In this paper, I argue for two principles to determine the temporal interpretation of modal sentences in English, given a theory in which modals are interpreted against double conversational backgrounds and an ontology in which possible worlds branch towards the future, The Disparity Principle requires that a modal sentence makes distinctions between worlds in the modal base. The Non- disparity Principle requires that a modal sentence does not make distinctions on the basis of facts settled at speech time. Selection of (...) the modal base will set these principles against each other, or allow for their cooperative interaction. For a root modal base, there is a conflict and disparity wins. The resulting interpretation is future. For a non-root modal base, the principles cooperate. Non-disparity determines a non-future interpretation and disparity requires the sentence to go beyond what is known by the speaker. (shrink)

The rise of causality and the attendant graph-theoretic modeling tools in the study of counterfactual reasoning has had resounding effects in many areas of cognitive science, but it has thus far not permeated the mainstream in linguistic theory to a comparable degree. In this study I show that a version of the predominant framework for the formal semantic analysis of conditionals, Kratzer-style premise semantics, allows for a straightforward implementation of the crucial ideas and insights of Pearl-style causal networks. I spell (...) out the details of such an implementation, focusing especially on the notions of intervention on a network and backtracking interpretations of counterfactuals. (shrink)

Judea Pearl won the 2010 Rumelhart Prize in computational cognitive science due to his seminal contributions to the development of Bayes nets and causal Bayes nets, frameworks that are central to multiple domains of the computational study of mind. At the heart of the causal Bayes nets formalism is the notion of a counterfactual, a representation of something false or nonexistent. Pearl refers to Bayes nets as oracles for intervention, and interventions can tell us what the effect of action will (...) be or what the effect of counterfactual possibilities would be. Counterfactuals turn out to be necessary to understand thought, perception, and language. This selection of papers tells us why, sometimes in ways that support the Bayes net framework and sometimes in ways that challenge it. (shrink)

The branch of philosophical logic which has become known as “belief change” has, in the course of its development, become alienated from its epistemological origins. However, as formal criteria do not suffice to defend a principled choice between competing systems for belief change, we do need to take their epistemological embedding into account. Here, on the basis of a detailed examination of Isaac Levi's epistemology, we argue for a new direction of belief change research and propose to construct systems for (...) belief change that can do without, but do not rule out, selection functions, in order to enable an *empirical* assessment of the relative merits of competing belief change systems. (shrink)

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have something to say on the (...) matter. (shrink)

Crosslinguistically, causative constructions conform to the following generalization: If the causal relation is syntactically concealed, then it is semantically direct. Concealed causatives span a wide syntactic spectrum, ranging from resultative complements in English to causative subjects in Miskitu. A unified type-driven theory is proposed which attributes the understood causal relation—and other elements of constructional meaning—to type lifting operations predictably licensed by type mismatch at LF. The proposal has far-reaching theoretical implications not only for the theory of compositionality and causation, but (...) also for the underlying theory of events, space, and time, in natural language discourse. (shrink)

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 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)

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)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual (...) engineering for intensions and hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal and hyperintensional expressivist approaches here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (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 counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (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)

Folklore has it that Sobel sequences favor a variably strict analysis of conditionals over its plainly strict alternative. While recent discussions for or against the lore have focussed on Sobel sequences involving counterfactuals, this paper draws attention to the fact that indicative Sobel sequences are just as felicitous as are their counterfactual cousins. The fact, or so I shall argue here, disrupts the folklore: given minimal assumptions about the semantics and pragmatics of indicative conditionals, a textbook variably strict analysis fails (...) to predict that indicative Sobel sequences are felicitous. The correct lesson to draw from Sobel sequences is that their felicity challenges classical implementations of the variably strict and of the plainly strict analysis alike. In response to this challenge I develop a dynamic strict analysis of conditionals that handles indicative Sobel sequences with grace while preserving intuitive constraints on the semantics and pragmatics of their members. A discussion of how such an analysis may handle the challenge from reverse Sobel sequences is provided. (shrink)

C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) (...) can do without extra-logical elements, and (5) only licenses consistent beliefs. (shrink)

Our preferences determine how we act and think, but exactly what the mechanics are and how they work is a central cause of concern in many disciplines. This book uses techniques from modern logics of information flow and action to develop a unified new theory of what preference is and how it changes. The theory emphasizes reasons for preference, as well as its entanglement with our beliefs. Moreover, the book provides dynamic logical systems which describe the explicit triggers driving preference (...) change, including new information, suggestions, and commands. In sum, the book creates new bridges between many fields, from philosophy and computer science to economics, linguistics, and psychology. For the experienced scholar access to a large body of recent literature is provided and the novice gets a thorough introduction to the action and techniques of dynamic logic. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines 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 and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (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} is 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 Elohim's 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. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher 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 two-dimensional 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 interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents 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 in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. 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)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines 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 and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (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} is 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 Elohim's 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. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher 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 two-dimensional 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 interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents 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 in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. 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)

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. (...) Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal. (shrink)

Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in ‘Cynthia will pass her exam’, will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are (...) jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents. (shrink)

This paper considers some questions related to the determination of epistemic modal domains. Specifically, given situations in which groups of agents have epistemic states that bear on a modal domain, how is the domain best restricted? This is a metasemantic project, in which I combine a standard semantics for epistemic modals, as developed by Kratzer, with a standard story about conversational dynamics, as developed by Stalnaker. I show how a standard framework for epistemic logic can model their interaction. I contend (...) that if groups have epistemic states that bear on the modal domain, as the data suggests, then careful attention must be paid to the method of combination selected for the epistemic states of the individuals within the group. Specifically, there should be some explanation of the flow of information in a group-deliberative setting. Through this study we find a novel explanation of modal disagreement and uptake. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

“Counterfactual” readings of might/could have were previously analyzed using metaphysical modal bases. This paper presents examples and scenarios where the assumptions of such a branching-time semantics are not met, because there are facts at the base world that preclude the complement of the modal becoming true. Additional arguments show that counterfactual readings are context dependent. These data motivate a semantics using a circumstantial (or factual) modal base, which refers to context-dependent facts about a world and time. The analysis is formulated (...) in a version of premise semantics for modality. (shrink)

Recent work on the interpretation of counterfactual conditionals has paid much attention to the role of causal independencies. One influential idea from the theory of Causal Bayesian Networks is that counterfactual assumptions are made by intervention on variables, leaving all of their causal non-descendants unaffected. But intervention is not applicable across the board. For instance, backtracking counterfactuals, which involve reasoning from effects to causes, cannot proceed by intervention in the strict sense, for otherwise they would be equivalent to their consequents. (...) We discuss these and similar cases, focusing on two factors which play a role in determining whether and which causal parents of the manipulated variable are affected: Speakers' need for an explanation of the hypothesized state of affairs, and differences in the ‘resilience’ of beliefs that are independent of degrees of certainty. We describe the relevant theoretical notions in some detail and provide experimental evidence that these factors do indeed affect speakers' interpretation of counterfactuals. (shrink)

This paper argues that just as full beliefs can constitute knowledge, so can properties of your credence distribution. The resulting notion of probabilistic knowledge helps us give a natural account of knowledge ascriptions embedding language of subjective uncertainty, and a simple diagnosis of probabilistic analogs of Gettier cases. Just like propositional knowledge, probabilistic knowledge is factive, safe, and sensitive. And it helps us build knowledge-based norms of action without accepting implausible semantic assumptions or endorsing the claim that knowledge is interest-relative.

Different similarity relations on sets are introduced, and their logical properties are investigated. Close relationships are shown to hold between similarity relations that are based on symmetrical difference and operators of belief contraction that are based on relational selection functions. Two new rationality criteria for minimal belief contraction, the maximizing property and the reducing property, are proposed.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)

This paper presents a new system of conditional logic B2, which is strictly intermediate in strength between the existing systems B1 and B3 from John Burgess (1981) and David Lewis (1973a). After presenting and motivating the new system, we will show that it is characterized by a natural class of frames. These frames correspond to the idea that conditionals are about which worlds are nearly closest, rather than which worlds are closest. Along the way, we will also give new characterization (...) results for B1 and B3, along with two other new systems B1.1 and B1.2. (shrink)

Based on the new experimental evidence, we argue that a link between a conditional antecedent and the consequent is semantically expressed rather than pragmatically conveyed. In our paper, we focus on particular kinds of links which conditionals may convey in a context. For instance, a conditional ‘If p, q’ may convey a thought equivalent to ‘p will cause q’, ‘p is the best explanation for q’, ‘q follows from p’, etcetera. The traditional theoretical literature on conditionals seems to imply that (...) these specific links are generated pragmatically and are akin to conversational implicatures. In order to test this hypothesis, we used a well-recognized linguistic test from ‘reinforceability’, which serves to distinguish between a semantic and pragmatic level of meaning, and we designed an experimental study based on that test. The outcome of our study is that specific links conveyed by conditionals exhibit features of semantic entailments rather than conversational implicatures. This result accords with some of the recent findings in empirical investigations on conditionals. In the final part of our paper, we discuss various accounts of conditionals which can accommodate the results of our study. (shrink)

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I claim that their argument fails to establish this result for two reasons. First, their assumptions force our hand on a controversial debate within counterfactual logic. In particular, they license counterfactual strengthening— the inference from ‘If A (...) were true then C would be true’ to ‘If A and B were true then C would be true’—which many reject. Second, the system they develop is provably equivalent to appending Deduction Theorem to a T modal logic. It is unsurprising that the combination of Deduction Theorem with T results in necessitation; indeed, it is precisely for this reason that many logicians reject Deduction Theorem in modal contexts. If Deduction Theorem is unacceptable for modal logic, it cannot be assumed to derive the necessity of mathematics. (shrink)

In this paper, I examine whether agents who commit testimonial injustice are morally responsible for their wrongdoing, given that they are ignorant of their wrongdoing. Fricker (2007) argues that agents whose social setting lacks the concepts or reasons necessary for them to correct for testimonial injustice are excused. I argue that agents whose social settings have these concepts or reasons available are also typically excused, because they lack the capacity to recognise those concepts or reasons. Attempts to trace this lack (...) of capacity back to an earlier culpable wrongdoing will often fail, due to there being no point at which these perpetrators knowingly chose to develop their prejudices. Attempts to ground culpability under Talbert’s (2008) Attributionist account of moral responsibility will also fail. This is because perpetrators’ lack of awareness of what they are doing makes it the case that they are not expressing objectionable evaluative judgments in the way required for blameworthiness. Finally, I argue that our temptation to blame agents who commit testimonial injustice is not completely unfounded. Appealing to Watson’s (1996) attributability/accountability distinction allows us to make sense of how some responses to the jurors are appropriate, despite their being excused. (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)

This paper presents a Ramsey account of conditionals within the framework of an implemented reason maintenance system. The reason maintenance system is built on top of a deductive reasoning engine based on relevance logic. Thus, the account of conditionals provided is not susceptible to the fallacies of relevance. In addition, it is shown that independently motivated requirements on practical relevant reason maintenance allow us to gracefully circumvent Gärdenfors's triviality result.

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)

The classic Lewis-Stalnaker semantics for counterfactuals captures that Sobel sequences are consistent sequences, for example: a.If Sophie had gone to the parade, she would have seen Pedro dance. b.But if Sophie had gone to the parade and been stuck behind someone tall, she would not have seen Pedro dance. But reverse a sequence like this one and it no longer sounds so good, which is surprising on the classic semantics. This observation motivated Kai von Fintel and Thony Gillies to propose (...) dynamic semantic accounts of counterfactual conditionals. Subsequently, Sarah Moss defended the classic semantics against the charge that it need be abandoned in the face of these order effects, arguing that the infelicity of the reverse sequences is pragmatic. I argue that both accounts are ultimately untenable, but each account has strengths. Seeing what works and what doesn't in each account points the way to the right positive view. With this in mind, I defend a contextualist account of counterfactuals that takes conversational relevance to play a central role. (shrink)

Whether there exist causal relations between guns firing and people dying, between pedals pressed and cars accelerating, or between carbon dioxide emissions and global warming, is typically taken to be a mind-independent, objective, matter of fact. However, recent contributions to the literature on causation, in particular theories of contrastive causation and causal modelling, have undermined this central causal platitude by relativising causal facts to models or to interests. This thesis flies against the prevailing wind by arguing that we must pay (...) greater attention to which elements of our causal talk vary with context and which elements track genuine features of the world around us. I will argue that once these elements are teased apart we will be in a position to better understand some of the most persistent problems in the philosophy of causation: pre-emption cases, absence causation, failures of transitivity and overdetermination. The result is a naturalist account of causation, concordant with the contextual variability we find in our ordinary causal talk, and parsimonious with respect to the theoretical entities posited. (shrink)

This paper investigates when and how children figure out the force of modals: that possibility modals (e.g., _can_/_might_) express possibility, and necessity modals (e.g., _must_/_have to_) express necessity. Modals raise a classic subset problem: given that necessity entails possibility, what prevents learners from hypothesizing possibility meanings for necessity modals? Three solutions to such subset problems can be found in the literature: the first is for learners to rely on downward-entailing (DE) environments (Gualmini and Schwarz in J. Semant. 26(2):185–215, 2009 ); (...) the second is a bias for strong (here, necessity) meanings; the third is for learners to rely on pragmatic cues stemming from the conversational context (Dieuleveut et al. in Proceedings of the 2019 Amsterdam colloqnium, pp. 111–122, 2019a ; Rasin and Aravind in Nat. Lang. Semant. 29:339–375, 2020 ). This paper assesses the viability of each of these solutions by examining the modals used in speech to and by 2-year-old children, through a combination of corpus studies and experiments testing the guessability of modal force based on their context of use. Our results suggest that, given the way modals are used in speech to children, the first solution is not viable and the second is unnecessary. Instead, we argue that the conversational context in which modals occur is highly informative as to their force and sufficient, in principle, to sidestep the subset problem. Our child results further suggest an early mastery of possibility—but not necessity—modals and show no evidence for a necessity bias. (shrink)

I draw upon Helen Steward's concept of agential settling to argue that freedom requires an ability to change the truth‐value of tenseless future contingents over time from false to true and that this ability requires a metaphysically open future.

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras comprise a materially adequate fragment of the language of thought, and endeavor to show how such algebras provide the resources necessary to resolve Russell's paradox of propositions. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dually isomorphic. I examine, in particular, the virtues (...) unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dual. I examine, in particular, the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast (...) to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)