2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive (...) reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket. (shrink)

Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

Repeatedly and successfully, the celebrated Harvard philosopher Robert Nozick has reached out to a broad audience beyond the confines of his discipline, addressing ethical and social problems that matter to every thoughtful person. Here Nozick continues his search for the connections between philosophy and "ordinary" experience. In the lively and accessible style that his readers have come to expect, he offers a bold theory of rationality, the one characteristic deemed to fix humanity's "specialness." What are principles for? asks Nozick. We (...) could act simply on whim, or maximize our self-interest and recommend that others do the same. As Nozick explores rationality of decision and rationality of belief, he shows how principles actually function in our day-to-day thinking and in our efforts to live peacefully and productively with each other. Throughout, the book combines daring speculations with detailed investigations to portray the nature and status of rationality and the essential role that imagination plays in this singular human aptitude. (shrink)

This article described three heuristics that are employed in making judgements under uncertainty: representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and adjustment from an anchor, which is usually employed in numerical prediction when a relevant value (...) is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty. (shrink)

Neuroethological investigations of mammalian and avian auditory systems have documented species-specific specializations for processing complex acoustic signals that could, if viewed in abstract terms, have an intriguing and striking relevance for human speech sound categorization and representation. Each species forms biologically relevant categories based on combinatorial analysis of information-bearing parameters within the complex input signal. This target article uses known neural models from the mustached bat and barn owl to develop, by analogy, a conceptualization of human processing of consonant plus (...) vowel sequences that offers a partial solution to the noninvariance dilemma the locus equations orderly output constraint”) is hypothesized based on the notion of an evolutionarily conserved auditory-processing strategy. High correlation and linearity between critical parameters in the speech signal that help to cue place of articulation categories might have evolved to satisfy a preadaptation by mammalian auditory systems for representing tightly correlated, linearly related components of acoustic signals. (shrink)

Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize figural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one (...) another, that tend to maintain their size and shape over motion, and that tend to act upon each other only on contact. These findings suggest that o general representation of object unity and boundaries is interposed between representations of surfaces and representations of objects of familiar kinds. The processes that construct this representation may be related to processes of physical reasoning. (shrink)

Throughout, the book combines daring speculations with detailed investigations to portray the nature and status of rationality and the essential role that...

The now-classic Metaphors We Live By changed our understanding of metaphor and its role in language and the mind. Metaphor, the authors explain, is a fundamental mechanism of mind, one that allows us to use what we know about our physical and social experience to provide understanding of countless other subjects. Because such metaphors structure our most basic understandings of our experience, they are "metaphors we live by"--metaphors that can shape our perceptions and actions without our ever noticing them. In (...) this updated edition of Lakoff and Johnson's influential book, the authors supply an afterword surveying how their theory of metaphor has developed within the cognitive sciences to become central to the contemporary understanding of how we think and how we express our thoughts in language. (shrink)

Hans Krebs' discovery, in 1932, of the urea cycle was a major event in biochemistry. This article describes a program, KEKADA, which models the heuristics Hans Krebs used in this discovery. KEKADA reacts to surprises, formulates explanations, and carries out experiments in the same manner as the evidence in the form of laboratory notebooks and interviews indicates Hans Krebs did. Furthermore, we answer a number of questions about the nature of the heuristics used by Krebs, in particular: How domain‐specific are (...) the heuristics? To what extent are they idiosyncratic to Krebs? To what extent do they represent general strategies of problem‐solving search?The relative generality of KEKADA allows us to view the control structure of KEKADA and its domain‐independent heuristics as a model of scientific experimentation that should apply over a broad domain. (shrink)

Considers that intuitive predictions follow a judgmental heuristic-representativeness. By this heuristic, people predict the outcome that appears most representative of the evidence. Consequently, intuitive predictions are insensitive to the reliability of the evidence or to the prior probability of the outcome, in violation of the logic of statistical prediction. The hypothesis that people predict by representativeness was supported in a series of studies with both naive and sophisticated university students. The ranking of outcomes by likelihood coincided with the ranking by (...) representativeness, and Ss erroneously predicted rare events and extreme values if these happened to be representative. The experience of unjustified confidence in predictions and the prevalence of fallacious intuitions concerning statistical regression are traced to the representativeness heuristic. (shrink)

Stanovich & West analyze individual differences with respect to response output (e.g., participants' numerical estimates). They do not analyze the underlying cognitive processes that led to the outputs; they thereby probably misclassify some non-normative responses as normative. Using base rate neglect and overconfidence as examples, I demonstrate the advantages of analyzing cognitive processes further.

I argue that explanation should be thought of as the phenomenological mark of the operation of a particular kind of cognitive system, the theory-formation system. The theory-formation system operates most clearly in children and scientists but is also part of our everyday cognition. The system is devoted to uncovering the underlying causal structure of the world. Since this process often involves active intervention in the world, in the case of systematic experiment in scientists, and play in children, the cognitive system (...) is accompanied by a theory drive, a motivational system that impels us to interpret new evidence in terms of existing theories and change our theories in the light of new evidence. What we usually think of as explanation is the phenomenological state that accompanies the satisfaction of this drive. However, the relation between the phenomenology and the cognitive system is contingent, as in similar cases of sexual and visual phenomenology. Distinctive explanatory phenomenology may also help us to identify when the theory-formation system is operating. (shrink)

[Correction Notice: An erratum for this article was reported in Vol 109 of Psychological Review. Due to circumstances that were beyond the control of the authors, the studies reported in "Models of Ecological Rationality: The Recognition Heuristic," by Daniel G. Goldstein and Gerd Gigerenzer overlap with studies reported in "The Recognition Heuristic: How Ignorance Makes Us Smart," by the same authors and with studies reported in "Inference From Ignorance: The Recognition Heuristic". In addition, Figure 3 in the Psychological Review article (...) was originally published in the book chapter and should have carried a note saying that it was used by permission of Oxford University Press.] One view of heuristics is that they are imperfect versions of optimal statistical procedures considered too complicated for ordinary minds to carry out. In contrast, the authors consider heuristics to be adaptive strategies that evolved in tandem with fundamental psychological mechanisms. The recognition heuristic, arguably the most frugal of all heuristics, makes inferences from patterns of missing knowledge. This heuristic exploits a fundamental adaptation of many organisms: the vast, sensitive, and reliable capacity for recognition. The authors specify the conditions under which the recognition heuristic is successful and when it leads to the counter-intuitive less-is-more effect in which less knowledge is better than more for making accurate inferences. (shrink)

I argue that psychologists interested in human causal judgment should understand and adopt a representation of causal mechanisms by directed graphs that encode conditional independence (screening off) relations. I illustrate the benefits of that representation, now widely used in computer science and increasingly in statistics, by (i) showing that a dispute in psychology between ‘mechanist’ and ‘associationist’ psychological theories of causation rests on a false and confused dichotomy; (ii) showing that a recent, much-cited experiment, purporting to show that human subjects, (...) incorrectly let large causes ‘overshadow’ small causes, misrepresents the most likely, and warranted, causal explanation available to the subjects, in the light of which their responses were normative; (iii) showing how a recent psychological theory (due to P. Cheng) of human judgment of causal power can be considerably generalized: and (iv) suggesting a range of possible experiments comparing human and computer abilities to extract causal information from associations. (shrink)

Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon's notion of satisficing, the authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the (...) authors held a competition between the satisficing "Take The Best" algorithm and various "rational" inference procedures. The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result is an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference. (shrink)

This is a book about how we see: the environment around us (its surfaces, their layout, and their colors and textures); where we are in the environment; whether or not we are moving and, if we are, where we are going; what things are good for; how to do things (to thread a needle or drive an automobile); or why things look as they do.The basic assumption is that vision depends on the eye which is connected to the brain. The (...) author suggests that natural vision depends on the eyes in the head on a body supported by the ground, the brain being only the central organ of a complete visual system. When no constraints are put on the visual system, people look around, walk up to something interesting and move around it so as to see it from all sides, and go from one vista to another. That is natural vision—and what this book is about. (shrink)

Proper linear models are those in which predictor variables are given weights such that the resulting linear composite optimally predicts some criterion of interest; examples of proper linear models are standard regression analysis, discriminant function analysis, and ridge regression analysis. Research summarized in P. Meehl's book on clinical vs statistical prediction and research stimulated in part by that book indicate that when a numerical criterion variable is to be predicted from numerical predictor variables, proper linear models outperform clinical intuition. Improper (...) linear models are those in which the weights of the predictor variables are obtained by some nonoptimal method. The present article presents evidence that even such improper linear models are superior to clinical intuition when predicting a numerical criterion from numerical predictors. In fact, unit weighting is quite robust for making such predictions. The application of unit weights to decide what bullet the Denver Police Department should use is described; some technical, psychological, and ethical resistances to using linear models in making social decisions are considered; and arguments that could weaken these resistances are presented. (shrink)

A review of the literature indicates that linear models are frequently used in situations in which decisions are made on the basis of multiple codable inputs. These models are sometimes used normatively to aid the decision maker, as a contrast with the decision maker in the clinical vs statistical controversy, to represent the decision maker "paramorphically" and to "bootstrap" the decision maker by replacing him with his representation. Examination of the contexts in which linear models have been successfully employed indicates (...) that the contexts have the following structural characteristics in common: each input variable has a conditionally monotone relationship with the output; there is error of measurement; and deviations from optimal weighting do not make much practical difference. These characteristics ensure the success of linear models, which are so appropriate in such contexts that random linear models may perform quite well. 4 examples involving the prediction of such codable output variables as GPA and psychiatric diagnosis are analyzed in detail. In all 4 examples, random linear models yield predictions that are superior to those of human judges. (shrink)

Can quite different values be rationally weighed against one another? Can the value of one thing always be ranked as greater than, equal to, or less than the value of something else? If the answer to these questions is no, then in what areas do we find commensurability and comparability unavailable? And what are the implications for moral and legal decision making? This book struggles with these questions, and arrives at distinctly different answers.".

Much research on judgment and decision making has focussed on the adequacy of classical rationality as a description of human reasoning. But more recently it has been argued that classical rationality should also be rejected even as normative standards for human reasoning. For example, Gigerenzer and Goldstein and Gigerenzer and Todd argue that reasoning involves “fast and frugal” algorithms which are not justified by rational norms, but which succeed in the environment. They provide three lines of argument for this view, (...) based on: the importance of the environment; the existence of cognitive limitations; and the fact that an algorithm with no apparent rational basis, Take-the-Best, succeeds in an judgment task. We reconsider –, arguing that standard patterns of explanation in psychology and the social and biological sciences, use rational norms to explain why simple cognitive algorithms can succeed. We also present new computer simulations that compare Take-the-Best with other cognitive models. Although Take-the-Best still performs well, it does not perform noticeably better than the other models. We conclude that these results provide no strong reason to prefer Take-the-Best over alternative cognitive models. (shrink)

A working assumption that processes of natural and cultural evolution have tailored the mind to fit the demands and structure of its environment begs the question: how are we to characterize the structure of cognitive environments? Decision problems faced by real organisms are not like simple multiple-choice examination papers. For example, some individual problems may occur much more frequently than others, whilst some may carry much more weight than others. Such considerations are not taken into account when (i) the performance (...) of candidate cognitive mechanisms is assessed by employing a simple accuracy metric that is insensitive to the structure of the decision-maker's environment, and (ii) reason is defined as the adherence to internalist prescriptions of classical rationality. Here we explore the impact of frequency and significance structure on the performance of a range of candidate decision-making mechanisms. We show that the character of this impact is complex, since structured environments demand that decision-makers trade off general performance against performance on important subsets of test items. As a result, environment structure obviates internalist criteria of rationality. Failing to appreciate the role of environment structure in shaping cognition can lead to mischaracterising adaptive behavior as irrational. (shrink)