Conditionals

We propose a novel approach to understanding conditional statements, viewing them as change descriptors within a standard nondeterministic framework. Our logical systems operate on a tree ordering, where the past is linear but the future is inherently uncertain and branching. We provide an axiomatization and demonstrate completeness for systems incorporating both a solely forward-looking conditional operator and a combination of backward and forward-looking operators. Additionally, we introduce and prove analogous results for the duals of these conditional operators, which naturally represent (...) update operators by detailing the transformations leading to the current state. (shrink)

This paper addresses the question of which normative standards apply in the psychology of reasoning. In a first strand, the present paper contributes to a debate concerning whether the New Paradigm in the psychology of reasoning really constitutes a paradigm shift by presenting an argument concerning the deductive competence presupposed by ideal Bayesian agents. On the construal of the New Paradigm as the replacement of deductive logic by probability theory, no such shift was possible: the standard probabilistic frameworks used in (...) the psychology of reasoning were never independent of logical principles to begin with. It is possible, however, to replace the treatment of a fragment of natural language (e.g., conditionals, quantifiers) in classical logic with probabilistic alternatives, as the paper discusses. Thus construed, the probabilistic turn was a major step forward in the psychology of reasoning but one that is better pruned of some of the misleading characterizations that surround it. When multiple norms apply to experimental tasks, a further practical problem presents itself: how should researchers arbitrate between them? In a second strand, an experimental research program is outlined which confronts this problem of arbitrating between competing rationality norms by presenting a way of making rationality assessments of participants based on verbal arguments. In this part, a recent attempt by Dewey (2022) to dissolve problems of arbitration in psychology is critically discussed. (shrink)

Counterfactual conditionals occupy a central position in philosophical analysis, yet attempts to provide a stable account of them have repeatedly failed to converge. Refinements of similarity relations, background conditions, causal dependencies, and related evaluative frameworks often succeed in resolving particular cases, only to generate new instabilities elsewhere. The resulting pattern is not accidental. Counterfactual analysis exhibits a persistent cycle of local stabilization followed by renewed counterexample production. -/- This paper argues that the source of this instability is structurally mislocated. Standard (...) approaches treat counterfactuals as objects of evaluation and seek increasingly precise conditions under which evaluation yields stable results. In doing so, they presuppose that the antecedent, consequent, and relevant background descriptions belong to a single evaluable configuration. The present paper challenges this presupposition. -/- The central claim is that counterfactual instability arises when evaluation is applied to descriptions that are not jointly maintainable within a unified configuration. To articulate this limitation, the paper introduces admissibility as a pre-evaluative condition governing configuration formation and co-satisfiability as a condition on joint realizability under extension. Within this framework, descriptions may be locally admissible while failing to be globally co-satisfiable. Counterfactual instability emerges precisely under these conditions. -/- The analysis is developed through a unified treatment of classical cases, including the struck match, switch-and-breaker, and ability conditionals. These cases are shown to exhibit the same structural pattern: locally stable configurations are repeatedly combined as though they formed a single evaluable domain, despite the absence of a jointly maintainable configuration. The resulting instability is therefore not best understood as disagreement within evaluation, but as a consequence of evaluation being activated where its configurational presuppositions are not secured. -/- The paper further explains why refinement strategies systematically fail to eliminate counterexamples. Refinement may stabilize particular configurations, but it does not alter the underlying structure of admissibility and co-satisfiability. As a result, instability is displaced rather than resolved, and new counterexamples remain structurally generable. -/- The contribution of the paper is re-locational rather than revisionary. It does not propose a new semantics for counterfactuals and does not replace existing evaluative frameworks. Instead, it identifies a structural condition that those frameworks presuppose but do not determine. By relocating instability from evaluation to the formation of evaluable configurations, the paper provides an explanation for both the persistence of counterfactual disagreement and the systematic non-convergence of counterfactual analysis. (shrink)

This thesis investigates whether natural language conditionals can be systematically organized into a coherent taxonomy based on their logical structures. Examining material, strict, probabilistic, counterfactual, and counterpossible conditionals, it explores both successful and failed attempts at reduction between types. While some reductions prove viable (notably from counterpossible to counterfactual conditionals) the project encounters fundamental limits. The thesis argues that English "if… then" statements likely do not possess a unified logical form but rather most likely represent a heterogeneous cluster unified by (...) pragmatic and linguistic convention. Attempts at clarification through formal logic cannot fully resolve what genuinely constitutes a conditional versus what merely appears to be one. The work concludes that the conditional problem resists complete taxonomic resolution, suggesting that conditionality may be better understood as a family of related but irreducibly distinct logical structures rather than variations on a single core concept. (shrink)

Curry’s paradox is often presented as a demonstration that ordinary inferential rules can be made to yield absurdity from a single self-referential conditional. This paper argues that the standard presentation mislocates the failure. The problem is not that logic proves too much, nor that arithmetic is placed in jeopardy, but that a malformed construction is granted inferential standing before it has earned assertoric legitimacy. Curry’s sentence is intelligible, grammatically followable, and proposition-shaped, but those features are not enough to confer the (...) right to function as a premise. Inferential force is not free. A structure must first land as a genuine assertion before it can bear valid consequence. On this view, the appearance of proof is generated by an illicit admission at the gate: the sentence is promoted into inference despite never becoming fit for inferential exposure at all. Curry’s paradox therefore does not reveal a wound in logic. It reveals a stricter condition on logical use. The wider lesson is that not every intelligible structure enters the inferential domain merely by looking propositional. Where assertion has not properly landed, consequence is already misframed. (shrink)

Inductivism is the conjoint thesis that there are genuine inductive inferences and that successful inductive inferences provide inductive knowledge. This paper presents two challenges to inductivism. The first is explaining how many observations are required for inductive inferences in a precise and non-arbitrary way. This is the threshold problem. The second is providing an account of how inductive knowledge can be a qualitative change from a mere quantity of observations. This is the qualitative leap problem. I anticipate and criticize some (...) attempts to solve these problems. One strategy is based on the idea that inferences are justification attempts and that different inference types require different theories of justification. Thus successful inductions can receive an externalist interpretation as reliable processes in which the evidential threshold isn't reflectively accessible. I object that this solution generates new versions of the threshold problem and doesn't address the qualitative leap problem. By relying on Galen's argument against induction, I also argue that any attempt to solve the two problems will be unsuccessful, since an evidential threshold for inductive inferences is implausible in principle. The conclusion is that inductive skepticism is justified. (shrink)

This paper aims to unify two puzzles. One is the puzzle of Heim sequences: while many Sobel sequences can be felicitously uttered, their reverses, i.e. Heim sequences, often sound bad. The other puzzle is that true-true counterfactuals, i.e. counterfactuals with both true antecedents and true consequents, are invariably true on the standard Stalnaker-Lewis semantics, while some of them appear to be infelicitous to utter. True-true counterfactuals are first divided into two categories, which I call “unconnected” and “insufficient” true-trues. The two (...) kinds, I argue, deserve distinct pragmatic accounts. Then, it is argued that the category of insufficient true-trues is a special case of Heim sequences, in the sense that whatever is responsible for the infelicity of Heim sequences should also account for the infelicity of insufficient true-trues. Evidence for this unification is that the (in)felicity of both insufficient true-trues and Heim sequences reacts in similar ways to a series of contextual variations. Given the unification, I review two existing pragmatic accounts of Heim sequences—Moss in Nouˆs 46:561–586, 2012 and Ippolito in Ling & Phil 43:633–671, 2020—and try to apply them to insufficient true-trues. As will be clear, both accounts solve the insufficient true-true puzzles to the same degree of success as they solve the puzzle of Heim sequences, and neither account is completely satisfactory. In comparison, Ippolito’s account is more promising, and I provide a modification of it, which is expected to be an improved solution to both puzzles. (shrink)

Belnap (1970, 1973) proposed to formalize the restriction of first-order quantifiers ∀ and ∃ by means of a single sentential connective: a trivalent conditional that takes the semantic value ‘void’ when the antecedent is false. Thus, ‘every A is B’ is represented as ∀x(Ax → Bx) and ‘some A is B’ is represented as ∃x(Ax → Bx)—a notable unification compared to the standard representation in first-order logic that uses distinct connectives. This paper implements Belnap’s program, henceforth called Conditional Reduction, in (...) full generality and applies it to all conservative ⟨1, 1⟩ quantifiers. By combining Conditional Reductions with the Conservativity Theorem, due to Keenan and Stavi, any conservative type ⟨1, 1⟩ quantifier turns out to be equivalent to Boolean combinations of three basic type ⟨1⟩ quantifiers (‘everything’, ‘at least λ many things’ and the possessives) scoping over a trivalent conditional. (shrink)

This paper investigates the logic of compatibility as a ground for the logic of conditionals. We identify a family of principles expressing key properties of compatibility, which can be coherently ordered. Assuming that conditionals are definable in terms of incompatibility — the negation of compatibility — each of the principles identified yields corresponding principles governing conditionals. Clarifying these derivability relations provides a new perspective on several existing accounts of conditionals.

Zhan and Wang (2025) claim that the relevance effect found in Skovgaard-Olsen et al. (2016) might be an artifact due to “boundary cases” of zero or one probabilities. The relevance effect refers to the finding that people’s expectations about the probabilistic relevance of the antecedent for the consequent influences people’s probability judgments of indicative conditionals, “If A, then C”. In Skovgaard-Olsen et al. (2016, 2017), this effect was found not by using probabilistic notions of relevance, like ∆P=P(C|A)-P(C|-A), as direct predictors (...) of P(if A, then C). Instead, stimulus materials were pre-validated to implement different qualitative reason relation assessments of whether A is a reason for C, A reason against C, or neither, which were operationalized via categories of probabilistic relevance (positive relevance ∆P>0, negative relevance ∆P<0, irrelevance ∆P=0). Despite this, this commentary addresses the fact that the binomial statistical model used by Zhan and Wang (2025) is invalid for the type of data collected. The purpose of this paper is to do a re-analysis of the two data sets of Zhan and Wang (2025). First, we reanalyze the new data that Zhan and Wang (2025) present. Then we re-analyze the data from Skovgaard-Olsen et al. (2016), which Zhan and Wang (2025) in turn re-analyze in Table 5 of their paper. In both cases, we find that invalid statistical models were applied and that the conclusions that Zhan and Wang (2025) draw must be rejected once valid statistical models are applied. (shrink)

You've just read the first sentence of this paper. Would you have read it if some butterfly in Brazil had had some extra nectar for breakfast? You probably think so. But this trivial observation apparently has very dramatic consequences. For instance, it seems to imply that you would have read that very sentence even if someone had offered you $1.000.000 not to do so. This paper is about what thus looks like a paradox in that a counterintuitive conclusion can seemingly (...) be derived from plausible premises and assumptions. The key is to recognise that ‘you would have read the sentence if the butterfly had feasted’ admits of distinct readings: one on which it is false, which is the traditional counterfactual implying causal relevance, and another on which it is true, which we call an irrelevant semifactual. While a fully satisfactory solution would need to develop and defend a semantic analysis of such conditional sentences, our modest aim is merely to sketch how the paradox might be solved. The underpinning theoretical work is for a different paper. (shrink)

This paper provides an inductive interpretation of the sorites paradox. It is argued that the sorites paradox is an inductive meta-meta-inference that future modus ponens applications in a soritical series will be sound. The root of the paradox lies in the fact that inductive inferences rely on evidence and epistemic norms that are insensitive to incremental differences, since they are low probability events. This prevents an epistemicist solution given that cut-off points are incremental differences. This diagnosis is also adapted to (...) epistemic paradoxes such as the lottery paradox, the prediction paradox and the preface paradox. The other main idea of this paper is that the soritical nature of inductive inferences in addition to epistemicism motivates some arguments for inductive skepticism, such as that the evidentiary threshold of inductive inferences is unknowable, which can generate another soritical series that requires another unknowable cut-off point, and so on. The conclusion is that inductive inferences are unjustified. (shrink)

I present an intractable puzzle for the currently popular view that belief is weak—the view that expressions like ‘S believes p’ ascribe to S a doxastic attitude towards p that is rationally compatible with low credence that p. The puzzle concerns issues that arise on considering beliefs in conditionals. I show that proponents of weak belief either cannot consistently apply their preferred methodology when accommodating beliefs in conditionals, or they must deny that beliefs in conditionals can be used in reasoning.

In conversation, we make use of shared information in order to communicate. But what shared information? In theorising about conversation, it’s popular to allot a privileged position to a single body of information: the common ground (roughly, what all participants in a conversation take for granted). I argue that we need a more nuanced view—a single body of information is not enough to characterise how conversation works. As proof of concept, I focus on indicative conditionals. Orthodoxy holds that indicative conditionals (...) are felicitous only when their antecedents are compatible with the common ground. I marshal linguistic data to show this can’t be right. Instead, different conversational goals may impose different constraints on the use of indicative conditionals. Nevertheless, I argue that the orthodox constraint on indicative conditionals may be ceteris paribus true, with violations to be explained on a case-by-case basis, and defend this kind of approach to pragmatics. (shrink)

Review of William Lycan, Real Conditionals.

The idea that abilities should be understood as a modal tie between one's motivational states and one's actions is at the core of the most prominent views of abilities. I develop a novel challenge against such views of ability arguing that all these accounts cannot properly account for inabilities and compulsions.

In this paper, I distinguish and compare three kinds of logical expressivism. The first, reminiscent of attitude expressivism in meta-ethics, holds that logic is expressive in that logical vocabulary serves to express attitudes. For instance, traditional attitude expressivism about negation, going back to the work of Frank Plumpton Ramsey, Huw Price and others, holds that 'not' expresses disbelief. The second kind of logical expressivism, reminiscent of deflationism about truth and championed by Robert Brandom, holds that logic is expressive in that (...) logical vocabulary serves to make explicit—typically, by expressing them as contents of assertions—the commitments that are implicit in our discursive practices. For instance, content expressivism about the conditional holds that 'if' expresses as content commitment to the goodness of certain inferential moves. The third kind of logical expressivism, and the one I will be arguing for, holds that, in a sense, logic is expressive in both ways: logical vocabulary serves to make explicit commitments to expressions of attitudes. (shrink)

According to Molinism, logically prior to his creative decree, God knows via middle knowledge the truth value of the counterfactuals or conditionals of creaturely freedom (CFs) and thus what any possible person would do in any given circumstance. Critics of Molinism have pointed out that the Molinist God gets lucky that the CFs allow him to actualize either a world of his liking or even a good-enough world at all. In this paper, I advance and strengthen the popular critique in (...) two ways. First, I specify the kind of luck to which God is subject, which is circumstantial moral luck. Second, and more importantly, I argue that exposure to this luck is problematic because something external to God and beyond his control determines the degree of praiseworthiness he deserves in relevant possible worlds. My main contention is that divine subjection to circumstantial moral luck raises the theoretical costs of Molinism. (shrink)

This chapter argues that in order to develop a semantics that encompasses conditionals both with and without ‘if’, an explanatorily adequate semantic theory of conditionals in discourse has to kick the object of semantic study beyond that of the sentence to the level of speech acts. It provides a brief history of the debate regarding the degree to which context can inform truth-conditional content before proposing the radical contextualist theory of Default Semantics as one that can adequately capture the meanings (...) of conditionals as they are used and understood by speakers; a brief introduction to the theory is offered at the end of the chapter. (shrink)

En este trabajo realizaré un análisis de la propuesta de Edgington en el artículo Do Conditionals have Truth-Conditions?, con énfasis en su crítica a la consideración veritativo-funcional del condicional y en su consideración positiva del mismo. Empezaré contextualizando del debate acerca del condicional en el que se sitúa el artículo de Edginton, luego resumiré el argumento central del artículo contra la consideración veritativo-funcional y a favor de su consideración positiva. Demostraré algunos puntos débiles del argumento de Edginton, puesto que la (...) consideración veritativo-funcional del condicional puede no ser tan contraintuitiva como la autora plantea, y su consideración positiva del condicional no satisface la posibilidad de ser la interpretación universal del mismo. Cierro el trabajo planteando la importancia explicitar la interpretación de cualquier sentencia condicional. (shrink)

This paper is concerned with disjunctions of universal modals, such as ‘You have to clean your room or you have to walk the dog’, and disjunctions of conditionals, such as ‘If Alice dances, Charlie will dance, or if Bob dances, Charlie will dance’. We aim to provide a uniform account of their surprising behaviour. Our proposal combines three independently attested components. Firstly, disjunction's dynamic effect, familiar from presupposition projection: when we evaluate a disjunction ‘A or B’, we typically interpret B (...) assuming the negation of A, and optionally, also interpret A assuming the negation of B. Secondly, the fact that disjunctions often receive a conjunctive interpretation, familiar from free choice phenomena. Thirdly, that modal bases are restricted to local contexts, what Mandelkern has called ‘bounded modality’. (shrink)

The propositional connectives – and, or, not, if–then, etc. – are fundamental building blocks in formal as well as natural languages. In the Western tradition, they were first studied as such by the Stoics, and Propositional Logic is the fundament of practically all current systems of logic; every beginning logic course starts with it. Still, the proof theory and semantics of systems of propositional logic are far from trivial, and have been studied intensely by logicians in the last one and (...) a half centuries, not least in recent decades. It is actually a vast area of research, as witnessed by Lloyd Humberstone’s 1500 page tome The Connectives (2011), which overviews much of that research. Perhaps the most familiar recent work in this area concerns conditionals in formal and natural languages. The 4th Tsinghua Interdisciplinary Workshop on Logic, Language, and Meaning (TLLM 2024) also focused on the apparently simpler connectives expressing (various versions of) conjunction, disjunction, and negation. -/- Researchers working from a cross-linguistic perspective also study how the connectives are encoded in different languages, and ask whether classical logic is capable of capturing the variations and universals exhibited. Even in well-studied languages such as English, there are intricate phenomena that remain challenging for classical logic, including free choice disjunction, non-Boolean conjunction, and metalinguistic negation, to name just a few. There is also growing interest in the acquisition and processing of natural language connectives. In the context of the hotly discussed Large Language Models (LLMs), understanding connectives presents novel challenges that deserve in-depth exploration. (shrink)

The aim of the paper is to discuss the problem of the assignment of the degree of belief to conditional sentences by a rational agent. After presenting the general methodological framework, we analyze two possible approaches. In both cases we assume that we have a non-conditional probabilistic system of beliefs expressed in a language L0, and modeled in some initial probability space S, which allows us to assign probabilities to sentences from L0. Our aim is to extend this system of (...) beliefs to a given class of sentences Φ containing conditionals. The first approach is what we call the “credence-like” approach: for a given class Φ, we define credence as a function defined directly on linguistic objects. The second approach consists in assuming the existence of a standard probability space, in which the sentences from the set Φ are interpreted as events. In this case, the degree of belief of α is defined as the probability of the corresponding event in the probability space SΦ. We present both of these approaches, indicating what their advantages and disadvantages are. The thesis of the article is that the probabilistic approach to the analysis of degrees of belief of sentences containing the conditional connective is by far the more universal one and preferable method, particularly in the context of more complex conditionals. (shrink)

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one should (...) expect on the view that logical form is determined by truth conditions. (shrink)

The dominant analyses of the logical form of natural-language conditionals take them to be “suppositional conditionals”. The latter are true or accepted if the consequent is true/accepted on the supposition of the antecedent. But this can happen although the antecedent is completely irrelevant (or even somewhat adverse) to the consequent. In natural-language conditionals, however, the antecedent is typically meant to support or be evidence for the consequent. The logical form of conditionals will thus be more complex than the suppositional theory (...) would have it. Recently some suggestions as to what this logical form might look like have been made. In this paper, I critically discuss Vincenzo Crupi and Andrea Iacona’s account of “evidential conditionals”, including its recent amendments. (shrink)

Franz Huber’s book addresses beliefs and counterfactuals and their relationship. Using a normative approach, the author explores how agents should believe and change their beliefs, given they have...

The epistemic thesis is the thesis that a 'might' counterfactual like 'If Matt had gone to the parade, David might have gone to the parade' has the same meaning as 'Maybe, if Matt had gone to the parade, David would have gone to the parade.' I offer a new theory of the counterfactual interpretation of the modal 'might' on which 'might' has the same meaning as 'maybe would'. And I show that, when coupled with a plausible semantics for 'if' clauses, (...) my theory validates the epistemic thesis. (shrink)

This article provides a defense of deductivism, the notion that all inferences are deductive. It is argued that all inferences are deductive according to the reasoner’s intended domain of quantification. This implicit range might include different modalities (logical, nomological, metaphysical), different numbers of intended worlds (all, some, twenty, one…), and different sets of objects referred to. These restrictions require a different conception of validity where inferences can be truth-preserving in different ranges. The main alternative to deductivism is inductivism, the view (...) that some inferences are genuinely inductive. Section 2 presents the problems of inductivism, highlighting its conceptual deficiencies and advancing deductivism as an alternative. In section 3, it is argued that the epistemic commitments of inductivism and deductivism are fallibilism and infallibilism, respectively. Infallibilism is defended as a matter of coherence. Section 4 considers the metaphysical commitments of deductivism. It is argued that deductivism implies determinism, which, in turn, requires only deductive explanations. Section 5 concludes. Throughout the paper, other conceptual innovations are offered such as modal indexes, a modal interpretation of probability and a distinction between type and token propositions. (shrink)

I argue that practically all vague language is context sensitive in a covert and unfamiliar way. I first outline a novel puzzle concerning the interaction of conditionals and vagueness. I then argue that the best way of resolving the puzzle is by positing context‐sensitive penumbral connections between sundry parts of language. I argue that these penumbral connections shift through a distinct form of Lewisian accommodation. The upshot is that meaning is a far shiftier thing than has typically been thought.

Causal pre-emption scenarios are problematic for the counterfactual framework of causation (CFC) because people judge an action to be the actual cause of an outcome although the outcome would have occurred anyway due to the action of a pre-empted alternative cause. We propose that commonsense causal questions typically probe specific events that actually happened as and how they did, and show that counterfactuals that probe specific events match selections of actual cause, and dissociations only occur with non-specific counterfactuals. In addition, (...) the pre-empted action is often selected as the or an actual cause when it causes the pre-empting action (auto-pre-emption). Judgements of an action’s responsibility for the outcome track judgements of actual cause following the legal sine qua non principle. Agent reproach is also influenced by the agent's intention. The effects of causal dependency structure and counterfactual question type are robust across the intentionality of the pre-empting action and scenario content. (shrink)

Lee Archie argued that if any truth-values are consistently assigned to a natural language conditional, where modus ponens and modus tollens are valid argument forms, and affirming the consequent is invalid, this conditional will have the same truth-conditions as a material implication. This argument is simple and requires few and relatively uncontroversial assumptions. We show that it is possible to extend Archie’s argument to three- and five-valued logics and vindicate a slightly weaker conclusion, but one that is still important: Even (...) if you do not believe in bivalence and the classical negation operator, you would still have good reasons to accept that natural language conditionals and the material implication share truth-conditions. (shrink)

This paper is about the logic of progressive aspect. We defend a new principle, which we call ‘Progressive Specificity’. Progressive Specificity says that if you are Ving, and to V is to X or Y, then you are Xing or you are Ying. We offer seven arguments for Progressive Specificity, which explore connections with credences, counterfactuals, indicatives, ‘wish’ reports, implicatures, and more. These arguments extend to the futurative progressive, showing that prevailing accounts of the futurative, which treat it as conveying (...) plans, must be rejected. We consider two types of apparent counterexamples to Progressive Specificity: verbs of selection, such as ‘decide’, and verbs of creation, such as ‘build’. We then respond to an objection that Progressive Specificity gives rise to objectionable arbitrariness about what things are doing. Our response appeals to the close connection between Progressive Specificity and the principle of Conditional Excluded Middle. This connection, previously unexplored, provides additional support for Progressive Specificity, and paves the way toward a conditional account of the progressive. (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)

This paper provides new examples of vagueness phenomena with comparatives. I show that comparatives of the form ‘x is ADJ-er than y’ can be vague due to a fuzziness in how much of some property makes for a difference in ADJ-ness. The sorites examples I provide cannot be assimilated to cases of indiscriminability or fuzziness in relevant dimensions, standards, or measurement procedures. A revised degree-based semantics with semiorders, a well-studied threshold structure, is developed. The treatment of equatives captures the truth (...) of the claim that adjacent items in the sorites series are not relevantly distinguishable in ADJ-ness; and it avoids validating transitivities that would yield paradoxical conclusions. (shrink)

In this article, I analyze historical counterfactuals. Historical counterfactuals are conditional statements in which the antecedent refers to some change in the past. We ask what would have happened, had that change occurred. I discuss the nature of such counterfactuals. I then identify important functions that historical counterfactuals have. I point out that they are at the heart of explanations and, therefore, reveal issues related to contingency and actual history. I then discuss counterfactual reasoning in historiography. I argue that the (...) problem of suitable antecedent conditions has been exaggerated, and more serious issues concern the tracking of counterfactual scenarios. Throughout the paper, I argue that the interventionist way of thinking about historical counterfactuals clarifies both historical explanations and the nature of historical counterfactuals and should be adopted as the standard. I conclude by noting that historical counterfactuals may not fundamentally differ from more familiar forms of historiography. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably strict theorist faces a question: why do (...) we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

This book provides a fully developed account of Frank Ramsey's theory of conditionals. No proper study of Ramsey's view of conditionals has been carried out so far. This work aims at filling this gap. The book is divided in two parts and in four chapters. The first part of the book is historical, investigating Ramsey’s texts and recovering his view on conditionals. The second part is systematic, updating and developing a unified account of conditionals following Ramsey’s ideas.

Today there is a wealth of fascinating studies of connexive logical systems. But sometimes it looks as if connexive logic is still in search of a convincing interpretation that explains in intuitive terms _why_ the connexive principles should be valid. In this paper I argue that difference-making conditionals as presented in Rott (_Review of Symbolic Logic_ 15, 2022) offer one principled way of interpreting connexive principles. From a philosophical point of view, the idea of difference-making demands full, unrestricted connexivity, because (...) neither logical truths nor contradictions or other absurdities can ever ‘make a difference’ (i.e., be relevantly connected) to anything. However, difference-making conditionals have so far been only partially connexive. I show how the existing analysis of difference-making conditionals can be reshaped to obtain full connexivity. The classical AGM belief revision model is replaced by a conceivability-limited revision model that serves as the semantic base for the analysis. The key point of the latter is that the agent should never accept any absurdities. (shrink)

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the formif not-A,thenA, should not hold, since the conditional’s antecedentnot-Acontradicts its consequentA. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event$${A| \overline{A}}$$A|A¯is$${p(A| \overline{A})=0}$$p(A|A¯)=0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms (...) of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles:Aristotle’s theses,Aristotle’s Second Thesis,Abelard’s First Principle, andBoethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (likenon-symmetry). Both approaches satisfyminimalrequirements for a connexive logic. Finally, we compare both approaches conceptually. (shrink)

Indicative conditionals - e.g. ‘If I was born in Glasgow, then I was born in Scotland’ - seem to express propositions. In other words, they seem to express thoughts that can be shared and evaluated as either true or false. For the past hundred years or so, analytic philosophers have commonly interpreted them as equivalent to disjunctions, e.g. ‘Either I was not born in Glasgow, or I was born in Scotland’. Those who dig a little deeper tend to agree that (...) this is not quite right, but they often come to the conclusion that indicative conditionals do not express propositions at all. I argue for an alternative theory according to which indicative conditionals express a type of strict implication. What this means is that they are modal statements - e.g. ‘Necessarily, either I was not born in Glasgow, or I was born in Scotland’ - an idea that used to be quite popular despite striking many contemporary philosophers as radical. More specifically, I defend the idea that indicative conditionals express metaphysical necessity. I argue that this view respects our intuitions in an important way, and I show that it can be incorporated into a promising view of natural language conditionals more generally. Lastly, I argue that it also has plausible consequences for the related concepts of conditional probability, causal explanation, and risk. (shrink)

The article exposes (in brief) the theories of the counterfactuals in analytical philosophy (metalinguistic, ontological and suppositionist) and discusses the conditions of assertability of counterfactuals in historiography. The conviction of some historians that the counterfactuals are essentially forbidden in the scientific historiography is critised on the ground that counterfactuals are implied by the causal statements and statements of the relative causal importance. The admission is made that the traditional (historist) historiography lacks adequate conceptual infrastructure for the detailed analysis of the (...) objectively possible historical alternatives because its only method for validation of such analysis is inference by analogy. The procedure for validation of counterfactuals in economtric history is discussed citing as an exemple the work of Robert Fogel about the impact of the railroads on the economic growth in USA. The irrelevance of Jon Elster's "basic paradox of counterfactuals" for the working historian is asserted on the ground that as a matter of fact there is no empirical social theory capable to endogenize all initial conditions in explanatory arguments where it is instrumental for deduction of explanandum. (shrink)

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate (...) so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Báñezian Grounding for Counterfactuals of Creaturely Freedom:A Response to James Dominic Rooney, O.P.Taylor Patrick O'NeillIntroductionIn a recently published article, James Rooney, O.P., critiques a fundamental aspect of Réginald Garrigou-Lagrange's articulation of the relation between divine causality and creaturely freedom, which I also defended in my recent book.1 Specifically, Rooney argues that at least some of what Garrigou-Lagrange holds is rooted in a Molinist rather than Báñezian understanding of (...) human freedom and divine causality. The aim of this paper is to articulate the basic objections raised by Rooney and to show why the objections fail. We shall not provide an exegetical or textual analysis of Báñez himself, but rather will establish a speculative grounding and agreement between basic principles of Báñezianism and Garrigou-Lagrange's articulation, ultimately affirming the necessity of positing creaturely counterfactuals for Báñezianism.Rooney makes two distinct (but related) objections to Garrigou-Lagrange's treatment. First, he claims that Báñezianism as a system rejects the notion of "alternative possibilities" when considering the creaturely will and its relation to divine causality, especially in regard to physical premotion. I shall argue that this is incorrect, and indeed misses one of the constitutive elements of Báñezianism—in fact the very grounding for its claim that infallibly moved actions remain free. Second, Rooney claims that Garrigou-Lagrange posits [End Page 651] a circular argument regarding the reality of sin. Garrigou-Lagrange's argument would be circular if it corresponded to a single order of causality or if counterfactuals of creaturely freedom were incompatible with Báñezianism. But we shall argue that they are not. As such, the argument is not only not circular, but rather elucidates a constitutive element of the Báñezian system, thereby refuting the objection. In short, Garrigou-Lagrange's articulation of Báñezian premotion admits of counterfactuals without relying upon divine passivity, and it remains internally coherent.Rooney's Critique of the So-called "Garrigou Manoeuvre"Rooney begins the essay by outlining a few of the major differences between a Molinist and Báñezian view of human freedom. Rooney's argument is that there is a potential "grounding problem" for Báñezianism, or at least for Báñezianism as articulated by Garrigou-Lagrange. As Rooney notes, Báñezianism posits that God's efficacious grace is ontologically antecedent to our good actions (and his permission of sin is ontologically antecedent to our sin). But how does this position retain free choice, if divine causation or permission is infallibly determinative and antecedent to creaturely choice? Rooney says:The Banezians need to account for how it is possible that a creature can do otherwise in the special case when God moves the creature to act through grace. Specifically, what grounds the truth of the claim that, even when God determines human free choices from eternity such that a human being has only one course of action open to them, those human beings are morally responsible for their actions? If the Banezian view entails that human beings, acting under grace, strictly lack any ability to do otherwise, then the view is incoherent.2As such, we can see that "the ability to do otherwise" is an essential, grounding element for defending Báñezianism against radically compatibilist or double-predestinarian views of human freedom, which have been condemned by the Church at Trent and in subsequent condemnations of Jansenism.3 Of course, the phrase "ability to do otherwise" is metaphysically [End Page 652] ambiguous, which Rooney admits. Various articulations of a more metaphysically precise grounding for the preservation of free choice under the influence of efficacious grace (or while efficacious grace is withheld) have been put forth, and Rooney focuses on a particular "strategy" which he associates with Garrigou-Lagrange and myself.4 He terms this strategy the "Garrigou Manoeuvre."Rooney notes that "Garrigou-Lagrange claims that there is something in virtue of which God denies someone efficacious grace, and that this is in the control of the sinner."5 He quotes Garrigou-Lagrange as saying that a person "is deprived of efficacious grace because by sinning he resists sufficient grace.... [Therefore,] God... (shrink)

Timothy Williamson contends that our primary cognitive heuristic for prospectively assessing conditionals, i.e., the suppositional procedure, is provably inconsistent. Our diagnosis is that stipulations about the nature of suppositional rejection are the likely source of these results. We show that on at least one alternative, and quite natural, understanding of the suppositional attitudes, the inconsistency results are blocked. The upshot is an increase in the reliability of our suppositional heuristics across a wider range of contexts. One interesting consequence of the (...) increased reliability is a proportional decrease in the plausibility of an error-theory that Williamson employs against widespread intuitions about the truth values of counterpossible conditionals. (shrink)

This paper concerns the semantics of coordinated if-clauses, as in (1)-(2). It is argued that the meanings of such sentences are explained straightforwardly on theories of conditionals that tie their non- monotonic behaviour to the if-clause itself (e.g. Schlenker 2004, but not theories that tie it to a (covert) modal operator (e.g. Kratzer 1981; 1991). Coordinated if-clauses are revealing of the fine-grained compositional semantics of conditionals.

It has been more than sixty years since R. D. Collison Black published his Economic Thought and the Irish Question, a book which ever since has been widely regarded as a classic in the history of e...

Kevin Dorst (2019) uses the ‘manifest unassertability’ of conditionals of the form ‘If I don’t know p, then p’ as a new motivation for the KK thesis. In this paper we show that his argumentation is misguided. Plausible heuristics offer a compelling and nuanced explanation of the relevant infelicity data. Meanwhile, Dorst relies on tools that, quite independently of KK, turn out to be rather poor predictors of the infelicity of indicative conditionals.