Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...) express mathematical concepts—they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition. (shrink)
This chapter examines a common objection to sex robots: the symbolic-consequences argument. According to this argument sex robots are problematic because they symbolise something disturbing about our attitude to sex-related norms such as consent and the status of our sex partners, and because of the potential consequences of this symbolism. After formalising this objection and considering several real-world uses of it, the chapter subjects it to critical scrutiny. It argues that while there are grounds for thinking that sex robots could (...) symbolically represent a troubling attitude toward women (and maybe children) and the norms of interpersonal sexual relationships, the troubling symbolism is going to be removable in many instances and reformable in others. What will ultimately matter are the consequences of the symbolism but these consequences are likely to be difficult to ascertain. This may warrant an explicitly experimental approach to the development of this technology. (shrink)
Symbols should be grounded, as has been argued before. But we insist that they should be grounded not only in subsymbolic activities, but also in the interaction between the agent and the world. The point is that concepts are not formed in isolation (from the world), in abstraction, or "objectively." They are formed in relation to the experience of agents, through their perceptual/motor apparatuses, in their world and linked to their goals and actions. This paper takes a detailed look at (...) this relatively old issue, with a new perspective, aided by our work of computational cognitive model development. To further our understanding, we also go back in time to link up with earlier philosophical theories related to this issue. The result is an account that extends from computational mechanisms to philosophical abstractions. (shrink)
Whether computational algorithms such as latent semantic analysis (LSA) can both extract meaning from language and advance theories of human cognition has become a topic of debate in cognitive science, whereby accounts of symbolic cognition and embodied cognition are often contrasted. Albeit for different reasons, in both accounts the importance of statistical regularities in linguistic surface structure tends to be underestimated. The current article gives an overview of the symbolic and embodied cognition accounts and shows how meaning induction attributed to (...) a specific statistical process or to activation of embodied representations should be attributed to language itself. Specifically, the performance of LSA can be attributed to the linguistic surface structure, more than special characteristics of the algorithm, and embodiment findings attributed to perceptual simulations can be explained by distributional linguistic information. (shrink)
Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill1,2. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations3,4, and their performance suffers if this nonsymbolic system is impaired5. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required6–10. Here (...) we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction11–15. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics. We presented children with approximate symbolic arithmetic problems in a format that parallels previous tests of non-symbolic arithmetic in preschool children8,9. In the first experiment, five- to six-year-old children were given problems such as ‘‘If you had twenty-four stickers and I gave you twenty-seven more, would you have more or less than thirty-five stickers?’’. Children performed well above chance (65.0%, t1952.77, P 5 0.012) without resorting to guessing or comparison strategies that could serve as alternatives to arithmetic. Children who have been taught no symbolic arithmetic therefore have some ability to perform symbolic addition problems. The children’s performance nevertheless fell short of performance on non-symbolic arithmetic tasks using equivalent addition problems with numbers presented as arrays of dots and with the addition operation conveyed by successive motions of the dots into a box (71.3% correct, F1,345 4.26, P 5 0.047)8.. (shrink)
A. Newell and H. A. Simon were two of the most influential scientists in the emerging field of artificial intelligence (AI) in the late 1950s through to the early 1990s. This paper reviews their crucial contribution to this field, namely to symbolic AI. This contribution was constituted mostly by their quest for the implementation of general intelligence and (commonsense) knowledge in artificial thinking or reasoning artifacts, a project they shared with many other scientists but that in their case was theoretically (...) based on the idiosyncratic notions of symbol systems and the representational abilities they give rise to, in particular with respect to knowledge. While focusing on the period 1956-1982, this review cites both earlier and later literature and it attempts to make visible their potential relevance to today's greatest unifying AI challenge, to wit, the design of wholly autonomous artificial agents (a.k.a. robots) that are not only rational and ethical, but also self-conscious. (shrink)
In the first section of the article, we examine some recent criticisms of the connectionist enterprise: first, that connectionist models are fundamentally behaviorist in nature (and, therefore, non-cognitive), and second that connectionist models are fundamentally associationist in nature (and, therefore, cognitively weak). We argue that, for a limited class of connectionist models (feed-forward, pattern-associator models), the first criticism is unavoidable. With respect to the second criticism, we propose that connectionist modelsare fundamentally associationist but that this is appropriate for building models (...) of human cognition. However, we do accept the point that there are cognitive capacities for which any purely associative model cannot provide a satisfactory account. The implication that we draw from is this is not that associationist models and mechanisms should be scrapped, but rather that they should be enhanced.In the next section of the article, we identify a set of connectionist approaches which are characterized by “active symbols” — recurrent circuits which are the basis of knowledge representation. We claim that such approaches avoid criticisms of behaviorism and are, in principle, capable of supporting full cognition. In the final section of the article, we speculate at some length about what we believe would be the characteristics of a fully realized active symbol system. This includes both potential problems and possible solutions (for example, mechanisms needed to control activity in a complex recurrent network) as well as the promise of such systems (in particular, the emergence of knowledge structures which would constitute genuine internal models). (shrink)
We are familiar with the idea of symbolic value in everyday contexts, and philosophers sometimes help themselves to it when discussing other topics. However, symbolic value itself has not been sufficiently studied. What is it for something to have symbolic value? How important is symbolic value? The present purpose is to shed some light on the nature and significance of symbolic value. Two kinds of symbolic value are distinguished, called the ‘symbolic mode of valuing’ and ‘symbolism as a ground of (...) value’. Their potential significance lies in making a thoroughly relational contribution to thought about values, compared to the individualistic nature of more familiar values. This relational contribution consists in the role of symbols in shared ways of living. (shrink)
Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...) brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components – not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored. (shrink)
We argue that one important aspect of the “cognitive neuroscience revolution” identified by Boone and Piccinini :1509–1534. doi: 10.1007/s11229-015-0783-4, 2015) is a dramatic shift away from thinking of cognitive representations as arbitrary symbols towards thinking of them as icons that replicate structural characteristics of their targets. We argue that this shift has been driven both “from below” and “from above”—that is, from a greater appreciation of what mechanistic explanation of information-processing systems involves, and from a greater appreciation of the problems (...) solved by bio-cognitive systems, chiefly regulation and prediction. We illustrate these arguments by reference to examples from cognitive neuroscience, principally representational similarity analysis and the emergence of dynamical models as a central postulate in neurocognitive research. (shrink)
The strong continuity thesis postulates that the properties of mind are an enriched version of the properties of life, and thus that life and mind differ in degree and not kind. A philosophical problem for this view is the ostensive discontinuity between humans and other animals in virtue of our use of symbols—particularly the presumption that the symbolic nature of human cognition bears no relation to the basic properties of life. In this paper, we make the case that a genuine (...) account of strong continuity requires the identification of some sort of correlate of symbol-use in basic life properties. Our strategy is three-fold: 1) we argue that examples of proto-symbolism in simple living systems would be consistent with an evolutionary trajectory that ultimately produced symbolic cognition in humans; 2) we introduce Gordon Tomkins’ biological notion of ‘symbol’ as something that represents to the organism a feature of its environment that is significant to its survival; and 3) we employ this biological understanding of symbol-use to suggest that the symbolic nature of human cognition can be understood as an enriched version of the basic symbolic properties of life, thus preserving life-mind continuity in this context. (shrink)
The two works reprinted in this volume are a unique fusion of logical thought and inimitable whimsy. Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.
Modern semiotics is a branch of logics that formally defines symbol-based communication. In recent years, the semiotic classification of signs has been invoked to support the notion that symbols are uniquely human. Here we show that alarm-calls such as those used by African vervet monkeys (Cercopithecus aethiops), logically satisfy the semiotic definition of symbol. We also show that the acquisition of vocal symbols in vervet monkeys can be successfully simulated by a computer program based on minimal semiotic and neurobiological constraints. (...) The simulations indicate that learning depends on the tutor-predator ratio, and that apprentice-generated auditory mistakes in vocal symbol interpretation have little effect on the learning rates of apprentices (up to 80% of mistakes are tolerated). In contrast, just 10% of apprentice-generated visual mistakes in predator identification will prevent any vocal symbol to be correctly associated with a predator call in a stable manner. Tutor unreliability was also deleterious to vocal symbol learning: a mere 5% of “lying” tutors were able to completely disrupt symbol learning, invariably leading to the acquisition of incorrect associations by apprentices. Our investigation corroborates the existence of vocal symbols in a non-human species, and indicates that symbolic competence emerges spontaneously from classical associative learning mechanisms when the conditioned stimuli are self-generated, arbitrary and socially efficacious. We propose that more exclusive properties of human language, such as syntax, may derive from the evolution of higher-order domains for neural association, more removed from both the sensory input and the motor output, able to support the gradual complexification of grammatical categories into syntax. (shrink)
There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the symbol grounding problem : How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their shapes, be grounded (...) in anything but other meaningless symbols? The problem is analogous to trying to learn Chinese from a Chinese/Chinese dictionary alone. A candidate solution is sketched: Symbolic representations must be grounded bottom-up in nonsymbolic representations of two kinds: iconic representations, which are analogs of the proximal sensory projections of distal objects and events, and categorical representations, which are learned and innate feature-detectors that pick out the invariant features of object and event categories from their sensory projections. Elementary symbols are the names of these object and event categories, assigned on the basis of their categorical representations. Higher-order symbolic representations, grounded in these elementary symbols, consist of symbol strings describing category membership relations. Connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations, thereby connecting names to the proximal projections of the distal objects they stand for. In this way connectionism can be seen as a complementary component in a hybrid nonsymbolic/symbolic model of the mind, rather than a rival to purely symbolic modeling. Such a hybrid model would not have an autonomous symbolic module, however; the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom-up grounding of categories ' names in their sensory representations. Symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens, but by the nonarbitrary shapes of the icons and category invariants in which they are grounded. (shrink)
The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over meaningful symbols or over meaningless symbols. If it is computing over meaningful symbols its functioning presupposes the existence of meaningful symbols in the system, i.e. it implies semantic nativism. If the mind is computing over meaningless symbols, no intentional cognitive processes are available prior to symbol grounding. (...) In this case, no symbol grounding could take place since any grounding presupposes intentional cognitive processes. So, whether computing in the mind is over meaningless or over meaningful symbols, computationalism implies semantic nativism. (shrink)
Against the view that symbol-based semiosis is a human cognitive uniqueness, we have argued that non-human primates such as African vervet monkeys possess symbolic competence, as formally defined by Charles S. Peirce. Here I develop this argument by showing that the equivocal role ascribed to symbols by “folk semiotics” stems from an incomplete application of the Peircean logical framework for the classification of signs, which describes three kinds of symbols: rheme, dicent and argument. In an attempt to advance in the (...) classifying semiotic processes, Peirce proposed several typologies, with different degrees of refinement. Around 1903, he developed a division into ten classes. According to this typology, symbols can be further analysed in three subclasses (rheme, dicent, argument). I proceed to demonstrate that vervet monkeys employ dicent symbols. There are remarkable implications of this argument since ‘symbolic species theory’ fails to explore the vast Peircean semiotic philosophy to frame questions regarding the emergence and evolution of symbolic processes. (shrink)
This paper presents a mutual confrontation of the oeuvres of Pierre Teilhard de Chardin (1881–1955) and Jacques Lacan (1901–1980), highlighting their relevance for the planetary challenges we are facing today. I will present their views on technoscience, environmental pollution and religious faith, focussing on human genomics as a case study. Both authors claim that technoscience reflects a tendency towards symbolisation: incorporating the biosphere (liv- ing nature) into the “symbolic order’ (Lacan) or ‘noosphere’ (Teilhard). On various occasions, Lacan refers to Teilhard’s (...) concept of the hominization of the planet and their dialogue culminates in a ‘final conversation’ between Teilhard and Lacan in 1954, during a reception organised by the journal Psyché. I will conclude that the Teilhard-Lacan dialogue is highly relevant for current debates concerning the Anthropocene, as a moment of global awakening and global crisis. Processes of hominization allowed humans to become literate beings, littering the planet as well: humans as literate litterers. Whereas Teilhard argues that technoscience and self-direc- ted evolution are about to culminate in what he refers to as point Omega, Lacan rather stresses the hazards involved in this optimistic desire towards all-encompassing synthesis, unification and fulfilment. (shrink)
Cognitive scientists have a variety of approaches to studying cognition: experimental psychology, computer science, robotics, neuroscience, educational psychology, philosophy of mind, and psycholinguistics, to name but a few. In addition, they also differ in their approaches to cognition - some of them consider that the mind works basically like a computer, involving programs composed of abstract, amodal, and arbitrary symbols. Others claim that cognition is embodied - that is, symbols must be grounded on perceptual, motoric, and emotional experience. The existence (...) of such different approaches has consequences when dealing with practical issues such as understanding brain disorders, designing artificial intelligence programs and robots, improving psychotherapy, or designing instructional programs. The symbolist and embodiment camps seldom engage in any kind of debate to clarify their differences. This book is the first attempt to do so. It brings together a team of outstanding scientists, adopting symbolist and embodied viewpoints, in an attempt to understand how the mind works and the nature of linguistic meaning. As well as being interdisciplinary, all authors have made an attempt to find solutions to substantial issues beyond specific vocabularies and techniques. (shrink)
This essay presents a phenomenological analysis of the functioning of symbols as elements of the life-world with the purpose of demonstrating the interrelationship of individual and society. On the basis of Alfred Schutz''s theory of the life-world, signs and symbols are viewed as mechanisms by means of which the individual can overcome the transcendences posed by time, space, the world of the Other, and multiple realities which confront him or her. Accordingly, the individual''s life-world divides itself into the dimensions of (...) time, space, the social world and various reality spheres which form the boundaries or transcendences that the I has to understand and integrate. Signs and symbols are described as appresentational modes which stand for experiences originating in the different spheres of the life-world within the world of everyday life, within which they can be communicated, thereby establishing intersubjectivity. Schutz''s theory of the symbol explains how social entities – such as nations, states or religious groups – are symbolically integrated to become components of the individual''s life-world. The following paper reconstructs Schutz''s concept of the symbol as a crucial component of his theory of the life-world, which is seen as an outstanding phenomenological contribution to the theory of the sign and the symbol in general. (shrink)
What is the relation between the material, conventional symbol structures that we encounter in the spoken and written word, and human thought? A common assumption, that structures a wide variety of otherwise competing views, is that the way in which these material, conventional symbol-structures do their work is by being translated into some kind of content-matching inner code. One alternative to this view is the tempting but thoroughly elusive idea that we somehow think in some natural language (such as English). (...) In the present treatment I explore a third option, which I shall call the "complementarity" view of language. According to this third view the actual symbol structures of a given language add cognitive value by complementing (without being replicated by) the more basic modes of operation and representation endemic to the biological brain. The "cognitive bonus" that language brings is, on this model, not to be cashed out either via the ultimately mysterious notion of "thinking in a given natural language" or via some process of exhaustive translation into another inner code. Instead, we should try to think in terms of a kind of coordination dynamics in which the forms and structures of a language qua material symbol system play a key and irreducible role. Understanding language as a complementary cognitive resource is, I argue, an important part of the much larger project (sometimes glossed in terms of the "extended mind") of understanding human cognition as essentially and multiply hybrid: as involving a complex interplay between internal biological resources and external non-biological resources. (shrink)
The author draws attention to gnoseologically not enough investigated phenomenon of automorphism thinking. In the widely known works of F. Varela, and U. Maturana automorphism is associated mainly with the study of the adaptation of biological organisms. It appears, however, that the possibilities of this approach are more significant. The author believes that the driving force of thinking activity is the constructive combination. Cognitive morphogenesis processes as a free combination of symbolic forms, managed by rules of mental experimentation over one’s (...) own resources, resulting in the development of the spiritual world of a person. The ‘generation of meanings through distinction of meanings‘ logic is a lever that starts independent-functioning automatic processes. Such a spiritual auto-modelling generates symbolic morphisms â what is referred to as drawing ‘castles in the air‘, creating constructions without basement. The author comes to the conclusion that in scientific knowledge, as in poetry, all abilities of associative consciousness on the basis of auto-modelling mechanism are involved and they serve as indicators for creation of form. In this process tools of internal semantic transformations aimed at paramorph exposure of reality are applied. (shrink)
The articles in this issue represent the pursuit of a new understanding of the human past, one that can replace the neo-saltationist view of a human revolution with models that can account for the complexities of the archaeological record and of human social lives. The articulation of archaeological, philosophical, and biological perspectives seems to offer a strong foundation for exploring available evidence, and this was the rationale for collecting these particular articles. Even at this preliminary stage there is a coherence (...) emerging in proposals: the origin and operation of symbolically rich, complexly signaling human social systems was the consequence of the long-term evolution of multiple components of perceiving and negotiating social interactions, a contingent outcome of myriad adaptive shifts rather than a single event. (shrink)
Over the past several decades, the philosophical community has witnessed the emergence of an important new paradigm for understanding the mind.1 The paradigm is that of machine computation, and its influence has been felt not only in philosophy, but also in all of the empirical disciplines devoted to the study of cognition. Of the several strategies for applying the resources provided by computer and cognitive science to the philosophy of mind, the one that has gained the most attention from philosophers (...) has been the Computational Theory of Mind (CTM). CTM was first articulated by Hilary Putnam (1960, 1961), but finds perhaps its most consistent and enduring advocate in Jerry Fodor (1975, 1980, 1981, 1987, 1990, 1994). It is this theory, and not any broader interpretations of what it would be for the mind to be a computer, that I wish to address in this paper. What I shall argue here is that the notion of symbolic representation employed by CTM is fundamentally unsuited to providing an explanation of the intentionality of mental states (a major goal of CTM), and that this result undercuts a second major goal of CTM, sometimes refered to as the vindication of intentional psychology. This line of argument is related to the discussions of derived intentionality by Searle (1980, 1983, 1984) and Sayre (1986, 1987). But whereas those discussions seem to be concerned with the causal dependence of familiar sorts of symbolic representation upon meaning-bestowing acts, my claim is rather that there is not one but several notions of meaning to be had, and that the notions that are applicable to symbols are conceptually dependent upon the notion that is applicable to mental states in the fashion that Aristotle refered to as paronymy. That is, an analysis of the notions of meaning applicable to symbols reveals that they contain presuppositions about meaningful mental states, much as Aristotle's analysis of the sense of healthy that is applied to foods reveals that it means conducive to having a healthy body, and hence any attempt to explain mental semantics in terms of the semantics of symbols is doomed to circularity and regress. I shall argue, however, that this does not have the consequence that computationalism is bankrupt as a paradigm for cognitive science, as it is possible to reconstruct CTM in a fashion that avoids these difficulties and makes it a viable research framework for psychology, albeit at the cost of losing its claims to explain intentionality and to vindicate intentional psychology. I have argued elsewhere (Horst, 1996) that local special sciences such as psychology do not require vindication in the form of demonstrating their reducibility to more fundamental theories, and hence failure to make good on these philosophical promises need not compromise the broad range of work in empirical cognitive science motivated by the computer paradigm in ways that do not depend on these problematic treatments of symbols. (shrink)
Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.
The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample quizzes and solutions. The (...) Symbolic Logic Study Guide is essential for all instructors and students who use LPL in their symbolic logic classes. (shrink)
In ethical reflections on new technologies, a specific type of argument often pops up, which criticizes scientists for “playing God” with these new technological possibilities. The first part of this article is an examination of how these arguments have been interpreted in the literature. Subsequently, this article aims to reinterpret these arguments as symbolic arguments: they are grounded not so much in a set of ontological or empirical claims, but concern symbolic classificatory schemes that ground our value judgments in the (...) first place. Invoking symbolic arguments thus refers to how certain new technologies risk undermining our fundamental symbolic distinctions by which we organize and evaluate our interactions with the world and in society. Such symbolic distinctions, moreover, tend to be resilient against logical argumentation, mainly because they themselves form the basis on which we argue in the cultural and ethical sphere in the first place. Therefore, effective strategies to evaluate and counter these arguments require another approach, showing that these technologies either do not challenge these classifications or, if they do, how they can be accompanied by the proper actions to integrate these technologies into our society. (shrink)
Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? -/- The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This (...) book is the first to offer a self-contained presentation of neural network models for a number of computer science logics, including modal, temporal, and epistemic logics. By using a graphical presentation, it explains neural networks through a sound neural-symbolic integration methodology, and it focuses on the benefits of integrating effective robust learning with expressive reasoning capabilities. -/- The book will be invaluable reading for academic researchers, graduate students, and senior undergraduates in computer science, artificial intelligence, machine learning, cognitive science and engineering. It will also be of interest to computational logicians, and professional specialists on applications of cognitive, hybrid and artificial intelligence systems. (shrink)
Ramscar and colleagues (2010, this volume) describe the “feature-label-order” (FLO) effect on category learning and characterize it as a constraint on symbolic learning. I argue that FLO is neither a constraint on symbolic learning in the sense of “learning elements of a symbol system” (instead, it is an effect on nonsymbolic, association learning) nor is it, more than any other constraint on category learning, a constraint on symbolic learning in the sense of “solving the symbol grounding problem.”.
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
This paper is concerned with the status of a symbol in Wittgenstein’s Tractatus. It is claimed in the first section that a Tractarian symbol, whilst essentially a syntactic entity to be distinguished from the mark or sound that is its sign, bears its semantic significance only inessentially. In the second and third sections I pursue this point of exegesis through the Tractarian discussions of nonsense and the context principle respectively. The final section of the paper places the forgoing work in (...) a secondary context, addressing in particular a debate regarding the realism of the Tractatus. (shrink)
The Zapatista Indigenous Movement from Chiapas, Mexico is an example of the anthropological dynamics between the visible and the invisible in Western culture and the possible revolution of perceiving reality as such since they had to cover their faces with masks in their rebel anti-system movement in order to be considered as having the same dignity as other human beings: they performed a revolutionary act that changed the symbolic order of the visible by the public exhibition of their colonial submission. (...) The mask gave them a face, disrupting the order of the visible with uncanny faces. In this article, a nondual model is proposed to capture the inessential ground of the given composed of endless perspectives in continuous transformation by the generation of ontological novelty: an open cognitive horizon of symbolically empty points of view irreducible to one perspective. For Krishnamurti, the revolutionary act is to see without an image in order to phenomenologically attend to things as they are beyond the known and the unknown such as Stilinovi? and Malevich pursued the dissolution of symbolic representations through art for the transformation of human reality. (shrink)
Perceptual symbol systems form a theoretically plausible alternative to amodal symbol systems. At this point it is unclear whether there is any truly diagnostic empirical evidence to decide between these systems. We outline some possible avenues of research in the domain of language comprehension that might yield such evidence. Language comprehension will be an important arena for tests of the two types of symbol systems.
As the accompanying articles in the Special Issue on Semiotic Scaffolding will attest, my colleagues in biosemiotics have done an exemplary job in showing us how to think about the critically generative role that semiotic scaffolding plays “vertically” – i.e., in evolutionary and developmental terms – by “allowing access to the upper floors” of biological complexity, cognition and evolution.In addition to such diachronic considerations of semiotic scaffolding, I wish to offer here a consideration of semiotic scaffolding’s synchronic power, as well (...) – and in particular the ability that it can afford its users to access new and other sign relations “horizontally” as a function of the way that multiple semiotically scaffolded relations intertwine to result in a “definite semantic topology that determines the ways that symbols modify each other’s referential functions in different combinations”.Taking up, in turn, Terrence Deacon’s later challenge that what the sciences of cognition – and biology more generally – needs to “come to grips with [is] the process of semiosis; the dynamic of interpretive activity by which semiotic relationships emerge from other semiotic relationships [as] intrinsically dynamic phases in a generative process”, I attempt here to show how Deacon’s own Peirce-inspired matrix of referential sign relations as presented in The Symbolic Species, when viewed as a semiotic scaffold of interactional constraints and possibility biases, provides the key to understanding the essentially thirdness-manifesting nature of symbol reference, formation and growth. (shrink)
This book will attempt to achieve a constructive and positive correla tion between mythic-symbolic language and philosophical anthropolo gy. It is intended as a reflection on the philosophical accomplishment of Paul Ricoeur. The term mythic-symbolic language in this context means the language of the multivalent symbol given in the myth with its psychological and poetic counterparts. The term symbol is not con ceived as an abstract sign as it is used in symbolic logic, but rather as a concrete phenomenon - (...) religious, psychological, and poetic. The task inherent in this correlation is monumental when one considers the dual dilemma of problematic and possibility which is at its heart. The prob lematic arises out of the apparent difficulty presented by the so-called challenge of modernity which seems to require the elimination of my thic-symbolic language as an intelligible mode of communication. Mythic-symbolic language is sometimes eliminated because in a world molded by abstract conceptualizations conceptUalizations of science, such a language is thought to be unintelligible. The claim is that its "primitive" explana tions have been transcended by our modernity. Others believe that the problem of mythic-symbolic language is the problem of the myth. If the mythic forms of language could be eliminated, the truth of such language could be preserved through its translation into an intelligible mode of discourse. The problematic is heightened further by the relation of consider ations of language to philosophical anthropology. (shrink)
Elementary Symbolic Logic: Concepts, Techniques, and Context introduces symbolic logic in a way that is accessible and yet rigorous enough to provide an adequate foundation for students who intend to further pursue studies in logic, or who work in areas of study—for example, philosophy or linguistics—where a serious understanding of logic is nonnegotiable. Moreover, while it is not a history book, it aims to provide some context for the development of symbolic logic.