An extraordinary, if circumscribed, positive shift has occurred since the mid-twentieth century in the perceived status of Hugh Everett III's 1956 theory of the universal wave function of quantum mechanics, now widely called the Many-Worlds Interpretation (MWI). Everett's starkly new interpretation denied the existence of a separate classical realm, contending that the experimental data can be seen as presenting a state vector for the whole universe. Since there is no state vector collapse, reality as a whole is strictly deterministic. Explained (...) jointly by the dynamical variables and the state vector, “this reality is not the reality we customarily think of, but is a reality composed of many worlds,” wrote Everett's colleague Bryce DeWitt. In this essay, I account briefly for the change of status in conventional scientific terms, yet chiefly in extended terms of three sets of ideas that I argue can be understood to affect believability in both scientific and religious contexts, illuminating helpfully the MWI phenomenon, and its engagement with theology: orthodoxy and heresy, language and reference, and faith and agnosticism. One's orientation relative to the variable content of these dynamic, socially oriented categories helps to make belief in ideas as metaphysically challenging as Everettian Quantum Mechanics, or particular ideas about God, either more or less believable. The categories will have the same function in a theology engaging Everett's theory, and in any theology at all written in a society deeply marked by what I further argue is a subtle, powerful, and pervasive mode of quasi-scientific thinking we can call societal constructive agnosticism, of which anyone doing theology today must be aware. (shrink)

Using a longitudinal case study design, we have tracked the recovery of motor function following severe traumatic brain injury (TBI) through a multimodal neuroimaging approach. In 2006, Canadian Soldier Captain (retired) Trevor Greene (TG) was attacked with an axe to the head while on tour in Afghanistan. TG continues intensive daily rehabilitation, which recently included the integration of physical therapy (PT) with neuromodulation using translingual neurostimulation (TLNS) to facilitate neuroplasticity. Recent findings with PT+TLNS demonstrated that recovery of motor function occurred (...) beyond conventional time limits, currently extending past 14-years post-injury. To investigate whether PT+TLNS similarly resulted in associated cognitive function improvements, we examined event-related potentials (ERPs) with the brain vital signs framework. In parallel with motor function improvements, brain vital signs detected significant increases in basic attention (as measured by P300 response amplitude) and cognitive processing (as measured by contextual N400 response amplitude). These objective cognitive improvements corresponded with TG’s self-reported improvements, including a noteworthy and consistent reduction in ongoing symptoms of post-traumatic stress disorder (PTSD). The findings provide valuable insight into the potential importance of non-invasive neuromodulation in cognitive rehabilitation, in addition to initial indications for physical rehabilitation. (shrink)

We consider extensions of Peano arithmetic suitable for doing some of nonstandard analysis, in which there is a predicate N(x) for an elementary initial segment, along with axiom schemes approximating ω 1 -saturation. We prove that such systems have the same proof-theoretic strength as their natural analogues in second order arithmetic. We close by presenting an even stronger extension of Peano arithmetic, which is equivalent to ZF for arithmetic statements.

A new method for obtaining lower bounds on the computational complexity of logical theories is presented. It extends widely used techniques for proving the undecidability of theories by interpreting models of a theory already known to be undecidable. New inseparability results related to the well known inseparability result of Trakhtenbrot and Vaught are the foundation of the method. Their use yields hereditary lower bounds . By means of interpretations lower bounds can be transferred from one theory to another. Complicated machine (...) codings are replaced by much simpler definability considerations, viz., the kinds of binary relations definable with short formulas on large finite sets. Numerous examples are given, including new proofs of essentially all previously known lower bounds for theories, and lower bounds for various theories of finite trees, which turn out to be particularly useful. (shrink)

In this paper we consider some axiomatic systems of set theory related to the system NF (New Foundations) of Quine. In particular we discuss the possible relations of cardinality between a finite set x and its subset class SC(x) = {y | y ∩ x} and also between x and its unit set class USC(x) = {{y} | y ε x}. Specker [5] has shown that in NF the cardinal of a finite set x can never be the same as (...) the cardinal of SC(x). (shrink)

We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes and Rosenthal [12]. In order to do this,•We study and compare three notions of convergence of types in a stable theory: logic convergence, i.e., formula by formula, metric convergence (both already well studied) and convergence of canonical bases. In particular, we characterise א0-categorical stable theories in which the last two agree.•We characterise sequences that admit almost indiscernible sub-sequences.•We apply these tools to the theory of (...) atomless random variables (ARV). We characterise types and notions of convergence of types as conditional distributions and weak/strong convergence thereof, and obtain, among other things, the Main Theorem of Berkes and Rosenthal. (shrink)

While we agree in broad strokes with the characterisation of rationalization as a “useful fiction,” we think that Fiery Cushman's claim remains ambiguous in two crucial respects: the reality of beliefs and desires, that is, the fictional status of folk-psychological entities and the degree to which they should be understood as useful. Our aim is to clarify both points and explicate the rationale of rationalization.

The main question that Firestone & Scholl (F&S) pose is whether “what and how we see is functionally independent from what and how we think, know, desire, act, and so forth” (sect. 2, para. 1). We synthesize a collection of concerns from an interdisciplinary set of coauthors regarding F&S's assumptions and appeals to intuition, resulting in their treatment of visual perception as context-free.

Presents a plethora of approaches to developing human potential in areas not conventionally addressed. Organized in two parts, this international collection of essays provides viable educational alternatives to those currently holding sway in an era of high-stakes accountability.

Critically significant parental effects in behavioral genetics may be partly understood as a consequence of maternal brain structure and function of caregiving systems recently studied in humans as well as rodents. Key parental brain areas regulate emotions, motivation/reward, and decision making, as well as more complex social-cognitive circuits. Additional key environmental factors must include socioeconomic status and paternal brain physiology. These have implications for developmental and evolutionary biology as well as public policy.

This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately.In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (...) (b) the definition of Bell’s locality condition does not rely on separability in any way; (c) the proof of Bell’s theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell’s theorem are weakened, what remains no longer embodies the locality principle. Teller’s argument for “relational holism” and Howard’s arguments concerning separability are criticised in the light of these results. Howard’s claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem. (shrink)

In 1984, Henson and Rubel [2] proved the following theorem: If p(x₁, ..., x n ) is an exponential polynomial with coefficients in with no zeroes in ℂ, then $p({x_1},...,{x_n}) = {e^{g({x_{1......}}{x_n})}}$ where g(x₁......x n ) is some exponential polynomial over ℂ. In this paper, I will prove the analog of this theorem for Zilber's Pseudoexponential fields directly from the axioms. Furthermore, this proof relies only on the existential closedness axiom without any reference to Schanuel's conjecture.

Critical thinking, defined as a person's ability and inclination to make and assess conclusions based on evidence is a commonly studied area of education. This issue focuses on using the case study method to promote critical thinking. The goal of critical thinking, i.e. leading others to become critical thinkers, can best be reached and, indeed, perhaps can only be reached in a learner-centered climate. Today's curriculum reform is calling for teachers to align their curricula with state and national standards, and (...) central to this goal is the ability to evaluate the curriculum. While the case study method is an ideal vehicle to promote critical thinking in the classroom, its application need not be limited to the classroom. (PsycINFO Database Record (c) 2007 APA, all rights reserved). (shrink)

Que signifie le fait d’avoir le statut de personne morale, c’est-à-dire d’avoir la capacité de responsabilité morale? Dans un important essai sur la question, Dennett a proposé six conditions qui définissent ce concept. Premièrement, l’entité à laquelle nous attribuerions le statut de personne morale doit être douée de rationalité. Deuxièmement, elle doit être capable d’adopter la position intentionnelle — c’est-à-dire qu’elle doit être capable d’attribuer des intentions aux autres. Troisièmement, elle doit pouvoir être l’objet d’une certaine attitude. Quatrièmement, elle doit (...) être capable de réciprocité de manière à pouvoir répondre à cette attitude. Cinquièmement, elle doit être capable de communiquer avec les autres. Les troisième, quatrième et cinquième conditions, de façon explicite et significative, impliquent des dimensions sociales, bien que, pour Dennett, la nature précise de ces dimensions sociales demeure une question encore ouverte. Enfin, ces cinq premières conditions sont nécessaires pour la sixième : l’entité doit être capable de conscience de soi. La conscience de soi est comprise ici comme étant un processus mental d’un ordre supérieur, dont, ainsi que le suggèrent Dennett et d’autres, les jeunes enfants sont incapables. Bien plus, dans une variété d’autres contextes, Dennett. (shrink)

We present a new modeling framework for recognition memory and repetition priming based on signal detection theory. We use this framework to specify and test the predictions of 4 models: (a) a single-system (SS) model, in which one continuous memory signal drives recognition and priming; (b) a multiple-systems-1 (MS1) model, in which completely independent memory signals (such as explicit and implicit memory) drive recognition and priming; (c) a multiple-systems-2 (MS2) model, in which there are also 2 memory signals, but some (...) degree of dependence is allowed between these 2 signals (and this model subsumes the SS and MS1 models as special cases); and (d) a dual-process signal detection (DPSD1) model, 1 possible extension of a dual-process theory of recognition (Yonelinas, 1994) to priming, in which a signal detection model is augmented by an independent recollection process. The predictions of the models are tested in a continuous-identification-with-recognition paradigm in both normal adults (Experiments 1–3) and amnesic individuals (using data from Conroy, Hopkins, & Squire,2005). The SS model predicted numerous results in advance. These were not predicted by the MS1 model, though could be accommodated by the more flexible MS2 model. Importantly, measures of overall model fit favored the SS model over the others. These results illustrate a new, formal approach to testing theories of explicit and implicit memory. (shrink)

Christopher Frith is a research professor at the Functional Imaging Laboratory of the Wellcome Department of Imaging Neuroscience at University College, London. He explores, experimentally, using the techniques of functional brain imaging, the relationship between human consciousness and the brain. His research focuses on questions pertaining to perception, attention, control of action, free will, and awareness of our own mental states and those of others. As the following discussion makes clear, Frith investigates brain systems involved in the choice of one (...) action over another and in the understanding of other people. Such investigations are aimed at understanding brain basis of autism and schizophrenia. In his widely cited study of schizophrenia, The Cognitive Neuropsychology of Schizophrenia , Frith argues that many of the positive symptoms of schizophrenia, such as delusions of control, auditory hallucinations, and thought insertion, involve problems of self-monitoring. Patients, in effect, lose track of their own intentions and mistakenly attribute agency for their own actions to someone else. Frith employs models of motor control, involving comparator mechanisms and efference copy, not only to explain delusions that involve movement, but also to develop a neurocognitive explanation of delusional cognition. (shrink)

We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K. In this paper we obtain a similar characterization of (...) approximability of a locally compact system A by systems from K using the language of nonstandard analysis. In the signature of A we introduce positive bounded formulas and their approximations; these are similar to those introduced by Henson [14] for Banach space structures (see also [15, 16]). We prove that a positive bounded formula φ holds in A if and only if all precise enough approximations of φ hold in all precise enough approximations of A. We also prove that a locally compact field cannot be approximated arbitrarily closely by finite (associative) rings (even if the rings are allowed to be non-commutative). Finite approximations of the field R can be considered as possible computer systems for real arithmetic. Thus, our results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings. (shrink)

We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with results from cite{BenYaacov:Perturbations} (...) regarding perturbations of bounded metric structures, we prove a Ryll-Nardzewski style characterisation of theories of Banach spaces which are separably categorical up to small perturbation of the norm. This last result is motivated by an unpublished result of Henson. (shrink)