Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency – as though these inferences were a reflexive response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuronlike elements represent a large (...) body of systemic knowledge and perform a range of inferences with such speed? We describe a computational model that takes a step toward addressing the cognitive science challenge and resolving the artificial intelligence paradox. We show how a connectionist network can encode millions of facts and rules involving n-ary predicates and variables and perform a class of inferences in a few hundred milliseconds. Efficient reasoning requires the rapid representation and propagation of dynamic bindings. Our model (which we refer to as SHRUTI) achieves this by representing (1) dynamic bindings as the synchronous firing of appropriate nodes, (2) rules as interconnection patterns that direct the propagation of rhythmic activity, and (3) long-term facts as temporal pattern-matching subnetworks. The model is consistent with recent neurophysiological evidence that synchronous activity occurs in the brain and may play a representational role in neural information processing. The model also makes specific psychologically significant predictions about the nature of reflexive reasoning. It identifies constraints on the form of rules that may participate in such reasoning and relates the capacity of the working memory underlying reflexive reasoning to biological parameters such as the lowest frequency at which nodes can sustain synchronous oscillations and the coarseness of synchronization. (shrink)

Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the (...) search for such examples of the structure mentioned above that do not stem from Jordan operator algebras; first natural candidates are matrix algebras over the octonions and other nonassociative rings. Therefore, the case when a nonassociative commutative multiplication exists is studied without assuming that it satisfies the Jordan condition. The characteristics of the resulting algebra are analyzed. This includes the uniqueness of the spectral resolution as well as a criterion for its existence, subalgebras that are Jordan algebras, associative subalgebras, and more different levels of compatibility than occurring in standard quantum mechanics. However, the paper cannot provide the desired example, but contribute to the search by the identification of some typical differences between the potential examples and the Jordan operator algebras and by negative results concerning some first natural candidates. The possibility that no such example exists cannot be ruled out. However, this would result in an unexpected new characterization of Jordan operator algebras, which would have a significant impact on quantum axiomatics since some customary axioms (e.g., power-associativity or the sum postulate for observables) might turn out to be redundant then. (shrink)

The present study investigates the types of verb and symbolic representational strategies used by 10 deaf signing adults and 13 deaf signing children who described in Italian Sign Language 45 video clips representing nine action types generally communicated by five general verbs in spoken Italian. General verbs, in which the same sign was produced to refer to several different physical action types, were rarely used by either group of participants. Both signing children and adults usually produced specific depicting predicates (...) by incorporating, through a representational strategy, the object and/or the modality of the action into the sign. As for the different types of representational strategies, the adults used the hand-as-object strategy more frequently than the children, who, in turn, preferred to use the hand-as-hand strategy, suggesting that different degrees of cognitive complexity are involved in these two symbolic strategies. Addressing the symbolic iconic strategies underlying sign formation could provide new insight into the perceptual and cognitive processes of linguistic meaning construction. The findings reported here support two main assumptions of cognitive linguistics applied to sign languages: there is a strong continuity between gestures and language; lexical units and depicting constructions derive from the same iconic core mechanism of sign creation. (shrink)

In this paper I argue that noun complement modality cannot be treated as dependent on the meanings of lexical embedding predicates or of abstract performatives. Using two types of complement modalities, I show that their meanings and restrictions remain distinct and invariable regardless of the meanings of their embedding predicates. Then, using embedding predicates that can take both types of modalities, I show that the embedding predicates retain their meanings, regardless of the different modalities of their (...) complements, and they can undergo deletions requiring their identity. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the spectral picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms -- for example, the Fourier transform. According to the "spectral" picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

We continue work of our earlier paper :219–241, 2009) where abstract logics and particularly intuitionistic abstract logics are studied.logics can be topologized in a direct and natural way. This facilitates a topological study of classes of concrete logics whenever they are given in abstract form. Moreover, such a direct topological approach avoids the often complex algebraic and lattice-theoretic machinery usually applied to represent logics. Motivated by that point of view, we define in this paper the category of intuitionistic abstract logics (...) with stable logic maps as morphisms, and the category of implicative spectral spaces with spectral maps as morphisms. We show the equivalence of these categories and conclude that the larger categories of distributive abstract logics and distributive sober spaces are equivalent, too. (shrink)

Interpretation of different writing styles, unconstrained cursiveness and relationship between different primitive parts is an essential and challenging task for recognition of handwritten characters. As feature representation is inadequate, appropriate interpretation/description of handwritten characters seems to be a challenging task. Although existing research in handwritten characters is extensive, it still remains a challenge to get the effective representation of characters in feature space. In this paper, we make an attempt to circumvent these problems by proposing an approach that (...) exploits the robust graph representation and spectral graph embedding concept to characterise and effectively represent handwritten characters, taking into account writing styles, cursiveness and relationships. For corroboration of the efficacy of the proposed method, extensive experiments were carried out on the standard handwritten numeral Computer Vision Pattern Recognition, Unit of Indian Statistical Institute Kolkata dataset. The experimental results demonstrate promising findings, which can be used in future studies. (shrink)

Why is a red face not really red? How do we decide that this book is a textbook or not? Conceptual spaces provide the medium on which these computations are performed, but an additional operation is needed: Contrast. By contrasting a reddish face with a prototypical face, one gets a prototypical ‘red’. By contrasting this book with a prototypical textbook, the lack of exercises may pop out. Dynamic contrasting is an essential operation for converting perceptions into predicates. The existence (...) of dynamic contrasting may contribute to explaining why lexical meanings correspond to convex regions of conceptual spaces. But it also explains why predication is most of the time opportunistic, depending on context. While off-line conceptual similarity is a holistic operation, the contrast operation provides a context-dependent distance that creates ephemeral predicative judgments that are essential for interfacing conceptual spaces with natural language and with reasoning. (shrink)

Abstract The notion of necessary new terms (predicates) is proposed. It is shown that necessary new predicates in first?order logic must be directly, recursively defined. I present a first?order inductive learning algorithm that introduces new necessary predicates to model scientific revolution in which a new language is adopted. I demonstrate that my learning system can learn a genetic theory with theoretical terms which, after being induced by my system, can be interpreted as either types of genetic properties (...) (dominant or recessive) or genes, depending on the representation of the hypotheses of the same theoretical terms. (shrink)

I defend a theory of mental representation that satisfies naturalistic constraints. Briefly, we begin by distinguishing (i) what makes something a representation from (ii) given that a thing is a representation, what determines what it represents. Representations are states of biological organisms, so we should expect a unified theoretical framework for explaining both what it is to be a representation as well as what it is to be a heart or a kidney. I follow Millikan in (...) explaining (i) in terms of teleofunction, explicated in terms of natural selection. -/- To explain (ii), we begin by recognizing that representational states do not have content, that is, they are neither true nor false except insofar as they both “point to” or “refer” to something, as well as “say” something regarding whatever it is they are about. To distinguish veridical from false representations, there must be a way for these separate aspects to come apart; hence, we explain (ii) by providing independent theories of what I call f-reference and f-predication (the ‘f’ simply connotes ‘fundamental’, to distinguish these things from their natural language counterparts). -/- Causal theories of representation typically founder on error, or on what Fodor has called the disjunction problem. Resemblance or isomorphism theories typically founder on what I’ve called the non-uniqueness problem, which is that isomorphisms and resemblance are practically unconstrained and so representational content cannot be uniquely determined. These traditional problems provide the motivation for my theory, the structural preservation theory, as follows. F-reference, like reference, is a specific, asymmetric relation, as is causation. F-predication, like predication, is a non-specific relation, as predicates typically apply to many things, just as many relational systems can be isomorphic to any given relational system. Putting these observations together, a promising strategy is to explain f-reference via causal history and f-predication via something like isomorphism between relational systems. -/- This dissertation should be conceptualized as having three parts. After motivating and characterizing the problem in chapter 1, the first part is the negative project, where I review and critique Dretske’s, Fodor’s, and Millikan’s theories in chapters 2-4. Second, I construct my theory about the nature of representation in chapter 5 and defend it from objections in chapter 6. In chapters 7-8, which constitute the third and final part, I address the question of how representation is implemented in biological systems. In chapter 7 I argue that single-cell intracortical recordings taken from awake Macaque monkeys performing a cognitive task provide empirical evidence for structural preservation theory, and in chapter 8 I use the empirical results to illustrate, clarify, and refine the theory. (shrink)

In this paper a conceptually based distinction between two classes of semantic predicates is proposed D–prediates, which encode object definig properties, and O–predicates, which encode optional properties. While the distinction between the properties is conceptually motivated, the two corresponding predicate classes are defined with reference to a logically based notion of ‘(predicate)field’. It is argued that on the basis of this distinction the differences in the grammatical behaviour of unaccusaive and unergative verbs in German can be derived and (...) do not require any form of syntactic representation because the properties that are usually taken to be an indication of the class membership of intransive verbs follow from the status of the properties encoded by the two types of semantic predicates. (shrink)

This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical quantifiers. As a (...) prerequisite, much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)

Do representational pictures have propositional contents? The current paper argues that the characteristic contents of pictures are predicative rather than propositional: pictures characterise things as looking certain ways, and they thereby express properties of visual perspectives. The paper argues that the characteristic predicative contents of pictures are nonetheless able to feature in fully-fledged propositional contents once they are combined with contents of other suitable sorts. Various facts about communicative uses of pictures are then explained. The paper concludes by considering the (...) bearing of its conclusions upon questions about the relationships between linguistic representation and pictorial representation. (shrink)

In this paper we attempt to develop a problem representation technique which enables the decomposition of a problem into subproblems such that their solution in sequence constitutes a strategy for solving the problem. An important issue here is that the subproblems generated should be easier than the main problem. We propose to represent a set of problem states by a statement which is true for all the members of the set. A statement itself is just a set of atomic (...) statements which are binary predicates on state variables. Then, the statement representing the set of goal states can be partitioned into its subsets each of which becomes a subgoal of the resulting strategy. The techniques involved in partitioning a goal into its subgoals are presented with examples. (shrink)

The aim of this study is to try to make use of real numbers for representing an infinite analysis of individual notions in an infinity of possible worlds.As an introduction to the subject, the author shows, firstly, the possibility of representing Boole's lattice of universal notions by an associate Boole's lattice of rational numbers.But, in opposition to the universal notions, definable by a finite number of predicates, an individual notion, cannot admits this sort of definition, because each state of (...) an individual subject is characterized by the values taken by an infinite number of predicates, each of whom may appear or disappear in the next state.The notion of “degree of identification of an individual notion” is then introduced and arithmetized by a rational number.As an individual notion can be defined by a convergent succession of degrees of identification, the real characteristic number of such an individual notion can be defined by the corresponding convergent succession of rational numbers, satisfying Cauchy's conditions for the convergence of successions. (shrink)

In this dissertation, I provide the logical foundation for a solution to the mind-body problem, a solution which is directly based upon Wilfrid Sellars' analogical theory of thought and sensation. Chapters I-IV are devoted to an interpretation, analysis, and constructive criticism of Sellars' notions of the inner thought episode and the sensing state. My analysis is offered in support of three general contentions: I argue that the postulation of inner thought episodes and sensing states is necessary for adequate explanations of (...) agent behavior; I hope to show how the analogical theory of inner thought episodes and sensing states actually generates a legitimate problem concerning the relationship between the mental and the physical; and I demonstrate the importance of the notion of analogy in philosophical theory construction. I suggest that the role of analogy provides the key for the solution to the mind-body problem. ;Chapter One is essentially introductory in nature. I offer an interpretation and reconstruction of Sellars' illustrative story entitled "The Jonesean Myth" . The "Myth" provides a suitable representation of Sellars' overall philosophy of mind. But perhaps more importantly, the "Myth" is a paradigm example of what I shall call the analogical method of inquiry, a method employed for the introduction of the notions of inner thought episodes and sensing states. In brief, I want to show how the "Myth" provides the logical basis for a theory adequate for explanations of the mental activity of agents. ;Chapters II and III are closely related. In Chapter II, I present a theory of linguistic representation which will serve as the analogical base for the introduction and characterization of the inner thought episode. In Chapter III, I develop the notion of the inner thought episode , and I examine its nature and status as a theoretical construct. Chapters II and III are thus related by the Sellarsian thesis that the concept of mental representation is to be understood in terms which apply, primarily, to characterizations of the features of the linguistic framework presented in Chapter II. ;In Chapter IV, I argue, again following Sellars' lead, that the explication of the notion of the perceptual thought episode requires the introduction of a second distinct sort of inner episode, namely, that of the sense experience or sensing state. The argument offered in Chapter IV is designed to show that sensing states are theoretical constructs, the reference to which is essential for explanations concerning the occurrence and nature of perceptual representations. Sensing states are introduced and characterized by an analogical extension of families of predicates which are suitable for the identification and description of ordinary physical objects . ;In Chapter V, I propose a solution to the mind-body problem, as the latter is generated by the analysis given to the thought episode and the sensing state . In general terms, I argue that any purported solution to the mind-body problem must provide an explanatory basis for agent behavior, and it is for this reason that I reject "reductionistic" theories of mind of the kind represented by logical behaviorism, type-identity physicalism, and Turing Machine functionalism. My solution, instead, involves a commitment to what I shall call token physicalism, a thesis which is contingent upon the development of a theory of neurophysiology which is rich enough to capture, in an analogical sense, both the intentional features of the thought episode, and the occurrent-like qualities which are exemplified by the sensing state. (shrink)

The use of circumscription for formalizing commonsense knowledge and reasoning requires that a circumscription policy be selected for each particular application: we should specify which predicates are circumscribed, which predicates and functions are allowed to vary, and what priorities between the circumscribed predicates are established. The circumscription policy is usually described either informally or using suitable metamathematical notation. In this paper we propose a simple and general formalism which permits describing circumscription policies by axioms, included in the (...) knowledge base along with the axioms describing the objects of reasoning. The new formalism is illustrated by recasting some of the familiar applications of circumscription in its terms. (shrink)

Debates about the semantics and pragmatics of predicates of personal taste have largely centered on contextualist and relativist proposals. In this paper, I argue in favor of an alternative, absolutist analysis of PPT. Theorists such as Max Kölbel and Peter Lasersohn have argued that we should dismiss absolutism due to its inability to accommodate the possibility of faultless disagreement involving PPT. My aim in the paper is to show how the absolutist can in fact accommodate this possibility by drawing (...) on an account of faultless disagreement that improves upon a recent proposal due to Karl Schafer. In amending Schafer’s proposal, I put forward an empirically informed view of our beliefs regarding matters of personal taste, as well as an account of our assertions concerning such matters. I also argue that absolutists should take disagreement about these matters to be conative, rather than doxastic, in nature. The anticipated result is an independently compelling account of faultless disagreement about matters of personal taste that fits naturally with absolutism. (shrink)

In the debate between contextualism and relativism about predicates of taste, the challenge from disagreement (the objection that contextualism cannot account for disagreement in ordinary exchanges involving such predicates) has played a central role. This paper investigates one way of answering the challenge consisting on appeal to certain, less focused on, uses of predicates of taste. It argues that the said thread is unsatisfactory, in that it downplays certain exchanges that constitute the core disagreement data. Additionally, several (...) arguments to the effect that the exchanges in question don’t amount to disagreement are considered and rejected. (shrink)

A new comprehensive framework for narrative understanding has been developed. Its centerpiece is a new situational logic calledEpisodic Logic, a knowledge and semantic representation well-adapted to the interpretive and inferential needs of general NLU. The most distinctive features of EL is its natural language-like expressiveness. It allows for generalized quantifiers, lambda abstraction, sentence and predicate modifiers, sentence and predicate reification, intensional predicates, unreliable generalizations, and perhaps most importantly, explicit situational variables linked to arbitrary formulas that describe them. These (...) allow episodes to be explicitly related in terms of part-whole, temporal and causal relations. Episodic logical form is easily computed from surface syntax and lends itself to effective inference. (shrink)

Current models of auditory verbal hallucinations tend to focus on the mechanisms underlying their occurrence, but often fail to address the content of the auditory experience. In other words, they tend to ask why there are AVHs at all, instead of asking why, given that there are AVHs, they have the properties that they have. One such property, which has been largely overlooked and which we will focus on here, is why the voices are often experienced as coming from agents, (...) and often specific, individualised agents. In this article, we argue not only that the representation of agents is important in accurately describing many cases of AVH, but also that deeper reflection on what is involved in the representation of agents has potentially vital consequences for our aetiological understanding of AVH, namely, for understanding how and why AVHs come about. (shrink)

The representation of Neg-Raising in the grammar is a matter of controversy. I provide evidence for representing Neg-Raising as a kind of presupposition associated with certain predicates by providing a detailed analysis of NPI-licensing in Neg-Raising contexts. Specific features of presupposition projection are used to explain the licensing of strict NPIs under Neg-Raising predicates. Discussion centers around the analysis of a licensing asymmetry noted in Horn (1971, Negative transportation: Unsafe at any speed? In CLS 7 (pp. 120–133)).Having (...) provided this analysis, I go on to discuss its implications for the theory of NPI-licensing more generally. In particular, I discuss how the present proposal reflects on von Fintel’s (1999, Journal of Semantics, 16, 97–148) proposal to use Strawson downward entailment in the statement of NPI-licensing principles. (shrink)

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found (...) to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed. (shrink)

The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine the existence of problem categories as a basis for representation; differences in the categories used by experts and novices; differences in the knowledge associated with the categories; and features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably (...) different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features. (shrink)

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group (...) R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

We claim that Kant's doctrine of the "transcendental ideal of pure reason" contains, in an anticipatory sense, a second-order theory of reality (as a second-order property) and of the highest being. Such a theory, as reconstructed in this paper, is a transformation of Kant's metatheoretical regulative and heuristic presuppositions of empirical theories into a hypothetical ontotheology. We show that this metaphysical theory, in distinction to Descartes' and Leibniz's ontotheology, in many aspects resembles Gödel's theoretical conception of the possibility of a (...) supreme being. The proposed second-order modal formalization of the Kantian doctrine of the "transcendental ideal" of the supreme being includes some specific features of Kantian general logic like "categorical", "hypothetical", and exclusive disjunctive propositions as basic forms. (shrink)

This paper revisits some foundational questions concerning the abstract representation of a discourse context. The context of a conversation is represented by a body of information that is presumed to be shared by the participants in the conversation – the information that the speaker presupposes a point at which a speech act is interpreted. This notion is designed to represent both the information on which context-dependent speech acts depend, and the situation that speech acts are designed to affect, and (...) so to be a representation of context that is appropriate for explaining the interaction of context and the contents expressed in them. After reviewing the motivating ideas and the outlines of the apparatus, the paper responds to a criticism of the framework, and considers the way it can help to clarify some phenomena concerning pronouns with indefinite antecedents. (shrink)

This article understands codes of ethics as written documents that represent social actors in specific ways through the use of language. It presents an empirical study that investigated the codes of ethics of the German Dax30 companies. The study adopted a critical discourse analysis-approach in order to reveal how the code-texts produce a particular understanding of the various internal social groups for the readers. Language is regarded as social practice that functions at creating particular understandings of individuals and groups, how (...) they are interrelated, and how they should behave. Findings show that codes of ethics do not represent employees as a group that is empowered or morally enlightened; instead they are positioned as passive receivers of rules and regulations. Furthermore, codes of ethics classify employees as having a need to be monitored and controlled by the higher levels of the corporate hierarchy. Overall, code language enforces compliance through maintaining existing and building new asymmetries between the different groups within a company. As a consequence, the article discusses a somewhat different understanding of code effectiveness. Reproducing and reemphasizing hierarchical relations could also lead to code compliance, perhaps without any need for developing the moral employee that is committed to ethical values. (shrink)

BackgroundIt is widely acknowledged that there is a global divide on health care and health research known as the 10/90 divide.MethodsA retrospective survey of articles published in the BMJ, Lancet, NEJM, Annals of Internal Medicine & JAMA in a calendar year to examine the contribution of the developing world to medical literature. We categorized countries into four regions: UK, USA, Other Euro-American countries and . OEAC were European countries other than the UK but including Australia, New Zealand and Canada. RoW (...) comprised all other countries.ResultsThe average contribution of the RoW to the research literature in the five journals was 6.5%. In the two British journals 7.6% of the articles were from the RoW; in the three American journals 4.8% of articles were from RoW. The highest proportion of papers from the RoW was in the Lancet . An analysis of the authorship of 151 articles from RoW showed that 104 involved authorship with developed countries in Europe or North America. There were 15 original papers in these journals with data from RoW but without any authors from RoW.ConclusionsThere is a marked under-representation of countries in high-impact general medical journals. The ethical implications of this inequity and ways of reducing it are discussed. (shrink)

One of the more powerful impressions created by vision is that of a coherent, richly-detailed world where everything is present simultaneously. Indeed, this impression is so compelling that we tend to ascribe these properties not only to the external world, but to our internal representations as well. But results from several recent experiments argue against this latter ascription. For example, changes in images of real-world scenes often go unnoticed when made during a saccade, flicker, blink, or movie cut. This "change (...) blindness" provides strong evidence against the idea that our brains contain a picture-like representation of the scene that is everywhere detailed and coherent. (shrink)

We consider the concept of entanglement for pure cases of finite dimensional state spaces. The criterion of unentangled states is related to demanding rank one of an associated eigenvalue problem. In addition to the conventional procedure based on the Schmidt decomposition, we devise a method based on the spectral resolution of unsymmetric matrices. In particular, we consider the case when all eigenvalues are zero, and find that the method still works.

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the problem of (...) old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)