This chapter deals with one of the common fallacies in Western philosophy called 'the gambler's fallacy (GF)'. GF is committed in the context of random, unconnected events. When (by chance) a certain outcome occurs very often in one period of time, the fallacious reasoner assumes that the opposite outcome will be more likely to occur in the future to “even out” the results. As with most fallacies, GF is prevalent because it is similar to a kind of good (...) reasoning. This chapter considers a case of flipping coin to understand this concept. GF covers situations where the results are based on chance. In a game of skill, for example, a streak may indicate the superiority of one player or team or it may cause the other players to adjust their strategy to stop the currently successful run. (shrink)

The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an (...) asymmetric way—ruling out “streaky” hypotheses more quickly than “switchy” ones. As a result, the majority (and the average) exhibit the gambler’s fallacy. If they have limited memory, this tendency persists even with arbitrarily-large amounts of data. Indeed, such Bayesians exhibit a variety of the empirical trends found in studies of the gambler’s fallacy: they expect switches after short streaks but continuations after long ones; these nonlinear expectations vary with their familiarity with the causal system; their predictions depend on the sequence they’ve just seen; they produce sequences that are too switchy; and they exhibit greater rates of gambler’s reasoning when forming binary predictions than when forming probability estimates. In short: what’s been thought to be evidence for irrationality may instead be rational responses to limited data and memory. (shrink)

The present study tests a gestalt explanation for the gambler's fallacy which posits that runs in random events will be expected to reverse only when the run is open or ongoing. This is contrasted with the law of small numbers explanation suggesting that people expect random outcomes to balance out generally. Sixty-one university students placed hypothetical guesses and bets on a series of coin tosses. Either heads or tails were dominant . In a closed run condition the run (...) ended prior to the critical trial , and in an open run condition the run remained open . As hypothesised, participants showed the gambler's fallacy in the open run condition, but not in the closed run condition. This difference is not due to differential memory for the outcomes. Men, and people with more previous experience gambling, were also found to be more prone to the gambler's fallacy. It is argued that the gestalt explanation best explains the results. (shrink)

The Therapeutic Misconception (TM) is a cognitive error with similarities to another cognitive error -- the Gambler's Fallacy (GF). This paper examines the similarities between TM and GF in an attempt to further illuminate the nature of TM, and to distinguish it from another cognitive error, Unrealistic Optimism (UO). Many cases of UO and mis-classified as TM.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. Here we get to grips with an everyday reasoning error: the gambler's fallacy.

Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs (...) about the base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of.50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin's version of Tversky & Kahneman's Law of Small Numbers. (shrink)

We conduct experiments to analyze investment behavior in decisions under risk. Subjects can bet on the outcomes of a series of coin tosses themselves, rely on randomized ‘experts’, or choose a risk-free alternative. We observe that subjects who rely on the randomized experts pick those who were successful in the past, showing behavior consistent with the hot hand belief. Obviously the term ‘expert’ suffices to attract some subjects. For those who decide on their own, we find behavior consistent with the (...) gambler’s fallacy, as the frequency of betting on heads (tails) decreases after streaks of heads (tails). (shrink)

Does the claimed fine-tuning of the constants of nature for life give reason to think that there are many other universes in which the constants have different values? Or does the inference from fine-tuning to a multiverse commit what Hacking calls the inverse gambler’s fallacy? The present paper considers two fine-tuning problems that seem promising to consider because they are in many respects analogous to the problem of the fine-tuned constants. Reasoning that parallels the inference from fine-tuning to a (...) multiverse seems prima facie adequate in these problems. However, it turns out that in both cases there are independent empirical reasons to believe the hypotheses that are analogous to the multiverse hypothesis. In the absence of such evidence, it would be coherent to raise the inverse gambler’s fallacy charge against the inference from fine-tuning to these multiverse-type hypotheses. In response to this finding, I suggest taking the possibility seriously that established standards of rationality may not allow us to decide whether the inference from fine-tuning to a multiverse is fallacious or not. The paper concludes by sceptically assessing the prospects for obtaining independent empirical evidence for concrete multiverse theories. (shrink)

The multiverse hypothesis is one of the leading proposed explanations of cosmic fine-tuning for life. One common objection to the multiverse hypothesis is that, even if it were true, it would not explain why this universe, our universe, is fine-tuned for life. To think it would so explain is allegedly to commit “the inverse gambler's fallacy.” This paper presents what the inverse gambler's fallacy is supposed to be, then surveys the discussion of it in the philosophical (...) literature of the last 35 years. (shrink)

In a recent article Ian Hacking argues that there can be cases where no probabilities may correctly be ascribed to individual members of a population, while probabilities are correctly ascribable to the population as a whole. In this paper a simple artificial coin-flipping model for such probabilities, not 'grounded from below' is constructed. The inferences licensed by this model and a consequence of the model for the theory of statistical tests is explored.

The gambler's fallacy and hot hand were studied in predictions about outcomes of coin tosses. A critical trial occurred when participants made predictions after a “run” of four heads or tails. Participants' attention was manipulated to focus on the person flipping the coin, the coin, or neither (control group) as a possible cause of the run. We also manipulated whether or not there was a change in who tossed the coin. In the control condition the standard reversal was (...) observed (gambler's fallacy); however, when participants focused on the person, and it was that same person who conducted the run and critical coin toss, more people chose in the direction of continuation (hot hand). Directing attention to the person tossing the run seemed to prompt participants to behave as if that individual was “hot” in terms of getting a specific outcome (e.g., heads), as if by sympathetic magic, thus eliminating the gambler's fallacy. (shrink)

A number of authors have claimed that the fact that our universe seems ’fine-tuned’ is evidence that there are many universes. Ian Hacking (1987) raised doubts about inferences to many sequential universes. More recently, Roger White has argued that it is a fallacy to infer that there are many universes, whether existing all at once or sequentially, from the fact that ours is fine-tuned. The upshot of our discussion will be that Hacking is right about the existence of certain (...) fallacious inferences, but that he (and White) are incorrect in their assimilation of arguments for many universes to these fallacious cases. (shrink)

This chapter contains sections titled: The False Cause Fallacy Hasty Generalizations Failure to Take Context into Account Suppressing Relevant Evidence The Gambler's Fallacy Affirming the Consequent/Denying the Antecedent The Fallacies of Composition and Division Missing the Forest for the Trees.

The most common objection to the Fine-Tuning Argument for the Multiverse is that the argument commits the Inverse Gambler’s Fallacy. Simon Friederich has recently composed an interesting version of this fine-tuning argument that avoids this fallacy and better-matches important scientific instances of anthropic reasoning. My thesis in this paper is that this new argument, while it may avoid the fallacy, contains a disputable premise concerning the prior probabilities of the hypotheses at issue. I consider various ways to (...) modify the argument to avoid this problem, but I argue that plausible replacements render other lines unjustified. I also briefly compare ‘indexical’ fine-tuning arguments such as Friederich’s, according to which our universe permits life, to ‘existential’ fine-tuning arguments, according to which some universe or other permits life. I conclude that while Friederich is correct that the new fine-tuning argument avoids the Inverse Gambler’s Fallacy, the argument nevertheless depends on an unjustified premise, and this is further reason for proponents of fine-tuning arguments for the multiverse to employ existential arguments rather than indexical arguments. (shrink)

When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference to real–world situations. (...) In lucid prose, he explores the many fallacies of probabilistic reasoning, such as the ‘gambler’s fallacy’ and the ‘inverse fallacy’, and shows how we can avoid falling into these traps by using the interpretations presented. He also illustrates the relevance of the interpretation of probability across disciplinary boundaries, by examining which interpretations of probability are appropriate in diverse areas such as quantum mechanics, game theory, and genetics. Using entertaining dialogues to draw out the key issues at stake, this unique book will appeal to students and scholars across philosophy, the social sciences, and the natural sciences. (shrink)

The universe appears fine-tuned for life. Bayesian confirmation theory is utilized to examine two competing explanations for this fine-tuning, namely design (theism) and the existence of many universes, in comparison with the ’null’ hypothesis that just one universe exists as a brute fact. Some authors have invoked the so-called ’inverse gambler’s fallacy’ to argue that the many-universes hypothesis does not explain the fine-tuning of ’this’ universe, but flaws in this argument are exposed. Nevertheless, the hypothesis of design, being simpler, (...) is arguably of higher prior probability and, therefore, to be preferred. The hypothesis of the single brute-fact universe is disconfirmed. (shrink)

In a number of recent papers I have been developing the theory of "nomic probability," which is supposed to be the kind of probability involved in statistical laws of nature. One of the main principles of this theory is an acceptance rule explicitly designed to handle the lottery paradox. This paper shows that the rule can also handle the paradox of the preface. The solution proceeds in part by pointing out a surprising connection between the paradox of the preface and (...) the gambler's fallacy. (shrink)

This paper has two aims. First, it points out a crucial difference between the standard argument from fine-tuning for the multiverse and paradigmatic instances of anthropic reasoning. The former treats the life-friendliness of our universe as the evidence whose impact is assessed, whereas the latter treat the life-friendliness of our universe as background information. Second, the paper develops a new fine-tuning argument for the multiverse which, unlike the old one, parallels the structure of paradigmatic instances of anthropic reasoning. The main (...) advantage of the new argument is that it is not susceptible to the inverse gambler’s fallacy charge. (shrink)

In this article I take a loose, functional approach to defining induction: Inductive forms of reasoning include those prima facie reasonable inference patterns that one finds in science and elsewhere that are not clearly deductive. Inductive inference is often taken to be reasoning from the observed to the unobserved. But that is incorrect, since the premises of inductive inferences may themselves be the results of prior inductions. A broader conception of inductive inference regards any ampliative inference as inductive, where an (...) ampliative inference is one where the conclusion ‘goes beyond’ the premises. ‘Goes beyond’ may mean (i) ‘not deducible from’ or (ii) ‘not entailed by’. Both of these are problematic. Regarding (i), some forms of reasoning might have a claim to be called ‘inductive’ because of their role in science, yet turn out to be deductive after all—for example eliminative induction (see below) or Aristotle’s ‘perfect induction’ which is an inference to a generalization from knowledge of every one of its instances. Interpretation (ii) requires that the conclusions of scientific reasoning are always contingent propositions, since necessary propositions are entailed by any premises. But there are good reasons from metaphysics for thinking that many general propositions of scientific interest and known by inductive inference (e.g. “all water is H2O”) are necessarily true. Finally, both (i) and (ii) fail to take account of the fact that there are many ampliative forms of inference one would not want to call inductive, such as counter-induction (exemplified by the ‘gambler’s fallacy’ that the longer a roulette wheel has come up red the more likely it is to come up black on the next roll). Brian Skyrms (1999) provides a useful survey of the issues involved in defining what is meant by ‘inductive argument’. Inductive knowledge will be the outcome of a successful inductive inference. But much discussion of induction concerns the theory of confirmation, which seeks to answer the question, “when and to what degree does evidence support an hypothesis?” Usually, this is understood in an incremental sense and in a way that relates to the rational credibility of a hypothesis: “when and by how much does e add to the credibility of h?”, although ‘confirms’ is sometimes used in an absolute sense to indicate total support that exceeds some suitably high threshold.. (shrink)

Cosmologists using the Anthropic Principle claim that if our universe had been much different then nobody would exist to observe it. This may become explanatory when one accepts the actual existence of multiple "universes": gigantic, largely or entirely separate systems having very varied properties. Ian Hacking has urged, though, that an Inverse Gambler's Fallacy is committed during many attempts to formulate anthropic explanations. Besides disagreeing with him, the paper makes several further points in support of such explanations, in (...) particular against the background of the Inflationary Universe. (shrink)

Erroneous gambling-related beliefs can be defined as beliefs that imply a failure to recognise how commercial gambling activities are designed to generate a guaranteed loss to players. In t...

The fine-tuning argument can be used to support the Many Universe hypothesis. The Inverse Gambler’s Fallacy objection seeks to undercut the support for the Many Universe hypothesis. The objection is that although the evidence that there is life somewhere confirms Many Universes, the specific evidence that there is life in this universe does not. I will argue that the Inverse Gambler’s Fallacy is not committed by the fine-tuning argument. The key issue is the procedure by which the universe (...) with life is selected for observation. Once we take account of the procedure, we find that the support for the Many Universe hypothesis remains. (shrink)

Randomness, a core concept of gambling, is seen in problem gambling as responsible for the formation of the math-related cognitive distortions, especially the Gambler’s Fallacy. In problem-gambling research, the concept of randomness was traditionally referred to as having a mathematical nature and categorized and approached as such. Randomness is not a mathematical concept, and I argue that its weak mathematical dimension is not decisive at all for the randomness-related issues in gambling and problem gambling, including the correction of the (...) misconceptions and fallacies about probability and statistical concepts applied in gambling. I distinguish between mathematical and nonmathematical dimensions of randomness (the epistemic, the theoretical-methodological, the functional, and the ethical) falling within the general concept, and I argue that both the studies having as object the math-related cognitive distortions among gamblers and the educational programs aiming at correcting them should employ this distinction in their design and content. (shrink)

Our best current science seems to suggest the laws of physics and the initial conditions of our universe are fine-tuned for the possibility of life. A significant number of scientists and philosophers believe that the fine-tuning is evidence for the multiverse hypothesis. This paper will focus on a much-discussed objection to the inference from the fine-tuning to the multiverse: the charge that this line of reasoning commits the inverse gambler’s fallacy. Despite the existence of a literature going back decades, (...) this philosophical debate has made little contact with scientific discussion of fine-tuning and the multiverse, which mainly revolves around a specific form of the multiverse hypothesis rooted in eternal inflation combined with string theory. Because of this, potentially important implications from science to philosophy, and vice versa, have been left underexplored. In this paper, I will take a first step at joining up these two discussions, by arguing that attention to the eternal inflation + string theory conception of the multiverse supports the inverse gambler’s fallacy charge. It does this by supporting the idea that our universe is contingently fine-tuned, thus addressing the concern that proponents of the inverse gambler’s fallacy charge have assumed this without argument. (shrink)

This paper defends the view that discovering that our universe is fine-tuned should make us more confident that other universes exist. My defense exploits a distinction between ideal and non-ideal evidential support. I use that distinction in concert with a simple model to disarm the most influential objection—the this-universe objection—to the view that fine-tuning supports the existence of other universes. However, the simple model fails to capture some important features of our epistemic situation with respect to fine-tuning. To capture these (...) features, I introduce a more sophisticated model. I then use the more sophisticated model to show that, even once those complicating factors are taken into account, fine-tuning should boost our confidence in the existence of other universes. (shrink)

Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed (...) as if reasonably reliable probability estimates were available for all possible outcomes, i.e. as if the prevailing epistemic conditions were analogous to those of gambling at the roulette table. This mistake can be called the tuxedo fallacy. It is argued that traditional engineering practices such as safety factors and multiple safety barriers avoid this fallacy and that they therefore manage uncertainty better than probabilistic risk analysis (PRA). PRA is a useful tool, but it must be supplemented with other methods in order not to limit the analysis to dangers that can be assigned meaningful probability estimates. (shrink)

Improving Your Reasoning is an expanded version of Chapter 10 of the author's larger work, Principles of Logic. The first chapter of Improving Your Reasoning is a general survey of arguments--deductive and inductive, valid and invalid, syllogistic and nonsyllogistic--and serves as an introduction for the rest of the book which deals only with fallacies. The types of fallacies are divided by chapter into the following principal categories: begging the question, pseudoauthority, irrelevant appeals, confusion, faulty classification, political fallacies, and inductive fallacies. (...) Each of these categories is further divided into a comprehensive range of sub-categories, with each sub-category presented in a short and easily understandable section. For example, inductive fallacies are divided into hasty generalization, accident, false cause, gambler's, faulty analogy, central tendency, misleading percentages, and misleading totals. Problems and answers are provided. This book may be used as a supplementary text for introductory logic.--T. G. N. (shrink)

In noting contemporary neglect of Mill's work on fallacy, Hansen and Pinto say that his account is tied more closely to scientific methodology than to problems of public discourse and everyday argumentation. This paper re-examines Mill's fallacies from a rhetorical perspective, assessing the extent to which his examples – drawn from the domains of popular superstition, science, philosophy, and public discussion – fit his theoretical structure. In articulating the relationship between Mill's philosophical assumptions and the discursive practices of the (...) fields from which he draws his examples, it will suggest the ambiguities in Mill's mentalistic, rationalistic, inductivist approach and the inescapable rhetoricity of his examples. (shrink)

According to the popular fitting attitude analysis of value, to be good is to be the object of a proattitude that it is fitting, in some sense, to have. One version of this analysis can be traced back to Franz Brentano, according to which “good” means “worthy of love.” In a review in Ethics of Brentano's The Origin of the Knowledge of Right and Wrong, G. E. Moore accuses Brentano of committing a fallacious inference, which I will call “Brentano's (...) class='Hi'>fallacy.” I shall show that Moore's accusation, properly formulated, hits the target and that his argument can be generalized so that it undermines other Brentano-like versions of the fitting attitude analysis. (shrink)

Adam's vision -- Gloomy science -- The severest critic -- On the margins -- Voices in the air -- Grand illusions.

David Hume has warned us not to endeavor to derive an “ought” from an “is” (1990, 469–70), reprimanding those who attempt to draw value judgments from empirical facts. But Judith Jarvis Thomson refuses to accept that values and facts are logically disjoint in this manner, primarily because of her worry that such a partition of our moral values from the “facts” will place a grave limitation on any ethical system, namely, that its claims apparently cannot be proven. Consequently, Thomson is (...) on the lookout for some provably true facts that can be used, contra Hume, to draw conclusions about moral values. Thomson begins by rejecting all generalist conceptions of the good (specifically, the utilitarian's identification of the good with pleasure) and proceeds to fracture the good into various kinds of “goodness in a way,” hoping to produce by this disintegration some moral facts that can be used to set ethics on an objective foundation. But I will argue that Thomson's so‐called objective facts are actually nothing but disguised moral claims, and that in attempting to sidestep the classic fallacy identified by Hume, she has blundered into another pitfall—the Smuggler's Fallacy, the offense of concealing her moral conclusions inside the premises of her argument. (shrink)

Amid undulating conceptions of the role and prowess of federalism emerges its central constitutional role: protecting American liberties against unwarranted governmental intrusions. To the extent that federalism is used as a guise for withdrawing fundamental rights to abortion by the U.S. Supreme Court in Dobbs v. Jackson Women’s Health Organization, individual rights are sacrificed in contravention of constitutional structural norms.

Argues against D. Hume's (1825) treatise "Of Miracles," which is often used to disprove the existence of psi. Hume states that a miracle is a violation of the laws of nature which are proved to be true by common experience, and that the only sufficient testimony for a miracle would be testimony whose falsehood would be even more miraculous than the miracle itself. The primary objections to Hume's argument are that (1) it is tautological, since it presupposes the nonexistence of (...) miraculous events, and (2) as a metaphysical statement, it is inappropriate when considering empirical evidence, which should be judged by its own rule. (shrink)

This paper reveals two fallacies in Turing's undecidability proof of first-order logic (FOL), namely, (i) an 'extensional fallacy': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a meaningful sentence is proven, and (ii) a 'fallacy of substitution': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a true sentence is proven. The first fallacy erroneously suggests that Turing's proof (...) of the non-existence of a circle-free machine that decides whether an arbitrary machine is circular proves a significant proposition. The second fallacy suggests that FOL is undecidable. (shrink)