We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We (...) also argue that discrete representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

Leibovich et al. propose that non-symbolic numerosity abilities develop from the processing of more basic, continuous magnitudes such as size, area, and density. Here I review similar arguments arising in the visual perception field and further propose that the evolvement of discrete representations from continuous stimulus properties may be a fundamental characteristic of cognitive development.

Intelligible speakers achieve specific vocal tract constrictions in rapid sequence. These constrictions are associated in theory with speech motor goals. Adult-focused models of speech production assume that discrete phonological representations, sequenced into word-length plans for output, define these goals. This assumption introduces a serial order problem for speech. It is also at odds with children's speech. In particular, child phonology and timing control suggest holistic speech plans, and so the hypothesis of whole word production. This hypothesis solves the serial (...) order problem by avoiding it. When the same solution is applied to adult speech the problem becomes how to explain the development of highly intelligible speech. This is the problem addressed here. A modeling approach is used to demonstrate how perceptual-motor units of production emerge over developmental time with the perceptual-motor integration of holistic speech plans that are also phonological representations; the specific argument is that perceptual-motor units are a product of trajectories (nearly) crossing in motor space. The model, which focuses on the integration process, defines the perceptual-motor map as a set of linked pairs of experienced perceptual and motor trajectories. The trajectories are time-based excursions through speaker-defined perceptual and motor spaces. By hypothesis, junctures appear where motor trajectories near or overlap one another in motor space when the shared (or extremely similar) articulatory configurations in these regions are exploited to combine perceptually-linked motor paths along different trajectories. Junctures form in clusters in motor space. These clusters, along with their corresponding (linked) perceptual points, represent perceptual-motor units of production, albeit at the level of speech motor control only. The units serve as pivots in motor space during speaking; they are points of transition from one motor trajectory to another along perceptually-linked paths that are selected to produce best approximations of whole word targets. (shrink)

The cultural turn has yet to fully reconfigure ‘class’ as a set of fictions, tropes, discourses and enduring culture-structures. Existing Durkheimian approaches have stalled at his middle period morphological reductionism. This paper constructs a more radical understanding in the late-Durkheimian idiom. It shows how class operates as a signifier in a language game of purity and pollution, virtue and vice. Taking a lead from studies of the ‘unruly’ working class, the paper opens up the more subtle pollution that attends to (...) the mythical ‘bourgeoisie’ and its associated and imagined ‘bourgeois’ culture. As a sign system this class location is deemed inauthentic, sybaritic, and as strangely deadening to cultural vitality. Although commonly found in contexts of gentrification and commodification that involve class conflict, this critical discourse is also applied within the bourgeois milieu. Such needless auto-critique suggests a relative autonomy from determination by class struggle. The possibilities for this approach are illustrated at length with reference to a paradigm case: the highly bourgeois milieu of the composer Richard Wagner and his Bayreuth Festival. (shrink)

The concept of representation has become almost inextricably bound to the concept of symbol systems. the concepts is nowhere more prevalent than in descriptions of "internal representations." These representations are thought to occur in an internal symbol system that allows the brain to store and use information. In this paper we explore a different approach to understanding psychological processes, one that retains a commitment to representations and computations but that is not based on the idea that information must be (...) stored and manipulated in symbol systems. In particular, we suggest that the notion of a symbol system as currently understood construes psychological processes in terms of a specific type of computational system, in which a control function "reads," "interprets," and manipulates discrete entities called "symbols." We argue that other types of computational systems may provide a more appropriate characterization of psychological processes. One implication of our argument is the need to consider the constraints placed on computational theories in psychology by the nature of the computing device itself, the human brain. Perhaps surprisingly, this implication leads us to the conclusion that a "functionalist" conception of psychological processes (discussed below) does not entail that physiology is irrelevant to psychology, as has been maintained by prominent adherents of the symbol-systems approach. (shrink)

Representation is central to contemporary theorizing about the mind/brain. But the nature of representation--both in the mind/brain and more generally--is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received view is that analog representations vary smoothly, while digital representations vary in a step-wise manner. I argue that this characterization is inadequate to account for the ways in which representation is used in cognitive science; in (...) its place, I suggest an alternative taxonomy. I will defend and extend David Lewis's account of analog and digital representation, distinguishing analog from continuous representation, as well as digital from discrete representation. I will argue that the distinctions available in this four-fold account accord with representational features of theoretical interest in cognitive science more usefully than the received analog/digital dichotomy. (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given (...) in Sendlewski (Studia Logica 43(3):257–280, 1984) to the tense case. (shrink)

Analog representation is often cast in terms of an engineering distinction between smooth and discrete systems. The engineering notion cuts across interesting representational categories, however, so it is poorly suited to thinking about kinds of representation. This paper suggests that analog representations support a pattern of interaction, specifically open-ended searches for content across levels of abstraction. They support the pattern by sharing a structure with what they represent. Continuous systems that satisfy the engineering notion are exemplars of (...) this kind because they are uninterpretable unless they are structure-preserving. Analog representations, so understood, include pictures, images, diagrams, and most graphs. This conception of analogicity also fits well with a line of thought about what makes perceptual states distinctive: they satisfy a “parts principle”. (shrink)

This short article discusses the nature of research and art practice and makes a case for the necessary intermingling of these activities. It does not attempt to define a space for art to operate as research, quite the opposite: research is an operating structure for the process and production of, among other things, art. It is regarded as integral to the processes of thinking, making, and reflecting, and it is important to note that curiosity, creative enquiry, and critical reflection underpin (...) much that is considered research in various fields. The author asserts that these processes are not necessarily discipline-specific although particular disciplines have specific procedures and goals. It is argued that "provisionality" is central to what art can offer other disciplines; it can make a virtue of incompleteness. The author suggests that art open itself up to quizzical scrutiny and help others to recognise that research has long been, and will continue to be, a driving force within its makeup. The article posits an expanded notion of the artwork that is essentially provisional and reliant on spectatorial involvement. (shrink)

In this paper we give a representation of the free MV-algebra over one generator as a structure of functions having finite domain.

In modern, Western societies the purpose of schooling is to ensure that school-goers acquire knowledge of pre-existing practices, events, entities and so on. The knowledge that is learned is then tested to see if the learner has acquired a correct or adequate understanding of it. For this reason, it can be argued that schooling is organised around a representational epistemology: one which holds that knowledge is an accurate representation of something that is separate from knowledge itself. Since the object (...) of knowledge is assumed to exist separately from the knowledge itself, this epistemology can also be considered ‘spatial.’ In this paper we show how ideas from complexity have challenged the spatial epistemology’ of representation and we explore possibilities for an alternative ‘temporal’ understanding of knowledge in its relationship to reality. In addition to complexity, our alternative takes its inspiration from Deweyan ‘transactional realism’ and deconstruction. We suggest that ‘knowledge’ and ‘reality’ should not be understood as separate systems which somehow have to be brought into alignment with each other, but that they are part of the same emerging complex system which is never fully ‘present’ in any (discrete) moment in time. This not only introduces the notion of time into our understanding of the relationship between knowledge and reality, but also points to the importance of acknowledging the role of the ‘unrepresentable’ or ‘incalculable’. With this understanding knowledge reaches us not as something we receive but as a response, which brings forth new worlds because it necessarily adds something (which was not present anywhere before it appeared) to what came before. This understanding of knowledge suggests that the acquisition of curricular content should not be considered an end in itself. Rather, curricular content should be used to bring forth that which is incalculable from the perspective of the present. The epistemology of emergence therefore calls for a switch in focus for curricular thinking, away from questions about presentation and representation and towards questions about engagement and response. (shrink)

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed (...) Symbol Systems, have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization–Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. (shrink)

I argue that dynamicism does not provide a convincing alternative to currently available cognitive theories. First, I show that the attractor dynamics of dynamicist models are inadequate for accounting for high-level cognition. Second, I argue that dynamicist arguments for the rejection of computation and representation are unsound in light of recent empirical findings. This new evidence provides a basis for questioning the importance of continuity to cognitive function, challenging a central commitment of dynamicism. Coupled with a defense of current (...) connectionist theory, these two critiques lead to the conclusion that dynamicists have failed to achieve their goal of providing a new paradigm for understanding cognition. (shrink)

Democracies that appoint legislators through elections in territorially defined, sub-national constituencies and simultaneously enfranchise expatriate citizens must either assign expatriate voters to in-country constituencies (assimilated representation) or group them into distinct overseas constituencies that elect their own legislators (discrete representation). This essay critically reviews extant normative discussions of the two models and develops a normative analysis of its own. This suggests that when expatriates form but a small part of a democracy’s overall demos, discrete representation (...) is the more attractive model of expatriate representation as it overall better satisfies four important standards of evaluation, namely: equal opportunities for political influence, deliberation within the legislature, deliberation among constituents, and partisan voter mobilisation. This argument is also defended against the potential objections that the said standards can be satisfied by other means than discrete expatriate representation and that the defence of discrete expatriate representation implies a proliferation of special constituencies. (shrink)

How internal categories influence how we perceive the world is a fundamental question in cognitive sciences. Yet, the relation between perceptual awareness and perceptual categorization has remained largely uncovered so far. Here, we addressed this question by focusing on face perception during subliminal and conscious perception. We used morphed continua between two face identities and we assessed, through a masked priming paradigm, the perceptual processing of these morphed faces under subliminal and supraliminal conditions. We found that priming from subliminal faces (...) followed linearly the information present in the primes, while priming from visible faces revealed a non-linear profile, indicating a categorical processing of face identities. Our results thus point to a special relation between perceptual awareness and categorical processing of faces, and support the dissociation between two modes of information processing: a subliminal mode involving analog treatment of stimuli information, and a supraliminal mode relying on discrete representation. (shrink)

In “Connectionism and the fats of folk psychology”, Forster and Saidel argue that the central claim of Ramsey, Stich and Garon (1991)—that distributed connectionist models are incompatible with the causal discreteness of folk psychology—is mistaken. To establish their claim, they offer an intriguing model which allegedly shows how distributed representations can function in a causally discrete manner. They also challenge our position regarding projectibility of folk psychology. In this essay, I offer a response to their account and show how (...) their model fails to demonstrate that our original argument was mistaken. While I will discuss several difficulties with their model, my primary criticism will be that the features of their model that are causally discrete are not truly distributed, while the features that are distributed are not really discrete. Concerning the issue of projectibility, I am more inclined to agree with Forster and Saidel and I offer a revised account of what we should have said originally. (shrink)

Robert Alexy has argued that the democratic objection to judicial review of legislation can be successfully addressed by assuming that judges exercise a special form of argumentative representation. In this article we argue that Alexy does not explain (as he should) under what circumstances judicial review tends to produce better decisions than parliamentary procedure, nor does he explain how judicial review can have a greater intrinsic value than parliamentary procedure. Subsequently, we argue that the intrinsic value of argumentative (...) class='Hi'>representation depends on the promotion of citizen deliberation, whereas its instrumental value depends on judges being committed to the rights of discrete and insular minorities in the face of hostile majorities. (shrink)

Relative to digital computation, analogue computation has been neglected in the philosophical literature. To the extent that attention has been paid to analogue computation, it has been misunderstood. The received view—that analogue computation has to do essentially with continuity—is simply wrong, as shown by careful attention to historical examples of discontinuous, discrete analogue computers. Instead of the received view, I develop an account of analogue computation in terms of a particular type of analogue representation that allows for discontinuity. (...) This account thus characterizes all types of analogue computation, whether continuous or discrete. Furthermore, the structure of this account can be generalized to other types of computation: analogue computation essentially involves analogue representation, whereas digital computation essentially involves digital representation. Besides being a necessary component of a complete philosophical understanding of computation in general, understanding analogue computation is important for computational explanation in contemporary neuroscience and cognitive science. (shrink)

In this work we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingale representation in case of discrete time and an application of the result for semi-continuous market model are also given.

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may (...) give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

A comparison of the literatures on how infants represent generic object classes, gender and race information in faces, and emotional expressions reveals both common and distinctive developments in the three domains. In addition, the review indicates that some very basic questions remain to be answered regarding how infants represent facial displays of emotion, including (a) whether infants form category representations for discrete classes of emotion, (b) when and how such representations come to incorporate affective meaning, (c) the developmental trajectory (...) for representation of emotional expression at different levels of inclusiveness (i.e., from broad to narrow or narrow to broad?), and (d) whether there is superior discrimination ability operating within more frequently experienced emotion categories. (shrink)

A comparison of the literatures on how infants represent generic object classes, gender and race information in faces, and emotional expressions reveals both common and distinctive developments in the three domains. In addition, the review indicates that some very basic questions remain to be answered regarding how infants represent facial displays of emotion, including (a) whether infants form category representations for discrete classes of emotion, (b) when and how such representations come to incorporate affective meaning, (c) the developmental trajectory (...) for representation of emotional expression at different levels of inclusiveness (i.e., from broad to narrow or narrow to broad?), and (d) whether there is superior discrimination ability operating within more frequently experienced emotion categories. (shrink)

We consider the first-order finite-difference expression of the commutator between d / dx and x. This is the appropriate setting in which to propose commutators and time operators for a quantum system with an arbitrary potential function and a discrete energy spectrum. The resulting commutators are identified as universal lowering and raising operators. We also find time operators which are finite-difference derivations with respect to the energy. The matrix elements of the commutator in the energy representation are analyzed, (...) and we find consistency with the equality \. We apply the theory to the particle in an infinite well and for the Harmonic oscillator as examples. (shrink)

Various theories of moral cognition posit that moral intuitions can be understood as the output of a computational process performed over structured mental representations of human action. We propose that action plan diagrams—“act trees”—can be a useful tool for theorists to succinctly and clearly present their hypotheses about the information contained in these representations. We then develop a methodology for using a series of linguistic probes to test the theories embodied in the act trees. In Study 1, we validate the (...) method by testing a specific hypothesis (diagrammed by act trees) about how subjects are representing two classic moral dilemmas and finding that the data support the hypothesis. In Studies 2–4, we explore possible explanations for discrete and surprising findings that our hypothesis did not predict. In Study 5, we apply the method to a less well‐studied case and show how new experiments generated by our method can be used to settle debates about how actions are mentally represented. In Study 6, we argue that our method captures the mental representation of human action better than an alternative approach. A brief conclusion suggests that act trees can be profitably used in various fields interested in complex representations of human action, including law, philosophy, psychology, linguistics, neuroscience, computer science, robotics, and artificial intelligence. (shrink)

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...) the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

This article presents a process account of some typicality effects and related similarity-dependent accuracy and response time phenomena that arise in the context of supervised concept acquisition. We describe Symbolic Concept Acquisition (SCA), a computational system that acquires and activates category prediction rules. In contrast to gradient representations, SCA performs by probing for prediction rules in a series of discrete steps. For learning new rules, it acquires general rules but then incrementally learns more specific ones. In describing SCA, we (...) emphasize its functionality in terms of accuracy and efficiency and motivate its design within the set of symbolic mechanisms and memory structures defined by the Soar architecture (Laird, Newell & Rosenbloom, 1987). For replicating human behavior, we first show how SCA exhibits some typicality effects in the course of learning responding faster and more accurately to more typical test examples. Then, using data from human experiments, we evaluate SCA's qualitative predictions on accuracy and response time on individual dataset instances. We show how SCA's predictions correlate with human data across three experimental conditions concerning the effect of instruction on learning strategy. (shrink)

The “folk” theory of democracy that typically justifies the administrative state cannot help but lead to a discourse of constraint. If agency action is only legitimate when it mechanically applies the will of the voters as transposed by Congress through statutes, then the norms guiding that action will inevitably restrain agency discretion. As a result, attempts to establish the democratic credentials of the administrative state ironically obstruct the application of collective power. But this “folk” theory of democracy is bad theory. (...) It is empirically incredible and, alarmingly, facilitates dangerous populist politics. Political theory instead suggests that a theory of democratic representation not only better explains legislative outcomes, but also deprives demagogues and deregulatory partisans of the fictions that prop up their agendas. After a brief survey of representative theory, this article will demonstrate that a model of trustee representation adequately describes administration, reinforces its democratic credentials and constitutes a space for politics in shaping the regulations that govern us all. (shrink)

It has been known for many years that the matrix representation of the one-dimensional position-momentum commutator calculated with the position and momentum matrices in a finite basis is not proportional to the diagonal matrix, contrary to what one expects from the continuous-space commutator. This discrepancy has correctly been ascribed to the incompleteness of any finite basis, but without the details of exactly why this happens. Understanding why the discrepancy occurs requires calculating the position, momentum, and commutator matrix elements in (...) the continuous position basis, in which all are generalized functions. The reason for the discrepancy is revealed by replacing the generalized functions with sequences approaching them as their parameter approaches zero. Besides explaining the discrepancy in the discrete and continuous models, this investigation finds an unusual double-peaked sequence for the Dirac delta function. (shrink)

Temporal stability and change in neutral contexts can transform continuous experiences into distinct and memorable events. However, less is known about how shifting emotional states influence these memory processes, despite ample evidence that emotion impacts non-temporal aspects of memory. Here, we examined if emotional stimuli influence temporal memory for recent event sequences. Participants encoded lists of neutral images while listening to auditory tones. At regular intervals within each list, participants heard emotional positive, negative, or neutral sounds, which served as “emotional (...) event boundaries” that divided each sequence into discrete events. Temporal order memory was tested for neutral item pairs that either spanned an emotional sound or were encountered within the same auditory event. Encountering a highly arousing event boundary led to faster response times for items encoded within the next event. Critically, we found that highly arousing sounds had different effects on binding ongoing versus ensuing sequential representations in memory. Specifically, highly arousing sounds were significantly more likely to enhance temporal order memory for ensuing information compared to information that spanned those boundaries, especially for boundaries with negative valence. These findings suggest that within aversive emotional contexts, fluctuations in arousal help shape the temporal organisation of events in memory. (shrink)

The ‘received view’ of the analog–digital distinction holds that analog representations are continuous while digital representations are discrete. In this paper I first provide support for the received view by showing how it (1) emerges from the theory of computation, and (2) explains engineering practices. Second, I critically assess several recently offered alternatives, arguing that to the degree they are justified they demonstrate not that the received view is incorrect, but rather that distinct senses of the terms have become (...) entrenched specific fields, perhaps most notably in the cognitive psychology of mental imagery. (shrink)

Based on Alasdair Urquhart’s representation of not necessarily distributive bounded lattices we exhibit several discrete dualities in the spirit of the “duality via truth” concept by Orłowska and Rewitzky. We also exhibit a discrete duality for Urquhart’s relevant algebras and their frames.

Formal models of cultural evolution analyze how cognitive processes combine with social interaction to generate the distributions and dynamics of ‘representations.’ Recently, cognitive anthropologists have criticized such models. They make three points: mental representations are non-discrete, cultural transmission is highly inaccurate, and mental representations are not replicated, but rather are ‘reconstructed’ through an inferential process that is strongly affected by cognitive ‘attractors.’ They argue that it follows from these three claims that: 1) models that assume replication or replicators are (...) inappropriate, 2) selective cultural learning cannot account for stable traditions, and 3) selective cultural learning cannot generate cumulative adaptation. Here we use three formal models to show that even if the premises of this critique are correct, the deductions that have been drawn from them are false. In the rst model, we assume continuously varying representations under the in uence of weak selective transmission and strong attractors. We show that if the attractors are suf ciently strong relative to selective forces, the continuous representation model reduces to the standard.. (shrink)

Enaction, as put forward by Varela and defended by other thinkers (notably Alva Noë, 2004; Susan Hurley, 2006; and Kevin O’Regan, 1992), departs from traditional accounts that treat mental processes (like perception, reasoning, and action) as discrete, independent processes that are causally related in a sequen- tial fashion. According to the main claim of the enactive approach, which Thompson seems to fully endorse, perceptual awareness is taken to be a skill-based activity. Our perceptual contact with the world, according to (...) the enactionists, is not mediated by representations but is enacted, and the notion of representation, belonging to the classic computational paradigm, has no place in this alternative approach. Though Thompson does not pronounce directly on the issue of representationalism, he is most definitely keeping the company of anti-representationalists, and in that context it is not unreasonable to take his silence for consent. In this paper, we will argue that the enactive approach to imagery is unworkable unless it makes appeal to representations, understood in a particular way. Not understood as pictures, to be sure. Or sentences for that matter. But those aren’t the only options. (shrink)

Electron redistribution is the cornerstone of our understanding of chemical reactivity. For the vast majority of organic reactions electrons are assumed to move in pairs providing explanatory mechanisms through the generation of intermediate structures. But for many transformations these discrete steps are idealized constructs, involving intermediates assumed but not empirically justified. This unitary perspective predicated on the curved arrow formalism has resulted in the scenario where for many organic transformations our supposed understanding far surpasses our growing knowledge. Reformulating organic (...) mechanisms to include single electron transfer as a component of, or an alternative to, the prevailing iconic descriptions can provide for a more empirically adequate mechanistic description. In addition using the language of SET presents an opportunity to unify mechanistic concepts under a common donor/acceptor framework. (shrink)

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the (...) cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes (...) C, that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

The representation of a rose varies considerably across philosophical, religious, and scientific schools of thought. While many would suggest that a rose exists objectively, as a physical object in geometric space reducible to fundamental particles such as atoms or quarks, others propose that a rose is an emergent whole that exists meaningfully when experienced subjectively for its sweet fragrance and red hue, its soft petals and thorny stem. Some might even maintain that a rose is “consciousness-only,” having no existence (...) apart from conscious perception. Thus, we find a spectrum of realist to idealist perspectives. Even in Dharma studies, with a common basis in Indian thought, the Vaiśeṣikas, Vaibhāṣikas, and the vijñaptimātra doctrine of the Yogācārin-Vijñānavādins entertain diverging perspectives. On one hand, the Vaiśeṣikas, a school of Vedic philosophy, propounded a theory of reality in the form of indivisible, eternal atoms, a metaphysical approach counter to the doctrine of not-self (anātman) in Buddhism. The Vaibhāṣikas, a school of early Buddhist atomism, on the other hand, denied the existence of a true self or eternal soul (ātman) as substratum for reality but maintained their own theory of atomism. For the Vaibhāṣikas, the flow of consciousness may be segmented into discrete moments, yet unlike many of their Buddhist contemporaries from other schools, they asserted that all cognizable phenomena are truly existent insofar as they consist of physically irreducible atoms. Among their objectors were the Yogācārin-Vijñānavādins who proposed the theory of consciousness-only (vijñaptimātra), rejecting the independent existence of indivisible atoms and discrete moments of time. This paper introduces the dialectic that formed between these schools through Vasubandhu’s fourth century C.E. text Twenty Verses on Consciousness-Only (Viṃśikāvijñaptimātratāsiddhi). While the gulf between the realist and idealist positions may seem, at times, irreconcilable, we integrate findings from the field of physics, particularly quantum mechanics (and several philosophical interpretations thereof) within the realm of modern science as a possible bridge between these otherwise seemingly disparate systems of Dharma. (shrink)

The purpose of this text is to analyze the social representations of feminism in divinatory practices. Our research in a few Moldavian counties has identified two main types of social representations of the relationship between magic/divination and feminism. Therefore, there are some dual representations of the feminine divinatory agents versus the masculine ones. Even though women are well represented among clairvoyants, clients, and spectators, these valorizations function as negative stereotypes and do not serve the women. Another representation of feminism (...) in divinatory practices that does not necessarily imply negativism and damnation is a more recent one. Old stereotypes are tamed and attenuated. The results of our research have shown that women continue to be associated with the survival of these practices. This is proof that old myths and representations are still alive. They are discretely present in social expressions. Finally, they will dominate us completely. (shrink)

For at least two centuries, democratic representation has been at the center of debate. Should elected representatives express the views of the majority, or do they have the discretion to interpret their constituents' interests? How can representatives balance the desires of their parties and their electors? What should be done to strengthen the representation of groups that have been excluded from the political system? Representative democracy itself remains frequently contested, regarded as incapable of reflecting the will of the (...) masses, or inadequate for today's global governance. Recently, however, this view of democratic representation has been under attack for its failure to capture the performative and constructive elements of the process of representation, and a new literature more attentive to these aspects of the relationship between representatives and the represented has arisen. In Creating Political Presence, a diverse and international group of scholars explores the implications of such a turn. Two broad, overlapping perspectives emerge. In the first section, the contributions investigate how political representation relates to empowerment, either facilitating or interfering with the capacity of citizens to develop autonomous judgment in collective decision making. Contributions in the second section look at representation from the perspective of inclusion, focusing on how representative relationships and claims articulate the demands of those who are excluded or have no voice. The final section examines political representation from a more systemic perspective, exploring its broader environmental conditions and the way it acquires democratic legitimacy. (shrink)

Projecting essence onto a social category means to think, talk, and act as if the category were a discrete natural kind and as if its members were all endowed with the same immutable attributes determined by the category's essence. Essentializing may happen implicitly or on purpose in representing ingroups and outgroups. We argue that essentializing is a versatile representational tool that is used to create identity in groups with chosen membership in order to make the group appear as a (...) unitary entity, that outsiders often draw on a group's essentialist self-construal in their judgements about the groups, that judgements about members of forced social categories are often informed by essentialist thinking that easily switches to discrimination and racism, and that under certain historical and political conditions members of social categories and groups may contest their essentialized identity, such as parts of the feminist movement, or that they may attempt to reconstruct an essentialized identity, such as parts of the homosexual movement or the largely defunct European nobility. Besides explicit political and power interests, we see communication processes and language use as a tacit force driving essentialization of social categories. (shrink)

Jeffery et al. characterize the egocentric/allocentric distinction as discrete. But paradoxically, much of the neural and behavioral evidence they adduce undermines a discrete distinction. More strikingly, their positive proposal reflects a more complex interplay between egocentric and allocentric coding than they acknowledge. Properly interpreted, their proposal about three-dimensional spatial representation contributes to recent work on embodied cognition.

The success of models of human behavior based on Bayesian inference over logical formulas or programs is taken as evidence that people employ a “language-of-thought” that has similarly discrete and compositional structure. We argue that this conclusion problematically crosses levels of analysis, identifying representations at the algorithmic level based on inductive biases at the computational level.

En 1928, à la suite d’une « conversion » qui le tourne vers des « valeurs spirituelles de poésie », le poète Pierre Jean Jouve renie tous ses ouvrages antérieurs à 1925 et proclame le début d’une « vita nuova ». Désormais, son œuvre ne cessera de représenter cette « scène originaire » de mort et de résurrection, mise sous le signe d’une « imitation du Christ ». Parmi ces représentations, le phénix occupe une place plutôt discrète mais significative. L’article (...) examine les différentes occurrences du symbole du phénix dans l’œuvre de traduction, de roman et de poésie de l’auteur, et y reconnaît une figure de la représentation, en tant que celle-ci exige la mort de l’objet tout en lui donnant une nouvelle vie. Le phénix jouvien apparaît comme une figure de l’« accomplissement » de cette représentation, aux multiples sens du mot. Il la montre en train de s’accomplir, via le sacrifice du corps « visible » comme présidant à un amour éternellement « audible » dans les mots. Il la représente sous une forme « accomplie » dans la prostituée qui, objet d’un meurtre sacrificiel, prend la figure d’un gouffre, lieu où toute représentation s’abîme, mais où toute représentation trouve aussi son origine et sa condition de possibilité. Il permet enfin d’en entrevoir le terme : l’oiseau, qui représente l’essence amoureuse et sacrificielle de la poésie, est d’autant plus « près » d’incarner cette essence qu’il renonce à se montrer ; il s’effacera derrière la représentation du lieu où son mystère s’est manifesté. In 1928, as a result of his “conversion” which turns him to “spiritual values of poetry”, the French poet Pierre Jean Jouve repels all the works he wrote before 1925 and announces the beginning of a “vita nuova”. From now on, his œuvre will never stop representing this “primitive scene” of death and resurrection, interpreted as an “imitation of Christ”. Among these representations, the Phoenix is a discrete but significant image. The article examines the different places where the Phoenix symbol appears, in Jouve’s translations, novels and poetry. The bird appears as a symbol of representation, based upon the death of the object and giving it a new life. Jouve’s Phoenix is a figure of the “accomplishment” of this representation. It shows representation in statu nascendi, as a sacrifice of the “visual” corporal appearance in order to realize a life and a love “hearable” in words. It represents representation as “accomplished” in the image of the prostitute, who was killed in a sacrificial way, and takes the appearance of an abyss, where every representation stops, but where every representation also finds its origin and its possibility. It finally puts in perspective the end of representation: the bird which represents the “essence” of poetry—an essence of love and sacrifice—is imagined “near to essences and God”, and the nearer as it becomes invisible and stops showing itself; in one of the last poems, it disappears behind the representation of the place where its mystery has revealed itself. (shrink)