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I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...) |
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The dynamical hypothesis states that cognitive systems are dynamical systems. While dynamical systems play an important role in many cognitive phenomena, the dynamical hypothesis as stated applies to every system and so fails both to specify what makes cognitive systems distinct and to distinguish between proposals regarding the nature of cognitive systems. To avoid this problem, I distinguish several different types of dynamical systems, outlining four dimensions along which dynamical systems can vary: total-state versus partial-state, internal versus external, macroscopic versus (...) |
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Dynamical systems play a central role in explanations in cognitive neuroscience. The grounds for these explanations are hotly debated and generally fall under two approaches: non-mechanistic and mechanistic. In this paper, I first outline a neurodynamical explanatory schema that highlights the role of dynamical systems in cognitive phenomena. I next explore the mechanistic status of such neurodynamical explanations. I argue that these explanations satisfy only some of the constraints on mechanistic explanation and should be considered pseudomechanistic explanations. I defend this (...) |
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At the end of the 19th century, Josiah Royce participated in what has come to be called the great debate (Royce, 1897; Armour, 2005).1 The great debate concerned issues in metaphysical theology, and, since metaphysics was primarily idealistic, it dealt considerably with the relations between the divine Self and lesser selves. After the great debate, Royce developed his idealism in his Gifford Lectures (1898-1900). These were published as The World and the Individual. At the end of the first volume, Royce (...) |
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I go deep into the biology of the human organism to argue that the psychological features and functions of persons are realized by cellular and molecular parallel distributed processing networks dispersed throughout the whole body. Persons supervene on the computational processes of nervous, endocrine, immune, and genetic networks. Persons do not go with brains. |
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The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system DS2 when DS1 exactly reproduces (...) |
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The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the (...) |
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Cognitive neuroscientists are turning to an increasingly rich array of neurodynamical systems to explain mental phenomena. In these explanations, cognitive capacities are decomposed into a set of functions, each of which is described mathematically, and then these descriptions are mapped on to corresponding mathematical descriptions of the dynamics of neural systems. In this paper, I outline a novel explanatory schema based on these explanations. I then argue that these explanations present a novel type of dynamicism for the philosophy of mind (...) |
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The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis. |
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According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, (...) |
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In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this (...) |
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According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. (...) |
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