We review the current status of fuzzy-trace theory. The presentation is organized around five topics. First, theoretical ideas that immediately preceded the development of fuzzy-trace theory are sketched. Second, experimental findings that challenged those ideas are summarized. Third, the core assumptions that comprised the initial version of fuzzy-trace theory are described. Fourth, some modifications to those assumptions are explored that were necessitated by subsequent experimental findings. Fifth, four areas of experimentation are considered in which research under the aegis of fuzzy-trace (...) theory is in progress: suggestibility and false memories; judgment and decision making; the development of forgetting; and the development of retrieval. (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)

It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, (...) fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic. (shrink)

First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.

Using everyday language, spatial concepts, visualizations and his renowned "Feynman diagrams," the author clearly and humorously communicates the substance and spirit of QED (quantum electodynamics).

The law of gravitation, an example of physical law The relation of mathematics to physics The great conservation principles Symmetry in physical law The distinction of past and future Probability and uncertainty: the quantum mechanical view of nature Seeking new laws.

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.

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...) show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation. (shrink)

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability (...) theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. (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)

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (shrink)

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

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.

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 outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...) here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (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 sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...) the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. (shrink)

A framework for the mind-matter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive non-Boolean description of a world without an a priori mind-matter distinction. Such a description in terms of a locally Boolean but globally non-Boolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are (...) no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely non-Boolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain.In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given a priori we have to expect correlations between these two domains. In physics it corresponds to Newton 's separation of universal laws of nature and contingent initial conditions Both descriptions have a non-Boolean structure and can be encompassed into a single non-Boolean description. Tensed and tenseless time can be synchronized by holistic correlations. (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)

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)