Carry on winning: The gamblers’ fallacy creates hot hand effects in online gambling

People suffering from the hot-hand fallacy unreasonably expect winning streaks to continue whereas those suffering from the gamblers’ fallacy unreasonably expect losing streaks to reverse. We took 565,915 sports bets made by 776 online gamblers in 2010 and analyzed all winning and losing streaks up to a maximum length of six. People who won were more likely to win again (apparently because they chose safer odds than before) whereas those who lost were more likely to lose again (apparently because they chose riskier odds than before). However, selection of safer odds after winning and riskier ones after losing indicates that online sports gamblers expected their luck to reverse: they suffered from the gamblers’ fallacy. By believing in the gamblers’ fallacy, they created their own hot hands.     

Countering conspiracy theory beliefs: Understanding the conjunction fallacy and considering disconfirming evidence

Research suggests that a number of cognitive processes—including pattern perception, intentionality bias, proportionality bias, and confirmation bias—may underlie belief in a conspiracy theory. However, there are reasons to believe that conspiracy theory beliefs also depend in part on a failure to understand the probability of actual events allegedly supporting those conspiracy theories as well as a failure to entertain disconfirming evidence that may contradict those beliefs. Study 1 examines the relationships between general beliefs in conspiracy theories, belief in a novel conspiracy theory, conjunctive error propensity, and the propensity to consider disconfirming evidence. Study 2 investigates the roles of confronting both the propensity to make conjunctive errors and the failure to consider disconfirming evidence in changing conspiracy theory beliefs as well as attitudes associated with those beliefs. The results of both studies suggest that corrections to one's propensity to make conjunctive errors and mindful consideration of disconfirming evidence may serve as viable methods of self-persuasion pertaining to conspiracy theory beliefs.     

Six types of fallaciousness: Toward a realistic theory of logical criticism

I begin by formulating the problem of the nature of fallacy in terms of the logic of the negative evaluation of argument, that is, in terms of a theory of logical criticism; here I discuss several features of my approach and several advantages vis-à-vis other approaches; a main feature of my approach is the concern to avoid both formalist and empiricist excesses. I then define six types of fallaciousness, labeled formal, explanatory, presuppositional, positive, semantical, and persuasive; they all involve arguments whose conclusion may be said not to follow from the premises, that is, they involve the logical evaluation of relationships among propositions. I also provide a set of data consisting of four historical cases or nine specific instances of fallacious arguments; these all pertain to the Copernican controversy about the earth's motion in the seventeenth century. I end with a discussion of further problems and inquiries that deserve attention.     

Pluralism, scientific knowledge, and the fallacy of overriding values

The paper examines one implication of pluralism, the view that all values are conditional and none are overriding. This implication is that since scientific knowledge is one of the conditional values, there are circumstances in which the pursuit of even the most basic scientific knowledge is legitimately curtailed. These circumstances occur when the pursuit of scientific knowledge conflicts with moral and political values which, in that context, are more important than it. The argument focuses on the case for and against space exploration in search of intelligent extraterrestrial life. The widely held supposition that search for pure scientific knowledge cannot be reasonably curtailed is identified as the fallacy of overriding values.     

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.     

Contexts of Begging the Question

In this paper a dialogical account of begging the question is applied to various contexts which are not obviously dialogues: - reading prose, working through a deductive system, presenting a legal case, and thinking to oneself. The account is then compared with that in chapter eight of D. Walton'sBegging the Question (New York; Greenwood, 1991).     

Deductive schemas with uncertain premises using qualitative probability expressions

The 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 (e.g., “the chances are high”) 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 (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Towards a pattern-based logic of probability judgements and logical inclusion “fallacies”

Probability judgements entail a conjunction fallacy (CF) if a conjunction is estimated to be more probable than one of its conjuncts. In the context of predication of alternative logical hypothesis, Bayesian logic (BL) provides a formalisation of pattern probabilities that renders a class of pattern-based CFs rational. BL predicts a complete system of other logical inclusion fallacies (IFs). A first test of this prediction is investigated here, using transparent tasks with clear set inclusions, varying in observed frequencies only. Experiment 1 uses data where BL makes dominant predictions; Experiment 2's predictions were less clear, and we additionally investigated judgements about the second-most probable hypotheses. The results corroborated a pattern-probability account and cannot be easily explained by other theories of CFs (e.g. inverse probability, confirmation). IFs were not limited to conjunctions, but rather occurred systematically for several logical connectives. Thus, pattern-based probability judgements about logical relations may constitute a basic class of intuitive but potentially rational probability judgements.     

Reductionism in Fallacy Theory

(1) The aim of the paper is to develop a reduction of fallacy theory, i.e. to 'deduce' fallacy theory from a positive theory of argumentation which provides exact criteria for valid and adequate argumentation. Such reductionism has several advantages compared to an unsystematic action, which is quite usual in current fallacy but which at least in part is due to the poor state of positive argumentation theory itself. (2) After defining 'fallacy' (3) some principle ideas and (4) the exact criteria for (argumentatively) valid and adequate arguments of the 'practical theory of argumentation' of the author are expounded. These criteria will be used as the positive basis for the following reduction. (5) In the main part of the paper a systematization, definition and explanation of the main types and many subforms of fallacies of argumentative validity and (6) adequacy is developed, following the list of positive conditions of validity and adequacy. In addition to many new types of fallacies, this systematization contains the most important of the traditionally known and named fallacies; these are explained and the criteria for some of them are corrected or put more precisely.