Nelson Goodman’s theory of symbol systems expounded in his Languages of Art has been frequently criticized on many counts (cf. list of secondary literature in the entry “Goodman’s Aesthetics” of Stanford Encyclopedia of Philosophy and Sect. 3 below). Yet it exerts a strong influence and is treated as one of the major twentieth-century theories on the subject. While many of Goodman’s controversial theses are criticized, the technical notions he used to formulate them seem to have been treated as neutral (...) tools. One such technical notion is that of the density of symbol systems. This serves to distinguish linguistic symbols from pictorial representations (after Goodman entirely rejected resemblance in that role) and is a crucial part of Goodman’s explanation of what constitutes aesthetic experience (and so indirectly what is art). Thus its significance for Goodman’s theory is fundamental. The aim of this paper is a detailed, logical analysis of this notion. It turns out that Goodman’s definition is highly problematic and cannot be applied to symbol systems in the way Goodman envisaged. To conclude, Goodman’s theory is problematic not just because of its controversial theses but also because of logical problems with the technical notions used at its very core. Hence the controversial claims are not simply contestable, but inaccurately expressed. (shrink)

This short paper grew out of an observation—made in the course of a larger research project—of a surprising convergence between, on the one hand, certain themes in the work of Mary Hesse and Nelson Goodman in the 1950/60s and, on the other hand, recent work on the representational resources of science, in particular regarding model-based representation. The convergence between these more recent accounts of representation in science and the earlier proposals by Hesse and Goodman consists in the recognition that, in (...) order to secure successful representation in science, collective representational resources must be available. Such resources may take the form of (amongst others) mathematical formalisms, diagrammatic methods, notational rules, or—in the case of material models—conventions regarding the use and manipulation of the constituent parts. More often than not, an abstract characterization of such resources tells only half the story, as they are constituted equally by the pattern of (practical and theoretical) activities—such as instances of manipulation or inference—of the researchers who deploy them. In other words, representational resources need to be sustained by a social practice; this is what renders them collective representational resources in the first place. (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)

This paper presents an original dialectical logic symbol system designed to transcend the limitations of traditional logical symbols in capturing subjectivity, qualitative aspects, and contradictions inherent in the human mind. By introducing new symbols, such as “ὄ” (being) and “⌀” (nothing), and arranging them based on principles of symmetry, the system’s operations capture complex dialectical relationships essential to both Hegelian philosophy and Buddhist thought. The operations of this system are primarily structured around the categories found in (...) Hegel’s Logic, and it allows users to incorporate their own subjectivity into the logical processes, opening up new possibilities in the philosophy of subjectivity. This symbol system also has the potential to help us explore fundamental questions of language and to precisely describe processes of consciousness transformation through symbols. This form of logic offers a new, irreducible tool for qualitative methods, and it will spark a new philosophical reflection on its relationship with traditional logic and mathematical symbols. (shrink)

The aim of this work is to develop a comparative analysis of the discursive structures that underlie the socialized formation of the interpretative paradigms of reality. We analyse how both political ideologies and the so-called “conspiracy theories” can be understood starting from the structure and functioning of Marc Augè's ideo-logic, namely the systemic-discursive device that defines the field of all possible sentences defining the real. -/- .

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)

Cognitive, or knowledge, agents, who are in some way aware of describing their own view of the world (based on their mental concepts), need to become concerned with the expressions of their own conceptions. My main supposition is that agents’ conceptions are mainly expressed in the form of linguistic expressions that are spoken, written, and represented based on e.g. letters, numbers, or symbols. This research especially focuses on symbolic conceptions (that are agents’ conceptions that are manifested in the form of (...) their symbols). I attempt to logically (and using ????LSYM) analyse symbolic conceptions in terminological systems. ????LSYM is an assertional fragment of my developed Conception Language (????L), which is utilised as a formal-logical system for representing and explicating agents’ conceptions of the world. Keywords: assertional logic; cognitive agent; knowledge agent; conception language; conception; symbol; symbolic conception. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

Thirty years ago, I elaborated on a position that could be seen as a compromise between an "extreme," symbol-based AI, and a "neurochemical reductionism" in AI. The present article recalls aspects of the espoused framework of schema theory that, it suggested, could provide a better bridge from human psychology to brain theory than that offered by the symbol systems of A. Newell and H. A. Simon.

Gottfried Leibniz embarked on a research program to prove all the Aristotelic categorical syllogisms by diagrammatic and algebraic methods. He succeeded in proving them by means of Euler diagrams, but didn’t produce a manuscript with their algebraic proofs. We demonstrate how key excerpts scattered across various Leibniz’s drafts on logic contained sufficient ingredients to prove them by an algebraic method –which we call the Leibniz-Cayley (LC) system– without having to make use of the more expressive and complex machinery of (...) first-order quantificational logic. In addition, we prove the classic categorical syllogisms again by a relational method –which we call the McColl-Ladd (ML) system– employing categorical relations studied by Hugh McColl and Christine Ladd. Finally, we show the connection of ML and LC with Boolean algebra, proving that ML is a consequence of LC, and that LC is a consequence of the Boolean lattice axioms, thus establishing Leibniz’s historical priority over George Boole in characterizing and applying (a sufficient fragment of) Boolean algebra to effectively tackle categorical syllogistic. (shrink)

The paper is a commentary on the target article by Christine A. Skarda & Walter J. Freeman, “How brains make chaos in order to make sense of the world”, in the same issue of the journal, pp.161–195. -/- I confine my comments largely to some philosophical claims that Skarda & Freeman make and to the relationship of their model to connectionism. Some of the comments hinge on what symbols are and how they might sit in neural systems.

As physical entities that translate symbols into physical actions, computers offer insights into the nature of meaning and agency. • Physical symbol systems, generically known as agents, link abstractions to material actions. The meaning of a symbol is defined as the physical actions an agent takes when the symbol is encountered. • An agent has autonomy when it has the power to select actions based on internal decision processes. Autonomy offers a partial escape from constraints imposed by (...) direct physical influences such as gravity and the transfer of momentum. Swimming upstream is an example. • Symbols are names that can designate other entities. It appears difficult to explain the use of names and symbols in terms of more primitive functionality. The ability to use names and symbols, i.e., symbol grounding, may be a fundamental cognitive building block. • The standard understanding of causality—wiggling X results in Y wiggling—applies to both physical causes (e.g., one billiard ball hitting another) and symbolic causes (e.g., a traffic light changing color). Because symbols are abstract, they cannot produce direct physical effects. For a symbol to be a cause requires that the affected entity determine its own response. This is called autonomous causality. • This analysis of meaning and autonomy offers new perspectives on free will. (shrink)

Inspired by the eminently successful physical theories and informed by commonplace experiences such as seeing a cat upon looking at a cat, conscious experience is thought of as a measurement or photocopy of given stimulus. Conscious experience, unlike a photocopy, is symbolic—like language—in that the relation between conscious experience and physical stimulus is analogous to that of the word "cat" and its meaning, i.e., arbitrary and yet systematic. We present arguments against the photocopy model and arguments for a symbolic conception (...) of conscious experience. Learning and the corresponding plasticity of the brain make a strong case for the symbolic conception of conscious experience, while many extra-ordinary conscious experiences argue against the formalisation of consciousness as a measuring device. The notions of place-value notation and grammar, which organise quantitative measurements and conscious experiences in the medium of numbers and language, respectively, are suggested as model systems for putting together a comprehensive theory of conscious experience. (shrink)

Floridi and Taddeo propose a condition of “zero semantic commitment” for solutions to the grounding problem, and a solution to it. I argue briefly that their condition cannot be fulfilled, not even by their own solution. After a look at Luc Steels' very different competing suggestion, I suggest that we need to re-think what the problem is and what role the ‘goals’ in a system play in formulating the problem. On the basis of a proper understanding of computing, I (...) come to the conclusion that the only sensible ground-ing problem is how we can explain and re-produce the behavioral ability and function of meaning in artificial computational agents. (shrink)

This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is finite. (...) But then, given fundamental results in recursion theory, the set will also be recursive, recursively enumerable, axiomatizable, and could be the output of a Turing machine. We then argue that it is impossible to produce a string of symbols that humans could possibly produce but no Turing machine could. Moreover, we show that any given string of symbols that we could produce could also be the output of a Turing machine. Our arguments have implications for Hilbert’s sixth problem and the possibility of axiomatizing particular sciences, they undermine at least two distinct arguments against the possibility of Artificial Intelligence, and they entail that expert systems that are the equals of human experts are possible, and so at least one of the goals of Artificial Intelligence can be realized, at least in principle. (shrink)

The extent of confusion between symbols and that which is symbolised is examined across five institutional spheres. Religion is the institution most marked by confusion of this type; indeed in some respects the symbolic mes- sage of religion may be the extent of the substantive reality. On the other hand, the very existence of the nation state may be judged to depend upon the exercise of the human imagination; hence providing a source of instability which may lead to the excesses (...) of nationalism. In regard to social status, the main problematical element is a certain circularity: it is necessary to get peo- ple to exhibit differences in behaviour which are then used to justify or con- stitute the status differences themselves. In politics, the symbolism of left and right threatens to strangle creative thinking, while in education the tendency on all sides to orient towards public systems of measurement and grading undermines the claim that what is really important is pupil and student learn- ing. A social cost is being paid for the failure to recognise and, where possible, address the issues identified. (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)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a (...) video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

A great deal of research has focused on the question of whether or not concepts are embodied as a rule. Supporters of embodiment have pointed to studies that implicate affective and sensorimotor systems in cognitive tasks, while critics of embodiment have offered nonembodied explanations of these results and pointed to studies that implicate amodal systems. Abstract concepts have tended to be viewed as an important test case in this polemical debate. This essay argues that we need to move beyond a (...) pretheoretical notion of abstraction. Against the background of current research and theory, abstract concepts do not pose a single, unified problem for embodied cognition but, instead, three distinct problems: the problem of generalization, the problem of flexibility, and the problem of disembodiment. Identifying these problems provides a conceptual framework for critically evaluating, and perhaps improving upon, recent theoretical proposals. (shrink)

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

The study of culture and cultural selection from a biological perspective has been hampered by the lack of any firm theoretical basis for how the information for cultural traits is stored and transmitted. In addition, the study of any living system with a decentralized or multi-level information structure has been somewhat restricted due to the focus in genetics on the gene and the particular hereditary structure of multicellular organisms. Here a different perspective is used, one which regards living systems (...) as self-constructing energy users that utilize their genome as a library of information, making the genetic system just another component that adds fitness to the overall integrated unit. In this framework, basic fitness is measured as the ability to gather energy for growth and reproduction, and the fitness of the genetic system is broken down into two aspects: first, the effectiveness in searching for new somatic functional information, and second, the effectiveness in searching for better structures to store and process information. With this more generalized perspective, major evolutionary transitions to higher levels of organization become competitions between different information structures; furthermore the functioning and fitness of cultural systems can be more easily described and compared with other modes of information storage within biological systems. Modern technological societies are self-constructing systems that rely on written (symbolic) information storage and very complex algorithms that effectively search for variation with a high probability of successful selection. These systems are currently competing with traditional organic systems, and this competition constitutes the latest major evolutionary transition. Upon comparison of the energy-gathering potential of symbolic-based systems with DNA-based life, it appears that symbolic systems have a tremendous fitness potential and the current shift to a higher level of selection may be as significant and far-reaching as any of the previous major evolutionary transitions. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were (...) exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

In this paper, we examine some basic linguistic abilities in a small sample of adults with minimal receptive vocabulary, whose receptive mental verbal age ranges from 1;2 to 3;10. In particular, we examine whether the participants in our study understand noun phrases consisting of a noun modified by an adjective. We use stimuli that they can recognise by name. Except for one participant, we find that, while all of them understand the noun and adjective in isolation, none seems to understand (...) these noun phrases, which means that they seem to not do linguistic composition. In order to test whether the difficulty is linguistic or conceptual, we ran two other studies, one on concept composition, and the other on iconic symbolic composition (composition of pictograms). Results suggest that linguistic composition is particularly difficult in this population, and that vocabulary breadth may not predict compositional abilities. (shrink)

Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...) (1980) and arguments from Gödel's Incompleteness theorems (e.g., Lucas, 1961; Penrose, 1989), both of which fall short of addressing the complete TM model. Both UTM-computers and formal systems provide an unsound basis for debate. In particular, their special natures easily foster the misconception that computation entails intrinsically meaningless symbol manipulation. This common view is incorrect with respect to full-fledged TM's, which can process inputs non-formally, i.e., in a subjective and dynamically evolving fashion. To avoid a distorted understanding of the theory of computation, philosophical judgments and discussions should be grounded firmly upon the complete Turing machine model, the proper model for real computers. (shrink)

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system (...) can be used with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

The field of AI has undergone a series of transformations, each marking a new phase of development. The initial phase emphasized curation of symbolic models which excelled in capturing reasoning but were fragile and not scalable. The next phase was characterized by machine learning models—most recently large language models (LLMs)—which were more robust and easier to scale but struggled with reasoning. Now, we are witnessing a return to symbolic models as complementing machine learning. Successes of LLMs contrast with their inscrutability, (...) inaccuracy, and hallucinations, which underwrite concerns over the reliability and trustworthiness of these systems, motivating investigations into commonsense reasoning, AI explainability, and formal verification techniques. Moreover, proper assessments of hybrid machine learning/symbolic systems require novel strategies to facilitate comparisons of performance and guide future AI progress. The EDGeS AAAI 2023 Spring symposium brought together researchers focusing on novel assessments and benchmarks for evaluating hybrid and artificial general intelligence (AGI) systems. This symposium revealed what was already suspected: research concerning evaluation of machine learning/symbolic hybrids and AGI is, unfortunately, lacking. Even so, the discussion was fruitful. (shrink)

The concept of symbolic power was first introduced by French sociologist Pierre Bourdieu to account for the tacit, almost unconscious modes of cultural/social domination occurring within the everyday social habits maintained over conscious subjects. Symbolic power accounts for discipline used against another to confirm that individual's placement in a social hierarchy, at times in individual relations but most basically through system institutions, in particular education.

The main aim of this article is to present and defend a thesis according to which conceptual representations of some types of mental states are encoded in the same neural structures that underlie the first-personal experience of those states. To support this proposal here, I will put forth a novel account of the cognitive function played by ‘shared representations’ of emotions and bodily sensations, i.e. neural structures that are active when one experiences a mental state of a certain type as (...) well as when one observes someone else experiencing a state of the same type. I will argue that shared representations in fact constitute vehicles of certain mental state concepts (more precisely, concepts of specific types of emotions and somatosensory states). The main line of arguing for this will consist in showing that shared representations exhibit specific, ‘conceptual’ functional properties:(1) causal effect on forming metacognitive judgments, (2) cognitive penetrability, (3) diversity of input types. (shrink)

In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.

The Turing Test (TT), the Chinese Room Argument (CRA), and the Symbol Grounding Problem (SGP) are about the question “can machines think?” We propose to look at these approaches to Artificial Intelligence (AI) by showing that they all address the possibility for Artificial Agents (AAs) to generate meaningful information (meanings) as we humans do. The initial question about thinking machines is then reformulated into “can AAs generate meanings like humans do?” We correspondingly present the TT, the CRA and the (...) SGP as being about generation of human-like meanings. We model and address such possibility by using the Meaning Generator System (MGS) where a system submitted to an internal constraint generates a meaning in order to satisfy the constraint. The system approach of the MGS allows comparing meaning generations in animals, humans and AAs. The comparison shows that in order to have AAs capable of generating human-like meanings, we need the AAs to carry human constraints. And transferring human constraints to AAs raises concerns coming from the unknown natures of life and human mind which are at the root of human constraints. Implications for the TT, the CRA and the SGP are highlighted. It is shown that designing AAs capable of thinking like humans needs an understanding about the natures of life and human mind that we do not have today. Following an evolutionary approach, we propose as a first entry point an investigation about the possibility for extending a “stay alive” constraint into AAs. Ethical concerns are raised from the relations between human constraints and human values. Continuations are proposed. (This paper is an extended version of the proceedings of an AISB/IACAP 2012 presentation). (shrink)

The dialogue develops arguments for and against a broad new world system - info-computationalist naturalism - that is supposed to overcome the traditional mechanistic view. It would make the older mechanistic view into a special case of the new general info-computationalist framework (rather like Euclidian geometry remains valid inside a broader notion of geometry). We primarily discuss what the info-computational paradigm would mean, especially its pancomputationalist component. This includes the requirements for a the new generalized notion of computing that (...) would include sub-symbolic information processing. We investigate whether pancomputationalism can provide the basic causal structure to the world and whether the overall research program of info-computationalist naturalism appears productive, especially when it comes to new approaches to the living world, including computationalism in the philosophy of mind. (shrink)

How the mind works is the ultimate mystery for human beings. To answer this question, one of the most significant insights is Kant’s argument that we can only perceive phenomena but not the essence of the external world. Following this idea, we formulated a novel computational framework to model the mind based on two assumptions: 1) There is no presupposition of the existence of the external objective world and the main task of the mind is to explore, establish and utilize (...) persistent relationships between senses and actions. 2) Symbolic intermediate-level representation is necessary. We call this framework the self-programming system. Based on the self-programming system, we interpreted the nature of concepts, time, space, causality, and consciousness. Besides that, we also draw a conclusion to the mind-body problem. Specifically, the perspective that considers subjective experience as fundamental is compatible with the existence of the external world and that the physical body serves as the substrate of the mind. However, since the relationship is “compatible” rather than “cause”, skepticism can never be ruled out in principle. Furthermore, we have elucidated the nature of interpretation within the context of reductive physicalism. This serves to provide a clear understanding as to why the hard problem of consciousness is inherently unsolvable. (shrink)

The Language of Thought program has a suicidal edge. Jerry Fodor, of all people, has argued that although LOT will likely succeed in explaining modular processes, it will fail to explain the central system, a subsystem in the brain in which information from the different sense modalities is integrated, conscious deliberation occurs, and behavior is planned. A fundamental characteristic of the central system is that it is “informationally unencapsulated” -- its operations can draw from information from any cognitive (...) domain. The domain general nature of the central system is key to human reasoning; our ability to connect apparently unrelated concepts enables the creativity and flexibility of human thought, as does our ability to integrate material across sensory divides. The central system is the holy grail of cognitive science: understanding higher cognitive function is crucial to grasping how humans reach their highest intellectual achievements. But according to Fodor, the founding father of the LOT program and the related Computational Theory of Mind (CTM), the holy grail is out of reach: the central system is likely to be non-computational (Fodor 1983, 2000, 2008). Cognitive scientists working on higher cognitive function should abandon their efforts. Research should be limited to the modules, which for Fodor rest at the sensory periphery (2000).1 Cognitive scientists who work in the symbol processing tradition outside of philosophy would reject this pessimism, but ironically, within philosophy itself, this pessimistic streak has been very influential, most likely because it comes from the most well-known proponent of LOT and CTM. Indeed, pessimism about centrality has become assimilated into the mainstream conception of LOT. (Herein, I refer to a LOT that appeals to pessimism about centrality as the “standard LOT”). I imagine this makes the standard LOT unattractive to those philosophers with a more optimistic approach to what cognitive science can achieve.. (shrink)

In sensorimotor integration, representation involves an anticipatory model of the action to be performed. This model integrates efferent signals (motor commands), its reafferent consequences (sensory consequences of an organism’s own motor action), and other afferences (sensory signals) originated by stimuli independent of the action performed. Representation, a form of internal modeling, is invoked to explain the fact that behavior oriented to the achievement of future goals is relatively independent from the immediate environment. Internal modeling explains how a cognitive system (...) achieves its goals despite variations in the environment with insufficient and noisy sensory–perceptual data. In a self that acts intentionally on the environment, knowledge is dependent upon the necessity to guide actions directed toward an aim. The self-inner model, a representation of internal and external environments (including reafferent and afferent messages) and also of the behavior plans and desirable future states (aims) and efferent intentions (motor planning and motor command messages), is intrinsically linked to a thinking capacity, which is supposed to emerge from the binding of multiple influences. Thinking emerges when higher behavior strategies are considered possible and capable of leading to aims or the fulfillment of intentions. In this model, symbolization processes are projective and anticipatory and, in this way, beyond present referents. Symbolization occurs linked to action planning, command, and regulation in mental simulation. Meaning is related to an inner sense of a self that acts over the environment. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics (...) education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

The present article is an attempt to bring together the development of mental activity and consciousness in the framework of the organism-environment theory (Jarvilehto, 1998a, 1998b, 1999); the main question is how the development of mental activity and consciousness can be formulated if the starting point is not the separation of man and environment as in traditional cognitive psychology, but a unitary organism-environment system. According to the present formulation, mental activity is conceived as activity of the whole organism-environment (...) class='Hi'>system and connected to the general development of life as a specific form of an organism-environment system comprising neurons. The advent of consciousness is regarded as a result of co-operation of such organism-environment systems. Consciousness is based on co-operation for the achievement of common results, and shared by the co-operating individuals (general consciousness), although each individual also makes it concrete from the perspective of his/her own body in the act of participation in common results (personal consciousness). Language is the means of formation of the co-operative system in the achievement of common results, and it is suggested that the use of language is related more to the type of co-operative system and intended common results than to any symbolic representation of the world. It is claimed that on this basis it is possible to develop psychology which takes seriously the concepts of mental activity and consciousness in the description of human action, but does not reduce these concepts either to biological or social factors. The present formulation should be regarded more as a conceptual outline than as a full-blown theory. (shrink)

Focusing on sin as a historical-cultural and socio-religious construction in a process that encompasses its mythical-religious aspects, the article points out that the concept that expresses its notion is rooted in the borders involving human failure to correspond to the paradigmatic framework and its system of taboos, laws and moral codes. Thus, converging on the etymological-literary and biblical-religious aspects of sin, the article emphasizes that, by ending the meaning of missing the mark, the translation of the aforementioned term as (...) “sin” corresponds to the textual transposition established by the Septuagintversion in a movement of abstraction from the notion of moral guilt. Based on Ricoeur's reading of the philosophical-theological aspects of sin, the article that points out that sin is not a term capable of exhausting the meaning of reality that it implies as a symbol of the rupture between essence and existence, converging to its characterization as a symbol of eviland “mythical grandeur” through a construction that marks sin as an intersection involving evil and the world and attributes its emergence tothe act and determines its identification as a product and simultaneously a cause. Thus, focusing on the biblical-theological aspects of sin in Tillich and on the construction of the concept as an alienation between “non-faith” and “non-love”, the articleemphasizes the irreducible character of the conception that, according to the Apostle Paul, encloses the condition of an almost personal powerthat controls this world, which implies the superposition of a state of affairs characterized by objectivity and the configuration of the event now designated as a rupture involving essence and existence in a movement that may represent the human separation from the “Being-in-itself” and expressing the element of personal responsibility imbricated in its existential dynamics. (shrink)

By defining both depictive and linguistic representation as kinds of symbol system, Nelson Goodman attempts to undermine the platitude that, whereas linguistic representation is mediated by convention, depiction is mediated by resemblance. I argue that Goodman is right to draw a strong analogy between the two kinds of representation, but wrong to draw the counterintuitive conclusion that depiction is not mediated by resemblance.

This study examines problems related to the representation of music. It constructs the sender/message/perceiver/result model, a prototype broad enough to incorporate a large variety of music and other notation systems, including those having to do with computers. The work defines music notation itself, describes various models for studying the subject--including the binary types prescriptive/descriptive, and symbolic/iconic--and assesses music notation as a contemporary practice. It encompasses a review of the actions and intentions of composers, performers, and audiences, and a consideration of (...) the message and how it is affected by media , reference systems , and meanings. Finally, through an examination of the possibilities of the self acting as a notation system within models posited by feminist and queer theory, I attempt to demonstrate the power of notation to affect other systems and worlds, including the worlds of music, art, and politics. ;The consideration of these topics draws on theories from linguistics, semiotics, structuralism, post-structuralism, cybernetics, and music, as well as the philosophies of John Cage, Jean-Jacques Nattiez, Nelson Goodman, and others. The work examines various languages and applications used to program computers for musical purposes, though this examination does not incorporate programs dedicated exclusively to printing music. Nor does the study focus on non-Western notations, suggestions for reforms of notation, or encyclopedic lists of notation devices. ;The expository writing is augmented by excerpts from material I gathered in numerous interviews. There are separate sections containing interviews of Leonard Meyer, Allan Kaprow, John Cage, Earle Brown, Roger Reynolds, and Heidi von Gunden. There is also a large, partially-annotated bibliography. ;My hope is that an inclusive, interdisciplinary exploration of music notation will be useful in broadening the theoretical and creative boundaries of the field, as well as bridging gaps among musicians using various music technologies, and artists and theorists from diverse fields and perspectives. (shrink)

Although formal thought disorder (FTD) has been for long a clinical label in the assessment of some psychiatric disorders, in particular of schizophrenia, it remains a source of controversy, mostly because it is hard to say what exactly the “formal” in FTD refers to. We see anomalous processing of terminological knowledge, a core construct of human knowledge in general, behind FTD symptoms and we approach this anomaly from a strictly formal perspective. More specifically, we present here a symbolic computational model (...) of storage in, and activation of, a human semantic network, or semantic memory, whose core element is logical form; this is normalized by description logic (DL), namely by CL, a DL-based language – Conception Language – designed to formalize conceptualization from the viewpoint of individual cognitive agency. In this model, disruptions in the rule-based implementation of the logical form account for the apparently semantic anomalies symptomatic of FTD, which are detected by means of a CL-based algorithmic assessment. (shrink)

Exactly how do the sign/symbol/token systems of endo- and exo-biosemiosis differ from those of cognitive semiosis? Do the biological messages that integrate metabolism have conceptual meaning? Semantic information has two subsets: Descriptive and Prescriptive. Prescriptive information instructs or directly produces nontrivial function. In cognitive semiosis, prescriptive information requires anticipation and “choice with intent” at bona fide decision nodes. Prescriptive information either tells us what choices to make, or it is a recordation of wise choices already made. Symbol systems (...) allow recordation of deliberate choices and the transmission of linear digital prescriptive information. Formal symbol selection can be instantiated into physicality using physical symbol vehicles (tokens). Material symbol systems (MSS) formally assign representational meaning to physical objects. Even verbal semiosis instantiates meaning into physical sound waves using an MSS. Formal function can also be incorporated into physicality through the use of dynamically-inert (dynamically-incoherent or -decoupled) configurable switch-settings in conceptual circuits. This paper examines the degree to which biosemiosis conforms to the essential formal criteria of prescriptive semiosis and cybernetic management. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

While Hegel’s influence on Arthur Danto has been examined in relation to specific parts of his thought, an overall analysis of said influence is still wanting. In this article, I analyze the presence of Hegelian influence in Danto’s complete thought from three perspectives: (1) Danto’s acceptance of Hegelian assumptions when it comes to the conception of history, narrative realism and historical progress, which allows him to combine timeless essentialism with historicism, (2) the cognitive aspect of art and the conception of (...) art as an embodied symbol, as well as the historical quality of said embodiment, and (3) the assumption that art’s trajectory coincides with the Hegelian prophecy that art will give way to philosophy, on which Danto’s “end of art” thesis is based. This examination not only illuminates the interrelation between the different parts of Dantian philosophy, but also reveals its systematic character. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

Throughout what is now the more than 50-year history of the computer many theories have been advanced regarding the contribution this machine would make to changes both in the structure of society and in ways of thinking. Like other theories regarding the future, these should also be taken with a pinch of salt. The history of the development of computer technology contains many predictions which have failed to come true and many applications that have not been foreseen. While we must (...) reserve judgment as to the question of the impact on the structure of society and human thought, there is no reason to wait for history when it comes to the question: what are the properties that could give the computer such far-reaching importance? The present book is intended as an answer to this question. The fact that this is a theoretical analysis is due to the nature of the subject. No other possibilities are available because such a description of the properties of the computer must be valid for any kind of application. An additional demand is that the description should be capable of providing an account of the properties which permit and limit these possible applications, just as it must make it possible to characterize a computer as distinct from a) other machines whether clocks, steam engines, thermostats, or mechanical and automatic calculating machines, b) other symbolic media whether printed, mechanical, or electronic and c) other symbolic languages whether ordinary languages, spoken or written or formal languages. This triple limitation, however, (with regard to other machines, symbolic media and symbolic languages) raises a theoretical question as it implies a meeting between concepts of mechanical-deterministic systems, which stem from mathematical physics, and concepts of symbolic systems which stem from the description of symbolic activities common to the humanities. The relationship between science and the humanities has traditionally been seen from a dualistic perspective, as a relationship between two clearly separate subject areas, each studied on its own set of premises and using its own methods. In the present case, however, this perspective cannot be maintained since there is both a common subject area and a new - and specific - kind of interaction between physical and symbolic processes. (shrink)

Casting a glance at philosophical inquiries of the last decades, with regard to human cognition (in a broad sense), we are witnesses to turns one after the other. The settings were based on the change of scope and perspective of investigations. The so-called linguistic turn refers to “the view that philosophical problems are problems which may be solved (or dissolved) either by reforming language or by understanding more about the language we presently use”. In the 90s, W. J. T. Mitchell (...) coined the phrase pictorial turn, calling attention to the fact that “pictures form a point of peculiar friction and discomfort across a broad range of intellectual inquiry”. In order to eliminate this intellectual discomfort, Mitchell considers exploratory and explicatory approaches that focus on non-linguistic symbol systems and do not consider language as the only source of a significant paradigm regarding meaning. Recently, there has been a shift of emphasis regarding the basis of cognitive skills. This may be the next turn, a sensorimotor or activist one. Although this turn has massive roots in the past, and there is some controversy regarding whether it is fully reconcilable with various findings of cognitive neurology, this view seems to be capable of providing a framework within which the verbalist approach can cease to be the dominant view. (shrink)

Nelson Goodman (1906-2007) approached the arts and other kinds of knowledge as forms of symbolism. His principal aim in philosophy was to advance understanding and remove confusions by verbal analysis and logical constructions. Goodman's philosophical theories encompass nominalism, constructivism and a version of radical relativism. In his Languages of Art, Goodman sets forth distinctions among the various art according to differences in the forms of symbols employed. He contributed as well to arts education and to philosophy of the museum. His (...) performance work, "Hockey Seen: A Nightmare in Three Periods and Sudden Death embodies his aesthetic theories. (shrink)

The perceptual symbol system view assumes that perceptual representations have a role-argument structure. A role-argument structure is often incorporated into amodal symbol systems in order to explain conceptual functions like abstraction and rule use. The power of perceptual symbol systems to support conceptual functions is likewise rooted in its use of structure. On Barsalou's account, this capacity to use structure (in the form of frames) must be innate.