``Neural computing'' is a research field based on perceiving the human brain as an information system. This system reads its input continuously via the different senses, encodes data into various biophysical variables such as membrane potentials or neural firing rates, stores information using different kinds of memories (e.g., short-term memory, long-term memory, associative memory), performs some operations called ``computation'', and outputs onto various channels, including motor control commands, decisions, thoughts, and feelings. We show a natural model of neural computing that (...) gives rise to hyper-computation. Rigorous mathematical analysis is applied, explicating our model's exact computational power and how it changes with the change of parameters. Our analog neural network allows for supra-Turing power while keeping track of computational constraints, and thus embeds a possible answer to the superiority of the biological intelligence within the framework of classical computer science. We further propose it as standard in the field of analog computation, functioning in a role similar to that of the universal Turing machine in digital computation. In particular an analog of the Church-Turing thesis of digital computation is stated where the neural network takes place of the Turing machine. (shrink)

In recent years the magnificent world of fractals has been revealed. Some of the fractal images resemble natural forms so closely that Benoit Mandelbrot's hypothesis, that the fractal geometry is the geometry of natural objects, has been accepted by scientists and non-scientists alike. The present paper critically examines Mandelbrot's hypothesis. It first analyzes the concept of a fractal. The analysis reveals that fractals are endless geometrical processes, and not geometrical forms. A comparison between fractals and irrational numbers shows that the (...) former are ontologically and epistemologically even more problematic than the latter. Therefore, it is argued, a proper understanding of the concept of fractal is inconsistent with ascribing a fractal structure to natural objects. Moreover, it is shown that, empirically, the so-called fractal images disconfirm Mandelbrot's hypothesis. It is conceded that the fractal geometry can be used as a useful rough approximation, but this fact has no bearing on the physical theory of natural forms. (shrink)

This paper challenges two orthodox theses: (a) that computational processes must be algorithmic; and (b) that all computed functions must be Turing-computable. Section 2 advances the claim that the works in computability theory, including Turing's analysis of the effective computable functions, do not substantiate the two theses. It is then shown (Section 3) that we can describe a system that computes a number-theoretic function which is not Turing-computable. The argument against the first thesis proceeds in two stages. It is first (...) shown (Section 4) that whether a process is algorithmic depends on the way we describe the process. It is then argued (Section 5) that systems compute even if their processes are not described as algorithmic. The paper concludes with a suggestion for a semantic approach to computation. (shrink)

Sections 3.16 and 3.23 of Roger Penrose's Shadows of the mind (Oxford, Oxford University Press, 1994) contain a subtle and intriguing new argument against mechanism, the thesis that the human mind can be accurately modeled by a Turing machine. The argument, based on the incompleteness theorem, is designed to meet standard objections to the original Lucas-Penrose formulations. The new argument, however, seems to invoke an unrestricted truth predicate (and an unrestricted knowability predicate). If so, its premises are inconsistent. The usual (...) ways of restricting the predicates either invalidate Penrose's reasoning or require presuppositions that the mechanist can reject. (shrink)

Computationalism, the notion that cognition is computation, is a working hypothesis of many AI researchers and Cognitive Scientists. Although it has not been proved, neither has it been disproved. In this paper, I give some refutations to some well-known alleged refutations of computationalism. My arguments have two themes: people are more limited than is often recognized in these debates; computer systems are more complicated than is often recognized in these debates. To underline the latter point, I sketch the design and (...) abilities of a possible embodied computer system. (shrink)

For a variety of reasons, consciousness and selfhood are beginning once again to be intensively studied in a scientific frame of reference. The notions of each which are emerging are extremely varied: in the case of selfhood, the lack of an adequate vocabulary to capture various aspects of subjectivity has led to deep confusion. The task of the first part of this article is to clear up this terminological confusion, while salvaging whatever is valuable from the contemporary discussion. The more (...) important task of the second part is to discuss the moral issues inevitably involved in any treatment, scientific or otherwise, of the modern identity. (shrink)

Turing's (1936) analysis of effective symbolic procedures is a model of conceptual clarity that plays an essential role in the philosophy of mathematics. Yet appeal is often made to the effectiveness of human procedures in other areas of philosophy. This paper addresses the question of whether Turing's analysis can be applied to a broader class of effective human procedures. We use Sieg's (1994) presentation of Turing's Thesis to argue against Cleland's (1995) objections to Turing machines and we evaluate her proposal (...) to understand the effectiveness of procedures in terms of their reliability and precision. A number of conditions for effectiveness are identified and these are used to provide a general argument against the possibility of a Leibnizian decision procedure. (shrink)

We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is (...) computable. (shrink)

The aim of this essay is to introduce philosophers of science to some recent philosophical discussions of the nature and origin of the direction of time. The essay is organized around books by Hans Reichenbach, Paul Horwich, and Huw Price. I outline their major arguments and treat certain critical points in detail. I speculate at the end about the ways in which the subject may continue to develop and in which it may connect with other areas of philosophy.

Existing work on the ultimate limits of computation has urged that the apparatus of real numbers should be eschewed as an investigative tool and replaced by discrete mathematics. The present paper argues for a radical extension of this viewpoint: not only the continuum but all infinitary constructs including the rationals and the potential infinite sequence of whole numbers need to be eliminated if a self-consistent investigative framework is to be achieved.

In this paper I attempt mainly to elucidate the claim, advanced by Woorward, that the key notion to characterize physical laws is that of invariance. I draw a distinction betwen two levels of invariance in order to elaborate that thesis. I maintain that distinctive marks of the nomic status of basic laws of physics are either that they hold invariantly, within a domain of applivation, or that they fulfill some principles of symmetry. The fomer mark relatesd to the manner in (...) which physical systems change invariantly whereas the latter concerns to the invariance of the laws themselves. This view contrats with the traditional philosophical thesis that physical laws are true universal statements with a necessary character which differentiate then from accidental true generalizations, which are contingent. (shrink)

(1991). Gödel, Turing, chaitin and the question of emergence as a meta‐principle of modern physics. some arguments against reductionism. World Futures: Vol. 32, Creative Evolution in Nature, Mind, and Society, pp. 185-195.

The dominant position in the field of artificial intelligence (AI) is computationalism where the operative principle is that cognition in general and consciousness in particular can be captured by identification of the proper set of computations. This position has been attacked from several angles, most effectively, in my opinion, by John Searle in his now famous Chinese Room thought experiment. I critique this Searlean perspective on the grounds that, while it is probably correct in its essentials, it does not go (...) far enough. Quite simply, it runs afoul of the problem of emergentism. The proffered solution to this problem is that consciousness (or very rudimentary forms of it) needs to be viewed as an inherent property of organic form. While this recasting of the problem solves the emergentist dilemma it opens up a number of other issues. However, the new problems, unlike the old, appear in principle to be amenable to scientific analysis. (shrink)

Some dichotomies related to modeling electrocortical activities are analyzed. Attractor neural networks versus biologically motivated models, near-equilibrium versus nonequilibrium processes, linear and nonlinear dynamics, stochastic and chaotic patterns, local and global scale simulation of cortical activities are discussed.

I present two arguments that aim to establish logical limits on what we can know. More specifically, I argue for two results concerning what we can know about questions that we cannot answer. I also discuss a line of thought, found in the writings of Pierce and of Rescher, in support of the idea that we cannot identify specific scientific questions that will never be answered.

The ?language of the gods? is conceived as a kind of language more complex than what we associate with human tongues in the strict sense of the term. Certain arbitrary regularities throughout the rational disciplines appear to indicate the existence of this language. The present article explores this new concept and applies it in an attempt to provide a logical clarification of the notions of individual consciousness and physical reality.

In the 70 years since Alan Turing’s ‘Computing Machinery and Intelligence’ appeared in Mind, there have been two widely-accepted interpretations of the Turing test: the canonical behaviourist interpretation and the rival inductive or epistemic interpretation. These readings are based on Turing’s Mind paper; few seem aware that Turing described two other versions of the imitation game. I have argued that both readings are inconsistent with Turing’s 1948 and 1952 statements about intelligence, and fail to explain the design of his game. (...) I argue instead for a response-dependence interpretation. This interpretation has implications for Turing’s view of free will: I argue that Turing’s writings suggest a new form of free will compatibilism, which I call response-dependence compatibilism. The philosophical implications of rethinking Turing’s test go yet further. It is assumed by numerous theorists that Turing anticipated the computational theory of mind. On the contrary, I argue, his remarks on intelligence and free will lead to a new objection to computationalism. (shrink)

Wright & Liley contrast their theory that the global dynamics of the EEG are linear with that of Freeman, who hypothesizes an EEG governed by (nonlinear) deterministic-chaotic dynamics. A “call for further discussion” on the part of the authors is made as to how either theory fits with experimental findings indicating that EEG dynamics are non-linear but stochastic.

This paper suggests a novel reinterpretation of the mathematical core of Wheeler-Feynman absorber theory, and hence a new route to the conclusion that the temporal asymmetry of classical electromagnetic radiation has the same origin as that of thermodynamics. The argument begins (Sec. 2) with a careful analysis of what the apparent asymmetry of radiation actually involves. Two major flaws in the standard version of the Wheeler-Feynman treatment of radiative asymmetry are then identified (Secs. 4–5), and the proposed reinterpretation is described (...) (Sec. 6). This avoids the two flaws previously mentioned, and also the problematic dependence of radiation on cosmological structure. (shrink)

Since the late nineteenth century, physics has been puzzled by the time-asymmetry of thermodynamic phenomena in the light of the apparent T-symmetry of the underlying laws of mechanics. However, a compelling solution to this puzzle has proved elusive. In part, I argue, this can be attributed to a failure to distinguish two conceptions of the problem. According to one, the main focus of our attention is a time-asymmetric lawlike generalisation. According to the other, it is a particular fact about the (...) early universe. This paper aims (i) to distinguish these two different conceptions of the time-asymmetric explanandum in thermodynamics; (ii) to argue in favour of the latter; and (iii) to show that whichever we choose, our rational expectations about the thermodynamic behaviour of the future must depend on what we know about the past: contrary to the common view, statistical arguments alone do not give us good reason to expect that entropy will always continue to increase. (shrink)

For some years there has been a controversy about whether brain state variables such as EEG or neuronal spike trains exhibit chaotic behaviour. Wright & Liley claim that the local dynamics measured by spike trains or local field potentials exhibit chaotic behaviour, but global measures like EEG should be governed by linear dynamics. We propose a different scheme. Based on simulation studies and various experiments, we suggest that the pointwise dimension of EEG time series may provide some valuable information about (...) underlying neuronal generators. (shrink)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

This account of the dynamical theory of chaos leads to a metaphysical picture of a world with an open future, in which the laws of physics are emergent‐downward approximations to a more subtle and supple reality and in which there is downward causation through information input as well as upward causation through energy input. Such a metaphysical picture can accommodate both human and divine agency.

Physics explores a universe of wonderful order, expressed in terms of beautiful mathematical equations. Mathematics itself is understood to be the exploration of a realm of noetic reality. Science describes matter in terms of concepts with mind-like qualities. The psychosomatic nature of human persons is best understood in terms of a dual-aspect monism, in which matter and mind are complementary aspects of a unitary being. The new science of complexity theory, with its dualities of parts/whole and energy/information, offers modest resources (...) for the speculative exploration of this idea. The intrinsic unpredictabilities present in nature afford the metaphysical opportunity to consider dissipative systems as exhibiting top–down causality. (shrink)

The original data reported by Benjamin Libet and colleagues are reinterpreted, taking into account the facilitation which is experimentally demonstrated in the first of their series of articles. It is shown that the original data equally well or better support a quite different set of conclusions from those drawn by Libet. The new conclusions are that it takes only 80 ms for stimuli to come to consciousness and that “subjective back-referral of sensations in time” to the time of the stimulus (...) does not occur. (shrink)

The duration of “now” is shown to be important not only for an understanding of how conscious beings sense duration, but also for the validity of the phenomenological enterprise as Husserl conceived it. If “now” is too short, experiences can not be described before they become memories, which can be considered to be transcendent rather than immanent phenomena and therefore inadmissible as phenomenological data. Evidence concerning (a) the objective duration of sensations in various sensory modalities, (b) the time necessary for (...) sensations to enter consciousness and (c) the variability in the subjective sense of time's passing under different conditions is used to conclude that the duration of “now” can actually vary under normal conditions from about 10 ms to several seconds and in extreme cases up to several hours. Thus the immanent moment can be long enough to encompass a report of the contents of consciousness, making phenomenology a viable project. A further speculation from the evidence described is that consciousness takes discrete samples of the external world, at a rate inversely proportional to the duration of the “now” moment. (shrink)