The life of Niels Bohr spanned times of revolutionary change in science itself as well as its impact on society. Along with Albert Einstein, Bohr can be considered to be this century's major driving force behind the new philosophical and mathematical descriptions of the structure of the atom and the nucleus. Abraham Pais, the acclaimed biogrpaher of Albert Einstein, here traces Bohr's progress from his well-to-do origins in late nineteenth-century Denmark to his position at centre stage in the world political (...) scene, particularly during the Second World War and the development of atomic weapons. Pais' description moves through the science as it was before Bohr, as it became because of Bohr, and thence to Bohr's scientific and philosophical legacy. That legacy is contained both in theory as it is now universally enshrined, as well as in its practice in such great Danish institutions as Riso. But more than that, Pais captures the essence of Bohr, the intensely private family figure who, despite appalling personal tragedy, became one of the most loved cultural figures of recent times. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.

In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making and response time. The quantum walk (...) model is compared to standard sequential sampling models, and the architectural assumptions of both are considered. In particular, we show that the quantum model has a natural interpretation in terms of a cognitive architecture that is both massively parallel and involves both co-operative and competitive interactions between units. Additionally, we introduce a family of models that includes aspects of the classical and quantum walk models. (shrink)

First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that (...) probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials. (shrink)

A clear and accessible presentation of quantum theory, suitable for researchers yet accessible to graduates.

The 'Evolution of Cooperation' addresses a simple yet age-old question; If living things evolve through competition, how can cooperation ever emerge? Despite the abundant evidence of cooperation all around us, there existed no purely naturalistic answer to this question until 1979, when Robert Axelrod famously ran a computer tournament featuring a standard game-theory exercise called The Prisoner's Dilemma. To everyone's surprise, the program that won the tournament, named Tit for Tat, was not only the simplest but the most "cooperative" entrant. (...) This unexpected victory proved that cooperation - one might even say altruism - is mathematically possible and therefore needs no hidden hand or divine agent to create and sustain it. A great roadblock to the understanding of all sorts of behavior was at last removed. The updated edition includes an extensive new chapter on cooperation in cancer cells and among terrorist organizations. (shrink)

Are people rational? This question was central to Greek thought and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus (...) of certain reasoning. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

Oxford Philosophical Texts Series Editor: John Cottingham The Oxford Philosophical Texts series consists of authoritative teaching editions of canonical texts in the history of philosophy from the ancient world down to modern times. Each volume provides a clear, well laid out text together with a comprehensive introduction by a leading specialist, giving the student detailed critical guidance on the intellectual context of the work and the structure and philosophical importance of the main arguments. Endnotes are supplied which provide further commentary (...) on the arguments and explain unfamiliar references and terminology, and a full bibliography and index are also included. The series aims to build up a definitive corpus of key texts in the Western philosophical tradition, which will form a reliable and enduring resource for students and teachers alike. David Hume's aim in writing An Enquiry concerning Human Understanding was to introduce his philosophy to a European culture in which many educated people read original works of philosophy. He gives an elegant and accessible presentation of strikingly original and challenging views about the limited powers of human understanding, the attractions of scepticism, the compatibility of free will and determinism, and weaknesses in the foundations of religion. Hume's philosophy was highly controversial in the eighteenth century and remains so today. The text printed in this edition is that of the Clarendon critical edition of Hume's works. A substantial introduction by the editor explains the intellectual background to the work and surveys its main themes. The volume also includes detailed explanatory notes on the text, a glossary of terms, a full list of references, and a section of supplementary readings. (shrink)

THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

In these essays the minimalist approach to linguistic theory is formulated and progressively developed.

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining (...) the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. (shrink)

David Hume's Enquiry concerning Human Understanding is the definitive statement of the greatest philosopher in the English language. His arguments in support of reasoning from experience, and against the "sophistry and illusion"of religiously inspired philosophical fantasies, caused controversy in the eighteenth century and are strikingly relevant today, when faith and science continue to clash. The Enquiry considers the origin and processes of human thought, reaching the stark conclusion that we can have no ultimate understanding of the physical world, or indeed (...) our own minds. In either sphere we must depend on instinctive learning from experience, recognizing our animal nature and the limits of reason. Hume's calm and open-minded skepticism thus aims to provide a new basis for science, liberating us from the "superstition" of false metaphysics and religion. His Enquiry remains one of the best introductions to the study of philosophy, and his edition places it in its historical and philosophical context. (shrink)

One of the main themes that has emerged from behavioral decision research during the past three decades is the view that people's preferences are often constructed in the process of elicitation. This idea is derived from studies demonstrating that normatively equivalent methods of elicitation (e.g., choice and pricing) give rise to systematically different responses. These preference reversals violate the principle of procedure invariance that is fundamental to all theories of rational choice. If different elicitation procedures produce different orderings of options, (...) how can preferences be defined and in what sense do they exist? This book shows not only the historical roots of preference construction but also the blossoming of the concept within psychology, law, marketing, philosophy, environmental policy, and economics. Decision making is now understood to be a highly contingent form of information processing, sensitive to task complexity, time pressure, response mode, framing, reference points, and other contextual factors. (shrink)

In this book, Newell makes the case for unified theories by setting forth a candidate.

Newell proposed that cognitive theories be developed in an effort to satisfy multiple criteria and to avoid theoretical myopia. He provided two overlapping lists of 13 criteria that the human cognitive architecture would have to satisfy in order to be functional. We have distilled these into 12 criteria: flexible behavior, real-time performance, adaptive behavior, vast knowledge base, dynamic behavior, knowledge integration, natural language, learning, development, evolution, and brain realization. There would be greater theoretical progress if we evaluated theories by a (...) broad set of criteria such as these and attended to the weaknesses such evaluations revealed. To illustrate how theories can be evaluated we apply these criteria to both classical connectionism and the ACT-R theory. The strengths of classical connectionism on this test derive from its intense effort in addressing empirical phenomena in such domains as language and cognitive development. Its weaknesses derive from its failure to acknowledge a symbolic level to thought. In contrast, ACT-R includes both symbolic and subsymbolic components. The strengths of the ACT-R theory derive from its tight integration of the symbolic component with the subsymbolic component. Its weaknesses largely derive from its failure, as yet, to adequately engage in intensive analyses of issues related to certain criteria on Newell's list. Key Words: cognitive architecture; connectionism; hybrid systems; language; learning; symbolic systems. (shrink)

Summary. We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epistemic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems, compatible, comparable, commensurable, and complementary descriptions can be precisely characterized and distinguished from each other. Some tentative examples are indicated that, we suppose, would have (...) been of interest to Pauli. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal (...) result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...) that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts. (shrink)

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

_Figure 1. Dendrites and cell bodies of schematic neurons connected by dendritic-dendritic gap junctions form a laterally connected input_ _layer (“dendritic web”) within a neurocomputational architecture. Dendritic web dynamics are temporally coupled to gamma synchrony_ _EEG, and correspond with integration phases of “integrate and fire” cycles. Axonal firings provide input to, and output from, integration_ _phases (only one input, and three output axons are shown). Cell bodies/soma contain nuclei shown as black circles; microtubule networks_ _pervade the cytoplasm. According to the (...) Orch OR theory, gamma EEG-synchronized integration phases include quantum computations in_ _microtubule networks which culminate with conscious moments. Insert closeup shows a gap junction through which microtubule quantum_ _states entangle among different neurons, enabling macroscopic quantum states in dendritic webs extending throughout cortex and other_ _brain regions._. (shrink)

The book is the first to give a systematic account, founded in fundamental quantum physical principles, of how the brain functions as a unified system.

Grush and Churchland (1995) attempt to address aspects of the proposal that we have been making concerning a possible physical mechanism underlying the phenomenon of consciousness. Unfortunately, they employ arguments that are highly misleading and, in some important respects, factually incorrect. Their article ‘Gaps in Penrose’s Toilings’ is addressed specifically at the writings of one of us (Penrose), but since the particular model they attack is one put forward by both of us (Hameroff and Penrose, 1995; 1996), it is appropriate (...) that we both reply; but since our individual remarks refer to different aspects of their criticism we are commenting on their article separately. The logical arguments discussed by Grush and Churchland, and the related physics are answered in Part l by Penrose, largely by pointing out precisely where these arguments have already been treated in detail in Shadows of the Mind (Penrose, 1994). In Part 2, Hameroff replies to various points on the biological side, showing for example how they have seriously misunderstood what they refer to as ‘physiological evidence’ regarding to effects of the drug colchicine. The reply serves also to discuss aspects of our model ‘orchestrated objective reduction in brain microtubules – Orch OR’ which attempts to deal with the serious problems of consciousness more directly and completely than any previous theory. (shrink)

The thirty-five chapters in this book describe various judgmental heuristics and the biases they produce, not only in laboratory experiments but in important...

One of the most notable aspects of Fodor's work is that it articulates features not only of speculative cognitive architectures but also of current research in ...

Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...

This volume tackles the slippery subject of 'meaning'.

To make progress on the problem of consciousness, we have to confront it directly. In this paper, I first isolate the truly hard part of the problem, separating it from more tractable parts and giving an account of why it is so difficult to explain. I critique some recent work that uses reductive methods to address consciousness, and argue that such methods inevitably fail to come to grips with the hardest part of the problem. Once this failure is recognized, the (...) door to further progress is opened. In the second half of the paper, I argue that if we move to a new kind of nonreductive explanation, a naturalistic account of consciousness can be given. I put forward my own candidate for such an account: a nonreductive theory based on principles of structural coherence and organizational invariance, and a double-aspect theory of information. (shrink)

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', (...) allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. (...) Additionally, the principle of semantic compositionality is underspecifi ed, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations. (shrink)

We propose a critique ofnormativism, defined as the idea that human thinking reflects a normative system against which it should be measured and judged. We analyze the methodological problems associated with normativism, proposing that it invites the controversial “is-ought” inference, much contested in the philosophical literature. This problem is triggered when there are competing normative accounts (the arbitration problem), as empirical evidence can help arbitrate between descriptive theories, but not between normative systems. Drawing on linguistics as a model, we propose (...) that a clear distinction between normative systems and competence theories is essential, arguing that equating them invites an “is-ought” inference: to wit, supporting normative “ought” theories with empirical “is” evidence. We analyze in detail two research programmes with normativist features – Oaksford and Chater's rational analysis and Stanovich and West's individual differences approach – demonstrating how, in each case, equating norm and competence leads to an is-ought inference. Normativism triggers a host of research biases in the psychology of reasoning and decision making: focusing on untrained participants and novel problems, analyzing psychological processes in terms of their normative correlates, and neglecting philosophically significant paradigms when they do not supply clear standards for normative judgement. For example, in a dual-process framework, normativism can lead to a fallacious “ought-is” inference, in which normative responses are taken as diagnostic of analytic reasoning. We propose that little can be gained from normativism that cannot be achieved by descriptivist computational-level analysis, illustrating our position with Hypothetical Thinking Theory and the theory of the suppositional conditional. We conclude that descriptivism is a viable option, and that theories of higher mental processing would be better off freed from normative considerations. (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)