Conditionals

The paper defends an account of the context-sensitivity of norms that draws on the resources of counterfactual conditionals. The account combines two assumptions: the assumption that permission is rule-abiding performance in some contextually relevant situations; and the assumption that the contextually relevant situations are picked out by the mechanism that selects the possible worlds relevant for the evaluation of counterfactual conditionals. The account explains the non-monotonicity of permissions and solves a puzzle, raised by Timothy Williamson, about the seeming failure of (...) permissions to distribute over conjunction. In the domain of epistemic norms, the account solves an analogous puzzle and deals successfully with so-called blindspot propositions. (shrink)

In this paper, I defend an updated account of functional kinds, initially presented by Daniel Weiskopf, from the criticism that functional kinds will not qualify as scientific kinds. An important part of Weiskopf’s account is that functional kinds are multiply realisable. The criticisms I consider avoid discussion of multiple realisability. Instead, it is argued that functional kinds carry inferior counterfactual profiles when compared to other accounts of kinds. I respond to this charge by arguing that this criticism fails to take (...) into consideration the role that multiple realisability can play in providing important explanatory counterfactuals. I do so by highlighting some points made by Lauren Ross that highlight where multiple realisability is explanatorily pertinent. I then argue that the criticisms of Weiskopf’s account fail to establish the explanatory inferiority of functional kinds. (shrink)

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

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...) outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (shrink)

This paper is on the problem of profligate omissions. The problem is that counterfactual definitions of causation identify as a cause anything that could have prevented an effect but that did not actually occur, which is a highly counterintuitive result. Many solutions of this problem appeal to normative, epistemic, pragmatic, or metaphysical considerations. These existing solutions are in some sense substantive. In contrast, this paper concentrates on the semantics of counterfactuals. I propose to replace Strong Centering with Weak Centering. This (...) allows that the actual world is not the only world that is closest to the actual world. As a result, some counterfactuals that would otherwise have been true, turn out to be false. When these counterfactuals concern causation, fewer causal claims are true. In addition to describing steps towards solving the problem of profligate omissions, the proposal captures an abstraction that is shared by many of the existing solutions: depending on how the distance ordering underlying the Weak Centering condition is constructed and interpreted, some of these existing solutions can be recovered. (shrink)

In natural language, conditionals are frequently used for giving explanations. Thus the antecedent of a conditional is typically understood as being connected to, being relevant for, or providing evidential support for the conditional's consequent. This aspect has not been adequately mirrored by the logics that are usually offered for the reasoning with conditionals: neither in the logic of the material conditional or the strict conditional, nor in the plethora of logics for suppositional conditionals that have been produced over the past (...) 50 years. In this paper I survey some recent attempts to come to terms with the problem of encoding evidential support or relevance in the logic of conditionals. I present models in a qualitative-modal and in a quantitative-probabilistic setting. Focussing on some particular examples, I show that no perfect match between the two kinds of settings has been achieved yet. (shrink)

This book presents and develops inferential expressivism, a novel approach to the study of meaning which combines elements of the expressivist and inferentialist programmes. Expressivists explain the meaning of words in terms of the attitudes that they are used to express; inferentialists explain the meaning of words in terms of the inferences that they are used to draw. The book lays out the philosophical foundations of inferential expressivism by articulating and defending the view that the meaning of an expression is (...) to be explained in terms of the inferences we draw involving the attitudes we express. The book, moreover, lays out the logical foundations of inferential expressivism by showing how to implement the view rigorously by means of novel formal systems which can deal with a variety of speech acts. As the book shows, by joining forces expressivism and inferentialism can meet their key challenges whilst retaining their distinctive insights and advantages. The book goes on to demonstrate the fruitfulness of the inferential expressivist approach to meaning by applying it to a diverse range of linguistic phenomena, including epistemic modals, probability operators, conditionals, moral predicates, the truth predicate, and propositional attitude predicates. (shrink)

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' (...) uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional \(p{{\,\mathrm{\hookrightarrow }\,}}q\) is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

Conditional constructions (if–then) enable us to express our thoughts about possible states of the world, and they form an important ingredient for our reasoning and argumentative capabilities. Different types and argumentative uses have been distinguished in the literature, but their applicability to actual language use is rarely evaluated. This paper focuses on the reliability of applying classifications of connections between antecedents and consequents of conditionals to discourse, and three issues are identified. First, different accounts produce incompatible results when applied to (...) language data. Second, a discrepancy between theory and data was observed in previous studies, which sometimes discard existing classifications for being detached from actual language use. Finally, language users construct various cognitive relations between clauses of conditionals without being able to rely on overt linguistic features, which poses problems for the annotation of conditionals in argumentation and discourse. This paper addresses these issues by means of comparing theoretical types and actual uses of conditionals, by inspecting the dispersion of types in natural-language corpora, and by conducting an experiment in which the inter-rater reliability of classifications was assessed. The results show that the reliability of classifications of conditionals when applied to language data is low. With respect to the aforementioned issues, different classifications produced incompatible results, a discrepancy between theory and data was indeed observed, and low reliability scores indicated a largely interpretative nature of types of conditionals. Given these results, suggestions for the enhancement of reliability in corpus studies of conditionals and beyond are provided to enhance future classification design. (shrink)

We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as (...) infinitely many ways that a sentence might receive both classical truth values in the latter. In order to obtain deductive systems that are very nearly classical, we need to utilize different conditionals (and different negations) in each logic. (shrink)

Conditionals with conditional constituents pose challenges for _the Thesis_, the idea that the probability of a conditional is the corresponding conditional probability. This note is concerned with two proposals for overcoming those challenges, both inspired by early work of van Fraassen: the _Bernoulli Semantics_ associated with Stalnaker and Jeffrey, and augmented with a mechanism for obtaining “local probabilities” by Kaufmann; and a proposal by Bacon which I dub _Ordinal Semantics_. Despite differences in mathematical details and emphasis of presentation, both proposals (...) lend themselves for use as a basis for a modal-theoretic interpretation of embedded conditionals. The goal of this note is to compare the two frameworks by implementing a model for the interpretation of conditionals in each, based on the same underlying probability model for non-conditional sentences. I show that in the Ordinal model, certain sentences are assigned probabilities that do not accord with intuitions. This problem is familiar from the literature on Bernoulli models and can be addressed by introducing Kaufmann-style local probabilities into Ordinal models. I then show that Bernoulli Semantics has other limitations, in that it assigns probabilities in violation of the Thesis to certain very complex formulas. The upshot is that a fusion of the theories may be our best shot at getting the predictions right. (shrink)

It can often seem like the attitude we hold towards a conditional should be our attitude in the consequent on the supposition of the antecedent. Following by Williamson (Suppose and Tell: The Semantics and Heuristics of Conditionals. Oxford University Press, 2020), we call this The suppositional rule (SR). The Adams-style non-propositional theories of indicatives upholds some key implications of SR, allowing, for instance, our credence in a conditional to be the probability of the consequent given the antecedent. Williamson (Suppose and (...) Tell: The Semantics and Heuristics of Conditionals. Oxford University Press, 2020) has recently provided a series of inconsistency arguments against SR. He thereby intends to undermine non-propositional views as well as other rivals to his favoured material conditional account. I outline a strategy which theorists of all stripes can employ to avoid Williamson’s arguments. I then show how non-propositionalists can implement this strategy. I show how they can uphold SR when it is intuitively compelling, whilst allowing it to fail when it is not. (shrink)

We put forth an account for when to believe causal and evidential conditionals. The basic idea is to embed a causal model in an agent’s belief state. For the evaluation of conditionals seems to be relative to beliefs about both particular facts and causal relations. Unlike other attempts using causal models, we show that ours can account rather well not only for various causal but also evidential conditionals.

Philosophical statements are often suppositions. Gottfried Wilhelm Leibniz proposes in Nouveaux Essais sur l’entendement humain, 1704, a method of the construction of assertive conditionals occurring between any philosophical suppositions. If we can infer a philosophical statement from any suppositions then the implication between these suppositions and the obtained statement is assertive. In the article, some examples of the application of Leibniz’s method are considered.

In this paper, I investigate whether the intuitions that make connexive logics seem plausible might lie in pragmatic phenomena, rather than the semantics of conditional statements. I conclude that pragmatics indeed underwrites these intuitions, at least for indicative statements. Whether this has any effect on logic choice (and what that effect might be), however, heavily depends on one’s semantic theory of conditionals and on how one chooses to logically treat pragmatic failures.

Logical connectives (otherwise known as 'logical constants' or 'logical particles') have seemed challenging to philosophers of language. This article gives a concise account of logical connectives.

This note presents a very brief history of the observation that the probability of the material conditional A⊃B is in general different from, but cannot be less than, the conditional probability of B given A. The difference between the two probabilities is significant for the interpretation of conditionals and for the possibility of inductive probability. It can be quantitatively specified in so-called ‘excess laws’ for which Popper appears to have claimed priority. I argue that such a priority claim should be (...) rejected and credit should instead be given, if to anyone, to Boole and Reichenbach instead. (shrink)

Conditional statements are ubiquitous, from promises and threats to reasoning and decision making. By now, logicians have studied them from many different angles, both semantic and proof-theoretic. This paper suggests two more perspectives on the meaning of conditionals, one dynamic and one geometric, that may throw yet more light on a familiar and yet in some ways surprisingly elusive and many-faceted notion.1.

"This book is the first of two volumes on belief and counterfactuals. It consists of six of a total of eleven chapters. The first volume is concerned primarily with questions in epistemology and is expository in parts. Among others, it provides an accessible introduction to belief revision and ranking theory. Ranking theory specifies how conditional beliefs should behave. It does not tell us why they should do so nor what they are. This book fills these two gaps. The consistency argument (...) tells us why conditional beliefs should obey the laws of ranking theory by showing them to be the means to attaining the end of holding true and informative beliefs. The conditional theory of conditional belief tells us what conditional beliefs are by specifying their nature in terms of non-conditional belief and counterfactuals. In addition, the book contains several novel arguments, accounts, and applications. These include an argument for the thesis that there are only hypothetical imperatives and no categorical imperatives; an account of the instrumentalist understanding of normativity, or rationality, according to which one ought to take the means to one's ends; as well as solutions to the problems of conceptual belief change, logical learning, and learning conditionals. A distinctive feature of the book is its unifying methodological approach: means-end philosophy. Means-end philosophy takes serious that philosophy is a normative discipline, and that philosophical problems are entangled with each other. It also explains the importance of logic to philosophy, without being a technical theory itself"--. (shrink)

Moritz Schulz explores counterfactual thought and language: what would have happened if things had gone a different way. Counterfactual questions may concern large scale derivations or small scale evaluations of minor derivations. A common impression, which receives a thorough defence in the book, is that oftentimes we find it impossible to know what would have happened. However, this does not mean that we are completely at a loss: we are typically capable of evaluating counterfactual questions probabilistically: we can say what (...) would have been likely or unlikely to happen. Schulz describes these probabilistic ways of evaluating counterfactual questions and turns the data into a novel account of the workings of counterfactual thought. (shrink)

The book is mainly concerned with the problem of the logical analysis of hypothetical (conditional) statements.

What are counterfactuals and what is their point? In many cases, none at all. It may be true that if kangaroos didn't have tails, they would fall over, but they do have tails and if they didn't they wouldn't be kangaroos (or would they?). This is the sort of thing that can give counterfactuals a bad name, as inhabitants of a La La Land of the mind. On the other hand, counterfactuals do useful service across a broad range of disciplines (...) in both the sciences and the humanities, including philosophy, history, cosmology, biology, cognitive psychology, jurisprudence, economics, art history, literary theory. They are also richly, albeit sometimes treacherously, present in the everyday human realm of how our lives are both imagined and lived: in the 'crossroads' scenario of decision-making, the place of regret in retrospective assessments of paths taken and not taken, and, at the outer limit, as the wish not to have been born. Christopher Prendergast take us on a dizzying exploratory journey through some of these intellectual and human landscapes, mobilizing a wide range of reference from antiquity to the present, and sustained by the belief that, whether as help or hindrance, and with many variations across cultures, counterfactual thinking and imagining are fundamental to what it is to be human. (shrink)

There is a vast class of things that science has so far almost entirely neglected. They are central to the understanding of physical reality both at an everyday level and at the level of the most fundamental phenomena in physics, yet have traditionally been assumed to be impossible to incorporate into fundamental scientific explanations. They are facts not about what is--the actual--but about what could be: counterfactuals. According to physicist Chiara Marletto, laws about things being possible or impossible may generate (...) an alternative way of providing explanations. This fascinating, far-reaching approach holds promise for revolutionizing the way fundamental physics is formulated, but also for providing essential tools to face existing technological challenges, from delivering the next generation of information-processing devices, beyond the universal quantum computer, to designing AIs. Each chapter in the book delineates how an existing vexed open problem in science can be solved by this radically different approach; and it is augmented by short fictional stories that explicate the main point of the chapter. As Marletto demonstrates, contemplating what is possible can give us a more complete and hopeful picture of the physical world. (shrink)

This title introduces the concept of "if this, then that" in coding by using relatable real-world examples. Vivid photographs and easy-to-read text aid comprehension for early readers. Features include an infographic, fun facts, Making Connections questions, a glossary, and an index. QR Codes in the book give readers access to book-specific resources to further their learning.

In _Suppose and Tell_, Williamson makes a new case for the material conditional account. He tries to explain away apparently countervailing data by arguing that these have been misinterpreted because researchers have overlooked the role of heuristics in the processing of conditionals. Cases involving the receipt of apparently conflicting conditionals play an important dialectical role in Williamson’s book: they are supposed to provide evidence for the material conditional account as well as for the defeasibility of a key procedure underlying our (...) everyday assessments of conditionals. We argue that they can serve neither of these purposes and that Williamson overestimates the reach of heuristics. We specifically challenge Williamson’s assumption that, in the kind of cases centrally at issue in his book, the recipient of conflicting conditionals will typically accept those at face value, even granting Williamson that conditionals can be freely passed among speakers under normal conditions of testimony. (shrink)

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

One of the open questions in Bayesian epistemology is how to rationally learn from indicative conditionals (Douven, 2016). Eva et al. (Mind 129(514):461–508, 2020) propose a strategy to resolve this question. They claim that their strategy provides a “uniquely rational response to any given learning scenario”. We show that their updating strategy is neither very general nor always rational. Even worse, we generalize their strategy and show that it still fails. Bad news for the Bayesians.

Recent literature on Stalnaker's Thesis, which seeks to vindicate it from Lewis (1976)'s triviality results, has featured linguistic data that is prima facie incompatible with Conditionalization in iterated cases (McGee 1989, 2000; Kaufmann 2015; Khoo & Santorio, 2018). In a recent paper (2021), Goldstein & Santorio make a bold claim: they hold that these departures light the way to a new, non-conditionalizing theory of rational update.Here, I consider whether this new form of update is subject to a Dutch book. On (...) the official, invariantist version of the theory, I show that the answer is “yes”. On a competing, contextualist theory of indicative conditionals (Bacon, 2015), the answer is “no”, for reasons that have familiar connections to the limits of textbook Bayesianism. After presenting a concrete case, I explore the dialectical ramifications. The upshot is some hard choices for theories that seek to save the linguistic phenomena. (shrink)

Deriving ethical conclusions from arguments that rely heavily on metaphysical foundations, as Parfit (1984) does in generating his Nonidentity Problem, is an approach fraught with problems. Sparrow...

Researchers, clinicians, and patients have good reasons for wanting answers to causal questions of disease and therapeutic intervention. This paper uses microbiologist Robert Koch’s pioneering work and famous postulates to extrapolate a logical sequence of evidence for confirming the causes of disease: association between individuals with and without a disease; isolation of causal agents; and the creation of a counterfactual. This paper formally introduces counter-counterfactuals, which appear to have been used, perhaps intuitively, since the time of Koch and possibly earlier. (...) An argument is presented that counter-counterfactuals are a useful tool for identifying necessary causes of disease, and sometimes must be used in place of isolation which is not always possible. In addition, a logical sequence of causal evidence for a therapeutic intervention is presented: creating a counterfactual, comparisons between subjects in receipt of treatment versus those who are not, and counter-counterfactuals. (shrink)

We present a method that generates two-sided sequent calculi for four-valued logics like "first degree entailment" (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators are truth-functional over the four truth-values 'none', 'false', 'true', and 'both', where 'true' and 'both' are designated.) First, we show that for every n-ary operator * every truth table entry f*(x1,...,xn) = y can be characterized in terms of a (...) pair of sequent rules. Secondly, we use these sequent rules to build sequent calculi and prove their completeness. With the help of two simplification procedures we then show that the 2⋅4^n sequent rules that characterize an n-ary operator can be systematically reduced to at most four sequent rules. Thirdly, we use our method to investigate the proof-theoretical consequences of including intuitive truth-functional implications in FDE-like logics. (shrink)

Claro R. Ceniza [1927-2001] is arguably one of the best philosophers that the Philippines has ever produced. However, it is quite unfortunate that some of his important contributions are not that well-known. This paper aims to rectify this by presenting an evaluation of his original insights on three outstanding problems in philosophy, viz., the paradoxes of material implication, the nature of probability, and the metaphysics of modality.