It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. (...) There is no bar to the quality of understanding being the result of natural selection, but only so long as the physical laws contain a non-computational ingredient. (shrink)

The relativistic quantum mechanics with Lorentz-invariant evolution parameter and indefinite mass is a very elegant theory. But it cannot be derived by quantizing the usual classical relativity in which there is the mass-shell constraint. In this paper the classical theory is modified so that it remains Lorentz invariant, but the constraint disappears; mass is no longer fixed—it is an arbitrary constant of motion. The quantization of this unconstrained theory gives the relativistic quantum mechanics in which wave functions are localized and (...) normalized in spacetime. Though many authors have published good works in support for such a localization in time, the latter has been generally considered as problematic. Here I show that wave packets restricted to a finite region of spacetime are not a nuisance, but just the contrary. They have the physical interpretation in the fact that an observer perceives a world line event by event, as his experience of “now” proceeds in spacetime. Quantum mechanically this means that at a certain value of the evolution parameter τ the event is most probably to occur within the spacetime region around {ie1005-1} occupied by the wave packet; at later value of τ the position {ie1005-2}—and hence the time coordinate t—of the wave packet is changed. This is closely related to the interpretation of quantum mechanics in general. (shrink)

Economic value additions to knowledge and demand provide practical, embedded and extensible meaning to philosophizing cognitive systems. Evaluation of a cognitive system is an empirical matter. Thinking of science in terms of distributed cognition (interactionism) enlarges the domain of cognition. Anything that actually contributes to the specific quality of output of a cognitive system is part of the system in time and/or space. Cognitive science studies behaviour and knowledge structures of experts and categorized structures based on underlying structures. Knowledge representation (...) through understanding of ‘epistemic cultures’ is an evolutionary stage. But cognition goes beyond knowledge representation. Notwithstanding the importance of epistemology of phenomena, the practicability cum philosophical aspects of machine learning needs to be seen in dynamic behaviour in socio-economic-technical value additions if human machine interaction processes that are context specific are incorporated into strong artificial intelligent systems. Cognitive Science is also studied from both computational and biological angles. Evolution of interactive forms of reasoning through understanding of meta-language of computations or biological learning processes is possible. But the limitation of historical cultures predefines the role of interactive processes in user-networks beyond technology networks. Despite this limitation, inclusive development notions of a heterogeneous national society such as India or Europe can be tested and incorporated. (shrink)

Abstract This paper explores the role of symbolic languages within and between positivist disciplines. Symbolic languages, of which mathematics is the most important example, consist of tautologically true statements, such as 2 + 2 = 4. These must be operationalized before being useful for positivist research agendas (i.e. two apples and two oranges make four fruit). Disciplines may borrow either the symbolic languages of another discipline or the symbolic language and the accompanying operationalizations. The choice has important theoretical effects, and (...) affects the kind of interdisciplinary community created. The game theory community is an example of a community based on the interdisciplinary exchange of symbolic language only, while the ? political economy? community exchanges both symbolic languages and operationalizations. (shrink)

The book presents the case that cognitive science should turn its attention to developing theories of human cognition that cover the full range of human perceptual, cognitive, and action phenomena. Cognitive science has now produced a massive number of high-quality regularities with many microtheories that reveal important mechanisms. The need for integration is pressing and will continue to increase. Equally important, cognitive science now has the theoretical concepts and tools to support serious attempts at unified theories. The argument is made (...) entirely by presenting an exemplar unified theory of cognition both to show what a real unified theory would be like and to provide convincing evidence that such theories are feasible. The exemplar is SOAR, a cognitive architecture, which is realized as a software system. After a detailed discussion of the architecture and its properties, with its relation to the constraints on cognition in the real world and to existing ideas in cognitive science, SOAR is used as theory for a wide range of cognitive phenomena: immediate responses ; discrete motor skills ; memory and learning ; problem solving ; language ; and development. The treatments vary in depth and adequacy, but they clearly reveal a single, highly specific, operational theory that works over the entire range of human cognition, SOAR is presented as an exemplar unified theory, not as the sole candidate. Cognitive science is not ready yet for a single theory – there must be multiple attempts. But cognitive science must begin to work toward such unified theories. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

There are a number of dispositionalist solutions to the free will problem based on freedom consisting in the agent's exercise of a power. But if a subject a is free when they exercise their power P, there is an objection to be overcome from the possibility of power implantation. A brainwasher, rather than directly manipulating a subject's movements, can instead implant in them a desire, to be understood as a disposition to act, and allow the subject to exercise such a (...) power. It seems that, according to the dispositionalist theory of freedom, such an agent would still count as acting freely. There is a strong non-consent intuition that a is not free in such a case because they did not consent to having the power P—the desire in question. Filling out this intuition is not straightforward. But it can be done in terms of the exercise of P being regulated by higher-order powers of self-reflection. Such regulation is what allows an agent to either take ownership of a power or to reject it. (shrink)

C HL is Noam Chomsky's shorthand for "Single Computational System of human language." C HL is that part of the faculty of language (FL) that integrates lexical information to form linguistic expressions at the interfaces where language interacts with other cognitive systems. In this paper, I am asking whether the elements of FL are dedicated to language alone, or whether significant parts of FL might apply beyond language. From a close examination of the properties of the principles of C HL (...) , I argue that they might well apply to a class of natural symbol systems that includes language and other cognitive systems. This issue of linguistic specificity differs from a similar issue raised recently by Chomsky. For Chomsky, while the "elements" of the linguistic system per se are drawn from all over nature, general principles of computational efficiency control the operation of the system. Currently, there is little empirical motivation for this vast generalization to all of nature. The more restricted generalization proposed here looks better suited to the current form of inquiry on language and related system. (shrink)

The authors present climate change and antibiotic resistance as emergent biosocial phenomena—ongoing products of massively multiple interactions among human lifestyles and broader life processes. They argue that response to climate change and antibiotic resistance is often framed by two varieties of biosocial imagination. Anthropocentric imaginations privilege the question of human distinctiveness. Anthropomorphic imaginations privilege the question of whether biosocial processes can be modeled in terms of centers of moral and causal responsibility. Together, these frame the matter of response in terms (...) of deliberate human action. The authors argue that, considered as emergent biosocial phenomena, climate change and antibiotic resistance “diffract” deliberate human action and thus limit the value of this frame by rendering the human/nonhuman and intended/nonintended distinctions that are crucial to its practical operation locally irrelevant. Alternative biosocial imaginations currently developing around climate change and antibiotic resistance that allow for “diffraction” and therefore frame response differently are considered. (shrink)

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the (...) intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand. (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)

This article introduces the concepts of System, Autonomous System, Intelligent System, Multiple System, and Collective Being. It deals with issues related to managing these different levels of systemic aggregation. The author then discusses applications related to Architecture and design with particular reference to cities.

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (shrink)

We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...) be either inconsistent or incomplete. Moreover, since humanly known mathematics is axiomatizable, it can be the output of a Turing machine. We then argue that any given mathematical claim that we could possibly know could be the output of a Turing machine, at least in principle. So the Lucas-Penrose (Lucas in Philosophy 36:112–127, 1961; Penrose, in The Emperor’s new mind. Oxford University Press, Oxford (1994)) argument cannot be sound. (shrink)

The study of human intelligence was once dominated by symbolic approaches, but over the last 30 years an alternative approach has arisen. Symbols and processes that operate on them are often seen today as approximate characterizations of the emergent consequences of sub- or nonsymbolic processes, and a wide range of constructs in cognitive science can be understood as emergents. These include representational constructs (units, structures, rules), architectural constructs (central executive, declarative memory), and developmental processes and outcomes (stages, sensitive periods, neurocognitive (...) modules, developmental disorders). The greatest achievements of human cognition may be largely emergent phenomena. It remains a challenge for the future to learn more about how these greatest achievements arise and to emulate them in artificial systems. (shrink)

The emergence of novelty in the realm of the living remains, despite the long tradition of evolutionary biology, unwelcome, calling for explanation by old, established knowledge. The prevailing neodarwinian evolutionary paradigm approaches living beings as passive outcomes of external (and extraneous, hence “blind”) formative forces. Many teachings opposing Darwinism also take the existence of eternal, immutable and external laws as a necessary prerequisite. Ironically enough, authors who oppose Darwinian theory, and admit that living beings possess a “self”, often accentuate internal, (...) ideal and eternal harmony,which is incompatible with historical changes; moreover such harmony is again imposed by external, atemporal “laws”. I describe here a third approach embodied by the names of two unrelated scholars, Stuart Kauffman (biology, physics) and Juri Lotman (semiotics, culturology). Their approach suggests thatthe evolution of organisms, minds, cultures — is a continuous negotiation (semiosis) of ‘laws’, driving to ever broader spaces of freedom and constantly larger autonomy of existence. (shrink)