Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M as a weighted (...) average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (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 paper 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)

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)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. 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 book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (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)

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)

While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits (...) of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality. (shrink)

We construct a causal-modeling semantics for both indicative and counterfactual conditionals. As regards counterfactuals, we adopt the orthodox view that a counterfactual conditional is true in a causal model M just in case its consequent is true in the submodel M∗, generated by intervening in M, in which its antecedent is true. We supplement the orthodox semantics by introducing a new manipulation called extrapolation. We argue that an indicative conditional is true in a causal model M just in case its (...) con- sequent is true in certain submodels M∗, generated by extrapolating M, in which its antecedent is true. We show that the proposed semantics can account for some important minimal pairs nicely and naturally. We also prove a theorem showing under what conditions intervention and extrapolation will yield the same result, and thus explain how counterfactual and indicative conditionals would behave in a causal-modeling semantics. (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)

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...) spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: that a conditional is logically independent from its antecedent; that a sequence of antecedents behaves like a single conjunctive antecedent ; and that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. (shrink)

Philosophy and Phenomenological Research, EarlyView.

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.

We show that five important elements of the ‘nomological package’— laws, counterfactuals, chances, dispositions, and counterfactuals—needn’t be a problem for the Growing-Block view. We begin with the framework given in Briggs and Forbes (in The real truth about the unreal future. Oxford studies in metaphysics. Oxford University Press, Oxford, 2012 ), and, taking laws as primitive, we show that the Growing-Block view has the resources to provide an account of possibility, and a natural semantics for non-backtracking causal counterfactuals. We show (...) how objective chances might ground a more fine-grained concept of feasibility, and furnished a places in the structure where causation and dispositions might fit. The Growing-Block view, thus understood, provides the resources to explain the close link between modality and tense, so that it predicts modal change as time passes. This account lets us capture not only what the future might hold for us, and also what might have been. (shrink)

In this paper, I consider a variant of the ancient Idle Argument involving so‐called “unconditionals” with interrogative antecedents. This new Idle Argument provides an ideal setting for probing the logic of these close relatives of if‐conditionals, which has been comparatively underexplored. In the course of refuting the argument, I argue that contrary to received wisdom, many unconditionals do not entail their main clauses, yet modus ponens is still unrestrictedly valid for this class of expressions. I make these lessons precise in (...) a formal system drawing on recent work in inquisitive semantics. My larger aim is to challenge standard truth preservation accounts of logic and deductive argumentation. (shrink)

An important question for the causal modeling approach is how to integrate non‐causal dependence relations such as asymmetric supervenience into the approach. The most prominent proposal to that effect (due to Gebharter) is to treat those dependence relationships as formally analogous to causal relationships. We argue that this proposal neglects some crucial differences between causal and non‐causal dependencies, and that in the context of causal modeling non‐causal dependence relationships should be represented as mutual dependence relationships. We develop a new kind (...) of model – “hybrid models” ‐ based on this suggestion, and formulate a set of axioms for those models. Our formalism has important implications for Kim's exclusion problem: whereas Gebharter's framework vindicates Kim's causal exclusion objection against nonreductive physicalism, our framework has no such implication, and can help non‐reductive physicalists vindicate the efficacy of high‐level properties. A further benefit of our formalism is that it yields a natural and plausible way of thinking about interventions in multi‐level contexts. (shrink)

Suppose that A explains B. Do A and B need to be true? Provided that we have metaphysical explanation in mind, orthodoxy answers “yes:” metaphysical explanation is factive. This article introduces and defends a non-factive notion of metaphysical explanation. I argue that we need a non-factive notion of explanation in order to make sense of explanationist arguments where we motivate a view by claiming that it offers better explanations than its competitors. After presenting and rejecting some initially plausible rivals, I (...) account for non-factive metaphysical explanation by drawing on existing applications of structural equation models to metaphysical grounding. (shrink)

Team semantics is a highly general framework for logics which describe dependencies and independencies among variables. Typically, the dependencies considered in this context are properties of sets of configurations or data records. We show how team semantics can be further generalized to support languages for the discussion of interventionist counterfactuals and causal dependencies, such as those that arise in manipulationist theories of causation. We show that the “causal teams” we introduce in the present paper can be used for modelling some (...) classical counterfactual scenarios which are not captured by the usual causal models. We then analyse the basic properties of our counterfactual languages and discuss extensively the differences with respect to the Lewisian tradition. (shrink)

We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically investigate the expressive power of these languages in causal team semantics, and we provide complete natural deduction calculi for each language. Furthermore, we introduce a generalized semantics which allows representing uncertainty about the causal laws, and we analyze the expressive power and proof theory of the causal-observational languages over this enriched semantics.

According to Woodward’s influential account of explanation, explanations have a counterfactual structure, and explanatory counterfactuals are analysed in terms of causal relations and interventions. In this paper, we provide a formal semantics of explanatory counterfactuals based on a Ramsey Test semantics of conditionals. Like Woodward’s account, our account is guided by causal considerations. Unlike Woodward’s account, it makes no reference to causal graphs and it also covers cases of explanation where interventions are impossible.

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)

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.

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)