An investigation into the online processing of counterfactual and indicative conditionals

The ability to represent conditional information is central to human cognition. In two self-paced reading experiments we investigated how readers process counterfactual conditionals (e.g., If Darren had been athletic, he could probably have played on the rugby team) and indicative conditionals (e.g., If Darren is athletic, he probably plays on the rugby team). In Experiment 1 we focused on how readers process counterfactual conditional sentences. We found that processing of the antecedent of counterfactual conditionals was rapidly constrained by prior context (i.e., knowing whether Darren was or was not athletic). A reading-time penalty was observed for the critical region of text comprising the last word of the antecedent and the first word of the consequent when the information in the antecedent did not fit with prior context. In Experiment 2 we contrasted counterfactual conditionals with indicative conditionals. For counterfactual conditionals we found the same effect on the critical region as we found in Experiment 1. In contrast, however, we found no evidence that processing of the antecedent of indicative conditionals was constrained by prior context. For indicative conditionals (but not for counterfactual conditionals), the results we report are consistent with the suppositional account of conditionals. We propose that current theories of conditionals need to be able to account for online processing differences between indicative and counterfactual conditionals.     

A plea for pragmatics

Let intentionalism be the view that what proposition is expressed in context by a sentence containing indexicals depends on the speaker’s intentions. It has recently been argued that intentionalism makes communicative success mysterious and that there are counterexamples to the intentionalist view in the form of cases of mismatch between the intended interpretation and the intuitively correct interpretation. In this paper, I argue that these objections can be met, once we acknowledge that we may distinguish what determines the correct interpretation from the evidence that is available to the audience, as well as from the standards by which we judge whether or not a given interpretation is reasonable. With these distinctions in place, we see that intentionalism does not render communicative success mysterious, and that cases of mismatch between the intended interpretation and the intuitively correct one can easily be accommodated. The distinction is also useful in treating the Humpty Dumpty problem for intentionalism, since it turns out that this can be treated as an extreme special case of mismatch.     

Betting on conditionals

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B, and conditional bets, I bet you that if A then B. The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional—true, false, or void for indicative conditionals and win, lose, or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis.     

Epistemic comparative conditionals

The interest of epistemic comparative conditionals comes from the fact that they represent genuine ‘comparative epistemic relations’ between propositions, situations, evidences, abilities, interests, etc. This paper argues that various types of epistemic comparative conditionals uniformly represent comparative epistemic relations via the comparison of epistemic positions rather than the comparison of epistemic standards. This consequence is considered as a general constraint on a theory of knowledge attribution, and then further used to argue against the contextualist thesis that, in some cases, considering a new counter- possibility can raise the epistemic standard of knowledge attribution. Instead, the paper shows that considering a new counter-possibility can only lower the epistemic position of a putative knower. Moreover, since the comparison, by the nature of conditionals, is free from any commitment to the truth-values of specific knowledge attributions, my conclusion is free from the debate between contextualism and invariantism on whether the truth-value of a knowledge attribution can actually vary with context.     

Abstract reasoning and the interpretation of basic conditionals

Studies examining the interpretation that is given to if–then statementstypically use what are referred to as basic conditionals, which give contextless relations between two unrelated concrete terms (If the ball is blue, then the shape is square). However, there is some evidence that basic conditionals require a more abstract form of representation. In order to examine this, we presented participants with truth-table tasks involving either basic conditionals or conditionals referring to imaginary categories (If it is a bori, then it has red wings), and standard conditional inference tasks with abstract and familiar premises. As expected, fewer typical defective conditional interpretations were given to basic conditionals. In addition, partial correlations showed a unique relationship between the interpretation of basic conditionals and abstract inferential reasoning. Results suggest that people process basic conditionals as a form of abstract reasoning, and that the interpretation of conditionals must consider the semantic context.     

The evidential support theory of conditionals

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.     

Advice conditionals about tips and warnings: interpretations and inferences

Two experiments examine how people interpret and reason about advice conditionals, such as tips, for example, “if you study more your grades will improve”, and warnings, for example, “if you stop exercising you will gain weight”. Experiment 1 showed that when participants reason about whether a tip or warning could be true in different situations, their judgments correspond to a biconditional or conditional interpretation on about half of all trials, but to an enabling or tautology interpretation on many others. Experiment 2 showed that participants make few modus ponens and tollens inferences from tips and warnings, and more modus ponens inferences from tips than warnings. The implications for alternative theories are discussed.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.     

A process model of the understanding of uncertain conditionals

To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction.     

Towards a semantics for the artifactual theory of fiction and beyond

In her book Fiction and Metaphysics (1999) Amie Thomasson, influenced by the work of Roman Ingarden, develops a phenomenological approach to fictional entities in order to explain how non-fictional entities can be referred to intrafictionally and transfictionally, for example in the context of literary interpretation. As our starting point we take Thomasson’s realist theory of literary fictional objects, according to which such objects actually exist, albeit as abstract and artifactual entities. Thomasson’s approach relies heavily on the notion of ontological dependence, but its precise semantics has not yet been developed. Moreover, the modal approach to the notion of ontological dependence underlying the Artifactual Theory has recently been contested by several scholars. The main aims of this paper are (i) to develop a semantic approach to the notion of ontological dependence in the context of the Artifactual Theory of fiction, and in so doing bridge a number of philosophical and logical gaps; (ii) to generalize Thomasson’s categorial theory of ontological dependence by reconstructing ontological categories of entities purely in terms of different structures of ontological dependence, rather than in terms of the basic kinds of entities the categorical entities depend on.     

A QBF-based formalization of abstract argumentation semantics

We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Furthermore, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.     

Linguistic communication and the semantics/pragmatics distinction

Most people working on linguistic meaning or communication assume that semantics and pragmatics are distinct domains, yet there is still little consensus on how the distinction is to be drawn. The position defended in this paper is that the semantics/pragmatics distinction holds between (context-invariant) encoded linguistic meaning and speaker meaning. Two other ‘minimalist’ positions on semantics are explored and found wanting: Kent Bach’s view that there is a narrow semantic notion of context which is responsible for providing semantic values for a small number of indexicals, and Herman Cappelen and Ernie Lepore’s view that semantics includes the provision of values for all indexicals, even though these depend on the speaker’s communicative intentions. Finally, some implications are considered for the favoured semantics/pragmatics distinction of the fact that there are linguistic elements (lexical and syntactic) which do not contribute to truth-conditional content but rather provide guidance on pragmatic inference.     

The effect of semantics on problem solving is to reduce relational complexity

This article reports a study carried out in order to measure how semantic factors affect reductions in the difficulty of the Chinese Ring Puzzle (CRP) that involves removing five objects according to a recursive rule. We hypothesised that semantics would guide inferences about action decision making. The study involved a comparison of problem solving for two semantic isomorphic variants of the CRP ( fish and fleas ) with problem solving for the puzzle's classic variant (the Balls and Boxes problem; Kotovsky & Simon, 1990 Kotovsky, K. and Simon, H. A. 1990. What makes some problems really hard: Exploration in the problem space difficulty. Cognitive Psychology, 22: 143–183. [Crossref], [Web of Science ®] , [Google Scholar]). Our results showed that the number of moves was reduced by 47% in the fish version and by 51% in the flea version. We discuss these results in terms of semantic inferences and reductions in relational complexity. During the exploratory stage of problem solving participants discover the dependent relations between elements in the puzzle. Initially these relations are processed separately; learning involves generalising the relations within a coherent, interconnected whole that makes up the puzzle's rules. It seems that semantics make it easier for the puzzle's elements to be grouped together within coherent, meaningful wholes, which reduces relational complexity and facilitates problem solving.     

The semantics and acquisition of number words: integrating linguistic and developmental perspectives

This article brings together two independent lines of research on numerally quantified expressions, e.g. two girls. One stems from work in linguistic theory and asks what truth conditional contributions such expressions make to the utterances in which they are used--in other words, what do numerals mean? The other comes from the study of language development and asks when and how children learn the meaning of such expressions. My goal is to show that when integrated, these two perspectives can both constrain and enrich each other in ways hitherto not considered. Specifically, work in linguistic theory suggests that in addition to their 'exactly n' interpretation, numerally quantified NPs such as two hoops can also receive an 'at least n' and an 'at most n' interpretation, e.g. you need to put two hoops on the pole to win (i.e. at least two hoops) and you can miss two shots and still win (i.e. at most two shots). I demonstrate here through the results of three sets of experiments that by the age of 5 children have implicit knowledge of the fact that expressions like two N can be interpreted as 'at least two N' and 'at most two N' while they do not yet know the meaning of corresponding expressions such as at least/most two N which convey these senses explicitly. I show that these results have important implications for theories of the semantics of numerals and that they raise new questions for developmental accounts of the number vocabulary.     

What exactly is a yait anyway: The role of semantics in orthographic learning

This study investigated whether semantic information presented along with novel printed nonwords facilitates orthographic learning and examined predictors of individual differences in this important literacy skill. A sample of 35 fourth graders was tested on a variety of language and literacy tests, and participants were then exposed to 10 target nonwords, 5 of which were presented with semantic information. Children were tested 1 and 4 days later on their ability to correctly recognize and spell the target nonwords. Results revealed a significant main effect on the recognition task, where items presented with semantic information were identified correctly more often than were words presented in isolation. No significant effect of training condition was found for the spelling posttests. Furthermore, multiple regression analyses revealed that both phonological and semantic factors were significant predictors of orthographic learning. The findings support the view that orthographic learning, as measured through visual recognition, involves the integration of phonological, orthographic, and semantic representations.     

Fresh Logic: proof-theory and semantics for FM and nominal techniques

In this paper we introduce Fresh Logic, a natural deduction style first-order logic extended with term-formers and quantifiers derived from the FM-sets model of names and binding in abstract syntax. Fresh Logic can be classical or intuitionistic depending on whether we include a law of excluded middle; we present a proof-normalisation procedure for the intuitionistic case and a semantics based on Kripke models in FM-sets for which it is sound and complete.     

Orthographic learning in learning to spell: The roles of semantics and type of practice

This study investigated the relevance of type of practice and presence of semantic representation for orthographic learning in learning to spell. A total of 36 students in Grade 2 (mean age = 7 years 10 months) were exposed to 10 novel nonwords, 5 of which were paired with semantic information. Half of the participants practiced reading these new items, whereas the others spelled them. The students were then tested 1 and 7 days later on a dictation task. Results revealed a significant main effect of practice type favoring spelling practice and a main effect of the teaching condition, where taught items paired with semantic information were spelled correctly more often than words presented without semantic support. There was no effect of testing time, with learned words being retained well over the 1-week delay, nor were there any significant interactions. The findings support the contention that spelling offers an excellent milieu for orthographic learning to occur. Furthermore, semantics are proposed as a relevant factor in learning to spell, supporting the view that orthographic learning involves the integration of phonological, orthographic, and semantic representations.     

Knowledge claims and context: loose use

There is abundant evidence of contextual variation in the use of “S knows p.” Contextualist theories explain this variation in terms of semantic hypotheses that refer to standards of justification determined by “practical” features of either the subject’s context (Hawthorne & Stanley) or the ascriber’s context (Lewis, Cohen, & DeRose). There is extensive linguistic counterevidence to both forms. I maintain that the contextual variation of knowledge claims is better explained by common pragmatic factors. I show here that one is variable strictness. “S knows p” is commonly used loosely to implicate “S is close enough to knowing p for contextually indicated purposes.” A pragmatic account may use a range of semantics, even contextualist. I use an invariant semantics on which knowledge requires complete justification. This combination meets the Moorean constraint as well as any linguistic theory should, and meets the intuition constraint much better than contextualism. There is no need for ad hoc error theories. The variation in conditions of assertability and practical rationality is better explained by variably strict constraints. It will follow that “S knows p” is used loosely to implicate that the condition for asserting “p” and using it in practical reasoning are satisfied.