined based only on scientific facts. Second, the objects of psychiatric classifications are interactive human kinds because people with disorders respond to their classifications through looping effects. Third, sociocultural factors can shape disorders in complex ways, which is indicated by their cross-cultural variation. I argue that these challenges can be overcome with a pluralistic explanatory account that grants an explicit role to value-sensitive considerations and social scientific research. Based on this, I argue that particular disorders can in principle support inductive inferences. ------------------------------------------------------------------------------------------ My key argument is that although whether a condition is considered pathological is partly a value-laden question, this does not rule out a realist account of particular psychiatric disorders as homeostatic property cluster kinds (HPC). I assert that causal mechanisms responsible for psychiatric kinds can be understood non-metaphysically based on the contrastive-counterfactual and interventionist theories of explanation. An advantage of this account is that it can address the concern that psychiatric explanations require one to relate heterogeneous causal factors on different levels, such as genetic, neurological, psychological, and social. My novel argument is that mechanistic explanations of scientific kinds have applicability domains over which they account for specific aspects of kinds and warrant inductive inferences. That is, identifying the applicability domain of an explanation spells out the conditions under which the explanation is expected to be reliable and when it can break down. This helps to understand how different discipline approaches, including social and cultural ones, can be complementary and make an explanation of a psychiatric kind more reliable. On the other hand, the account also shows how the complex nature of psychiatric kinds can license re-classifications for different epistemic and non-epistemic purposes. Finally, in the light of the social implications of psychiatric classifications, I suggest a value-sensitive or ameliorative approach to engineering the concept of psychiatric disorder. In conclusion, my account shows that research on the social and cultural factors that shape psychiatric disorders, and weighing the non-epistemic values that influence classificatory practices, can and should inform classificatory choices as well as policy and treatment interventions. (shrink)

Let’s consider the following paradox (Fodor [1989], Jackson and Petit [1988] [1992], Drestke [1988], Block [1991], Lepore and Loewer [1987], Lewis [1986], Segal and Sober [1991]): i) The intentional content of a thought (or any other intentional state) is causally relevant to its behavioural (and other) effects. ii) Intentional content is nothing but the meaning of internal representations. But, iii) Internal processors are only sensitive to the syntactic structures of internal representations, not their meanings. Therefore it seems that if we (...) want to defend the idea -absolutely plausible from an intuitive point of view- that mental / intentional states are causally responsible for behavioural outputs and we want to do it on the physicalist basis of any scientific methodology, we will have to give up the conviction that such intentional states qua intentional, i. e. as having a particular meaning, are the ones causally responsible for our behaviour. The path that takes us to mental epiphenomenalism is clear: 1) the causal powers of any event are completely determined by its physical properties; 2) although intentional properties supervene on physical properties, they can’t be identified with them; 3) intentional properties, as intentional, are not causally responsible for behaviour, because they don’t take part in the causal powers of the states to which they belong, i. e., intentional properties are epiphenomenal. Let’s consider now a different yet parallel position to the one just described. There is an important debate in cognitive science about whether the class of mechanisms to which we belong and which the computational modelling project of cognitive processes refers to is best represented by classical or connectionist approaches (McClelland, Rumelhart et. al [1986], Smolensky [1987] [1988], Fodor and Pylyshyn [1988], Pinker and Prince [1988], Clark [1989], Ramsey, Stich and Rumelhart [1991], Clark and Karmiloff-Smith [forthcoming]).In classical, serial processing models, information is encoded in terms of rules that have a linguistic character. In connectionist or parallel distributed processing (PDP) models, the causal relationships among the units that constitute the system determine how the information is processes by the network, although these units don’t have a direct semantic interpretation. But, for both, classical and connectionist models, all the computations can be explained without any reference to the content of the processed information, i.e., in both cases the properties that seem to be responsible for the system’s behaviour are ultimately physical properties nor intentional ones. This situation mirrors thus, within cognitive science, the philosophical discussion concerning the causal efficacy of semantic properties. Now, if in this debate we opt for the classical paradigm, there is a way of finding a solution to the computational version of the epiphenomenalism paradox. This solution is based mainly on the notion of supervenience or, more precisely, on the notion of mereological supervenience (Kim [1984] [1988])1 . The idea of intentional properties supervening on physical properties makes sense within the classical context because there exists an easily isolable supervenience base comprising the syntactic items in the socalled language of thought. But, what happens if we opt for the connectionist paradigm?. The situation here doesn’t seem to favour the use of the same supervenience strategy. For it has been argued (Ramsey, Stich and Garon [1991]) that beliefs, desires, and other mental states are nor, in the connectionist paradigm, individuable as weight or activation states of the system. This is because information is encoded by the network in distributed and superpositional representations, i.e., there are no straightforwardly isolable vehicles at the physical level that can be identified as the articulated supervenience base on which the semantic properties supervene2 . If this is true, then the connectionist not only loses the battle against epiphenomenalism but more drastically, seems to offer a standing invitation to eliminativism, since talk of beliefs and desires, etc. now seems to be floating free of any acceptable scientific underpinning, i.e., she has lost the necessary theoretical apparatus for supporting the intuitive idea that propositional attitudes -beliefs, desires and any mental states with semantic content- are physically realized. This second line of argumentation doesn’t take us to a paradox but to a dilemma: either we accept eliminativism, if connectionist hypothesis are correct or we defend the causal efficacy of mental states with semantic content by showing that, after all, connectionist networks are not plausible cognitive models (Davies [1991]). From my point of view, however, both lines of argumentation need to be revised. The aim of this paper is to find an account of the causal efficacy of content that avoids the aforementioned epiphenomenalist objections and that doesn’t require the discovery of inner symbols in the computational modelling of such contentful mental states. In short, the aim is to find a meeting point where a philosophical story about content and cause and the connectionist computational model can be brought together (Cfr. Clark [1989]). (shrink)

What is our epistemic access to metaphysical modality? Timothy Williamson suggests that the epistemology of counterfactuals will provide the answer. This paper challenges Williamson's account and argues that certain elements of the epistemology of counterfactuals that he discusses, namely so called background knowledge and constitutive facts, are already saturated with modal content which his account fails to explain. Williamson's account will first be outlined and the role of background knowledge and constitutive facts analysed. Their key role is (...) to restrict our imagination to rule out irrelevant counterfactual suppositions. However, background knowledge turns out to be problematic in cases where we are dealing with metaphysically possible counterfactual suppositions that violate the actual laws of physics. As we will see, unless Williamson assumes that background knowledge corresponds with the actual, true laws of physics and that these laws are metaphysically necessary, it will be difficult to address this problem. Furthermore, Williamson's account fails to accommodate the distinction between conceivable yet metaphysically impossible scenarios, and conceivable and metaphysically possible scenarios. This is because background knowledge and constitutive facts are based strictly on our knowledge of the actual world. Williamson does attempt to address this concern with regard to metaphysical necessities – as they hold across all possible worlds – but we will see that even in this case the explanation is questionable. These problems, it will be suggested, cannot be addressed in a counterfactual account of the epistemology of modality. The paper finishes with an analysis of Williamson's possible rejoinders and some discussion about the prospects of an alternative account of modal epistemology. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation (...) in inquisitive semantics: truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

The use of counterfactuals for considerations of algorithmic fairness and explainability is gaining prominence within the machine learning community and industry. This paper argues for more caution with the use of counterfactuals when the facts to be considered are social categories such as race or gender. We review a broad body of papers from philosophy and social sciences on social ontology and the semantics of counterfactuals, and we conclude that the counterfactual approach in machine learning fairness and social explainability (...) can require an incoherent theory of what social categories are. Our findings suggest that most often the social categories may not admit counterfactual manipulation, and hence may not appropriately satisfy the demands for evaluating the truth or falsity of counterfactuals. This is important because the wide- spread use of counterfactuals in machine learning can lead to misleading results when applied in high-stakes domains. Accordingly, we argue that even though counterfactuals play an essential part in some causal inferences, their use for questions of algorithmic fairness and social explanations can create more problems than they resolve. Our positive result is a set of tenets about using counterfactuals for fairness and explanations in machine learning. (shrink)

A certain type of counterfactual is thought to be intimately related to causation, control, and explanation. The time asymmetry of these phenomena therefore plausibly arises from a time asymmetry of counterfactual dependence. But why is counterfactual dependence time asymmetric? The most influential account of the time asymmetry of counterfactual dependence is David Albert’s account, which posits a new, time-asymmetric fundamental physical law, the so-called “past hypothesis.” Albert argues that the time asymmetry of (...) class='Hi'>counterfactual dependence arises from holding fixed the past hypothesis when evaluating counterfactuals. In this paper, I argue that Albert’s account misconstrues the time asymmetry of counterfactual dependence. (shrink)

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; (...) a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal; and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps to unify essential concepts of biological networks. (shrink)

David Lewis introduced the idea of a quasi-miracle to overcome a problem in his initial account of counterfactuals. Here we put the notion of a quasi-miracle to a different and new use, showing that it offers a novel account of the phenomenon of poetic justice, where characters in a narrative get their due by happy accident. The key to understanding poetic justice is to see what makes poetically just events remarkable coincidences. We argue that remarkable coincidence is to (...) be understood in terms of a distinctive type of experience quasi-miracles offer. Cases of poetic justice offer a dual awareness of the accidental nature of the events and of a non-accidental process, involving intention, which it appears would explain them. We also extend this account to incorporate how we might experience magic tricks. An account of poetic justice as quasi-miraculous allows us to account for the experience of encounters with poetic justice, as involving the incongruity of seeing design in accident. (shrink)

The pattern of credences we are inclined to assign to counterfactuals challenges standard accounts of counterfactuals. In response to this problem, the paper develops a semantics of counterfactuals in terms of the epsilon-operator. The proposed semantics stays close to the standard account: the epsilon-operator substitutes the universal quantifier present in standard semantics by arbitrarily binding the open world-variable. Various applications of the suggested semantics are explored including, in particular, an explanation of how the puzzling credences in counterfactuals come (...) about. (shrink)

The most compelling extant accounts of explanation casts all explanations as causal. Yet there are sciences, theoretical population biology in particular, that explain their phenomena by appeal to statistical, non-causal properties of ensembles. I develop a generalised account of explanation. An explanation serves two functions: metaphysical and cognitive. The metaphysical function is discharged by identifying a counterfactually robust invariance relation between explanans event and explanandum. The cognitive function is discharged by providing an appropriate description of this (...) relation. I offer examples of explanations from portfolio theory and population genetics that meet this characterisation. In each case the invariance relation holds between a statistical property of an ensemble and a change in structure of the ensemble. In neither case, however, does the statistical property cause the outcome it explains. There are genuine statistical, non-causal scientific explanations. (shrink)

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)

In non-causal explanations, some non-causal facts (such as mathematical, modal or metaphysical) are used to explain some physical facts. However, precisely because these explanations abstract away from causal facts, they face two challenges: 1) it is not clear why would one rather than the other non-causal explanantia be relevant for the explanandum; and 2) why would standing in a particular explanatory relation (e.g., “counterfactual dependence”, “constraint”, “entailment”, “constitution”, “grounding”, and so on), and not in some other, be explanatory. I (...) develop an explanatory relevance account which is based on erotetic constraints and show how it addresses these two challenges. (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)

This work consists of two parts. Part I will be a contribution to a philo- sophical discussion of the nature of causal explanation. It will present my contrastive counterfactual theory of causal explanation and show how it can be used to deal with a number of problems facing theories of causal explanation. Part II is a contribution to a discussion of the na- ture of interest explanation in social studies of science. The aim is to (...) help to resolve some controversies concerning interest explanation by explicating the concept of interest and its explanatory uses by using the account of explanation developed in Part I. (shrink)

Causal selection is the task of picking out, from a field of known causally relevant factors, some factors as elements of an explanation. The Causal Parity Thesis in the philosophy of biology challenges the usual ways of making such selections among different causes operating in a developing organism. The main target of this thesis is usually gene centrism, the doctrine that genes play some special role in ontogeny, which is often described in terms of information-bearing or programming. This paper (...) is concerned with the attempt of confronting the challenge coming from the Causal Parity Thesis by offering principles of causal selection that are spelled out in terms of an explicit philosophical account of causation, namely an interventionist account. I show that two such accounts that have been developed, although they contain important insights about causation in biology, nonetheless fail to provide an adequate reply to the Causal Parity challenge: Ken Waters's account of actual-difference making and Jim Woodward's account of causal specificity. A combination of the two also doesn't do the trick, nor does Laura Franklin-Hall's account of explanation (in this volume). We need additional conceptual resources. I argue that the resources we need consist in a special class of counterfactual conditionals, namely counterfactuals the antecedents of which describe biologically normal interventions. (shrink)

Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally, counterfactually-altered circumstances have been treated as "small miracles" that locally violate the laws of nature while sharing the same initial conditions. In Pearl's structural causal model (SCM) framework this is made mathematically rigorous via interventions that modify the causal laws while the values of exogenous variables are shared. In recent years, however, this purely (...) interventionist account of counterfactuals has increasingly come under scrutiny from both philosophers and psychologists. Instead, they suggest a backtracking account of counterfactuals, according to which the causal laws remain unchanged in the counterfactual world; differences to the factual world are instead "backtracked" to altered initial conditions (exogenous variables). In the present work, we explore and formalise this alternative mode of counterfactual reasoning within the SCM framework. Despite ample evidence that humans backtrack, the present work constitutes, to the best of our knowledge, the first general account and algorithmisation of backtracking counterfactuals. We discuss our backtracking semantics in the context of related literature and draw connections to recent developments in explainable artificial intelligence (XAI). (shrink)

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

According to one large family of views, scientific explanations explain a phenomenon (such as an event or a regularity) by subsuming it under a general representation, model, prototype, or schema (see Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441; Churchland, P. M. (1989). A neurocomputational perspective: The nature of mind and the structure of science. Cambridge: MIT Press; Darden (2006); Hempel, C. G. (1965). Aspects of (...) scientific explanation. In C. G. Hempel (Ed.), Aspects of scientific explanation (pp. 331–496). New York: Free Press; Kitcher (1989); Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25). My concern is with the minimal suggestion that an adequate philosophical theory of scientific explanation can limit its attention to the format or structure with which theories are represented. The representational subsumption view is a plausible hypothesis about the psychology of understanding. It is also a plausible claim about how scientists present their knowledge to the world. However, one cannot address the central questions for a philosophical theory of scientific explanation without turning one’s attention from the structure of representations to the basic commitments about the worldly structures that plausibly count as explanatory. A philosophical theory of scientific explanation should achieve two goals. The first is explanatory demarcation. It should show how explanation relates with other scientific achievements, such as control, description, measurement, prediction, and taxonomy. The second is explanatory normativity. It should say when putative explanations succeed and fail. One cannot achieve these goals without undertaking commitments about the kinds of ontic structures that plausibly count as explanatory. Representations convey explanatory information about a phenomenon when and only when they describe the ontic explanations for those phenomena. (shrink)