Source reliability and the conjunction fallacy

Information generally comes from less than fully reliable sources. Rationality, it seems, requires that one take source reliability into account when reasoning on the basis of such information. Recently, Bovens and Hartmann (2003) proposed an account of the conjunction fallacy based on this idea. They show that, when statements in conjunction fallacy scenarios are perceived as coming from such sources, probability theory prescribes that the "fallacy" be committed in certain situations. Here, the empirical validity of their model was assessed. The model predicts that statements added to standard conjunction problems will change the incidence of the fallacy. It also predicts that statements from reliable sources should yield an increase in fallacy rates (relative to unreliable sources). Neither the former (Experiment 1) nor the latter prediction (Experiment 3) was confirmed, although Experiment 2 showed that people can derive source reliability estimates from the likelihood of statements in a manner consistent with the tested model. In line with the experimental results, model fits and sensitivity analyses also provided very little evidence in favor of the model. This suggests that Bovens and Hartmann's present model fails to explain fully people's judgements in standard conjunction fallacy tasks.     

Who is susceptible to conjunction fallacies in category-based induction?

Recent evidence suggests that the conjunction fallacy observed in people’s probabilistic reasoning is also to be found in their evaluations of inductive argument strength. We presented 130 participants with materials likely to produce a conjunction fallacy either by virtue of a shared categorical or a causal relationship between the categories in the argument. We also took a measure of participants’ cognitive ability. We observed conjunction fallacies overall with both sets of materials but found an association with ability for the categorical materials only. Our results have implications for accounts of individual differences in reasoning, for the relevance theory of induction, and for the recent claim that causal knowledge is important in inductive reasoning.     

The conjunction fallacy?

Tversky and Kahneman (1983) showed that when subjects are asked to rate the likelihood of several alternatives, including single and joint events, they often make a "conjunction fallacy." That is, they rate the conjunction of two events as being more likely than one of the constituent events. This, they claim, is a fallacy, since the conjunction of two events can never be more probable than either of the component events. In addition, they found that prior training in probability theory does not decrease the likelihood of making this fallacy. We argue that in some contexts, an alternative that contains the conjunction of two events can be more probable than an alternative that contains only one of the conjunction's constituent events. We carried out four experiments in which we manipulated this context. The frequency of making a conjunction fallacy was affected by the manipulation of context. Furthermore, when the context was clearly specified, prior training in statistics influenced the ratings.     

A case of confusing probability and confirmation

Tom Stoneham put forward an argument purporting to show that coherentists are, under certain conditions, committed to the conjunction fallacy. Stoneham considers this argument a reductio ad absurdum of any coherence theory of justification. I argue that Stoneham neglects the distinction between degrees of confirmation and degrees of probability. Once the distinction is in place, it becomes clear that no conjunction fallacy has been committed.     

Begging what is at issue in the argument

This paper objects to treating begging the question as circular reasoning. It argues that what is at issue in the argument is not to be confused with the claim or position that the arguer is adopting, and that logicians from Aristotle on give the wrong definition and have difficulty making sense of the fallacy because they try to define it in terms of how an argument is defined by logical theory - as a sequence consisting of premises followed by a conclusion. That the problematic about begging the question depends on treating an argument as a context-less sequence of statements seems to be anticipated by the pragma-dialectical approach. The paper offers a critique of this dialogical approach, as exemplified by Douglas Walton in his recent book on begging the question, on the grounds that it raises more problems than it solves. It concludes with the suggestion that what is really at issue in discussions of begging the question is the need for a theory of fallacy.     

Of faculties, fallacies, and freedom: dilemma and irony in the secularization of American psychology

In The Principles of Psychology, William James (1890) articulated an influential, boundary-setting argument against faculty psychology, subsequently dubbed the Fallacy of the Faculty Psychology. This argument was reiterated in American psychology textbooks for the next several decades, arguably solidifying and simplifying American perceptions of the "old" faculty psychology and establishing belief in the superiority of the "New Psychology." When placed in the context of American theological and philosophical history, however, the New Psychology argument appears unoriginal, somewhat unfair, and deeply (and even tragically) ironic. Despite their best intentions, a fallacy did emerge in the old psychology as they sought psychological foundations for libertarian free will. For those members of the New Psychology still committed to free will, then, the Fallacy argument cut both ways - refuting the fallacy also meant tearing down a long-standing foundation for free will in American psychology. Offering no viable alternative to fill the moral void, the New Psychology appeared at times conflicted with its new deterministic identity.     

Cognitive Spread: Under What Conditions Does the Mind Extend Beyond the Body?

The extended mind hypothesis (EMH) is the claim that the mind can and does extend beyond the human body. Adams and Aizawa (A&A) contend that arguments for EMH commit a ‘coupling constitution fallacy’. We deny that the master argument for EMH commits such a fallacy. But we think that there is an important question lurking behind A&A's allegation: under what conditions is cognition spread across a tightly coupled system? Building on some suggestions from Haugeland, we contend that the system must exhibit a distinctive sort of semantic activity, semantic activity that the system as a whole takes responsibility for.     

Breaking Out of the Circle

What’s wrong with begging the question? Some philosophers believe that question-begging arguments are inevitably fallacious and that their fallaciousness stems from a shared “formal” deficiency. In contrast, some philosophers, like Robinson (Analysis 31:113–117, 1971) deny that begging the question is fallacious at all. And others characterize begging the question as an “informal” fallacy of reasoning that can only be understood with the aid of epistemic (as opposed to syntactic and semantic) notions. Sorensen (Analysis 56:51–55, 1996) joins this last camp by offering a powerful argument against both Robinson’s skepticism and fully formal approaches to the phenomenon. According to Sorensen’s view, question-begging is fallacious because it compromises the rationality of the question-beggar’s position. Though his argument forces Robinson into a peculiar dialectical position, it does little to elucidate the reasons why Robinson’s position is unstable and it fails to embody Sorensen’s own conception of rationally persuasive argumentation. I utilize this conception to show how Robinson is left with no easily identifiable grounds on which to deny the fallaciousness of begging the question. By advancing the dialectic between Sorensen and Robinson, I aim to show that our argumentative practices must take the perspectives of others seriously, whether or not those perspectives are rational.     

On the reality of the conjunction fallacy

Attributing higher "probability" to a sentence of form p-and-q, relative to p, is a reasoning fallacy only if (1) the word probability carries its modern, technical meaning and (2) the sentence p is interpreted as a conjunct of the conjunction p-and-q. Legitimate doubts arise about both conditions in classic demonstrations of the conjunction fallacy. We used betting paradigms and unambiguously conjunctive statements to reduce these sources of ambiguity about conjunctive reasoning. Despite the precautions, conjunction fallacies were as frequent under betting instructions as under standard probability instructions.     

On the nature of the conjunction fallacy

In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). This belief violates the conjunction rule in probability theory. Tversky and Kahneman called this phenomenon the “conjunction fallacy”. Since the discovery of the phenomenon in 1983, researchers in psychology and philosophy have engaged in important controversies around the conjunction fallacy. The goal of this paper is to explore the most important of these controversies, namely, the controversy about the nature of the conjunction fallacy. Is the conjunction fallacy mainly due to a misunderstanding of the problem by participants (misunderstanding hypothesis) or is it mainly due to a genuine reasoning bias (reasoning bias hypothesis)? A substantial portion of research on the topic has been directed to test the misunderstanding hypothesis. I review this literature and argue that a stronger case can be made against the misunderstanding hypothesis. Thus, I indirectly provide support for the reasoning bias hypothesis.     

The conjunction fallacy and the many meanings of and

According to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator wedge, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language "and" can convey a wide range of relationships between conjuncts such as temporal order ("I went to the store and bought some whisky"), causal relationships ("Smile and the world smiles with you"), and can indicate a collection of sets rather than their intersection (as in "He invited friends and colleagues to the party"). When "and" is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator wedge, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people's understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator wedge. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.     

The Fallacy of Many Questions: On the Notions of Complexity, Loadedness and Unfair Entrapment in Interrogative Theory

The traditional fallacy of many questions, also known as the fallacy of complex question, illustrated by the question, "Have you stopped sexually harassing your students?", has been known since ancient times, but is still alive and well. What is of practical importance about this fallacy is that it represents a tactic of entrapment that is very common in everyday argumentation, as well as in special kinds of argumentation like that in a legal trial or a parliamentary debate. The tactic combines the use of loaded questions with the complexity of the question. A key notion is that of the presupposition of the question. How to deal with such questions is a point of departure for interrogative theory, and for any attempts to construct formal dialogues of a kind that can be used as normative models of argumentation.     

Many questions Begs the Question (but questions do not Beg the Question)

The fallacy of many questions or the complex question, popularized by the sophism ‘Have you stopped beating your spouse?’ (when a yes-or-no answer is required), is similar to the fallacy of begging the question orpetitio principii. Douglas N. Walton inBegging the Question has recently argued that the two forms are alike in trying unfairly to elicit an admission from a dialectical opponent without meeting burden of proof, but distinct because of the circularity of question-begging argument and noncircularity of many questions. I offer a reconstruction of the many questions fallacy according to which it is just as circular as begging the question, concluding that many questions begs the question. The same analysis contradicts Walton's claim that questions can beg the question, drawing a distinction between questions as the instruments of question-begging, and as vehicles for categorical noninterrogative presuppositions that beg the question.     

The illusion of replacement in research into the development of thinking biases: the case of the conjunction fallacy

The conjunction fallacy is a violation of a very basic rule of probability. Interestingly, although committing the fallacy seems irrational, adults are no less susceptible to the fallacy than young children. In Experiment 1, by employing tasks where the conjunctive response option involved two non-representative items, we found a large reduction in fallacy rates as compared to traditional conjunction fallacy problems. Nevertheless, fallacy rates remained relatively high in both adolescents and adults, although adults showed more consistency in their normative responses. In Experiment 2, we demonstrated that children’s relatively good performance on the task was not the consequence of their missing knowledge of social stereotypes. Additionally, children were more strongly affected by explicitly presented frequency information than adults. Indeed, adults only took frequency information into account when frequencies were made relevant by a training in probabilistic reasoning. Overall, the results suggest that whereas the potential for normative reasoning increases with development, this potential is often overshadowed by a pervasive tendency in adolescence and adulthood to rely on contextual information, knowledge, and beliefs, even when conflicting information is available. By contrast, children are more strongly influenced by explicitly presented information than relevant knowledge cued by the tasks.     

The conjunction fallacy and interference effects

In the present article we consider the conjunction fallacy, a well known cognitive fallacy experimentally tested in cognitive science, which occurs for intuitive judgments. We show that the quantum formalism can be used to describe, in a very simple way, this fallacy, in terms of interference effect. We provide evidence that the quantum formalism leads quite naturally to violations of the joint probability rule of classic probability when considering the estimated probability of the conjunction of two events. By defining the concept of maximal conjunction error, we find a good agreement with experimental results. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a quantum regime, where the cognitive fallacies and heuristics are valid.     

On the Theoretical Unification and Nature of Fallacies

I argue in a non-reductive sense for a plausible epistemic principle, which can (1) theoretically and instrumentally unify or systematize all fallacies, and (2) provide a justification for using such a principle for characterizing an erroneous argument as a fallacy. This plausible epistemic principle involves the idea of an error in the method of justification, which results in a failure to provide relevant evidence to satisfy certain standards of adequate proof. Thus, all fallacies are systematically disguised failures to provide substantive proof: a failure in the attempt to persuade rationally, as opposed to emotionally or rhetorically. I argue that the epistemic idea of begging the question is essential to this idea of a fallacy as an inadequate proof.     

I. Psychologism,Functionalism, and the modal status of logical Laws

In a recent article (Inquiry, Vol. 19 [1976]), J. W. Meiland addresses the issue of psychologism in logic, which holds that logic is a branch of psychology and that logical laws (such as the Principle of Non‐Contradiction) are contingent upon the nature of the mind. Meiland examines Husserl's critique of psychologism, argues that Husserl is not convincing, and offers two new objections to the psychologistic thesis. In this paper I attempt to rebut those objections. In question are the acceptable criteria for determining the possibility or impossibility of systems of logic significantly different from our own. I argue that a criteriological application of our accepted laws of logic to this question commits a circular fallacy. I then argue that, even if we accept logical consistency as a criterion for possibility, a plausible argument for the possibility of valid alternative logics can be constructed by using the functionalist analogy between minds and automata. Finally, I attempt to rebut the claim that in logic the only changes possible are conceptual changes that would not permit a proposition to be both true and false.