The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counterfactual probabilities--conditional probabilities where the condition has zero probability. (...) Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation. (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)

The aim is to motivate theoretically a relevance approach to conditionals in a comparative discussion of the main alternatives. In particular, it will be argued that a relevance approach to conditionals is better motivated than the suppositional theory currently enjoying wide endorsement. In the course of this discussion, an argument will be presented for why failures of the epistemic relevance of the antecedent for the consequent should be counted as genuine semantic defects. Furthermore, strategies for dealing with compositionality and the (...) perceived objective purport of indicative conditionals will be put forward. (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)

Coherence in conversations and in texts can be partially characterized by a set of coherence relations, motivated ultimately by the speaker's or writer's need to be understood. In this paper, formal definitions are given for several coherence relations, based on the operations of an inference system; that is, the relations between successive portions of a discourse are characterized in terms of the inferences that can be drawn from each. In analyzing a discourse, it is frequently the case that we would (...) recognize it as coherent, in that it would satisfy the formal definition of some coherence relation, if only we could assume certain noun phrases to be coreferential. In such cases, we will simply assume the identity of the entities referred to, in what might be called a “petty conversational implicature,” thereby solving the coherence and coreference problems simultaneously. Three examples of different kinds of reference problems are presented. In each, it is shown how the coherence of the discourse can be recognized, and how the reference problems are solved, almost as a by‐product, by means of these petty conversational implicatures. (shrink)

A conversational implicature is an inference that consists in attributing to a speaker an implicit meaning that goes beyond the explicit linguistic meaning of an utterance. This paper experimentallyinvestigates scalar implicature, a paradigmatic case of implicature in which a speaker's use of a term like Some indicates that the speaker had reasons not to use a more informative one from the samescale, e.g. All; thus, Some implicates Not all. Pragmatic theorists like Grice would predict that a pragmatic interpretation is determined (...) only after its explicit, logical meaning is incorporated (e.g. whereSome means at least one). The present work aims to developmentally unpack this prediction by showing how younger, albeit competent, reasoners initially treat a relatively weak term logically beforebecoming aware of its pragmatic potential. Three experiments are presented. Experiment 1 presents a modal reasoning scenario offering an exhaustive set of conclusions; critical among these isparticipants' evaluation of a statement expressing Might be x when the context indicates that the stronger Must be x is true. The conversationally-infelicitous Might be x can be understood logically(e.g. as compatible with Must) or pragmatically (as exclusive to must). Results from five-, seven-, and nine-year-olds as well as adults revealed that a) seven-year-olds are the youngest to demonstratemodal competence overall and that; b) seven- and nine-year-olds treat the infelicitous Might logically significantly more often than adults do. Experiment 2 showed how training with the modal taskcan suspend the implicatures for adults. Experiment 3 provides converging evidence of the developmental pragmatic effect with the French existential quantifier Certains (Some). Whilelinguistically-sophisticated children (eight- and ten-year-olds olds) typically treat Certains as compatible with Tous (All), adults are equivocal. These results, which are consistent with unanticipatedfindings in classic developmental papers, reveal a consistent ordering in which representations of weak scalar terms tend to be treated logically by young competent participants and morepragmatically by older ones. This work is also relevant to the treatment of scalar implicatures in the reasoning literature. (shrink)

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by (...) presenting data that cast doubt on an assumption underlying all triviality arguments. (shrink)

Over the last two decades, William Lycan’s work on the semantics of conditionals has been distinguished by his careful attention to the connection between syntax and semantics, and more generally by his impeccable methodology. Lycan takes compositionality seriously, so he requires that the meaning of compound expressions like ‘even if’ be a combination of the constituent expressions, here ‘even’ and ‘if’. After reading his work, it’s hard to take seriously work that does not share this methodology.

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)

Reasoning with conditionals is central to everyday life, yet there is long-standing disagreement about the meaning of the conditional. One example is the puzzle of so-called missing-link conditionals such as "if raccoons have no wings, they cannot breathe under water." Their oddity may be taken to show that conditionals require a connection between antecedent ("raccoons have no wings") and consequent ("they cannot breathe under water"), yet most accounts of conditionals attribute the oddity to natural language pragmatics. We present an experimental (...) study disentangling the pragmatic requirement of discourse coherence from a stronger notion of connection: probabilistic relevance. Results indicate that mere discourse coherence is not enough to make conditionals assertable. (shrink)

Conditionals whose antecedent and consequent are not somehow internally connected tend to strike us as odd. The received doctrine is that this felt oddness is to be explained pragmatically. Exactly how the pragmatic explanation is supposed to go has remained elusive, however. This paper discusses recent philosophical and psychological work that attempts to account semantically for the apparent oddness of conditionals lacking an internal connection between their parts.

ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical (...) expressions and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, the rate of conjunction fallacy was consistently low (not exceeding 20%,.. (shrink)

Three experiments investigated the processing of the implicature associated with some using a “gumball paradigm.” On each trial, participants saw an image of a gumball machine with an upper chamber with 13 gumballs and an empty lower chamber. Gumballs then dropped to the lower chamber and participants evaluated statements, such as “You got some of the gumballs.” Experiment 1 established that some is less natural for reference to small sets and unpartitioned sets compared to intermediate sets. Partitive some of was (...) less natural than simple some when used with the unpartitioned set. In Experiment 2, including exact number descriptions lowered naturalness ratings for some with small sets but not for intermediate size sets and the unpartitioned set. In Experiment 3, the naturalness ratings from Experiment 2 predicted response times. The results are interpreted as evidence for a Constraint-Based account of scalar implicature processing and against both two-stage, Literal-First models and pragmatic Default models. (shrink)

This paper addresses the question of whether the appearance ofthen in a conditional construction has any effect on the meaning of the sentence as a whole. It will be suggested thatthen does make a contribution by way of a particular presupposition associated with it. This also results inthen sometimes conflicting with the intended meaning of the sentence; in such cases its appearance is precluded. Certain aspects of the syntax ofthen will be discussed in parallel.

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.