How probability theory explains the conjunction fallacy

The conjunction fallacy occurs when people judge a conjunctive statement B‐and‐A to be more probable than a constituent B, in contrast to the law of probability that P(B ∧ A) cannot exceed P(B) or P(A). Researchers see this fallacy as demonstrating that people do not follow probability theory when judging conjunctive probability. This paper shows that the conjunction fallacy can be explained by the standard probability theory equation for conjunction if we assume random variation in the constituent probabilities used in that equation. The mathematical structure of this equation is such that random variation will be most likely to produce the fallacy when one constituent has high probability and the other low, when there is positive conditional support between the constituents, when there are two rather than three constituents, and when people rank probabilities rather than give numerical estimates. The conjunction fallacy has been found to occur most frequently in exactly these situations. Copyright © 2008 John Wiley & Sons, Ltd.     

Linda问题:"齐当别"抉择模型的解释

大量有关人类归因判断的研究表明,人类经常违反理性概率公理.Tversky和Kahneman(1983)使用Linda问题等特定场景的研究发现,人们系统性地表现出违反理性推断标准,判断合取事件发生概率大于其组成事件发生概率,称之为合取谬误,并用人们使用代表性启发式判断概率来解释该现象产生的原因.然而使用启发式观点对合取谬误现象进行解释过于模糊不清.该文首先介绍了合取谬误现象及其解释模型,然后应用Li(1994,2004)提出的不确定情形下决策理论--"齐当别"抉择模型对Linda问题中合取谬误产生的原因进行了新的解释.     

Affirming the consequent

The thesis of this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its premises at all favorably relevant to its conclusion. In support of this thesis I assume two premises and argue for a third. My two assumptions are these: (1) that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion certain relative to its premises (this is widely, if not universally, acknowledged by writers on logic), and (2) premises are favorably relevant to a conclusion only if it is certain or probable relative to them (I argued for this in an earlier paper). The premise I argue for in this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion probable relative to its premises. To establish this third premise, I first refute a defense of the contrary position (namely, that an argument's possessing the form of affirming the consequent suffices to make its conclusion probable relative to its premises), then offer counterexamples to that position, and finally demonstrate the failure of several attempts to save it.An earlier draft of this paper was read at the meeting of the Association for Informal Logic and Critical Thinking at the meeting of the American Philosophical Association in Portland on March 27, 1992. I am indebted to Terry Parsons, John Woods, and this journal's anonymous referees for their comments.     

A critique of Tversky and Kahneman's distinction between fallacy and misunderstanding

Tversky and Kahneman explain cognitive errors in terms of either misunderstanding or fallacy , but have failed to define these concepts. Therefore, they are unable to derive strict diagnostic criteria for distinguishing between them. The lack of conceptual clarification also has prevented them from recognizing the circular relationship between understanding and logicality. Diagnosis of understanding presupposes logicality, and diagnosis of logicality presupposes understanding. This circularity follows when understanding is defined as grasping what is and is not logically implied by a given expression as intended, and when fallacy is defined as logical error. Alternative definitions are discussed and rejected. Tversky and Kahneman fail to realize that one cannot explain and understand what is genuinely illogical, and that, therefore, errors must always be regarded as failure to understand, that is, as logical inference from erroneous premises.     

May the force be with you

This paper is a critical assessment of argumentum ad baculum, or appeal to force. Its principal contention is that, contrary to common opinion, there is no general fallacy of ad baculum. Most real-life ad baculums are, in fact, fairly strong. A basic logical form for reconstructed ad baculums is proposed, and a number of heterodoxical conclusions are also advanced and argued for. They include that ad baculum is not necessarily a prudential argument, that ad baculum need not involve force, violence, or threats, and that one can argue ad baculum to oneself. The starting point of the paper, however, is a critical evaluation of three ad baculums from the exercise sets of Irving Copi's well-known Introduction to Logic.     

The fallacy of fallacies

Several of the so-called fallacies in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of fallacies ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the fallacies mentioned by Aristotle can in fact be diagnosed by means of the interrogative model, including petitio principii, multiple questions, babbling, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether fallacies are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games.     

Naming our concerns about neuroscience: a review of Bennett and Hacker's philosophical foundations of neuroscience

Bennett and Hacker use conceptual analysis to appraise the theoretical language of modern cognitive neuroscientists, and conclude that neuroscientific theory is largely dualistic despite the fact that neuroscientists equate mind with the operations of the brain. The central error of cognitive neuroscientists is to commit the mereological fallacy, the tendency to ascribe to the brain psychological concepts that only make sense when ascribed to whole animals. The authors review how the mereological fallacy is committed in theories of memory, perception, thinking, imagery, belief, consciousness, and other psychological processes studied by neuroscientists, and the consequences that fallacious reasoning have for our understanding of how the brain participates in cognition and behavior. Several behavior-analytic concepts may themselves be nonsense based on thorough conceptual analyses in which the criteria for sense and nonsense are found in the ways the concepts are used in ordinary language. Nevertheless, the authors' nondualistic approach and their consistent focus on behavioral criteria for the application of psychological concepts make Philosophical Foundations of Neuroscience an important contribution to cognitive neuroscience.     

Evolutionary Ethics: Its Origin and Contemporary Face

The development of modern evolutionary ethics began shortly after the publication of Charles Darwin's On the Origin of Species by Natural Selection . Early discussions were plagued by several problems. First, evolutionary ethical explanations were dependent on group-selection accounts of social behavior (especially the explanation of altruism). Second, they seem to violate the philosophical principle that "ought" statements cannot be derived from "is" statements alone (values cannot be derivedfrom facts alone). Third, evolutionary ethics appeared to be biologically deterministic, deemed incompatible with the free will required for ethics to be possible. Fourth, social policies based on evolutionary theory (for example, eugenics in the early part of this century) seemed patently unethical. Sociobiology (which coalesced as a field of study with Edward O. Wilson's Sociobiology: The New Synthesis , 1975) addressed several of these problems and provided a rich framework and a new impetus for evolutionary ethics. The lingering problems were the philosophical is-ought barrier and biological determinism. After tracing the early and more recent development of evolutionary ethics, I argue that the remaining problems can be surmounted and an incipient evolutionary ethics can be defended. Thoroughgoing evolutionaryethics must await theoretical developments in neurobiology and cognitive science.     

Once (but not twice) upon a time: Narrative inoculation against conjunction errors indirectly reduces conspiracy beliefs and improves truth discernment

Psychological inoculation has proven effective at reducing susceptibility to misinformation. We present a novel storytelling approach to inoculation against susceptibility to the conjunction fallacy (d_{meta-analysis} = 0.82), a known cognitive predictor of conspiracy beliefs. In Study 1 (Pilot; N = 161), a narrative inoculation (vs. control) reduced susceptibility to conjunction errors, and in turn, conspiracy beliefs regarding government malfeasance. In Study 2 (main experiment; N = 141; pre-registered), two separate narrative inoculations (vs. control) directly reduced susceptibility to conjunction errors, and indirectly reduced conspiracy beliefs regarding extra-terrestrial cover-ups. In addition, the inoculation messages improved detection of both real and fake news (‘truth discernment’). We discuss theoretical and practical implications, including the use of inoculation to induce critical thinking styles, and tailoring inoculations that may suit storytelling mediums.