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, (...) and only sustained empirical research in cognitive science will determine the extent to which that is true. (shrink)

If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They (...) have infinitely complex bodies. Transfinite games anchor their social relations. (shrink)

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 (...) added a Supplementary Essay. The Essay, continuing themes from the great debate, developed an intriguing mathematical model of the relations between the divine Self and lesser selves. The second volume went on to.. (shrink)

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 (...) are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

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.

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 (...) fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic. (shrink)

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 (...) paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. (shrink)

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. (...) I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction. (shrink)

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 (...) microscopic, and systemic versus componential, and illustrate these with examples. I conclude with two illustrations of partial-state, internal, microscopic, componential dynamicism. (shrink)

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 (...) and neuroscience, componential dynamicism, that focuses on the parts of cognitive systems that fill certain functional roles in producing cognitive phenomena. (shrink)

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 (...) argument against three alternative interpretations of the neurodynamical explanatory schema. The independent interpretation holds that neurodynamical explanations and mechanisms are independent. The constitutive interpretation holds that neurodynamical explanations are constitutive but otherwise non-mechanistic. Both the independent and constitutive interpretations fail to account for all the features of neurodynamical explanations. The partial interpretation assumes that the targets of dynamical systems models are mechanisms and so holds that neurodynamical explanations are incomplete because they lack mechanistic details. I contend instead that the targets of those models are dynamical systems distinct from mechanisms and defend this claim against several objections. I conclude with a defense of the pseudomechanistic interpretation and a discussion of the source of their explanatory power in relation to a causal-mechanical description of the world. (shrink)

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 (...) and neuroscience, componential dynamicism, that focuses on the parts of cognitive systems that fill certain functional roles in producing cognitive phenomena. (shrink)

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 (...) the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones. (shrink)