Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...

Robert Stalnaker explores the contexts in which speech takes place, the ways we represent them, and the roles they play in explaining the interpretation and dynamics of speech. His central thesis is the autonomy of pragmatics: the independence of theory about structure and function of discourse from theory about mechanisms serving those functions.

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

The Taming of the True poses a broad challenge to realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant argues compellingly that every truth is knowable, and that an effective logical system can be based on this principle. He lays the foundations for global semantic anti-realism and extends its consequences from the philosophy of mathematics and logic to the theory of meaning, metaphysics, and epistemology.

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this book, making it the fullest and most authoritative treatment of the subject.

Wolfgang Spohn presents the first full account of the dynamic laws of belief, by means of ranking theory. This book is his long-awaited presentation of ranking theory and its ramifications.

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes of anaphora (...) resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

This article rebuts Ramsey's earlier theory, in 'Universals of Law and of Fact', of how laws of nature differ from other true generalisations. It argues that our laws are rules we use in judging 'if I meet an F I shall regard it as a G'. This temporal asymmetry is derived from that of cause and effect and used to distinguish what's past as what we can know about without knowing our present intentions.

This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...) presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists. (shrink)

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology (...) and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

Conditionals are sentences of the form 'If A, then B', and they play a central role in scientific, logical, and everyday reasoning. They have been in the philosophical limelight for centuries, and more recently, they have been receiving attention from psychologists, linguists, and computer scientists. In spite of this, many key questions concerning conditionals remain unanswered. While most of the work on conditionals has addressed semantical questions - questions about the truth conditions of conditionals - this book focuses on the (...) main epistemological questions that conditionals give rise to, such as: what are the probabilities of conditionals? When is a conditional acceptable or assertable? What do we learn when we receive new conditional information? In answering these questions, this book combines the formal tools of logic and probability theory with the experimental approach of cognitive psychology. It will be of interest to students and researchers in logic, epistemology, and psychology of reasoning. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that (i)utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) standard Bayesian conditionalization, (ii) is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, (iii) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (iv) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (shrink)

This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates or (...) graduates, but also of interest to professional philosophers. There are well-thought-out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means, it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature. (shrink)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

More than a decade of research has found strong evidence for P(if A, then C) = P(C|A) (“the Equation”). We argue, however, that this hypothesis provides an overly simplified picture due to its inability to account for relevance. We manipulated relevance in the evaluation of the probability and acceptability of indicative conditionals and found that relevance moderates the effect of P(C|A). This corroborates the Default and Penalty Hypothesis put forward in this paper. Finally, the probability and acceptability of concessive conditionals (...) (“Even if A, then still C”) were investigated and it was found that the Equation provides a better account of concessive conditionals than of indicatives across relevance manipulations. (shrink)

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as (...) well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content. (shrink)

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (...) (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities. (shrink)

The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process (...) of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases. (shrink)

The new paradigm in the psychology of reasoning adopts a Bayesian, or prob- abilistic, model for studying human reasoning. Contrary to the traditional binary approach based on truth functional logic, with its binary values of truth and falsity, a third value that represents uncertainty can be introduced in the new paradigm. A variety of three-valued truth table systems are available in the formal literature, including one proposed by de Finetti. We examine the descriptive adequacy of these systems for natural language (...) indicative condi- tionals and bets on conditionals. Within our framework the so-called “defective” truth table, in which participants choose a third value when the antecedent of the indicative conditional is false, becomes a coherent response. We show that only de Finetti’s system has a good descriptive fit when uncer- tainty is the third value. (shrink)

The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well. In this paper a particular notion of dependence is proposed. It is shown that under both a forward causal and a backward evidential reading of the conditional, this appropriateness condition reduces to conditional probability under some natural circumstances. Because this is in particular the case for the so-called diagnostic reading of the conditional, this analysis might help (...) to explain some of Douven and Verbrugge’s empirical observations. (shrink)

This paper examines precursors and consequents of perceived relevance of a proposition A for a proposition C. In Experiment 1, we test Spohn's assumption that ∆P = P − P is a good predictor of ratings of perceived relevance and reason relations, and we examine whether it is a better predictor than the difference measure − P). In Experiment 2, we examine the effects of relevance on probabilistic coherence in Cruz, Baratgin, Oaksford, and Over's uncertain “and-to-if” inferences. The results suggest (...) that ∆P predicts perceived relevance and reason relations better than the difference measure and that participants are either less probabilistically coherent in “and-to-if” inferences than initially assumed or that they do not follow P = P. Results are discussed in light of recent results suggesting that the Equation may not hold under conditions of irrelevance or negative relevance. (shrink)

In this study we investigate the influence of reason-relation readings of indicative conditionals and ‘and’/‘but’/‘therefore’ sentences on various cognitive assessments. According to the Frege-Grice tradition, a dissociation is expected. Specifically, differences in the reason-relation reading of these sentences should affect participants’ evaluations of their acceptability but not of their truth value. In two experiments we tested this assumption by introducing a relevance manipulation into the truth-table task as well as in other tasks assessing the participants’ acceptability and probability evaluations. Across (...) the two experiments a strong dissociation was found. The reason-relation reading of all four sentences strongly affected their probability and acceptability evaluations, but hardly affected their respective truth evaluations. Implications of this result for recent work on indicative conditionals are discussed. (shrink)

We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given (...) a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds (...) that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals. (shrink)

It is argued that the "inner" negation $\mathord{\sim}$ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: $\mathord{\sim}$ is read '$A$ is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g., "If Jim went to the party he had a (...) good time"). It is shown that the logic induced by the semantics shares many familiar properties with classical negation, but is orthogonal to both intuitionistic and classical negation: it differs from both in validating the inference from $A \rightarrow \nega B$ to $\nega(A\rightarrow B)$ to. (shrink)

entry for the Entry for the Stanford Encyclopedia of Philosophy, 2007.