Directional Bias

There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) some of the counter-examples to classical argumentative forms and known conditional puzzles are unsound.

The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be rendered invalid. If we maintain the context fixed, the counterexamples to the material account are disarmed. Throughout the paper I also consider the ramifications of this defence, make suggestions to prevent contextual fallacies, and anticipate some possible misunderstandings and objections.

This is the first part of two in a study on the logic and semantics of the indicative conditional. This first part provides a global expressivist analysis of the indicative conditional along the lines of the Ramsey Test. The analysis is a form of 'global' expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege-Geach problem). The resulting mental usage semantics is provably not susceptible to triviality results and completely characterises a logic for the indicative conditional that respects many of its well known logical quirks (the failure of modus ponens, etc.). The second part provides a semantic analysis of the resulting structure and logic.

Journal of Philosophical Logic, 2015

The Spanish Journal of Psychology, 2015

Directionality effect in deductive reasoning is a very well-known phenomenon that shows that the percentage of forward or backward inferences that participants make depends on the conditional form used. A new extension of the semantic hypothesis (Oberauer & Wilhelm, 2000) is presented to explain the directionality effect in double conditionals with different directionality. This hypothesis claims that the directional effect depends on which term plays the role of relatum. It also makes several novel claims which have been confirmed in three experiments: Experiments 1 and 2 showed there were more forward than backward inferences when the end-term that played the role of relatum was in the first premise, experiment 1:t(45) = 2.73,p< .01, experiment 2:t(38) = 12.06,p< .05, but there were more backward than forward inferences when the end-term that played the role of relatum was in the second premise, experiment 1: t(45) = 2.84,p< .01, experiment 2:t(38) = 2.21,p< .04. Exper...

Studia Logica, 2008

I argue that indicative conditionals are best viewed as having truth conditions (and so they are in part factual) but that these truth conditions are `gappy' which leaves an explanatory gap that can only be ¯lled by epistemic considerations (and so indicative conditionals are in part epistemic). I argue that this dual nature of indicative conditionals forces us to rethink the relationship between logic viewed as a descriptive discipline (focusing on semantics) and logic viewed as a discipline with a normative import (focusing on epistemic notions such as `reasoning', `beliefs' and `assumptions'). In particular, I argue that the development of formal models for epistemic states can serve as a starting point for exploring logic when viewed as a normative discipline.

Topoi, 2009

This paper replies to criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the 'paradoxes' of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.

The goal of this paper is to test the main predictions of the semantic hypothesis about the directional effect in double conditionals (such as, 'A only if B/only if C, B') with a construction task. The semantic hypothesis claims that directional effect can be explained by the inherent directionality of the relation between the relatum and the target object of the premises. According to this hypothesis, a directional effect should occur if only one of the end-terms of the premises takes the role of relatum: a) if the end-term that plays the role of relatum is in the first premise, a forward directional effect is predicted (from A to C); and b) if the end-term that plays the role of relatum is in the second premise, a backward directional effect is predicted (from C to A). On the other hand, it claims that there should be no directional effect when both end-terms take the role of relatum or when neither of the end-terms plays the role of relatum. Three experiments confirmed the main predictions of the semantic hypothesis in a construction task.

Adam Rieger (2013) has carried out a survey of arguments in favour of the material account of indicative conditionals. These arguments involve simple and direct demonstrations of the material account. I extend the survey with new arguments and clarify the logical connections among them. I also show that the main counterexamples against these arguments are not successful either because their premises are just as counter-intuitive as the conclusions, or because they depend on contextual fallacies. The conclusion is that the unpopularity of the material account is unjustified and that a more systematic approach in the analysis of arguments is long overdue in our attempts to understand the nature of conditionals.

This simple defense of material implication helps clarify the debate between the orthodox logicians, who claim 'If p then q' and 'p |horseshoe| q' are not interderivable and the nonorthodox logicians, who claim that the two expressions are interderivable. The paper shows the orthodox logician must deny that ordinary language arguments of the form modus ponens and modus tollens are truth-functional in any consistent sense on three lines of the truth-table.