In the 1960’s, both Montague (e.g. 1970, 222) and Grice (1975, 24) famously declared that natural languages were not so different from the formal languages of logic as people had thought. Montague sought to comprehend the grammars of both within a single theory, and Grice sought to explain away apparent divergences as due to the fact that the former, but not the latter, were used for conversation. But, if we confine our concept of logic to first order predicate logic (or (...) FOPL) with identity (that is, omitting everything which is not required for the pursuit of mathematical truth), then there are of course many other aspects, in addition to its use in conversation, which distinguish natural language from logic. Conventional implicature, information structure (including presupposition), tense and time reference, and the expression of causation and inference are several of these, which combine as well with syntactic complexities which are unnecessary in first order predicate logic. In this paper I will argue that such distinguishing aspects should be more fully exploited to explain the differences between the material conditional of logic and the indicative conditional of one natural language (English). (shrink)

Conditional promises and threats are speech acts that are used to manipulate other people's behaviour. Studies on human reasoning typically use propositional logic to analyse what people infer from such inducements. While this approach is sufficient to uncover conceptual features of inducements, it fails to explain them. To overcome this limitation, we propose a multilevel analysis integrating motivational, linguistic, deontic, behavioural, and emotional aspects. Commonalities and differences between conditional promises and threats on various levels were examined in two experiments. The (...) first shows that both types of inducements are understood as being complementary on the linguistic level, but not reversible, due to the specific temporal order of their actions. In addition, it gives a first assessment of emotional reactions. The second experiment investigated the novel question of whether complementary promises and threats, despite semantic differences, both imply an obligation to cooperate on the deontic level. The data corroborate this hypothesis, and they support various appraisal-theoretical assumptions on the elicitation of emotions. They also reveal that content affects not only the attribution of emotions, but also the deontic interpretation. (shrink)

Causal conditional reasoning means reasoning from a conditional statement that refers to causal content. We argue that data from causal conditional reasoning tasks tell us something not only about how people interpret conditionals, but also about how they interpret causal relations. In particular, three basic principles of people's causal understanding emerge from previous studies: the modal principle, the exhaustive principle, and the equivalence principle. Restricted to the four classic conditional inferences—Modus Ponens, Modus Tollens, Denial of the Antecedent, and Affirmation of (...) the Consequent—causal conditional reasoning data are only partially able to support these principles. We present three experiments that use concrete and abstract causal scenarios and combine inference tasks with a new type of task in which people reformulate a given causal situation. The results provide evidence for the proposed representational principles. Implications for theories of the na ve understanding of causality are discussed. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

In this paper I examine and question Marc Lange’s account of laws, and his claim that the law delineating the range of natural kinds of fundamental particle has a lesser grade of necessity that the laws connecting the fundamental properties of those kinds with their derived properties.

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief (...) and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. (shrink)

Conditionals that contain a modality in the consequent give rise to a particular semantic phenomenon whereby the antecedent of the conditional blocks possibilities when interpreting the modality in the consequent. This explains the puzzling logical behaviour of constructions like "If you don't buy a lottery ticket, you can't win", "If you eat that poison, it is unlikely that you will survive the day" and "If you kill Harry, you ought to kill him gently". In this paper it is argued that (...) a semantic version of the Ramsey Test provides a key in the analysis of such constructions. The logic for this semantics is axiomatized and some examples are studied, among them a well-known puzzle for contrary-to-duty obligations. (shrink)

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)

One of the main applications of the logic of theory change is to the epistemic analysis of conditionals via the so-called Ramsey test. In the first part of the present note this test is studied in the limiting case where the theory being revised is inconsistent, and it is shown that this case manifests an intrinsic incompatibility between the Ramsey test and the AGM postulate of success. The paper then analyses the use of the postulate of success, and a weakening (...) of it, generating axioms of conditional logic via the test, and it is shown that for certain purposes both success and weak success are quite superfluous. This suggests the proposal of abandoning both success and weak success entirely, thus permitting retention of the postulate of preservation discarded by Gärdenfors. (shrink)

The present study is part of recent attempts to specify the characteristics of the counterexample retrieval process during causal conditional reasoning. The study tried to pinpoint whether the retrieval of stored counterexamples (alternative causes and disabling conditions) for a causal conditional is completely automatic in nature or whether the search process also demands executive working memory (WM) resources. In Experiment 1, participants were presented with a counterexample generation task and a measure of WM capacity. We found a positive relation between (...) search efficiency, as measured by the number of generated counterexamples in limited time, and WM capacity. Experiment 2 examined the effects of a secondary WM load on the retrieval performance. As predicted, burdening WM with an attention-demanding secondary task decreased the retrieval efficiency. Both low and high spans were affected by the WM load but load effects were less pronounced for the most strongly associated counterexamples. Findings established that in addition to an automatic search component, the counterexample retrieval draws on WM resources. (shrink)

Work in progress — but after having all the main ideas in my head for at least 5 years now, I at least finally have a complete draft finished!

Work in progress. Will probably split into two papers, and then, perhaps, later, will be brought back together, along with other material, into something larger. (All this only if it works out OK!).

Conditionality is a modal feature (in only the trivial sense, in the case of the material conditional). For φ to be conditioned on ψ is for the appearance of φ and ψ to be connected in some way over some region of modal space.

Some philosophical positions maintain that some aspect of reality depends on human practices, cognitive attitudes or sentiments. This paper presents a framework for understanding such positions in a way that renders them immune to a number of natural but allegedly devastating objections.

I defend a formulation of the Ramsey Test with a condition for accepting negations of conditionals. It is implicit in the assumptions of the triviality theorems of Gärdenfors, Harper, and Lewis; and it allows for a unified proof of those theorems, from weaker assumptions about belief revision. This leads to a proof of McGee’s thesis that iterated conditionals do not obey modus ponens. †To contact the author, please write to: Institute of Philosophy, University of Leuven, Kardinaal Mercierplein 2, B‐3000 Leuven, (...) Belgium; e‐mail: etlin@alum.mit.edu. (shrink)

We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order (...) accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation. (shrink)

There are many ways in which language can describe the dependency of one occurrence on another and hence many varieties of conditional construction, including conditionals in ‘if’, ‘when’, ‘since’, and ‘as’, the absolutive conditionals of Stump (1985), and the correlative conditional construction (‘the more, the merrier’) discussed in Fillmore (1986). This paper will be concerned with investigating one species illustrated in (1a) and (1b).

Conditional sentences with quantifying expressions are systematically ambigous. In one reading, the if -clause restricts the domain of the overt quantifier; in the other, the if -clause restricts the domain of a covert quantifier, which defaults to epistemic necessity. Although the ambiguity follows directly from the Lewis- Kratzer line on if, it is not generally acknowledged, which has led to pseudoproblems and spurious arguments.

I’ll describe a range of systems for nonmonotonic conditionals that behave like conditional probabilities above a threshold. The rules that govern each system are probabilistically sound in that each rule holds when the conditionals are interpreted as conditional probabilities above a threshold level specific to that system. The well-known preferential and rational consequence relations turn out to be special cases in which the threshold level is 1. I’ll describe systems that employ weaker rules appropriate to thresholds lower than 1, and (...) compare them to these two standard systems. (shrink)