Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

This paper discusses comparison classes—sets that relativize the interpretation of gradable adjectives, often specified with for-clauses as in John is smart for a linguist. Such a discussion ultimately lends support to the thesis that scales, degrees, measure functions, and linear orders are grammatically derived from more basic relations between individuals. Three accounts of comparison classes are compared and evaluated. The first proposes that such classes serve as an argument to a function that determines a standard of comparison. The second maintains (...) that these classes restrict the domain of a measure function used to map entities to degrees. The third proposes that these classes limit the kind of individuals that participate in a binary relation; this relation is then used in the construction of a scale and a measure function. It is this third account that is most consistent with the empirical data. It can explain how comparison classes fix a standard of comparison, induce presuppositions concerning the comparative subjects, and induce incommensurability in comparative constructions. (shrink)

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

I propose that the meanings of vague expressions render the truth conditions of utterances of sentences containing them sensitive to our interests. For example, 'expensive' is analyzed as meaning 'costs a lot', which in turn is analyzed as meaning 'costs significantly greater than the norm'. Whether a difference is a significant difference depends on what our interests are. Appeal to the proposal is shown to provide an attractive resolution of the sorites paradox that is compatible with classical logic and semantics.

The mathematical theory of communication.

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Herbert Clark argues that language use is more than the sum of a speaker speaking and a listener listening. It is the joint action that emerges when speakers and listeners, writers and readers perform their individual actions in coordination, as ensembles. In contrast to work within the cognitive sciences, which has seen language use as an individual process, and to work within the social sciences, which has seen it as a social process, the author argues strongly that language use embodies (...) both individual and social processes. (shrink)

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)

In this paper, we provide a comprehensive survey of the space of possible analyses of the phenomenon of quantifier domain restriction, together with a set of considerations which militate against all but our own proposal. Among the many accounts we consider and reject are the ‘explicit’ approach to quantifier domain restric‐tion discussed, for example, by Stephen Neale, and the pragmatic approach to quantifier domain restriction proposed by Kent Bach. Our hope is that the exhaustive discussion of this special case of (...) context‐dependence will provide guidelines for how to decide, for an arbitrary case of context‐dependent discourse, whether it should be treated syntactically, semantically, or pragmatically. (shrink)

Sorites arguments employ an induction step such as ‘Small numbers have small successors’. People deduce that there must be an exception to the generalization but are reluctant to conclude that the generalization is false. My hypothesis is that the reluctance is due to the "Generic Overgeneralization Effect". Although the propounder of the sorites paradox intends the induction step to be a universal generalization, hearers assimilate universal generalizations to generic generalizations (for instance, ‘All birds fly’ tends to be remembered as ‘Birds (...) fly’). Most generic generalizations tolerate exceptions – especially when those exceptions are rare, abnormal, or difficult to imagine. Any counterexample to the induction step will have all of these features. (shrink)

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B p|E (T), for (...) every E such that p(E) > 0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The "Lockean" rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1-2):221-262, 1975; Alchourrón et al., J Symb Log 50:510-530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987). (shrink)

_ Convention_ was immediately recognized as a major contribution to the subject and its significance has remained undiminished since its first publication in 1969. Lewis analyzes social conventions as regularities in the resolution of recurring coordination problems-situations characterized by interdependent decision processes in which common interests are at stake. Conventions are contrasted with other kinds of regularity, and conventions governing systems of communication are given special attention.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept label (...) can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept label (...) can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

A speaker often decides whether or not to saysomething based on his assessment of the impact itwould have on his hearer's beliefs. If he thinks itwould bring them more in line with the truth, he saysit; otherwise he does not. In this paper, I developa model of these judgments, focusing specifically onthose of vague sentences. Under the simplifyingassumption that an utterance only conveys a speaker'sapplicability judgments, I present a Bayesian model ofan utterance's impact on a hearer's beliefs. Fromthis model I (...) derive a model of a speaker's judgment ofwhether or not an utterance would be informative. Iillustrate it with several examples of judgments ofvague and non-vague sentences. For instance, I showthat it models the common judgment that assertingeither ``George is tall'' or ``George is not tall'' wouldbe misleading if George were borderline tall, butasserting ``George is tall and he isn't tall'' would notbe. (shrink)

This paper investigates the way that linguistic expressions influence vagueness, focusing on the interpretation of the positive (unmarked) form of gradable adjectives. I begin by developing a semantic analysis of the positive form of ‘relative’ gradable adjectives, expanding on previous proposals by further motivating a semantic basis for vagueness and by precisely identifying and characterizing the division of labor between the compositional and contextual aspects of its interpretation. I then introduce a challenge to the analysis from the class of ‘absolute’ (...) gradable adjectives: adjectives that are demonstrably gradable, but which have positive forms that relate objects to maximal or minimal degrees, and do not give rise to vagueness. I argue that the truth conditional difference between relative and absolute adjectives in the positive form stems from the interaction of lexical semantic properties of gradable adjectives—the structure of the scales they use—and a general constraint on interpretive economy that requires truth conditions to be computed on the basis of conventional meaning to the extent possible, allowing for context dependent truth conditions only as a last resort. (shrink)

The Montagovian hypothesis of direct model-theoretic interpretation of syntactic surface structures is supported by an account of the semantics of binding that makes no use of variables, syntactic indices, or assignment functions & shows that the interpretation of a large portion of so-called variable-binding phenomena can dispense with the level of logical form without incurring equivalent complexity elsewhere in the system. Variable-free semantics hypothesizes local interpretation of each surface constituent; binding is formalized as a type-shifting operation on expressions that denote (...) functions, & sentences containing a free pronoun are analyzed as a function from individuals to propositions having a meaning of type (e,t). Standard weak crossover effects & binding patterns in sentences with multiple pronouns are shown to submit to straightforward type-theoretic treatments that do not rely on indexation. The variable-free semantics smoothly implements full surface compositionality & requires less machinery than standard accounts to handle functional questions, their answers, sloppy inferences, & across-the-board binding. 73 References. J. Hitchcock. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

Is language understanding a special case of social cognition? To help evaluate this view, we can formalize it as the rational speech-act theory: Listeners assume that speakers choose their utterances approximately optimally, and listeners interpret an utterance by using Bayesian inference to “invert” this model of the speaker. We apply this framework to model scalar implicature (“some” implies “not all,” and “N” implies “not more than N”). This model predicts an interaction between the speaker's knowledge state and the listener's interpretation. (...) We test these predictions in two experiments and find good fit between model predictions and human judgments. (shrink)

The paper is in two parts. In Part I, a semantics for embedded and query uses of interrogatives is put forward, couched within a situation semantics framework. Unlike many previous analyses,questions are not reductively analysed in terms of their answers. This enables us to provide a notion of ananswer that resolves a question which varies across contexts relative to parameters such as goals and inferential capabilities. In Part II of the paper, extensive motivation is provided for an ontology that distinguishes (...) propositions, questions, and facts, while at the same time the semantics provided captures an important commonality between questions and propositions: factsprove propositions andresolve questions. This commonality is exploited to provide an explanation for why predicates such as know carry presuppositions such as factivity and for a novel account of the behaviour of adverbially modified predicates with interrogative, declarative and fact-nominal arguments. (shrink)

CHAPTER 1. INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, ...

We present an argument for revising the theory of alternatives for Scalar Implicatures and for Association with Focus. We argue that in both cases the alternatives are determined in the same way, as a contextual restriction of the focus value of the sentence, which, in turn, is defined in structure-sensitive terms. We provide evidence that contextual restriction is subject to a constraint that prevents it from discriminating between alternatives when they stand in a particular logical relationship with the assertion or (...) the prejacent, a relationship that we refer to as symmetry. Due to this constraint on contextual restriction, discriminating between alternatives in cases of symmetry becomes the task of focus values. This conclusion is incompatible with standard type-theoretic definitions of focus values, motivating our structure-sensitive definition instead. (shrink)

Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (shrink)

Are people rational? This question was central to Greek thought and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus (...) of certain reasoning. (shrink)

This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horn's masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the book's original publication.

Book synopsis: Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms-such as "tall", "red", "bald", and "tadpole"—have borderline cases ; and they lack well-defined extensions. The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate. Another striking problem to which vagueness gives rise is the sorites paradox. If you remove one grain from a heap of (...) sand, surely you must be left with a heap. Yet apply this principle repeatedly as you remove grains one by one, and you end up, absurdly, with a solitary grain that counts as a heap. This anthology collects papers in the field. After an introduction that surveys the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent current work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity. (shrink)