This paper provides a general introduction to the use of causal models in the metaphysics of causation, specifically structural equation models and directed acyclic graphs. It reviews the formal framework, lays out a method of interpretation capable of representing different underlying metaphysical relations, and describes the use of these models in analyzing causation.

This paper addresses the question of what constitutes an apt interpreted model for the purpose of analyzing causation. I first collect universally adopted aptness principles into a basic account, flagging open questions and choice points along the way. I then explore various additional aptness principles that have been proposed in the literature but have not been widely adopted, the motivations behind their proposals, and the concerns with each that stand in the way of universal adoption. I conclude that the remaining (...) work of articulating aptness for a SEM analysis of causation is tied up with issue to do with modality, ontology, and mereology. Continuing this work is therefore likely to shed light on the relationship between these areas and causation more generally. (shrink)

Any counterfactual with a true antecedent and a true consequent is invariably predicted to be true by the standard Stalnaker–Lewis semantics. But many such true–true counterfactuals appear false to ordinary speakers, which is considered by many authors as evidence that the standard semantics should be revised. However, Walters and Williams prove that allowing true–true counterfactuals to be false would unacceptably invalidate some very plausible logical principles. The objective of this paper is to provide a pragmatic account of seemingly false true–true (...) counterfactuals, which explains why such counterfactuals seem false to ordinary speakers while being true semantically. In particular, a pluralistic pragmatic account is pursued: I argue that some true–trues seem false because they conversationally implicate some falsehood, and some others seem false because the focus (intonation stress) involved in them invokes some pragmatic re‐interpretation that affects speakers' truth‐value judgments. (shrink)

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.

I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

Halpern and Hitchcock appealed to the normality of witness worlds to solve the problem of isomorphism in the Halpern-Pearl definition of actual causality. This paper first proposes a new isomorphism counterexample, called “bogus permission,” to show that their approach is unsuccessful. Then, to solve the problem of isomorphism, I propose a new improvement over the Halpern-Pearl definition by introducing default worlds. Finally, I demonstrate that my new definition can resolve more potential counterexamples than similar approaches in the current literature, including (...) the Lewisian causal dependence, Menziesian causal dependence, and modified version of the Halpern-Pearl definition. Some other advantages of my definition are also discussed. (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)

Philosophy and statistics have studied two causal species, deterministic and probabilistic. There's a third species, however, hitherto unanalysed: underdeterministic causal phenomena, which are non-deterministic yet non-probabilistic. Here, I formulate a framework for modelling them. -/- Consider a simple case. If I go out, I may stumble into you but also may miss you. If I don’t go out, we won't meet. I go out. We meet. My going out is a cause of our encounter even if there was no determinate (...) probability of us meeting conditional on my going out. The cause is neither deterministic (it didn't necessitate the effect) nor probabilistic (the relevant conditional probabilities are undefined). Rather, it's underdeterministic: it raises the modal status of the effect from causally impossible to possible. -/- Here, I won't offer a theory of such token causes but develop the prerequisite for any such theory: the underdeterministic framework. The framework is like the deterministic structural-equations framework but with one consequential difference---an equation can return multiple values. This change allows me to define causal possibility and necessity, and corresponding notions of interventionist might- and would-counterfactuals. I also define conditional independence, which obeys the graphoid axioms, and prove that underdeterministic models satisfy the causal Markov condition. The framework can causally model situations that other frameworks cannot: decision-making under bounded uncertainty, games with multiple equilibria, infinite fair lotteries, and any other non-deterministic situation where indeterminacies are essentially non-probabilistic, or where we have a reason not to use probabilities. (shrink)

This article defends the notion of downward causation, relating it to a notion of conditional independence.

There is a systematic and suggestive analogy between grounding and causation. In my view, this analogy is no coincidence. Grounding and causation are alike because grounding is a type of causation: metaphysical causation. In this paper I defend the identification of grounding with metaphysical causation, drawing on the causation literature to explore systematic connections between grounding and metaphysical dependence counterfactuals, and I outline a non-reductive counterfactual theory of grounding along interventionist lines.

According to Interventionism, explanations cite invariant relations which hold among multiple variables. Interventionism incorrectly implies, however, that many common scientific explanations—which cite single‐variable boundary constraints—are not actually explanatory. So I propose a different account of explanation, similar in spirit to Interventionism, which gets those cases of scientific explanation right.

This paper outlines a non-reductive counterfactual account of grounding along interventionist lines, and uses the account to argue that taking grounding seriously requires ascribing non-trivial truth-conditions to a range of counterpossible counterfactuals. This result allows for a diagnosis of a route to scepticism about grounding, as deriving at least in part from scepticism about non-trivial counterpossible truth and falsity.

Conditional learning, where agents learn a conditional sentence ‘If A, then B,’ is difficult to incorporate into existing Bayesian models of learning. This is because conditional learning is not uniform: in some cases, learning a conditional requires decreasing the probability of the antecedent, while in other cases, the antecedent probability stays constant or increases. I argue that how one learns a conditional depends on the causal structure relating the antecedent and the consequent, leading to a causal model of conditional learning. (...) This model extends traditional Bayesian learning by incorporating causal models into agents’ epistemic states. On this theory, conditional learning proceeds in two steps. First, an agent learns a new causal model with the appropriate relationship between the antecedent and the consequent. Then, the agent narrows down the set of possible worlds to include only those which make the conditional proposition true. This model of learning can incorporate both standard cases of Bayesian learning and the non-uniform learning required to learn conditional information. (shrink)

Causal models show promise as a foundation for the semantics of counterfactual sentences. However, current approaches face limitations compared to the alternative similarity theory: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This article addresses these difficulties using exogenous interventions, where causal interventions change the values of exogenous variables rather than structural equations. This model accommodates judgments about backtracking counterfactuals, extends to logically complex counterfactuals, and validates familiar principles of counterfactual (...) logic. This combines the interventionist intuitions of the causal approach with the logical advantages of the similarity approach. (shrink)

Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, problems arise for using safety as a condition on knowledge: safety is not necessary for knowledge and cannot always explain the Gettier cases and cases of statistical evidence it is meant to address. In this paper, I argue for a new modal condition designed to capture the non-accidental relationship between facts and evidence required for knowledge: (...) causal safety. I argue that possible errors in belief can be captured by accounting for deviations in causal relationships and that there is a natural way to characterize which causal errors are relevant in an epistemic situation. Using this, I develop a causal analogue to safety, where one’s belief in p is causally safe if it is true in all causally relevant worlds where one believes p. Causal safety, I argue, can better explain the cases safety is meant to address and can avoid the arguments raised against the necessity of safety. (shrink)

In this paper, we develop a novel response to counterfactual scepticism, the thesis that most ordinary counterfactual claims are false. In the process we aim to shed light on the relationship between debates in the philosophy of science and debates concerning the semantics and pragmatics of counterfactuals. We argue that science is concerned with many domains of inquiry, each with its own characteristic entities and regularities; moreover, statements of scientific law often include an implicit ceteris paribus clause that restricts the (...) scope of the associated regularity to circumstances that are ‘fitting’ to the domain in question. This observation reveals a way of responding to scepticism while, at the same time, doing justice both to the role of counterfactuals in science and to the complexities inherent in ordinary counterfactual discourse and reasoning. (shrink)

A number of authors have recently used causal models to develop a promising semantics for non-backtracking counterfactuals. Briggs shows that when this semantics is naturally extended to accommodate right-nested counterfactuals, it invalidates modus ponens, and therefore violates weak centering given the standard Lewis/stalnaker interpretation of the counterfactual in terms of nearness or similarity of worlds. In this paper, I explore the possibility of abandoning the Lewis/stalnaker interpretation for some alternative that is better suited to accommodate the causal modeling semantics. I (...) argue that a revision of McGee’s semantics can accommodate CM semantics without sacrificing weak centering, and that CM semantics can therefore be situated within a general semantics for counterfactuals that is based on the nearness or similarity of worlds. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

The paper focuses on a recent challenge brought forward against the interventionist approach to the meaning of counterfactual conditionals. According to this objection, interventionism cannot account for the interpretation of right-nested counterfactuals, the problem being its strict interventionism. We will report on the results of an empirical study supporting the objection. Furthermore, we will extend the well-known logic of intervention with a new operator expressing an alternative notion of intervention that does away with strict interventionism. This new notion of intervention (...) operates on the valuation of the variables in a causal model, and not on their functional dependencies. (shrink)

Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.

A much-discussed idea in the causation literature is that it is preferable to invoke causes which are proportional to—neither too general nor too specific for—the effect. This article presents various ways of understanding this idea. In what sense are such causal claims ‘preferable’? And what is it for one event to be ‘proportional’ to another? In a companion article, ‘Proportionality in Causation, Part II: Applications and Challenges’, I discuss the principal applications of the resulting theories of proportionality, and the challenges (...) they face. (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 we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...) this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update. (shrink)

This paper aims to bridge philosophical and psychological research on causation, counterfactual thought, and the problem of backtracking. Counterfactual approaches to causation such as that by Lewis have ruled out backtracking, while on prominent models of causal inference interventionist counterfactuals do not backtrack. However, on various formal models, certain backtracking counterfactuals end up being true, and psychological evidence shows that people do sometimes backtrack when answering counterfactual questions in causal contexts. On the basis of psychological research, I argue that while (...) ordinarily both kinds of counterfactuals may be employed, non-backtracking counterfactuals are more easily used in causal inference because they are consistent with temporal order information embedded in the mental simulation heuristic, and they match reasoners’ experience of causation. While this approach is incompatible with the ambitions of counterfactual theories that seek to establish the non-backtracking interpretation as the only legitimate one, it can provide support for perspectival views on causation and open further inquiry on the functions of causal and counterfactual thought in the context of causal models. (shrink)

Some recent arguments defending the genuine causal efficacy of the mental have been relying on empirical research on neuroprosthetics. This essay presents a critical analysis of these arguments. The problem of mental causation, and the basic idea and results of neuroprosthetics are reviewed. It is shown how appealing to the research on neuroprosthetics can be interpreted to give support to the idea of mental causation. However, it does so only in a rather deflationary sense: by holding the mental identical with (...) the neural. So contrary to what the arguments have been assuming, neuroprosthetics cannot be used to argue for nonreductive physicalism. It can rather be taken to illustrate just the opposite: how the mental and the physical are identical. (shrink)

E. J. Lowe argues that the mental event token cannot be identical to the complex neural event token for they have different counterfactual properties. If the mental event had not occurred, the behavior would not have ensued, while if the neural event had not occurred, the behavior would have ensued albeit slightly differently. Lowe's argument for the neural counterfactual relies on standard possible world semantics, whose evaluation of such counterfactuals is problematic. His argument for the mental counterfactual relies on a (...) premise that is plausibly false. My arguments support other counterfactuals, which are consistent with identity theories. (shrink)

Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we have a (...) sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals". (shrink)

Walking through the supermarket, I see the avocados. I know they are avocados. Similarly, if you see a pumpkin on my office desk, you can know it’s a pumpkin from its looks. The phenomenology in such cases is that of “just seeing” that such and such. This phenomenology might suggest that the knowledge gained is immediate. This paper argues, to the contrary, that in these target cases, the knowledge is mediate, depending as it does on one’s knowledge of what the (...) relevant kind of thing looks like. To make the case requires examining the nature of knowing what Fs look like. Is such knowledge to be understood as knowledge of a fact, or rather as a kind of ability? From the conclusion that the knowledge in the target cases is not immediate, the paper concludes that perception does not afford us immediate knowledge concerning objects’ kinds. (shrink)

Rubin and Pearl offered approaches to causal effect estimation and Lewis and Pearl offered theories of counterfactual conditionals. Arguments offered by Pearl and his collaborators support a weak form of equivalence such that notation from the rival theory can be re-purposed to express Pearl’s theory in a way that is equivalent to Pearl’s theory expressed in its native notation. Nonetheless, the many fundamental differences between the theories rule out any stronger form of equivalence. A renewed emphasis on comparative research can (...) help to guide applications, further develop each theory, and better understand their relative strengths and weaknesses. (shrink)

McGee argued that modus ponens was invalid for the natural language conditional ‘If…then…’. Many subsequent responses have argued that, while McGee’s examples show that modus ponens fails to preserve truth, they do not show that modus ponens fails to preserve rational full acceptance, and thus modus ponens may still be valid in the latter informational sense. I show that when we turn our attention from indicative conditionals to subjunctive conditionals, we find that modus ponens does not preserve either truth or (...) rational full acceptance, and thus is not valid in either sense. In concluding I briefly consider how we can account for these facts. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...) reduced to probabilities, but deriving these probabilities involves more than just statistics. (shrink)

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals (...) with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (shrink)

I discuss three observations about backtracking counterfactuals not predicted by existing theories, and then motivate a theory of counterfactuals that does predict them. On my theory, counterfactuals quantify over a suitably restricted set of historical possibilities from some contextually relevant past time. I motivate each feature of the theory relevant to predicting our three observations about backtracking counterfactuals. The paper concludes with replies to three potential objections.

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (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)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

Biological modalities (e.g., biological possibility, necessity and counterfactuality) play an important explanatory role in biological practice. However, biological modalities lack truth conditions and the inferential relationship between biological and other modalities is unclear. This thesis addresses these problems, first, by improving upon Daniel Dennett's Library of Mendel. Second, a family of modal logics is introduced. In the simplest model, states are interpreted as codons, the binary relation is interpreted as single substitution mutation and the valuation induces a partition of blocks (...) of codons that code for some amino acid. In addition, the proposed framework allows for a grading of biological possibility and captures various competing notions of biological possibility. Applications include a model checker and a lawless Lewis-style semantics for biological counterfactuals. In short, this thesis lays the groundwork for a theory of biological modalities. (shrink)

Judea Pearl (2000) was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure but also to considerations of normality. In Halpern and Hitchcock (2011), we offer a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this study, we show how it (...) is possible to achieve a compact representation of extended causal models. (shrink)

Many have accepted that ordinary counterfactuals and might counterfactuals are duals. In this paper, I show that this thesis leads to paradoxical results when combined with a few different unorthodox yet increasingly popular theses, including the thesis that counterfactuals are strict conditionals. Given Duality and several other theses, we can quickly infer the validity of another paradoxical principle, ‘The Counterfactual Direct Argument’, which says that ‘A> ’ entails ‘A> ’. First, I provide a collapse theorem for the ‘counterfactual direct argument’. (...) The counterfactual direct argument entails the logical equivalence of the subjunctive and material conditional, given a variety of assumptions. Second, I provide a semantics that validates the counterfactual direct argument without collapse. This theory further develops extant dynamic accounts of conditionals. I give a new semantics for disjunction, on which A or B is only true in a context when A and B are both unsettled. The resulting framework validates CDA while invalidating other commonly accepted principles concerning the conditional and disjunction. (shrink)

Many defend the thesis that when someone knows p, they couldn’t easily have been wrong about p. But the notion of easy possibility in play is relatively undertheorized. One structural idea in the literature, the principle of Counterfactual Closure (CC), connects easy possibility with counterfactuals: if it easily could have happened that p, and if p were the case, then q would be the case, it follows that it easily could have happened that q. We first argue that while CC (...) is false, there is a true restriction of it to cases involving counterfactual dependence on a coin flip. The failure of CC falsifies a model where the easy possibilities are counterfactually similar to actuality. Next, we show that extant normality models, where the easy possibilities are the sufficiently normal ones, are incompatible with the restricted CC thesis involving coin flips. Next, we develop a new kind of normality theory that can accommodate the restricted version of CC. This new theory introduces a principle of Counterfactual Contamination, which says roughly that any world is fairly abnormal if at that world very abnormal events counterfactually depend on a coin flip. Finally, we explain why coin flips and other related events have a special status. A central take home lesson is that the correct principle in the vicinity of Safety is importantly normality-theoretic rather than (as it is usually conceived) similarity-theoretic. (shrink)

According to the theory developed here, we may trace out the processes emanating from a cause in such a way that any consequence lying along one of these processes counts as an effect of the cause. This theory gives intuitive verdicts in a diverse range of problem cases from the literature. Its claims about causation will never be retracted when we include additional variables in our model. And it validates some plausible principles about causation, including Sartorio's ‘Causes as Difference Makers’ (...) principle and Hitchcock's ‘Principle of Sufficient Reason’. (shrink)